text:
Translation:On bodies that are to be designated as "rigid"

by G.

In his paper "The theory of the rigid electron in the kinematics of the principle of relativity", has tried in an obvious way to give a definition of those types of motion of a three-fold extended deformable continuum, that are to be designated as "rigid" from the standpoint of the relativity principle. However, this was actually formulated by him only in one special and easily executed case. In particular the question remained untouched, whether six degrees of freedom can be ascribed to a "rigid" body defined in this way, as it may be wished by us if we want to ascribe the same fundamental meaning to this new "rigid" body in the system of the electromagnetic world-view, as it is ascribed to the ordinary rigid body in the system of the mechanical world-view.

Exactly this question will find its answer in the following lines in so far, as it will be proven that the motion of that "rigid" body is in general — i.e. neglecting special, more specified exceptions — unequivocally defined by the arbitrarily specified motion of a single of its points.

Particularly the fact may be mentioned for the purpose of illustration, that when one of its points is fixed, the body of can only uniformly rotate around a fixed axis that goes through that point.

I. Definition of the "rigid" body from the standpoint of the relativity principle.
Following 's lines of thought, the right angled coordinates x,y,z of a material particle, in connection with time t when it is located at this point, should be interpreted as the four coordinates of a point of the four-fold extended manifold $$R_{4}(x,y,z,t)$$.

Furthermore, a measure-determination should be introduced in this $$R_4$$ as well, according to which the square of the distance ds of two infinitely adjacent points is (the speed of light should from now on be set equal to 1)

The line elements of real length $$\left(ds^{2}>0\right)$$ are denoted as space-like, and such of purely imaginary length $$\left(ds^{2}<0\right)$$ are denoted as time-like. The directions of the line elements of length zero that emerge from one point constitute a real cone — the minimal cone of the relevant point — whose two surfaces are separated by $$dt>0$$ and $$dt<0$$, and shall be denoted as front-cone and back-cone.

Two directions $$(dx:dy:dz:dt)$$ and $$(dx':dy':dz':dt')$$ are normal to each other according to that measure-determination, if

The elements that are normal to the time-like elements are necessarily space-like, but not vice versa.

The group of those $$\infty^{10}$$ affine transformations (the functional determinant +1) of x,y,z,t shall be denoted as motions in $$R_4$$, which leave $$ds^2$$ unchanged and which don't mutually permute the front- and back-cones. The Lorentz transformations are thus the group of $$\infty^{6}$$ motions, which leave the zero point $$x=y=z=t=0$$ fixed — the rotations around the zero point, — and conversely the group of motions emerges from it by addition of the $$\infty^{4}$$ translations.

After these generally known definitions we think of any deformable continuum as in motion in ordinary three-dimensional space $$R_{3}(x,y,z)$$ — the coordinates at time t of any material particle (individualized by three parameters $$\xi,\eta,\zeta$$) may be:

To achieve a greater symmetry, some kind of local time τ may be introduced in some way:

by which it can be written in a more uniform way instead of (3):

The successive values of x,y,z,t for a specified material particle $$(\xi,\eta,\zeta)$$ now correspond in $$R_4$$ to a certain curve $$C_{\xi,\eta,\zeta}$$ – the world-line of that particle – and its equations in (5) are given for $$\xi,\eta,\zeta$$ (regarded as fixed) and τ (regarded as variable).

The motion of the entire continuum is thus represented in $$R_4$$ by a three-parameter family of curves $$C(\xi,\eta,\zeta)$$, which is exactly the $$\infty^{3}$$ world-lines of the particles of the continuum.

If we additionally presuppose that no particle of the continuum can travel by the speed of light or faster then the speed of light, then every line element of any curve is time-like. The definition of the "rigid" body that was given by M. from the standpoint of the relativity principle, can thus be formulated:

"The continuum is moving as a "rigid body", when in $$R_4$$ the world-lines $$C(\xi,\eta,\zeta)$$ of its points are equidistant curves."

This means, the normal-distance of two infinitely adjacent curves should be constant along themselves, or in other words, the strip that is formed by two infinitely adjacent curves shall everywhere be of equal thickness.

To formulate this condition analytically, we calculate the line element ds by (5) in curvilinear coordinates $$\xi,\eta,\zeta,\tau$$. If we write for uniformities sake:

then it shall be

Since after general presupposition of subluminal velocities, the elements of the curves $$C(\xi,\eta,\zeta)$$ are time-like, it is given:

by introduction of the linear differential form

and the quadratic one that only contains $$d\xi,d\eta,d\zeta$$:

we can write:

If the element ds shall be normal to curve $$C_{\xi,\eta,\zeta}$$, then it must be:

and the normal-distance of curves $$C_{\xi,\eta,\zeta}$$ and $$C_{\xi+d\xi,\eta+d\eta,\zeta+d\zeta}$$ are equal to $$d\sigma^{2}$$.

The condition of rigidity thus reads:

in other words, the six coefficients of the quadratic differential form $$d\sigma^{2}$$ must be independent from τ.

But also physically, that definition of rigidity can be formulated equally simple.

If the velocity of the particle $$(\xi,\eta,\zeta)$$ at time t is denoted by s, and its components by u,v,w:

then

If we put dt = 0 and consider all particles of the continuum at the same time t, then

thus

Obviously $$d\sigma^{2}=\epsilon^{2}$$ is now the equation of an infinitely small ellipsoid of revolution of semi-axes $$\epsilon,\epsilon,\epsilon\sqrt{1-s^{2}}$$, with the particle $$(\xi,\eta,\zeta)$$ as its center and its velocity direction as its figure-axis. The requirement $$(\partial/\partial\tau)d\sigma^{2}=0$$ thus means, that the volume elements (which are infinitely small spheres of radius ε in the state of rest) are transformed into an oblate ellipsoid of revolution, with a semi-minor axis $$\epsilon\sqrt{1-s^{2}}$$ in the direction of velocity and a semi-major axis ε normally to it. In other words, the definition of a "rigid" body given by can be brought into this extremely suggesting form:

 * "If the velocity within the body is changing in space and time, then the contraction hypothesis shall be valid for every single volume element."

By that, the single volume element possesses a six-fold freedom of motion, because the ellipsoid additionally allows $$\infty^{3}$$ linear homogeneous deformations in it. But is the same true for a body continuously formed by such elements of finite extension throughout? This question shall be dealt with in the following section.

II. Determination of the equidistant families of curves of $$R_4$$, that contain an arbitrary given curve.
We imagine that within such a family of curves $$C(\xi,\eta,\zeta)$$, a certain curve $$C_0$$ is somehow chosen, and the parameter values $$(\xi_{0},\eta_{0},\zeta_{0})$$ may be attributed to it.

Then we use the quadratic differential form $$d\sigma^{2}$$ in $$d\xi,d\eta,d\zeta$$, whose components only depend on $$\xi,\eta,\zeta$$, and which, as the square of the length of a space-like line element, has a definite positive character, and we introduce in it the variables a,b,c instead of $$\xi,\eta,\zeta$$ in the following way:

In the three-fold extended manifold of $$(\xi,\eta,\zeta)$$, we imagine the drawing of the two-parameter dependent family of curves of the extremal (propagating from point $$(\xi_{0},\eta_{0},\zeta_{0})$$) of the integral $$\int d\sigma$$ – the geodesic lines of form $$d\sigma^{2}$$ –, and let b,c be the values of both parameters for a line that goes through the point $$(\xi,\eta,\zeta)$$ of that family of curves, and a is the integral $$\int d\sigma$$ taken along it from $$(\xi_{0},\eta_{0},\zeta_{0})$$ to $$(\xi,\eta,\zeta)$$ – the geodesic distance of both points. If (for that geodesic polar coordinate system a,b,c) it is given:

then the differences $$\xi-\xi_{0},\ \eta-\eta_{0},\ \zeta-\zeta_{0}$$ for a = 0 and all b,c will vanish, but when divided by a (with convenient choice of b,c) then for a = 0 and all b,c it will remain finite, and if $$d\sigma^{2}$$ is expressed by this variables, it will assume the form:

where $$\varphi(db,dc)$$ also means a definite positive quadratic differential in db, dc alone, whose components still contain a,b,c, but like the previous of $$d\sigma^{2}$$ don't contain τ. And instead of τ another magnitude ϑ of the following kind shall be introduced as well:

We imagine as determined that solution of the differential equation:

which assumes the value $$\tau=\vartheta$$ for a = 0:

and by this last equation, instead of τ we have introduced the parameter ϑ which becomes identical with τ specifically along the curve $$C_0$$.

Expressed by a,b,c,τ it will be:

and da will vanish from the linear differential expression dν.

If we replace in this way the parameter $$(\xi,\eta,\zeta)$$ [which are constant along any curve] by (a,b,c), and the parameter τ [which is variable along any curve] by ϑ, then it will be

From this form we can immediately conclude, that the curves:

b = const., c = const., ϑ = const.

in $$R_{4}(x,y,z,t)$$ are extremals of the integral $$\int ds$$, which means that they are straight lines. Those $$\infty^{3}$$ straight lines $$G(b,c,\vartheta)$$ thus found, orthogonally intersect the equidistant curves C(a,b,c), because of the missing term with $$da\ d\vartheta$$ in $$ds^2$$. If we especially take from them the $$\infty^{2}$$ straight line that belongs to the same ϑ-value, and imagine the point a = 0 as marked on any of them, then this point is nothing else than the point $$\tau=\vartheta$$ on the curve $$C_0$$ through which they all go, and because they must be perpendicular to curve $$C_0$$ at this point, they are exactly the $$\infty^{2}$$ perpendiculars of curve $$C_0$$ at point $$\tau=\vartheta$$. They together form the normal plane of curve $$C_0$$ at this point, with which the surface ϑ = const. is consequently identical.

The magnitude a is the length $$\int ds$$, calculated along the straight line $$G_{b,c,\vartheta}$$ beginning at the intersection point with curve $$C_0$$ – being the distance of the corresponding space point of curve $$C_0$$.

The summary of that yields, that the expressions of x,y,z,t by a,b,c,ϑ are necessarily of the form:

{{MathForm1|(25)|$$\left\{ \begin{align} x= & x_{0}(\vartheta)+ax_{1}(b,c,\vartheta),\\ y= & y_{0}(\vartheta)+ay_{1}(b,c,\vartheta),\\ z= & z_{0}(\vartheta)+az_{1}(b,c,\vartheta),\\ t= & t_{0}(\vartheta)+at_{1}(b,c,\vartheta). \end{align}\right.$$}}

To simplify the notation, $$\mathrm{S}$$ shall be momentarily denoting a sum that is extended over the four coordinates x,y,z,t, in which, however, the term that is related to the t-coordinate has to be considered as negative.

Since the straight lines $$G(b,c,\vartheta)$$ are the normals of the curve $$C_0$$ (a = 0), it follows

and from that by differentiation to b and c it must be:

If the form $$ds^2$$ made by (25) will be identified with the expression (24), then the equations follow:

in which the coefficients of the binary, quadratic differential form $$\psi(db,dc)$$ and the magnitudes β and γ are evidently independent from a.

Especially we think of ϑ as the "proper time" along the curve $$C_0$$, thus

which can always be achieved by a convenient choice of τ, with which ϑ coincides along $$C_0$$.

From equations (28, $$\delta,\beta,\gamma$$) it follows for a = 0, one after the other:

and by recognizing, that

in the same way from (28,α):

and this eventually gives by (28,α):

However, as the coefficients of $$\varphi(db,dc)$$ are free from ϑ, then it follows that the magnitudes B,C and thus β, γ are independent from ϑ.

Now there are two possibilities:

A. We have B = 0, C = 0. Then

from which we can see, that the areas ϑ = const. – i.e. the normal planes of curve $$C_0$$ – were orthogonally intersected by the curves C(a,b,c). Thus it can be said:

The equidistant curves are the orthogonal-trajectories of a family of planes.

Conversely, also the orthogonal-trajectories of any family of planes form an equidistant family of curves, since also with respect to the measure-determination $$ds^2$$ in $$R_4$$, the theorem remains valid according to which the distance between two moving points is constant when their velocities are always normal to the connecting line.

