text:
Page:LorentzGravitation1916.djvu/4

 coordinates will be of secondary importance; with a single exception (§ 13) it only serves for short calculations which we have to intercalate (for the proof of certain geometric propositions) and for establishing the final equations, which have to be used for the solution of special problems. In the discussion of the general principles coordinates play no part; and it is thus seen that the formulation of these principles can take place in the same way whatever be our choice of coordinates. So we are sure beforehand of the general covariancy of the equations that was postulated by.

§ 4. ascribes to a line-element $$PQ$$ in the field-figure a length $$ds$$ defined by the equation

Here $$dx_{1},\dots dx_{4} $$ are the changes of the coordinates when we pass from $$P$$ to $$Q$$, while the coefficients $$g_{ab} $$ depend in one way or another on the coordinates. The gravitation field is known when these 10 quantities are given as functions of $$x_{1},\dots x_{4} $$. Here it must be remarked that in all real cases the coordinates can be chosen in such a way that for one point arbitrarily chosen (1) becomes

$ds^{2}=-dx_{1}^{2}-dx_{2}^{2}-dx_{3}^{2}+dx_{4}^{2} $

This requires that the determinant $$g$$ of the coefficients of (1) be always negative. The minor of this determinant corresponding to the coefficient $$g_{ab} $$ will be denoted by $$G_{ab} $$.

Around each point $$P$$ of the field-figure as a centre we may now construct an infinitesimal surface, which, when $$P$$ is chosen as origin of coordinates, is determined by the equation

where $$\epsilon $$ is an infinitely small positive constant which we shall fix once for all. This surface, which we shall call the indicatrix, is a hyperboloid with one real axis and three imaginary ones. We shall also introduce the surface determined by the equation

which differs from (2) only by the sign of $$\epsilon^{2} $$. We shall call this the conjugate indicatrix. It is to be understood that the indicatrices and conjugate indicatrices take part in the changes to which the field-figure may be subjected. As these surfaces are infinitely small,

title: Page:LorentzGravitation1916.djvu/4


text:
Page:LorentzGravitation1916.djvu/5

 they always remain hyperboloids of the said kind. The gravitation field will now be determined by these indicatrices, which we can imagine to have been constructed in the field-figure without the introduction of coordinates. When we have occasion to use these latter, we shall so choose them that the "axes" $$x_{1},x_{2},x_{3} $$ intersect the conjugate indicatrix constructed around their starting point, while the indicatrix itself is intersected by the axis $$x_{4} $$. This involves that the coefficients $$g_{11},g_{22},g_{33} $$ are negative and that $$g_{44} $$ is positive.

§ 5. The indicatrices will give us the units in which we shall express the length of lines in the field-figure and the magnitude of two-, three or four-dimensional extensions. When we use these units we shall say that the quantities in question are expressed in natural measure.

In the case of a line-element $$PQ$$ the unit might simply be the radius-vector in the direction $$PQ$$ of the indicatrix or the conjugate indicatrix described about $$P$$. It is however desirable to distinguish the two cases that $$PQ$$ intersects the indicatrix itself or the conjugate indicatrix. In the latter case we shall ascribe an imaginary length to the line-element. Besides, by taking as unit not the radius-vector itself but a length proportional to it, the numerical value of a line-element may be made to be independent of the choice of the quantity $$\epsilon $$.

These considerations lead us to define the length that will be ascribed to line-elements by the assumption that each radius-vector of the indicatrix has in natural measure the length $$\epsilon $$, while each radius-vector of the conjugate indicatrix has the length $$i\epsilon $$.

It will now be clear that the length of an arbitrary line in the field-figure can be found by integration, each of its elements being measured by means of the indicatrix or the conjugate indicatrix belonging to the position of the element. In virtue of our definitions a deformation of the field-figure will not change the length of lines expressed in natural measure and a geodetic line will remain a geodetic line.

§ 6. We are now in a position to indicate the first part $$H_{1} $$ of the principal function (§ 1). Let $$\sigma $$ be a closed surface in the field-figure and let us confine ourselves to the principal function

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

title: Page:LorentzGravitation1916.djvu/5


text:
Page:LorentzGravitation1916.djvu/6

 so far as it belongs to the space $$\Omega $$ enclosed by that surface. Then the quantity $$H_{1} $$ is the sum, taken with the negative sign, of the lengths of all world-lines of material points so far as they lie within $$\Omega $$, each length multiplied by a constant $$m$$, characteristic of the point in question and to be called its mass.

It must be remarked that the elements of the world-lines of material points intersect the corresponding indicatrices themselves. The lengths of these lines are therefore real positive quantities.

A deformation of the field-figure leaves $$H_{1} $$ unchanged.

§ 7. We shall now pass on to the part of the principal function belonging to the gravitation field. The mathematical expression for this part was communicated to me by in our correspondence. It is