B. At least one of the magnitudes B,C is not zero. Then it follows from (28,β,γ), that also Θ is independent from ϑ, and thus in the expression:

all coefficients are free from ϑ at all.

In this case, let us consider the one-parameter group of transformations of $$R_4$$, in which the point with parameter values (a,b,c,ϑ) goes over to those, to which the following parameter values belong:

According to the things recognized above, it is given for those transformations:

therefore they are motions in $$R_4$$, and since in those motions any single curve C(a,b,c) is evidently moved in itself, then the following statement can be made:

The equidistant curves are the trajectories of a one-parametric group of motion.

Conversely, also the trajectories of a one-parameter motion group always form an equidistant family of curves, since the sector that is limited by two infinitely adjacent curves can be moved in itself, thus it must have the same extensions everywhere.

Having noticed this, we think of the curve $$C_0$$ as arbitrarily given, and we pose the exercise to find out all equidistant families of curves that belong to that curve.

By (A) we have an unequivocally defined solution in the orthogonal trajectories of the normal planes of $$C_0$$ in all cases. Shall there be others besides those, then the related families will necessarily be summarized under (B) and therefore curve $$C_0$$ must form a one-parameter group of motions in itself. Conversely, also the trajectories of any one-parameter group of motions of curve $$C_0$$ in itself (which don't fix $$C_0$$ pointwise) give a solution of the exercise, and by all existing groups of this kind also all other solutions are given.

In order to move $$C_0$$ in itself, it is necessary and sufficient, that the three curvatures of that curve – that are invariants of motion and that let the curve remain fixed except its position in space – are constant along the curve, so that the curve is, so to speak, a helix. In addition, if $$C_0$$ shall have more than one such group of motions in itself, then there must be motions that let $$C_0$$ pointwise remain fixed, and any single one of such motion corresponds to another group of motions of the curve in itself. The fixpoints of any motion in $$R_4$$ now forms (here we can neglect the case of a single fixpoint) either a straight line or a plane $$R_3$$, and in reverse these formations remain fixed pointwise at $$\infty^{3}$$ or $$\infty^{1}$$ motions.

Depending on whether curve $$C_0$$ (with constant curvatures) exists in no space lower than $$R_3$$ or $$R_2$$ or eventually is a straight line, it has 1 or $$\infty^{1}$$ or $$\infty^{3}$$ one-parameter motion groups in itself, and exactly that is the number of the additional solutions of the exercise, that are given by the trajectories of that group.

If one takes into consideration, that $$C_0$$ is the image of a point of a "rigid" body – its world-line – then the answer can be given to the question after the freedom of motion of a "rigid" body:

In 's kinematics of rigid bodies, the motion of the whole body is generally unequivocally determined by the arbitrarily defined motion of a single point of it.

An exception only takes place, when the world-line of that point in $$R_4$$ has constant curvatures, namely in this case – depending on the condition that it doesn't lie in a lower space than (at the most) $$R_3$$ or $$R_2$$, or eventually it is a straight line – there additionally exist 1 or $$\infty^{1}$$ or $$\infty^{3}$$ possible motions.

However, although by this result the immediately given purpose – the determination of the degrees of freedom of a "rigid" body – is achieved, it is apparently necessary to particularly consider all the possible forms of motion, especially also in the special cases. Although they cannot be used for a general definition of a "rigid" body, they have a special meaning from the standpoint of the relativity principle. It is therefore convenient to incorporate some simple facts of non-Euclidean geometry, which in any case can be used with advantage for questions concerning the theory of relativity – for example for the composition of velocities – as it will be shown at a specific place.

III. The Lorentz transformation and hyperbolic geometry in $$R_3$$.
The measure-determination introduced in $$R_{4}(x,y,z,t)$$ coincides in the bundle of $$\infty^{3}$$ – for example, the lines that emanate from the origin $$O(x=y=z=t=0)$$ – with 's metric that is based on the real minimal cone of that point as absolute cone. By projective representation of the line bundle at the points of $$R_3$$, it goes over into a real plane of second order, the measure-determination therefore goes over into 's metric that is based on that real $$F_2$$. The rotations around O in $$R_4$$ – the Lorentz transformations – correspond to the motions in $$R_3$$ which are related to this hyperbolic measure-determination. To give this obvious connection a certain form and take advantage from it for the current purpose, we have to remind some known things of hyperbolic geometry.

To project a line bundle of $$R_4$$ through O upon $$R_3$$ in a simple manner, one only has to set x,y,z,t equal to the homogeneous right angled coordinates $$z_{1},z_{2},z_{3},z_{4}$$ in $$R_3$$:

by which the minimal cone in $$R_3$$ corresponds to the unit sphere around the origin:

so that it has to serve as absolute plane of the measure-determination that has to be introduced in $$R_3$$.

The one- two- and three-dimensional structures of $$R_4$$ (which are plane and directed through O), are corresponding to the points, straight lines and planes of $$R_3$$. By their orientation in relation to the sphere, they visualize the orientation of the corresponding structures to the minimal cone (for example time-like lines = inner points, space-like lines = outer points). Any such structure of $$R_4$$ is normal to each other, if the corresponding structures of $$R_3$$ are conjugated to each other as regards the polar connectivity at the sphere (for example, two lines perpendicular to each other = two lines of which all are located at the polar plane of the other). The four edges of a polar tetrahedron of the sphere are corresponding in $$R_4$$ to four straight lines that pass through O and that are mutually normal; if we choose them in a convenient order and take the $$x',y',z',t'$$-axis as direction (the corresponding edge in the interior of the sphere, of course, as $$t'$$-axis) of a new coordinate system, then those new coordinates $$x',y',z',t'$$ are connected with the old ones x,y,z,t by a Lorentz transformation.

If in addition

are the components of a vector of second kind, then its two invariants are:

{{MathForm1|(41)|$$\left\{ \begin{align} D= & p_{23}p_{14}+p_{31}p_{24}+p_{12}p_{34},\\ \Delta= & p_{23}^{2}+p_{31}^{2}+p_{12}^{2}+p_{14}^{2}+p_{24}^{2}+p_{34}^{2} \end{align}\right.$$}}

and if one puts, in accordance with the reality relations of $$p_{ik}$$ (where $$f_{ik}$$ are to be understood as real magnitudes):

{{MathForm1|(42)|$$\left\{ \begin{align} & p_{23}:p_{31}:p_{12}:ip_{14}:ip_{24}:ip_{34}\\ & \qquad=f_{23}:f_{31}:f_{12}:f_{14}:f_{24}:f_{34},\\ & \qquad f_{ik}+f_{ki}=0, \end{align}\right.$$}}

then the vector of second kind can, regarding the relations of its components, illustrated by the linear complex of $$R_3$$:

As long as $$D\ne0$$, one has a general complex, and then there are two specified real straight lines that are conjugated polars, either with respect to the sphere or with respect to the complex. If one chooses a polar-tetrahedron of the sphere, from which two opposite edges coincide with this straight line, then in the corresponding system $$x',y',z',t'$$ all components $$p'_{ik}$$ of the vector of second kind will vanish, except of two whose values can immediately expressed by D and Δ.

However, if D = 0 (singular vector according to ), then this complex becomes a special one, consisting of all straight lines that intersect a specified straight line. This intersects, or is tangent to, or misses the sphere, depending ($$p_{23},p_{31},p_{12}$$ considered as real) on whether $$\Delta>0,\ \Delta=0,\ \Delta<0$$. The corresponding two-dimensional plane of $$R_4$$ can be used for clarification of the vector with respect to the relations of its components. Simultaneously, analogous to the preceding, by its aid the coordinate systems of $$R_4$$ can immediately be given in which as much as possible of the vector components will vanish.

Especially any infinitely small Lorentz transformation can be illustrated by a vector of second kind, the points of $$R_4$$ are all moving through it perpendicularly to its complex plane. Depending on whether $$D\ne0$$ or = 0, then in $$R_4$$ only the origin or also the points of the two-dimensional plane (used above) remain fixed. The latter intersects, or is tangent to, or misses the minimal cone depending on whether $$\Delta>0,=0,<0$$.

If one eventually imagine an arbitrary Lorentz transformation that transforms $$(x',y',z',t')$$ into (x,y,z,t), then this obviously corresponds to a collineation of $$R_3$$ that transforms the unit sphere in itself - exactly a hyperbolic motion of $$R_3$$.

Conversely, all of such collineations correspond to two linear homogeneous transformations in x,y,z,t with determinant 1 which leave $$ds^2$$ unchanged. The identical collineation of $$z_i$$ particularly corresponds to the two transformations:

{{MathForm1|(44)|$$\left\{ \begin{array}{crcrcrcr} x= & x', & y= & y', & z= & z', & t= & t'\\ x= & -x', & y= & -y', & z= & -z', & t= & -t'\end{array}\right.$$}}

From these, only the first is a Lorentz transformation, since the second one replaces the front- and back-cone of the point O against each other. The Lorentz transformations correspond one-to-one to hyperbolic motions in $$R_3$$.

Now in addition, the sphere will be transformed in itself by any of such a motion, so that the complex parameter (imagined as extended upon it):

is subjected to a linear substitution with generally complex coefficients (the additionally conjugated complex parameter, the conjugated complex substitution), and to all such substitutions corresponds a specified hyperbolic motion in $$R_3$$.

If $$x',y',z',t'$$ are transformed into x,y,z,t by a Lorentz transformation, then the magnitudes:

are connected to each other by a linear substitution (with complex coefficients)

and all such substitutions are corresponding to a certain Lorentz transformation.

If one wants, as it is necessary for the following, to write the one-parameter group of Lorentz transformations, then one only has to take the one-parameter group of linear substitutions in $$\mathsf{Z}$$, and to form the corresponding Lorentz transformation. The first ones are now (by ϑ we think of the [real] parameter, by λ of an arbitrary real magnitude):

$$\begin{align} \mathsf{I.} & &  & \mathsf{Z}=\mathsf{Z}'e^{(1+i\lambda)\vartheta} &  & \mathrm{loxodromic} & \mathrm{group}\\ \mathsf{II.} & &  & \mathsf{Z}=\mathsf{Z}'e^{i\vartheta} &  & \mathrm{elliptical} & ''\\ \mathsf{III.} & &  & \mathsf{Z}=\mathsf{Z}'e^{\vartheta} &  & \mathrm{hyperbolic} & ''\\ \mathsf{IV.} & &  & \mathsf{Z}=\mathsf{Z}'+\vartheta &  & \mathrm{parabolic} & '' \end{align}$$

They correspond to the following groups of Lorentz transformation (for the sake of convenience they shall be denoted by the same names):

I. Loxodromic group

$$\begin{align} x+iy= & (x'+iy')e^{i\lambda\vartheta}, & t-z= & (t'-z')e^{\vartheta},\\ x-iy= & (x'-iy')e^{-i\lambda\vartheta}, & t+z= & (t'+z')e^{-\vartheta}, \end{align}$$

II. Elliptic group

$$\begin{align} x+iy= & (x'+iy')e^{i\vartheta}, & z= & z',\\ x-iy= & (x'-iy')e^{-i\vartheta}, & t= & t'. \end{align}$$

III. Hyperbolic group

$$\begin{align} x= & x', & t-z= & (t'-z')e^{\vartheta}\\ y= & y', & t+z= & (t'+z')e^{-\vartheta} \end{align}$$

IV. Parabolic group

$$\begin{align} x= & x'+\vartheta(t'-z'), & y= & y'\\ z= & z'+\vartheta x'+\frac{1}{2}\vartheta^{2}(t'-z'), & t-z= & t'-z'. \end{align}$$

One notices at once, that these four groups are only different from each other by the kind of vector of second kind that illustrates the corresponding infinitesimal transformation.

IV. The one-parametric groups of motions in $$R_4$$ and the corresponding forms of motion of "rigid" bodies.
If one writes for the sake of symmetry:

{{MathForm1|(48)|$$\left\{ \begin{align} x_{1}= & x, & x_{2}= & y, & x_{3}= & z, & x_{4}= & it,\\ x'_{1}= & x', & x'_{2}= & y', & x'_{3}= & z', & x'_{4}= & it', \end{align}\right.$$}}

then any motion in $$R_4$$ can be analytically expressed in the form of a linear substitution:

Then $$\left|a_{ij}\right|$$ is an orthogonal determinant of value +1, additionally $$a_{44}$$ is real positive and the remaining magnitudes $$a_{i},a_{ij}$$ are purely imaginary or real, depending on whether they have the index 4 or not.

If one has by (49) a continuous family of motions that depend on parameter ϑ, that is, $$a_i$$ and $$a_{ij}$$ are functions of ϑ, then by differentiation with respect to ϑ while $$x_i$$ remains constant:

where it is put:

{{MathForm1|(51)|$$\left\{ \begin{align} q_{i}= & \sum\limits _{1}^{4}j\ a_{ij}\frac{da_{ij}}{d\vartheta},\\ & &  & (i,j=1,2,3,4)\\ p_{ij}= & \sum\limits _{1}^{4}k\ a_{ki}\frac{da_{kj}}{d\vartheta}, & p_{ij}+p_{ji}=0 \end{align}\right.$$}}

therefore also the magnitudes $$q_i$$ and $$p_{ij}$$ are purely imaginary or real, depending on whether they have the index 4 or not.

If we interpret (49) as equations of the coordinate transformation from system S(x,y,z,t) into a system $$S'(x',y',z',t')$$ moving against it, then consequently $$-q_{i}$$ would be the components of the vector (first kind) of velocity of the origin $$O'$$ of $$S'$$ and $$-p_{ij}$$ would be the components of the vector (second kind) of the angular velocity of $$S'$$ around $$O'$$, both times taken by the axis of $$S'$$.

If the family of motions forms a group, then (by convenient choice of ϑ) $$q_i$$ and $$p_{ij}$$ are independent from ϑ, and conversely the integration of equations (50) always gives a group of motions for arbitrary values of $$p_i$$ and $$p_{ij}$$.

The trajectories of the group – the trajectories of the points fixed at $$S'$$ according to the interpretation above – which (as we know) form an equidistant family of curves, are illustrated by (49) with constant $$x'_{i}$$ and variable ϑ; they of course only apparently depend on four parameters, but actually they depend only on three parameters.

Now, after these remarks, in order to write down the possible one-parameter groups of motion of $$R_4$$, and consequently in order to simultaneously write down the corresponding equidistant family of curves, one has to note that when the motions (49) form a group, then the same is true for the rotations:

and this must be – in general only after performing a suitable Lorentz transformation to $$x_i$$ and of the same to $$x'_{i}$$ – identical with one of the four groups of Lorentz transformations specified in the preceding section; namely with the group I. II. III. IV., depending on whether it applies to the invariant D and Δ of the vector $$p_{ij}$$:

{{MathForm1|(53)|$$\left\{ \begin{array}{rllrll} \mathrm{I}. & D\ne0, & & \mathrm{II}. & D=0, & \Delta>0,\\ \mathrm{II}. & D=0, & \Delta<0, & \mathrm{IV}. & D=0, & \Delta=0.\end{array}\right.$$}}

By that, the possible value systems of $$a_{ij}$$ can immediately be given, though the values associated with $$a_i$$ in all cases follow from (51):

and specifically we can chose arbitrary constants for $$q_j$$, as long as:

at least for a certain field of values of $$x'_{j}$$. Now, furthermore the values of $$p_{ij}$$ for the four groups are one after the other:

$$\left.\begin{align} \mathrm{I}. & & p_{21}= & -p_{12}=\lambda, & p_{34}= & -p_{43}=i\\ \mathrm{II}. & & p_{21}= & -p_{12}=1,\\ \mathrm{III}. & & p_{34}= & -p_{43}=i,\\ \mathrm{IV}. & & q_{31}= & -p_{13}=1, & p_{41}= & -p_{14}=i \end{align}\right\} $$ the remaining $$p_{ij}$$ are always equal to zero

and in connection with (50) they teach us, that by a convenient change of system $$S'$$ (as well as of the system S) we always can achieve to following more simple value systems of $$q_i$$:

$$\begin{align} \mathrm{I}. & & q_{1}= & 0 & q_{2}= & 0, & q_{3} & =0, & q_{4} & =0,\\ \mathrm{II}. & & = & 0, & = & 0, &  & =0, &  & =\delta i,\\ \mathrm{III}. & & = & \alpha, & = & 0, &  & =0, &  & =0,\\ \mathrm{IV}. & & = & 0, & = & \beta, &  & =0, &  & =\delta i, \end{align}$$

Now, all this gives the following groups of motion, named after the rotation groups that are contained in them, together with the corresponding equidistant family of curves and motion types of the "rigid" body:

I. Loxodromic group

If t = 0:

$$x=x_{0},\ y=y_{0},\ z=z_{0},\ \vartheta=\vartheta_{0},$$

then for the corresponding motion of a "rigid" body it follows:

{{MathForm1|(57)|$$\left\{ \begin{align} x+iy= & \left(x_{0}+iy_{0}\right)e^{i\lambda u}, & u=\lg\frac{\sqrt{z_{0}^{2}+t^{2}}-t}{z_{0}}\\ x-iy= & \left(x_{0}-iy_{0}\right)e^{-i\lambda u},\\ z= & \sqrt{z_{0}^{2}+t^{2}}. \end{align}\right.$$}}

If one uses cylindrical coordinates $$\varrho,\varphi,z,\left(x+iy=\varrho e^{i\varphi}\right)$$, then these equations can also be written:

{{MathForm1|(58)|$$\left\{ \begin{align} \varrho= & \varrho_{0},\\ z= & \frac{1}{2}u_{0}\left(e^{\frac{\varphi-\varphi_{0}}{\lambda}}+e^{-\frac{\varphi-\varphi_{0}}{\lambda}}\right),\\ t= & \sqrt{z^{2}-z_{0}^{2}}. \end{align}\right.$$}}

Thus the points of a "rigid" body are moving upon sphere cylinders around the Z-axis along curves, and which, by unwinding of the cylinder on a plane, go over into catenaries with the velocity:

The points on the Z-axis are moving in this plane by the law denoted by as "hyperbolic motion": $$z=\sqrt{z_{0}^{2}+t^{2}}$$

Their world-lines are lying in $$R_2$$, while those of all other points belong to a space not lower than $$R_4$$.

II. Elliptic group

$$\begin{align} x+iy= & (x'+iy')e^{i\vartheta}, & z= & z',\\ x-iy= & (x'-iy')e^{-i\vartheta}, & t= & t'+\delta\vartheta. \end{align}$$

If t = 0:

$$x=x_{0},\ y=y_{0},\ z=z_{0},\ \vartheta=\vartheta_{0},$$

then for the corresponding motion of the "rigid" body it follows:

{{MathForm1|(60)|$$\left\{ \begin{align} x+iy= & \left(x_{0}+iy_{0}\right)e^{i\frac{t}{\delta}},\\ x-iy= & \left(x_{0}-iy_{0}\right)e^{-i\frac{t}{\delta}},\\ z= & z_{0}. \end{align}\right.$$}}

Thus this body rotates like an ordinary rigid body uniformly around the Z-axis.

The world-line of the points on the Z-axis are straight lines, the world-lines of all other points belong each to $$R_3$$, but not to a space lower than it.

III. Hyperbolic group.

$$\begin{align} x= & x'+\alpha\vartheta, & t-z= & (t'-z')e^{\vartheta},\\ y= & y', & t+z= & (t'+z')e^{-\vartheta}, \end{align}$$

If t = 0:

$$x=x_{0},\ y=y_{0},\ z=z_{0},\ \vartheta=\vartheta_{0},$$

then for the corresponding motion of the "rigid" body it follows:

{{MathForm1|(61)|$$\left\{ \begin{align} x= & x_{0}+\alpha\lg\frac{\sqrt{z_{0}^{2}+t^{2}}-t}{z_{0}},\\ y= & y_{0},\\ z= & \sqrt{z_{0}^{2}+t^{2}} \end{align}\right.$$}}

Thus its points are moving in planes normal to the Y-axis along catenaries:

with the velocity:

the world-lines of all points belong each to $$R_3$$, but not to a space lower than it.

IV. Parabolic group.

$$\begin{align} x= & x'+\vartheta\left(t'-z'\right)+\frac{1}{2}\delta\vartheta^{2}, & y= & y'+\beta\vartheta,\\ z= & z'+\vartheta x'+\frac{1}{2}\vartheta^{2}(t'-z')+\frac{1}{6}\delta\vartheta^{3}, & t-z= & t'-z'+\delta\vartheta. \end{align}$$

Here:

thus it is necessarily $$\delta\ne0$$.

If we put $$\vartheta=\vartheta_{0}$$:

$$x=x_{0},\ y=y_{0},\ z=z_{0},\ t=t_{0},$$

then the expressions above remain unchanged due to the group property, as long as one replaces $$x',y',z',t',\vartheta$$ by $$x_{0},y_{0},z_{0},t_{0},\vartheta-\vartheta_{0}$$ within them. If one particularly takes:

$$\vartheta_{0}=-\frac{1}{\delta}(t'-z'),$$

then $$t_{0}=z_{0}$$.

Since for the motion of a rigid body only the trajectories of the group are of importance, instead of

$\vartheta+\frac{1}{\delta}(t'-z')$,

one can again write ϑ and then formulate the equations for the motion of a "rigid" body as follows:

{{MathForm1|(65)|$$\left\{ \begin{align} x= & x_{0}+\frac{1}{2}\delta\vartheta^{2}, & y= & y_{0}+\beta\vartheta,\\ z= & z_{0}+x_{0}\vartheta+\frac{1}{6}\delta\vartheta^{3}, & t-z= & \delta\vartheta \end{align}\right.$$}}

Thus all its points are moving along space curves of third order with the velocity:

The world-lines of all points belong each to $$R_3$$, but not to a space lower than it.

If one poses for clarities sake the question, which of the formed equidistant families of curves of class (B) simultaneously also belong to class (A), i.e, which are orthogonal trajectories of a family of planes, then for the magnitudes $$q_i$$ and $$p_{ij}$$ that belong to the corresponding group, it is given:

and for that it is necessary and sufficient, that the 4×5 matrix which emerges from the determinant $$\left|p_{ij}\right|$$ by addition of row $$q_i$$, has the rank 1 or 2. The related discussion teaches, that this only occurs for the hyperbolic group II. with α = 0, by which indeed the trajectories are the orthogonal trajectories of the planes $$Az+Bt=0$$. The corresponding motion of the "rigid" body reads:

This most simple translational motion, which was also discussed by and denoted as "hyperbolic motion", it thus the only type of motion that simultaneously belong to classes (A) and (B).

Of course, the four types of motion of class (B) formed at this place, can be transformed by an arbitrary Lorentz transformation.

Anyway, due to the given composition it is easy (by a given motion of a point of the "rigid" body) to immediately and explicitly give the possible types of motion of class (B) in addition to the motion of class (A). If, for example, a point of the body is fixed, then its world-line is a straight line, but such one arises as a trajectory only in group II – which immediately gives the fact mentioned at the beginning, that a "rigid" body with a fixed point only can rotate around an axis that goes through it, like an ordinary rigid body.

It may be noticed at the end, that the determination of the always possible motion of a "rigid" body from the motion of one of its points that belong to class (A) – i.e, the determination in $$R_4$$ of the orthogonal trajectories of the normal planes of that point's world-line – can be traced back to the integration of a an equation.

Leipzig, December 1, 1909.

Received December 7, 1909


text:
Page:Title 3 CFR 2005 Compilation.djvu/97

 Proc. 7912 Title 3--The President Annex I (continued) 2916.39.08 29 ! 7.32.00 2918.21.10 2920.10.40 2916.39.12 2917.33.00 2918.23.10 2920.10.50 2916.39.16 2917.34.00 2918.23.20 2920.90.10 2916.39.20 2917.35.00 2918.29.22 2920.90.50 2917.11.00 2917.37.00 2918.29.25 2921.11.00 2917.12.20 2917.39.20 2918.29.30 2921.12.00 2917.13.00 2918.11.10 29l 8.30.90 2921.19.10 2917.14.10 2918.11.50 2918.90.18 2921.[9.60 2917.19.10 2918.13.50 2918.90.20 2921.21.00 29 ] 7.19.15 2918.14.00 2918.90.30 2921.22.05 2917.19.17 2918.15.10 2918.90.35 292[.22.50 2917.19.23 29I 8.15.50 2918.90.50 2921.29.00 2917.19.30 2918.16.10 2919.00.25 2921.30.50 2917.19.70 2918.16.50 2919.00.50 2921.42.15 2917.31.00 2918.19.60 2920. ! O. 10 2921.42.21 2921.42.55 2924.29.47 293 ! .00.25 2933.61.00 2921.43.15 2924.29.52 2931.00.90 2933.69.60 2921.43.19 2924.29.62 2932.11.00 2933.71.00 2921.43.22 2924.29.65 2932.13.00 2933.79.20 2921.49.32 2924.29.95 2932.19.50 2933.79.30 2921.51.20 2925.t 1.00 2932.21.00 2933.79.85 2921.59.20 2925.19.90 2932.29.10 2933.99.06 2922.11.00 2925.20.90 2932.29.25 2933.99.14 2922.12.00 2926.10.00 2932.29.50 2933.99.17 2922.13.00 2926.90.08 2932.94.00 2933.99.22 2922.19.95 2926.90.14 2932.99.08 2933.99.24 2922.29.26 2926.90.17 2932.99.20 2933.99.85 2922.29.29 2926.90.21 2933.11.00 2933.99.87 2922.39.14 2926.90.23 2933.19.23 2933.99.90 2922.39.50 2926.90.25 2933.19.30 2933.99.97 2922.41.00 2926.90.30 2933.19.35 2934.10.90 2922.42.50 2927.00.15 2933.19.45 2934.20.05 2922.49.40 2927.00.25 2933.19.90 2934.20.10 2922.49.80 2927.00.30 2933.21.00 2934.20.15 2922.50.11 2928.00.30 2933.29.20 2934.20.35 2922.50.19 2928.00.50 2933.29.45 2934.99.08 2922.50.50 2929.10.30 2933.29.90 2934.99.11 2923.10.00 2929.90.50 2933.39.21 2934.99.12 2923.20.20 2930.10.00 2933.39.25 2934.99.15 2923.90.00 2930.20.10 2933.39.27 2934.99.16 2924.19.10 2930.20.90 2933.49.08 2934.99. l 8 2924\17721.04 2930.30.60 2933.49.10 2934.99.20 2924.21.18 2930.90.10 2933.59.10 2934.99.30 2924.21.50 2930.90.24 2933.59. l 5 2934\17799.47 2924.29.10 2930.90.30 2933.59.18 2934.99.90 2924.29.36 2930.90.44 2933.59.59 2935.00.06 2924.29.43 2930.90.90 2933.59\17795 2935.00\17720 84

�

license: Creative Commons - Attribution Share-Alike - https://creativecommons.org/licenses/by-sa/4.0/


text:
Page:Title 3 CFR 2005 Compilation.djvu/98

 Proclamations Proc. 7912 Annex I (continued) 2935.00.32 3206.11.00 3208.90.00 3307.10.10 2938.10.00 3206.19.00 3209.10.00 3307.10.20 2938.90.00 3206.20.00 3210.00.00 3307.30.10 2940.00.60 3206.30.00 3212.10.00 3307.30.50 294!.20.10 3206.41.00 3213.10.00 3307.41.00 2942.00.50 3206.42.00 3213.90.00 3307.90.00 320 1.90.10 3206.43.00 3214.10.00 3401.30.10 3201.90.50 3206.49.10 3215.11.00 3402.11.20 3202.10.10 3206.49.30 3215.19.00 3402.11.40 3202.90.50 3206.49.50 3215.90.10 3402.11.50 3203.00.80 3207.10.00 3215.90.50 3402.12.10 3204.19.35 3207.20.00 3301.24.00 3402.12.50 3204.20.10 3207.30.00 330!.29.10 3402.13.10 3204.20.80 3207.40.10 3301.29.20 3402.13.20 3204.90.00 3208.10.00 3302.10.40 3402.13.50 3205.00.15 3208.20.00 3302. I 0.50 3402.19.10 3402.19.50 3701.99.60 3805.!0.00 3823.19.20 3402.20.11 3702.20.00 3806.10.00 3824.20.00 3402.90.10 3702.31.00 3806.20.00 3824.30.00 3402.90.30 3702.32.00 3806.30.00 3824.60.00 3402.90.50 3702.39.00 3806.90.00 3824.90.19 3403.11.40 3702.4!.00 3807.00.00 3824.90.22 3403.11.50 3702.42.00 3808.10. lO 3824.90.25. 3403.19.50 3702.43.00 3808.10.25 3824.90.28 3403.91.10 3702.44.00 3808.10.30 3824.90.31 3404.20.00 3702.51.00 3808.20.15 3824.90.32 3501.10.10 3702.52.00 3808.20.28 3824.90.33 3501.90.60 3702.53.00 3808.20.30 3824.90.34 3503.00.10 3702.54.00 3808.30.15 3824.90.36 3503.00.55 3702.91.01 3808.30.20 3824.90.40 3504.00.10 3702.93.00 3808.40.10 3824.90.46 3505. ! 0.00 3702.95.00 3808.40.50 3926.20.30 3505.20.00 3703.10.30 3808.90.08 4101.20.35 3506.10.50 3703.10.60 3808.90.70 4101.50.35 3506.91.00 3703.20.30 3809.10.00 4101.90.35 3601.00.00 3703.20.60 3809.91.00 4104.11.30 3603.00.30 3703.90.30 3812.10.10 4104.19.30 3603.00.60 3703.90.60 3812.20.10 4104.41.30 3603.00.90 3707.1'0.00 3812.30.20 4104.49.30 3604.10.10 3707.90.60 3812.30.60 4203.21.20 3604.10.90 3801.10.10 3813.00.50 4203.21.55 3604.90.00 3801.30.00 3814.00.20 4203.21.60 3606.90.80 380!.90.00 381190.20 4203.21.80 3701.20.00 3802.10.00 3816.00.00 4412.13.40 3701.30.00 3802.90.10 3817.00.15 4601.91.05 3701.91.00 3802.90.20 3823.11.00 4601.99.05 3701.99.30 3802.90.50 3823.12.00 6304.99.10 85

�


text:
Page:Title 3 CFR 2005 Compilation.djvu/99

 Proc. 7912 Title 3--The President Annex I (continued) 6304.99.25 7113.19.25 8516.50.00 9506.91.00 6304.99.40 7116.20.05 9001.30.00 7012.00.00 7116.20.15 9009.12.00 7113.11.50 7615.19.30 9506.62.80 (5). For the following provisions, the Rates of Duty 1-Special subc01umn is modified by deleting the symbol "A" and inserting an "A*" in lieu thereoff 0603.10.80 2306.50.00 6406.91.00 7408.19.00 0710.29.15 2611.00.60 6802.21.10 8544.30.00 0804.50.80 4101.50.70 6802.91.20 1702.90.10 4t03.20.20 7202.49.50 2008.30.96 4412.19.40 7408.11.60 Section D. Effective with respect to articles entered, or withdrawn from warehouse for consumption, on or after July 1,2005, general note 4(a) of the Harmonized Tariff Schedule of the United States is modified by adding to the "Associations of Countries (treated as one country)", the following: "Member countries of the South Asian Association for Regional Cooperation (SAARC) Currently qualifying: Bangladesh Bhutan India Nepal Pakistan Sri Lanka" Annex II HTS subheading and countries for which the competitive need limitation provided in section 503(c)(2)(A)(i)(II) is waived 0202.30.02 Uruguay 0813.40.80 Thailand 0302.69.10 Philippines 1102\17730.00 Thailand 0305.20.20 Russia 1202.10.40 Egypt 0410.00.00 Indonesia 1301.90.40 India 071 1.40.00 India 1401.90.40 Argentina 0712.90.70 Egypt 1517.90.10 Argentina 0713.90.60 India 1601.00.40 Brazil 0713.90.80 India 1602.50.09 Argentina 0802.50.20 Turkey 170I \17791.80 Brazil 0804.10.60 Pakistan 1702.90.35 Brazil 0810.60.00 Thailand 1806.10.43 Brazil 0813.40.10 Thailand t 901.20.45 Argentina

�


text:
Page:Title 3 CFR 2005 Compilation.djvu/100

 Proclamations Proc. 7912 Annex II (continued) 2006.00.70 Thailand 4107.11.40 India 2008.99.35 Thailand 4107.11.60 Brazil 2008.99.50 Thailand 4107.12.40 India 2009.39.20 Brazil 4107.91.40 India 2305.00.00 Argentina 4107.99.40 India 2306.30.00 Argentina 4202.92.04 Philippines 2515.12.20 Turkey 5007.10.30 India 2804.29.00 Russia 5208.31.20 India 2826.20.00 Brazil 5208.41.20 India 2840.11.00 Turkey 5208.42.10 India 2840.19.00 Turkey 5209.31.30 India 2841.50.10 Kazakhstan 5209.41.30 India 2841.90.20 Kazakhstan 7113.20.25 India 2850.00.20 Russia 7202.1 I. 10 Georgia 2903.51.00 Romania 7307.21.10 India 2903.69.08 Brazil 7413.00.90 Turkey 2909.50.40 Indonesia 8112.12.00 Kazakhstan 2915.34.00 Russia 8112.19.00 Kazakhstan 2934.99.18 Brazil 8406.90.30 Brazil 3808.40.10 Argentina 8410.13.00 Brazil 410 ! .20.40 Brazil 8528.12.16 Thailand 4101.50.50 Brazil 8528.30.50 India 4101.90.35 Argentina 9016.00.40 Thailand 4101.90.40 Argentina 9614.20.60 Turkey 4106.21.90 India 4106.22.00 Pakistan Annex III HTS Subheading and Country Granted A Waiver of the Application of Section 503(c)(2)(A) of the 1974 Act HTS Subheading Country 3823.19.20 Philippines 4107.19.50 Argentina 4107.92.80 Argentina 4412.13.40 Indonesia 7113.11.50 Thailand 9001.30.00 Indonesia 9009.12.00 Thailand 87

�


text:
Page:Title 3 CFR 2005 Compilation.djvu/101

 Proc. 7912 Title 3--The President Annex IV Effective with respect to goods of Canada under the terms of general note 12 that are entered, or withdrawn from warehouse for consumption, on or after July 1, 2005, general note 12(t) to the Harmonized Tariff Schedule of the United States is hereby modified as follows: 1. Tariff classification rule (TCR) 3 to chapter 51 is redesignated as 3B, and the following new provisions are inserted immediately below TCR 2 to such chapter: "Note: The following TCRs 3 and 3A apply only to goods of Canada under the terms of this note. 3. A change to woven fabrics (other than tapestry fabrics or upholstery fabrics of a weight not exceeding 140 grams per square meter) of combed fine animal hair of subheading 5112.11 from yam of combed camel hair or combed cashmere of subheading 5108.20 or any other heading, except from headings 5106 through 5107, any other good of heading 5108 or headings 5109 through 5111, 5113, 5205 through 5206, 5401 through 5404 or 5509 through 5510. 3A. A change to woven fabrics, other than tapestry fabrics or upfiolstery fabrics, of combed fine animal hair of subheading 5112.19 from yarn of combed camel hair or combed cashmere of subheading 5108.20 or any other heading, except grom headings 5106 through 5107, any other good of heading 5108 or headings 5109 through 5111, 5113, 5205 through 5206, 5401 through 5404 or 5509 through 5510." 2. TCR 4 to chapter 54 is redesignated as 4A, and the following new provisions are inserted immediately below TCR 3 to such chapter: "Note: The following TCR 4 applies only to goods of Canada under the terms of this note. 4. A change to heading 5408 from filament yams of viscose rayon of heading 5403 or any other chapter, except from headings 5106 through 5110, 5205 through 5206 or 5509 through 5510." 3. TCR 1 to chapter 55 is redesignated as 1A, and the following new provisions are inserted immediately below the side heading "Chapter 55.": "Note: The following TCR 1 applies only to goods of Canada under the terms of this note. 1. A change to subheading 5509.31 from acid-dyeable acrylic tow of subheading 5501.30 or any other chapter, except from headings 5201 through 5203 or 5401 through 5405." 4. The text of the TCR to chapter 56 is designated as TCR 3 to such chapter and shall be included in general note 12(t) below the side heading "Chapter 56.", and the following new provisions are inserted immediately below such side heading: "Note: The following TCRs 1 and 2 and heading rule apply only to goods of Canada under the terms of this note. 1. A change to sanitary towels or tampohs of subheading 5601.10 from tfi-lobal rayon staple fiber (38 mm, 3.3 decitex) of subheading 5504.10 or any other chapter, except from headings 5106 through 5113, 5204 through 5212, 5307 through 5308 or 5310 through 5311 or chapters 54 through 55. Heading rule: For the purposes of TCR 2 to this chapter, the tem\177 "fiat yams" means multifilament yams of nylon 66 of subheading 5402.41, the foregoing whmh are untextured (flat) semi-dull yams, either untwisted or with a twist not exceeding 50 trans per meter, comprising 7 denier/5 filament, 10 demer/7 filament or 12 dedier/5 filament. 2. A change to heading 5606 from flat yams of subheading 5402.41 or any other chapter, except from headings 5106 through 5113, 5204 through 5212, 5307 through 5308 or 5310 through 5311 or chapters 54 through 55."

�


text:
Page:Title 3 CFR 2005 Compilation.djvu/102

 Proclamations Proc. 7912 Annex IV (continued) 5. The text of the TCR to chapter 58 is designated as TCR 2 to such chapter and shall be included in general note 12(0 below the side heading "Chapter 58.", and the following new provisions are inserted immediately below such side heading: "Note: The following TCR I applies only to goods of Canada under the terms of this note. I. A change to warp pile fabrics, cut, of subheading 5801\17735 (the foregoing fabrics with pile of d\177y-spun acrylic staple fibers of subheading 5503.30 and dyed in the piece to a single uniform color) from any other chapter, except from headings 5106 through 5113, 5204 through 5212, 5307 through 5308 or 5310 through 531 I, chapter 54, headings 5501 through 5502, subheadings 5503.10 through 5503.20 or 5503.40 through 5503.90 or headings 5504 through 5515." Annex V Effective with respect to goods entered, or withdrawn from warehouse for consumption, on or after December 18, 2004, the Harmonized Tariff Schedule of the United States (HTS) is hereby modified as follows: 1. General note 7 to the HTS is modified by inserting at the end thereof the following new subdivision: "(h) The duty-free treatment provided under the CBERA shall not apply to any footwear provided for in any of subheadings 6401.10.00, 6401.91.00, 6401.92.90, 6401.99.30, 6401.99.60, 6401.99.90, 6402.30.50, 6402.30.70, 6402.30.80, 6402.91.50, 6402.91.80, 6402.91.90, 6402.99.20, 6402.99.80, 6402.99.90, 6403.59.60, 6403.91.30, 6403.99.60, 6403.99.90, 6404.11.90 and 6404.19.20 of the tarlff schedule that was not designated on December 18, 2004, as eligible articles for purposes of the GSP under general note 4 to the tariff schedule." 2. General note 17 to the HTS is modified as follows: (A) by redesignating subdivision (d) of such note as subdivision (e); (B) deleting "Articles" at the beginning of the text of subdivision (b) of such note and by inserting in lieu themof"Except as pmvided in subdivision (d) of this note, articles"; and (C) by inserting the following new subdivision (d) in sequence: "(d) Subdivision (b)(ii) of this note shall not apply to footwear provided for in any of subheadings 6403.59\17760, 6403.91.30, 6403.99.60 and 6403.99.90 of the tariff schedule, and footwear provided for in any such subheading shall be eligible for the rate of duty set forth in the "Special" rates of duty subcolumn followed by the symbol "R" in parentheses if-- (i) the article of footwear is the growth, product or manufacture of a designated beneficiary country enumerated in subdivision (a) of this note; and (ii) the article meets all requirements of general note 7 to the tariff schedule other than being the growth, product or manufacture of a beneficiary country set forth in subdivision (a) of such general note 7." 3\177 For each of the following subheadings of HTS chapter 64, the symbol "E," is inserted in alphabetical sequence in the parenthetical expression following the duty rate of"Free" in the Rates of Duty 1-Special subcolumn: 89

�


text:
Page:Title 3 CFR 2005 Compilation.djvu/103

 Proc. 7912 Title 3--The President Annex V (continued) 6401.92.60, 6402.19.05, 6402.19.15, 6402.19.50, 6402.19.70, 6402.19.90, 6402.30.30, 6402.91.40, 6402.91.60, 6402.91.70, 6402.99.05, 6402.99. I 0, 6402.99.14, 6402.99.18, 6402.99.30, 6402.99.60, 6402.99.70, 6403.19.10, 6403.19.30, 6403.19.40, 6403.19.50, 6403.40.30, 6403.40.60, 6403.51.30, 6403.51.60, 6403.51.90, 6403.59.30, 6403.59.90, 6403.91.60, 6403.91.90, 6403.99.20, 6403.99.40, 6403.99\17775, 6404.11.20, 6404.11.40, 6404.11.50, 6404.11.60, 6404. l 1.70, 6404.11.80, 6404.19.15, 6404.19.25, 6404.19.30, 6404.19.35, 6404.19.40, 6404.19.50, 6404.19.60, 6404.19.70, 6404.19.80, 6404.19.90, 6404.20.20, 6404.20.40, 6404.20.60, 6405.10.00, 6405.20.30, 6405.20.60, 6405.20.90, 6405.90.90. Annex VI Section A. Effective with respect to goods of Singapore under the terms of general note 25 to the tariff schedule that are entered, or withdrawn from warehouse for consumption, on or after January 1, 2004, general note 25(c)(ii)(B) is modified by inserting the expression "herein" after the word "enumerated" and by striking out "in subdivision (m) of this note", and by inserting at the end of such subdivision (c)(ii)(B) the following new text and tabulation: "For purposes of this note, a "remanufactared good" must, in its condition as imported, be ciassifiable in a tariff provision enumerated in the first colunto below and be described opposite such provision: Heading/Subheading Articles Eligible for Treatment as Remanufactured Goods Under this Note (1) 8408 Compression-ignition internal combustion engines (diesel or semi-diesel engines) (2) 8409.91, 8409.99 Parts (other than aircrat\177 engines) for use solely or principally wi\177 the engines of hcadlng 8407 or 8408 (3) 8412.21 Linear acting hydraulic power engines and motors (cylinders) (4) 8412.29 Other hydraulic power engines and motors (5) 8412.39 Pneumatic power engines and motors (other than linear acting (cylinders)) (6) 8412.90 Parts of engines and motors of heading 8412 (7) 8413.30 Fuel, lubricating or cooling medium pumps for internal combustion engines (8) 8413.50 Other reciprocating positive displacement pumps (9) 8413.60 Other rotary positive displacement pumps (10) 8413.91 Parts of pumps for liquids, whether or not fitted with a measuring device; parts of liquid elevators (11) 8414.30 Compressors of a kind used in refrigerating equipment (including air conditioning) (12) 8414.80 Other air or vacuum pumps, air or other gas compressors 9O

�


text:
Page:Title 3 CFR 2005 Compilation.djvu/104

 Proclamations Proc. 7912 Annex VI (continued) and fans not elsewhere enumerated in heading 8414; other ventilating or recycling hoods incorporating a fan, whether or not fitted with filters, the foregoing notelsewhere enumerated in heading 8414 ( 13 ) 8414.90 Parts of air or vacuum pumps, air or other gas compressors and fans; parts of other ventilating or recycling hoods incorporating a fan, whether or not fitted with fittings (14) 8419.89 Other machinery, plant or equipment of heading 8419 (15) 8431.20 Parts of machinery of heading 8427 (16) 8431.49 Other par\177 of machinery, not elsewhere enumerated in heading 8431 (17) 8481.20 Valves for oleohydraulic or pneumatic transmissions (18) 8481.40 Safety or relief valves (19) 8481.80 Other appliances, not elsewhere enumerated in heading 848 I (20) 8481.90 Pa\177s of taps, cocks, valves and similar appliances for pipes, boiler shells, tanks, vats or the like, including pressure-reducing valves and thermostatically controlled valves (21 ) 8483.10 Transmission shafts (including camshafts and crankshafts) and cranks (22) 8483.30 Bearing housings, not incorporating ball or roller bearings; plain shaft bearings (23) 8483.40 Gears and gearing, other than toothed wheels, chain sprockets and other transmission elements entered separately; ball or roller screws; gear boxes and other speed changers, including torque converters (24) 8483.50 Flywheels and pulleys, including pulley blocks (25) 8483.60 Clutches and shaft couplings (including universal joints) (26) 8483.90 Toothed wheels, chain sprockets and other transmission elements presented separately; parts of goods of heading 8483 (27) 8503 Parts suitable for use solely or principally with the machines of heading 8501 or 8502 (28) 8511.40 Starter motors and dual purpose starter-generators (29) 8511.50 Other generators, not elsewhere enumerated in heading 8511 (30) 8526.10 Radar apparatus (31) 8537.10 Boards, panels, consoles, desks, cabinets and other bases, equipped with two or more apparatus of heading 8535 or 8536, for electric control or the distribution of electricity, including those incorporating instruments or apparatus of chapter 90, and numerical control apparatus, other than switching apparatus of heading 8517, all the foregoing for a voltage not exceeding 1,000 V

�


text:
Page:Title 3 CFR 2005 Compilation.djvu/105

 Proc. 7912 Title 3--The President knnex VI (continued) (32) 8542.21 Digital monolithic integrated circuits (33) 8708.31 Mounted brake limngs for the motor vehicles of headings 8701 to 8705 (34) 8708.39 Brakes and servo-brakes for the motor vehicles of headings 8701 to 8705, and parts thereof (other than mounted brake linings of subheading 8708.31) (35) 8708.40 Gear boxes for the motor vehicles of headings 8701 to 8705 (36) 8708.60 Non-driving axles and parts thereof for the motor vehicles of headings 8701 to 8705 (37) 8708.70 Road wheels and parts and accessories thereof for the motor vehicles of headings 8701 to 8705 (38) 8708.93 Clutches and parts thereof for the motor vehicles of headings 8701 to 8705 (39) 8708.99 Other parts and accessories of the motor vehicles of headings 8701 to 8705, not elsewhere enumerated in heading 8708 (40) 9031.49 Other optical instruments and appliances (except for inspecting semiconductor wafers or devices or for inspecting photomasks or reticles used in manul:acturing semicoaductor devices), not specified or included elsewhere in chapter 90." Section B. Effective with respect to goods entered, or withdrawn from warehouse for consumption, on or after July 1, 2005, subheadings 1604.16.10 and 1604.16.30 are deleted and the following new provision is inserted in lieu thereof, with the material inserted in the columns entitled "Heading/Subheading", "Article Description", "Rates of Duty I General", "Rates of Duty 1 Special", and "Rates of Duty 2", respectively: [16041 :(Prepared...:] : : :
 * (Fish,...:]

[1604.16]: [Anchovies:] : : : "1604.16.20 : In oil, in airtight containers ; Free : : 30%" Section C. Effective with respect to goods of Australia under the terms of general note 28 to the tariff schedule that are entered, or withdrawn from warehouse for consumption, on or after January 1, 2005, such general note 28 is modified as set forth below: 1. Subdivision (b) is modified by deleting the word "note," at the of clause (iv) and the expression "and is iruported directly into the customs territory of the United States from the territory of Australia" and by inserting at the end of clause (iv) the word "note." 2. Subdivision (m)(vi) of such note is deleted, and subdivisions (vii), (viii), (ix), (x), (xi), (xii), (xiii) and (xiv) are redesignated as (vi), (vii), (viii), (ix), (x), (xi), (xii) and (xiii), respectively. 3. Tariff classification rule (TCR) I to chapter 56, as set forth in subdivision (n) of such note, is modified by deleting "chapter 54" and by inserting in lieu thereof "chapters 54". 92

�


text:
Page:Title 3 CFR 2005 Compilation.djvu/106

 Proclamations Proc. 7912 Annex VI (continued) 4. TCRs I0 and 11 to chapter 61 are each modified by deleting "53.07 through 53.08 or 53.10 through 53.11" and by inserting in lieu thereof"5307 through 5308 or 5310 through 5311 ". Section D. Effective with respect to goods of Chile under the terms of general note 26 to the tariff schedule that are entered, or withdrawn from warehouse for consumption, on or after January 1, 2004, general note 26(n) to the HTS is modified by deleting from tariff classification rule 63 of Chapter 29 "2926.45" and by inserting in lieu thereof"2921.45". Section E. Effective with respect to goods entered, or withdrawn from warehouse for consumption, on or after Decmnber 18, 2004, the HTS is \177nodified by inserting, in the Rates of Duty 1-Special subcolumn for subheadings 8510.20.10, 8510.20.90, and 8708.29.25, the symbols "CL," and "SG" in alphabetical sequence in the parenthetical expression following the "Free" rate of duty. Section F. Effective with respect to goods of Singapore under the terms of general note 25 to the HTS that are entered, or withdrawn from warehouse for consumption, on or after January 1, 2004, U.S. note 13 to subchapter X of chapter 99 of the HTS is modified as follows: by striking from subdivision (a) the word "man=made" and by inserting in lieu thereof"man-made"; and by striking from subdivision (d) the word "ttherto" and by inserting in lieu thereof "thereto". Section G. Effective with respect to goods entered, or withdrawn from warehouse for consumption, on or after the date of signature of this notice, the subheadings enmnerated below are each modified as provided herein: (i) For the following subheadings, the symbol ", MX" is deleted from the parenthetical expression following the duty rate "The rate applicable to each garment in the ensemble if separately entered" from the Rates of Duty 1-Special subcolumn and the symbol "MX," is inserted in alphabetical sequence in the parenthetical expression following the duty rate "Free" in such subcolumn: 6103.21.00, 6103.22.00, 6103.23.00, 6103.29.10, 6103.29.20, 6104.21.00, 6104.22.00, 6104.23.00, 6104.29.10, 6104.29.20, 6203.21.30, 6203.21.90, 6203.22.30, 6203.23.00, 6203.29.20, 6203.29.30, 6204.21.00, 6204.22.30, 6204.23.00, 6204.29.20, 6204.29.40. (2) For heading 9817.61.01, the symbol "MX," is deleted from the parenthetical expression following the duty rate "The rate applicable in the absence of this heading" in the Rates of Duty l-Special subcolumn and the symbol ", MX" is inserted in alphabetical sequence in the parenthetical expression following the duty rate "Free" in such subcolumn. Section H. Effective with respect to goods entered, or withdrawn from warehouse for consumption, on or after January 1, 2005, the tariff classification rules (TCRs) set forth in general note 12(t) to the HTS are modified as provided herein: (1) TCRs 8A and 8B to chapter 85 are deleted. (2) The following language is inserted immediately above TCR 9 to chapter 85: "Note: The following TCRs 8A and 8B apply only to goods of Canada under the terms of this note, 93

�


text:
Page:Title 3 CFR 2005 Compilation.djvu/107

 Proc. 7912 Title 3--The President Annex VI (continued) 8A. A change to tariff item 8504.90.65 tiom any other tariff item. 8B. (A) A change to subheading 8504.90 from any other heading; or (B) No required change in tariff classification to subheading 8504.90, provided there is a regional value content of not less than: ( 1 ) 60 percent where the transaction value method is used, or (2) 50 percent where the net cost method is used. Note: The following TCR 8B applies only to goods of Mexico under the terms of this note: 8B. A change to subheadlng 8504.90 from any other heading." Section I. Effective with respect to goods entered, or withdrawn from warehouse for consumption, on or after January 1, 2005, the HTS is modified by inserting, in the Rates of Duty l-Special subcolunm for subheading 8708.29.25, the symbol "AU" in alphabetical sequence in the parenthetical expression following the "Free" rate of duty.

�


text:
Page:Title 3 CFR 2005 Compilation.djvu/108

 Proclamations Proc. 7913 Proclamation 7913 of July 15, 2005 Captive Nations Week, 2005 By the President of the United States of America A Proclamation America stands for freedom and supports those who are oppressed. During Captive Nations Week, we reaffirm our commitment to advancing democ- racy, defending liberty, and protecting human rights around the world. When President Eisenhower issued the first Captive Nations Week procla- mation in 1959, freedom was being denied by communist regimes in Eu- rope, Asia, and Latin America. Millions were deprived of their rights to freely practice religion, assemble in public, and exercise freedom of speech. The Cold War and the captivity of millions of people in Central and East- ern Europe have since ended, and we have witnessed the rise of democratic governments in countries across the globe. Building a free and peaceful world is the work of generations, and this work continues. America believes that freedom is God's gift to each man and woman in this world and that spreading freedom's blessings is the call- ing of our time. We are continuing to work to help spread liberty and de- mocracy to people who have known fear and oppression. The gains in places like Afghanistan, Iraq, Ukraine, and Georgia have been achieved through the courage, determination, and sacrifice of millions of men and women in those countries, with the assistance of the United States and other allies. As a Nation forged from the ideals of freedom, justice, and human dignity, we will continue speaking out on behalf of oppressed people. We will sup- port the growth of democratic movements and institutions in every nation. This young century will be ]iberty's century, and during Captive Nations Week, we pledge to advance the cause of liberty for all people. The Congress, by Joint Resolution approved July 17, 1959 (73 Stat. 212), has authorized and requested the President to issue a proclamation desig- nating the third week in July of each year as "Captive Nations Week." NOW, THEREFORE, I, GEORGE W. BUSH, President of the United States of America, do hereby proclaim July 17 through July 23, 2005, as Captive Nations Week. I call upon the people of the United States to observe this week with appropriate ceremonies and activities and to reaffirm their com- mitment to all those seeking liberty, justice, and self-determination. IN WITNESS WHEREOF, I have hereunto set my hand this fifteenth day of July, in the year of our Lord two thousand five, and of the Independence of the United States of America the two hundred and thirtieth. GEORGE W. BUSH 95

�


text:
Page:A short history of social life in England.djvu/124

104 meats, such as that of oxen, goats, horses, camels, and water-fowl, rich fish, pastry, new bread, and old or moist cheese. Let him take moderate exercise before eating and rest entirely after it, and then ride horses or gently-trotting mules, avoiding rapid ascents or descents. Frequent combing of the hair is a great help, especially after sleep, for it assists the evaporation of the humours which ascend to the head."

In the same book there is an elaborate receipt for driving away mice: "Take realgar, salt, pomegranite bark, hellebore root, sulphur, litharge, and shells of shrimps, equal parts, rub together, and sprinkle on hot coals through the house. All mice will flee and will never come back. But do you also avoid that fume, for it is horrible exceedingly!"

One paragraph is specially funny. "In this book," says the author, "I propose with God's help to consider diseases peculiar to women, and since women are, for the most part, poisonous creatures, I shall then proceed to treat of the bites of venomous beasts."

Such, briefly, were the crude ideas surrounding the art of medicine, while surgery was chiefly in the hands of the barbers, when the terrible Black


text:
Page:Title 3 CFR 2005 Compilation.djvu/109

 Proc. 7914 Title 3--The President Proclamation 7914 of July 21, 2005 Parents' Day, 2005 By the President of the United States o/America A Proclamation Parents are role models for their children. With patience, sacrifice, and love, they teach their children life lessons and prepare them for the future. On Parents' Day, we express our gratitude for the hard work of parents throughout America and reaffirm our commitment to promoting a culture of responsible parenthood. Mothers and fathers love their children unconditionally and make daily sacrifices to provide for them. Parents create a safe, nurturing environment in which their children can grow and learn. By instructing their children to make right choices, parents instill lifelong values and prepare their chil- dren for the challenges and opportunities ahead. Parents experience the great joy of watching their sons and daughters mature into responsible adults and good citizens. On Parents' Day, we recognize the boundless love and generosity of all par- ents, including the foster and adoptive parents who demonstrate the com- passionate spirit of America. We honor parents for their dedication to pro- viding our Nation's children with the love and support they need. NOW, THEREFORE, I, GEORGE W. BUSH, President of the United States of America, by virtue of the authority vested in me by the Constitution and laws of the United States and consistent with Public Law 103-362, as amended, do hereby proclaim Sunday, July 24, 2005, as Parents' Day. I en- courage all Americans to express love, respect, and appreciation to parents across our Nation. I also call upon citizens to obse\177've this day with appro- priate programs, ceremonies, and activities. IN WITNESS WHEREOF, I have hereunto set my hand this twenty-first day of July, in the year of our Lord two thousand five, and of the Independence of the United States of America the two hundred and thirtieth. GEORGE W. BUSH Proclamation 7915 of July 26, 2005 Anniversary of the Americans with Disabilities Act, 2005 By the President of the United States of America A Proclamation On July 26, 1990, President George H. W. Bush signed into law the Ameri- cans with Disabilities Act (ADA). This historic legislation provides a clear and comprehensive national mandate for the elimination of discrimination against individuals with disabilities. The ADA reflects our Nation's faith in the promise of all individuals and helps to ensure that our Nation's oppor- tunities are more accessible to all. 96

�


text:
Page:Title 3 CFR 2005 Compilation.djvu/110

 Proclamations Proc. 7915 The ADA has been a great success in expanding opportunity for disabled Americans. By reducing barriers and changing perceptions, the ADA has increased participation in community life and given greater hope to mil- lions of Americans. Because of the ADA, individuals with disabilities are better able to develop skills for school, work, and independent living. Our Nation has more to do to further the goals of the ADA. Through the New Freedom Initiative, my Administration is building on the progress of the ADA to increase the use of technology and expand educational and employment opportunities. We are promoting the development and dissemination of assistive and univer- sally designed technology. We have launched DisabilityInfo.gov, an online resource of programs and technology relevant to the daily lives of people with disabilities and their families, employers, selazice providers, and other community members. We also require electronic and information tech- nologies used by the Federal Government to be accessible to people with disabilities. To ensure that no child with a disability is left behind, I have requested $11.1 billion for the Individuals with Disabilities Education Act in my FY 2006 budget--S4.7 billion above the FY 2001 level. The Depart- ment of Education is seeking new and effective ways for students with dis- abilities to learn. My Administration is also working to educate employers on ADA requirements and further assisting persons with disabilities by im- plementing the "Ticket to Work" program and strengthening training and employment services at One-Stop Career Centers. Through all of these ef- forts, we are helping individuals with disabilities have the opportunity to live and work with greater freedom. On the 15th anniversary of the Americans with Disabilities Act, we cele- brate the progress that has been made and reaffirm our commitment to ful- filling the ADA's mission of bringing greater hope and opportunity to our Nation's disabled Americans. NOW, THEREFORE, I, GEORGE W. BUSH, President of the United States of America, by virtue of the authority vested in me by the Constitution and laws of the United States, do hereby proclaim July 26, 2005, as a day in celebration of the 15th Anniversary of the Americans with Disabilities Act. I call on all Americans to celebrate the many contributions individuals with disabilities have made to our country, and I urge our citizens to fulfill the promise of the ADA to give all people the opportunity to live with dig- nity, work productively, and achieve their dreams. IN WITNESS WHEREOF, I have hereunto set my hand this twenty-sixth day of July, in the year of our Lord two thousand five, and of the Independ- ence of the United States of America the two hundred and thirtieth. GEORGE W. BUSH 97

�


text:
Page:Title 3 CFR 2005 Compilation.djvu/111

 Proc. 7916 Title 3--The President Proclamation 7916 of August 5, 2005 40th Anniversary of the Votin\365 Ri\365hts Act of 1965 By the President of the United States o/America A Proclamation In America, we believe in the freedom of every individual. This freedom includes the ability to participate in one of the most cherished rights and fundamental responsibilities of citizenship: the right to vote. The Voting Rights Act of 1965 helped ensure that all citizens would have the oppor- tunity to vote, regardless of race. As President Lyndon Johnson said when he signed the Act, "Millions of Americans are denied the right to vote be- cause of their color. This law will ensure them the right to vote. The wrong is one which no American, in his heart, can justify. The right is one which no American, true to our principles, can deny." As we celebrate the 40th anniversary of this historic act, we reaffirm this bedrock commitment to equality and justice for all. America's history is a story of people working for freedom, justice, and equality. We have made great progress toward achieving these ideals. In the middle of the 20th century, the conscience of America was awakened by the struggles and the courage of those who overcame racial slurs, fire hoses, and burning crosses. Brave men and women held sit-ins at lunch counters, rode buses on Freedom Rides, and marched in our Nation's Capital and throughout our country to demand the full promise of the Declaration of Independence. The work of these courageous Americans led to the Voting Rights Act of 1965, and we remember their heroism on this anniversary. America is a stronger and better Nation because of the Voting Rights Act of \177965. As President Johnson said upon signing the Act, it is "a triumph for freedom as huge as any victory that has ever been won on any battle- field." The Act was a great step forward in the history of our Nation, and it remains essential as we continue our progress toward a society in which every person of every background can realize the American Dream. NOW, THEREFORE, I, GEORGE W. BUSH, President of the United States of America, by virtue of the authority vested in me by the Constitution and Laws of the United States, do hereby proclaim August 6, 2005, as a day of celebration in honor of the 40th Anniversary of the Voting Rights Act of \177965. I call upon all Americans to obse\177've this day with appropriate pro- grams, ceremonies, and activities. IN WITNESS WHEREOF, I have hereunto set my hand this fifth day of Au- gust, in the year of our Lord two thousand five, and of the Independence of the United States of America the two hundred and thirtieth. GEORGE W. BUSH 98

�


text:
Page:Title 3 CFR 2005 Compilation.djvu/112

 Proclamations Proc. 7918 Proclamation 7917 of August 15, 2005 National Airborne Day, 2005 By the President of the United States o/America A Proclamation Americans live in freedom because of the extraordinary bravery, sacrifice, and dedication to duty of the members of our Armed Forces. From the first official Army parachute jump 65 years ago, our country's Airborne troops have played a crucial role in the defense of our Nation and our liberty. On National Airborne Day, we pay special tribute to these courageous soldiers who served with honor and integrity. On August 16, 1940, the successful first jump of the Army Parachute Test Platoon laid the foundation for a new and innovative method of combat that helped contribute to an Allied victory in World War II. These bold pio- neers answered the call of duty and set an example for future generations to follow. Since the designation of the Army's first Airborne division, the 82nd Airborne, on August 15, 1942, our Airborne troops have performed with valor. The brave men and women of our Airborne forces have worked to defeat tyranny, advance the cause of liberty, and build a safer world. Today a new generation of Airborne forces is fighting a war against an enemy that threatens the peace and stability of the world. At this critical time, Airborne forces of the Army, Navy, Marines, and Air Force are con- tinuing the noble tradition of the first sky soldiers. Americans are grateful for the service of our Airborne forces and all our troops, and we are in- spired by the strength and sacrifice of our military members and their fami- lies. NOW, THEREFORE, I, GEORGE W. BUSH, President of the United States of America, by virtue of the authority vested in me by the Constitution and laws of the United States, do hereby proclaim August 16, 2005, as National Airborne Day. I encourage all Americans to honor those who have se\177'ved in the Airborne forces, and I also call upon all citizens to observe this day with appropriate programs, ceremonies, and activities. IN WITNESS WHEREOF, I have hereunto set my hand this fifteenth day of August, in the year of our Lord two thousand five, and of the Independ- ence of the United States of America the two hundred and thirtieth. GEORGE W. BUSH Proclamation 7918 of August 25, 2005 Women's Equality Day, 2005 By the President of the United States of America A Proclamation On August 26, 1920, the 19th Amendment to the Constitution was adopted, guaranteeing American women the right to vote. The passage of this amendment was the culmination of a long struggle that reached back to the 99

�


text:
Page:Title 3 CFR 2005 Compilation.djvu/113

 Proc. 7919 Title 3--The President founding of the country and was furthered by the 1848 women's rights con- vention in Seneca Falls, New York. By celebrating Women's Equality Day, we commemorate the adoption of this amendment and honor the visionary women who fought tirelessly for women's suffrage. Led by women such as Elizabeth Cady Stanton, Susan B. Anthony, and Lucretia Mott, the suffragists stood up against iniustice and persevered until, as Susan B. Anthony wrote, the handful who first took a stand for suffrage grew into an army. The efforts of these pioneers helped secure for American women the right to vote. Since the adoption of the 19th Amendment, women have continued to make great contributions to our Nation. Women today are leaders in medi- cine, law, iournalism, business, government, and other professions. They are doctors and mothers, teachers and lawyers, homemakers and pilots, art- ists and entrepreneurs. Women also are serving with great honor in our Armed Forces as we fight a war on terror and defend our freedoms. The hard work of American women is essential to the strength and vitality of our country. One hundred and fifty-seven years after the Seneca Falls Convention, we continue to work so that all people can enjoy their God-given rights. This Women's Equality Day, as we celebrate the 85th anniversary of the 19th Amendment, we honor the perseverance, leadership, and achievements of the suffragists and all of America's women, and we renew our commitment to equal justice and dignity for all. NOW, THEREFORE, I, GEORGE W. BUSH, President of the United States of America, by virtue of the authority vested in me by the Constitution and laws of the United States, do hereby proclaim August 26, 2005, as Women's Equality Day. I call upon the people of the United States to observe this day with appropriate programs and activities. IN WITNESS WHEREOF, I have hereunto set my hand this twenty-fifth day of August, in the year of our Lord two thousand five, and of the Independ- ence of the United States of America the two hundred and thirtieth. GEORGE W. BUSH Proclamation 7919 of August 29, 2005 National Ovarian Cancer Awareness Month, 2005 By the President of the United States of America A Proclamation Ovarian cancer is one of the leading causes of cancer deaths among women in the United States. Each year, thousands of women are diagnosed with ovarian cancer, and thousands die from the disease. During National Ovar- ian Cancer Awareness Month, we strive to raise awareness of ovarian can- cer and promote early detection and treatment of this disease. Early detection is essential to the successful treatment of ovarian cancer. The 5-year survival rate is higher than 90 percent for ovarian cancer pa- tients whose disease is caught during the first stage of development. Most 100

�


text:
Page:Title 3 CFR 2005 Compilation.djvu/114

 Proclamations Proc. 7920 ovarian cancer cases are diagnosed at an advanced stage, however, because no reliable screening test exists for the disease. Because the early signs of ovarian cancer are easy to miss and often resemble the signs of other condi- tions, it is important for women to talk with their doctors about detection and be aware of the risk factors and symptoms of this cancer. There is more we need to learn about how best to prevent, detect, and treat ovarian cancer. The National Cancer Institute (NCI) is currently sponsoring a study on genetic and environmental factors that may increase the risk of ovarian cancer. In addition, the NCI is sponsoring clinical trials to explore new ways to screen for and detect ovarian cancer. Researchers are studying new treatment options, including biological therapies, anticancer drugs, vaccines, and other therapies to treat resistant forms of ovarian cancer. The Centers for Disease Control and Prevention will spend almost $4.6 million, and the Department of Defense's Ovarian Cancer Research Program will in- vest an estimated $10 million. As we observe National Ovarian Cancer Awareness Month, we recognize the courage and strength of women battling ovarian cancer, and of their families and friends who love and support them. Our Nation is grateful for the hard work and commitment of our dedicated researchers and medical professionals. With continued effort, we can raise awareness of ovarian cancer and find new ways to prevent and treat this deadly disease. NOW, THEREFORE, I, GEORGE W. BUSH, President of the United States of America, by virtue of the authority vested in me by the Constitution and laws of the United States, do hereby proclaim September 2005 as National Ovarian Cancer Awareness Month. I call upon government officials, busi- nesses, communities, health care professionals, educators, volunteers, and all people of the United States to continue our Nation's strong commitment to preventing and treating ovarian cancer. IN WITNESS WHEREOF, I have hereunto set my hand this twenty-ninth day of August, in the year of our Lord two thousand five, and of the Inde- pendence of the United States of America the two hundred and thirtieth. GEORGE W. BUSH Proclamation 7920 of August 29, 2005 National Prostate Cancer Awareness Month, 2005 By the President of the United States of America A Proclamation Prostate cancer is the second leading cause of cancer-related deaths among American men. This year, thousands of men will be diagnosed with pros- tate cancer, and thousands will die from the disease. While great strides have been made in the battle against prostate cancer, we have more work to do. During National Prostate Cancer Awareness Month, we renew our commitment to fight prostate cancer by finding better ways to prevent, de- tect, and treat this deadly disease. My Administration is committed to funding research for prevention and better treatments for prostate cancer. This year, the National Institutes of 101

�


text:
Page:Title 3 CFR 2005 Compilation.djvu/115

 Proc. 7921 Title 3--The President Health will invest an estimated $381 million in prostate cancer research, including $310 million at the National Cancer Institute. The Department of Defense's Prostate Cancer Research Program will spend an estimated $85 million, and the Centers for Disease Control and Prevention will devote an estimated $14 million toward prostate cancer research. Scientists are exam- ining risk factors to identify ways to prevent prostate cancer, and they are finding ways to detect this disease earlier, when it is easier to treat. In ad- dition, newer treatments are helping to slow or stop the spread of prostate cancer in men with advanced stages of the disease. This progress offers hope to men who are living with prostate cancer and those who are at risk. As we observe National Prostate Cancer Awareness Month, I encourage all men, especially those over the age of 50, to talk with their doctors about the risk of prostate cancer and the appropriate screenings. I commend those who fight this disease, and I applaud the dedication of researchers, health care providers, and all who are working to increase our knowledge of pros- tate cancer. By raising awareness and supporting research, we can save lives. NOW, THEREFORE, I, GEORGE W. BUSH, President of the United States of America, by virtue of the authority vested in me by the Constitution and laws of the United States, do hereby proclaim September 2005 as National Prostate Cancer Awareness Month. I call upon government officials, busi- nesses, communities, health care professionals, educators, volunteers, and all people of the United States to reaffirm our Nation's strong and con- tinuing commitment to treat and prevent prostate cancer. IN WITNESS WHEREOF, I have hereunto set my hand this twenty-ninth day of August, in the year of our Lord two thousand five, and of the Inde- pendence of the United States of America the two hundred and thirtieth. GEORGE W. BUSH Proclamation 7921 of August 29, 2005 National Alcohol and Drug Addiction Recovery Month, 2005 By the President of the United States of America A Proclamation The devastating effects of alcohol and drug addiction have destroyed the lives and families of countless Americans. During National Alcohol and Drug Addiction Recovery Month, we recognize the dangers of substance abuse and renew the hope of overcoming addiction for individuals across our Nation. This year's theme, "Join the Voices for Recovery: Healing Lives, Families and Communities," encourages those striving to recover from this disease and recognizes the many families, support organizations, faith- based and community groups, and volunteers working to help overcome addiction. Substance abuse leads to a cycle of addiction and despair that too often causes disease and death among young people. The Helping America's Youth initiative, led by First Lady Laura Bush, is promoting positive youth development and combating alcohol and drug addiction. This initiative is 102

�


text:
Page:Title 3 CFR 2005 Compilation.djvu/116

 Proclamations Proc. 7922 helping our children to make healthy choices and build lives of purpose. To aid citizens seeking treatment and recovery for substance abuse, my Ad- ministration also has provided $200 million over the past 2 years for the Access to Recovery program. My 2006 budget requests an additional $150 million for this program to further expand treatment choices. Directing re- sources to individuals allows them to choose a program that suits their needs and increases their chances of success. In addition, we have in- creased opportunities for communities and faith-based providers to aid those suffering from addiction. I encourage all Americans to support individuals striving to overcome ad- diction and the groups that are helping to fight alcohol and drug addiction. By working together, we can continue to build a more compassionate soci- ety that transforms lives and provides health, hope, and healing to those who hurt. NOW, THEREFORE, I, GEORGE W. BUSH, President of the United States of America, by virtue of the authority vested in me by the Constitution and laws of the United States, do hereby proclaim September 2005 as National Alcohol and Drug Addiction Recovery Month. I call upon the people of the United States to observe this month with appropriate programs and activi- ties. IN WITNESS WHEREOF, I have hereunto set my hand this twenty-ninth day of August, in the year of our Lord two thousand five, and of the Inde- pendence of the United States of America the two hundred and thirtieth. GEORGE W. BUSH Proclamation 7922 of September 4, 2005 Death of William H. Rehnquist By the President of the United States of America A Proclamation As a mark of respect for William H. Rehnquist, Chief Justice of the United States, I hereby order, by the authority vested in me by the Constitution and laws of the United States of America, including section 7 of title 4, United States Code, that the flag of the United States shall be flown at half- staff at the White House and on all public buildings and grounds, at all military posts and naval stations, and on all naval vessels of the Federal Government in the District of Columbia and throughout the United States and its Territories and possessions until sunset, Tuesday, September 13, 2005. I also direct that the flag shall be flown at half-staff for the same pe- riod at all United States embassies, legations, consular offices, and other fa- cilities abroad, including all military facilities and naval vessels and sta- tions. IN WITNESS WHEREOF, I have hereunto set my hand this fourth day of September, in the year of our Lord two thousand five, and of the Independ- ence of the United States of America the two hundred and thirtieth. GEORGE W. BUSH 103

�


text:
Page:Title 3 CFR 2005 Compilation.djvu/117

 Proc.7923 Title 3--The President Proclamation 7923 of September 4, 2005 Honoring the Memory of the Victims of Hurricane Katrina By the President of the United States o/America A Proclamation As a mark of respect for the victims of Hurricane Katrina, I hereby order, by the authority vested in me by the Constitution and laws of the United States of America, that the flag of the United States shall be flown at half- staff at the White House and on all public buildings and grounds, at all military posts and naval stations, and on all naval vessels of the Federal Government in the District of Columbia and throughout the United States and its Territories and possessions until sunset, Tuesday, September 20, 2005. I also direct that the flag shall be flown at half-staff for the same pe- riod at all United States embassies, legations, consular offices, and other fa- cilities abroad, including all military facilities and naval vessels and sta- tions. IN WITNESS WHEREOF, I have hereunto set my hand this fourth day of September, in the year of our Lord two thousand five, and of the Independ- ence of the United States of America the two hundred and thirtieth. GEORGE W. BUSH Proclamation 7924 of September 8, 2005 To Suspend Subchapter IV of Chapter 31 of Title 40, United States Code, Within a Limited Geographic Area in Response to the National Emergency Caused by Hurricane Katrina By the President of the United States of America A Proclamation 1. Section 3142(a) of title 40, United States Code, provides that "every con- tract in excess of $2,000, to which the Federal Government or the District of Columbia is a party, for construction, alteration, or repair, including painting and decorating, of public buildings and public works of the Gov- ernment or the District of Columbia that are located in a State or the Dis- trict of Columbia and which requires or involves the employment of me- chanics or laborers shall contain a provision stating the minimum wages to be paid various classes or laborers and mechanics." 2. Section 3142(b) of title 40, United States Code, provides that such "min- imum wages shall be based on the wages the Secretary of Labor determines to be prevailing for the corresponding classes of laborers and mechanics employed on projects of a character similar to the contract work in the civil subdivision of the State in which the work is to be performed..." 3. Under various other related acts, the payment of wages is made depend- ent upon determinations by the Secretary of Labor under section 3142 of title 40, United States Code. 104

�


text:
Page:Title 3 CFR 2005 Compilation.djvu/118

 Proclamations Proc. 7924 4. Section 3147 of title 40, United States Code, provides that "[t]he Presi- dent may suspend the provisions of this subchapter during a national emer- gency." 5. Several areas of the Nation have been recently devastated by Hurricane Katrina. The devastation from the hurricane has resulted in the largest amount of property damage from a natural disaster in the history of the Na- tion. An enormous but undetermined number of lives have been lost, and hundreds of thousands of homes and business establishments either de- stroyed or severely damaged. Hundreds of thousands of individuals have lost their jobs and their livelihood. An unprecedented amount of Federal assistance will be needed to restore the communities that have been rav- aged by the hurricane. Accordingly, I find that the conditions caused by Hurricane Katrina constitute a "national emergency" within the meaning of section 3147 of title 40, United States Code. (a) Hurricane Katrina has resulted in unprecedented property damage. (b) The wage rates imposed by section 3\17742 of title 40, United States Code, increase the cost to the Federal Government of providing Fed- eral assistance to these areas. (c) Suspension of the subchapter IV of chapter 3\177 of title 40, United States Code, 40 U.S.C. 3\1774\177-3148, and the operation of related acts to the extent they depend upon the Secretary of Labor's determina- tions under section 3\17742 of title 40, United States Code, will result in greater assistance to these devastated communities and will per- mit the employment of thousands of additional individuals. NOW, THEREFORE, I, GEORGE W. BUSH, President of the United States of America, do by this proclamation suspend, as to all contracts entered into on or after the date of this proclamation and until otherwise provided, the provisions of subchapter IV of chapter 3\177 of title 40, United States Code, 40 U.S.C. 3\1774\177-3148, and the provisions of all other acts providing for the payment of wages, which provisions are dependent upon determina- tions by the Secretary of Labor under section 3\17742 of title 40, United States Code, as they apply to contracts to be performed in the following jurisdic- tions: the counties of Baldwin, Choctaw, Clarke, Mobile, Sumter, and Washington in the State of Alabama; the counties of Broward, Miami-Dade, and Monroe in the State of Florida; the parishes of Acadia, Allen, Ascen- sion, Assumption, Avoyelles, Beauregard, Bienville, Bosslet, Caddo, Calcasieu, Caldwell, Cameron, Catahoula, Claiborne, Concordia, De Soto, East Baton Rouge, East Carroll, East Feliciana, Evangeline, Franklin, Grant, Iberia, Iberville, Jackson, Jefferson, Jefferson Davis, La Salle, Lafayette, Lafourche, Lincoln, Livingston, Madison, Morehouse, Natchitoches, Orle- ans, Ouachita, Plaquemines, Pointe Coupee, Rapides, Red River, Richland, Sabine, St. Bernard, St. Charles, St. Helena, St. James, St. John the Baptist, St. Landry, St. Martin, St. Mary, St. Tammany, Tangipahoa, Tensas, Terrebonne, Union, Vermilion, Vernon, Washington, Webster, West Baton Rouge, West Carroll, West Feliciana, and Winn in the State of Louisiana; and the counties of Adams, Alcorn, Amite, Attala, Benton, Bolivar, Cal- houn, Carroll, Chickasaw, Choctaw, Claiborne, Clarke, Clay, Coahoma, Coplab, Covington, DeSoto, Forrest, Franklin, George, Greene, Grenada, Hancock, Harrison, Hinds, Holmes, Humphreys, Issaquena, Itawamba, Jack- son, Jasper, Jefferson, Jefferson Davis, Jones, Kemper, Lafayette, Lamar, Lau- derdale, Lawrence, Leake, Lee, Leftore, Lincoln, Lowndes, Madison, Mar- ion, Marshall, Monroe, Montgomery, Neshoba, Newton, Noxubee, 105

�


text:
Page:Title 3 CFR 2005 Compilation.djvu/119

 Proc. 7925 Title 3--The President Oktibbeha, Panola, Pearl River, Perry, Pike Pontotoc, Prentiss, Quitman, Rankin, Scott, Shatkey, Simpson, Smith, Stone, Sunflower, Tallahatchie, Tate, Tippah, Tishomingo, Tunira, Union, Walthall, Warren, Washington, Wayne, Webster, Wilkinson, Winston, Yalobusha, Yazoo in the State of Mississippi. And, as to such contracts to be performed in such iurisdictions, I do hereby suspend, until otherwise provided, the provisions of any Executive Order, proclamation, rule, regulation, or other directive providing for the payment of wages, which provisions are dependent upon determinations by the Sec- retary of Labor under section 3142 of title 40, United States Code; IN WITNESS WHEREOF, I have hereunto set my hand this eighth day of September, in the year of our Lord two thousand five, and of the Independ- ence of the United States of America the two hundred and thirtieth. GEORGE W. BUSH Proclamation 7925 of September 8, 2005 National Day of Prayer and Remembrance for the Victims of Hurricane Katrina By the President of the United States of America A Proclamation Hurricane Katrina was one of the worst natural disasters in our Nation's history and has caused unimaginable devastation and heartbreak through- out the Gulf Coast Region. A vast coastline of towns and communities has been decimated. Many lives have been lost, and hundreds of thousands of our fellow Americans are suffering great hardship. To honor the memory of those who lost their lives, to provide comfort and strength to the families of the victims, and to help ease the burden of the survivors, I call upon all Americans to pray to Almighty God and to perform acts of service. As we observe a National Day of Prayer and Remembrance for the Victims of Hurricane Katrina, we pledge our support for those who have been in- jured and for the communities that are struggling to rebuild. We offer thanks to God for the goodness and generosity of so many Americans who have come together to provide relief and bring hope to fellow citizens in need. Our Nation is united in compassion for the victims and in resolve to overcome the tremendous loss that has come to America. We will strive together in this effort, and we will prevail through perseverance and pray- er. Americans are reaching out to those who suffer by opening their hearts, homes, and communities. Their actions demonstrate the greatest compas- sion one person may show to another: to love your neighbor as yourself. Across our Nation, so many selfless deeds reflect the promise of the Scrip- ture: "For I was hungry and you gave Me food; I was thirsty and you gave Me drink; I was a stranger and you took Me in." I encourage all Americans to respond with acts of kindness in the days ahead. By contributing time, 106

�


text:
Page:Title 3 CFR 2005 Compilation.djvu/120

 Proclamations Proc. 7926 money, or needed goods to a relief organization and by praying for the sur- vivors and those in recovery efforts, we can make a tremendous difference in the lives of those in need. Hurricane Katrina and its aftermath resulted in a considerable loss of life. We pray that God will bless the souls of the lost, and that He will comfort their families and friends and all lives touched by this disaster. As the American people unite to help those who are hurting, we share a deter- mination to stand by those affected by Hurricane Katrina in the months and years ahead as they rebuild their lives and reclaim their future. We are de- termined that the Gulf Coast region will rise again. The tasks before us are enormous, and so is the heart of America. We will continue to comfort and care for the survivors. We will once again show the world that the worst adversities bring out the best in the American people. NOW, THEREFORE, I, GEORGE W. BUSH, President of the United States of America, by virtue of the authority vested in me by the Constitution and laws of the United States, do hereby proclaim Friday, September 16, 2005, as a National Day of Prayer and Remembrance for the Victims of Hurricane Katrina. I ask that the people of the United States and places of worship mark this National Day of Prayer and Remembrance with memorial services and other appropriate observances. I also encourage all Americans to re- member those who have suffered in the disaster by offering prayers and giving their hearts and homes for those who now, more than ever, need our compassion and our support. IN WITNESS WHEREOF, I have hereunto set my hand this eighth day of September, in the year of our Lord two thousand five, and of the Independ- ence of the United States of America the two hundred and thirtieth. GEORGE W. BUSH Proclamation 7926 of September 9, 2005 Minority Enterprise Development Week, 2005 By the President of the United States of America A Proclamation Across our country, the entrepreneurial spirit of minority businesses is strong and growing. By creating jobs and advancing opportunities, these businesses improve lives and transform neighborhoods throughout our Na- tion. During Minority Enterprise Development Week, we recognize minor- ity entrepreneurs and their employees for their commitment to free enter- prise and equal opportunity. Minority businesses are an essential part of a society in which personal ini- tiative is encouraged and in which opportunity is within the reach of all of our citizens. Significant increases in minority business ownership are providing an engine for economic growth and helping more of our citizens succeed. By fueling job creation and providing goods and services to con- sumers, these businesses are helping to lift communities and provide hope. 107

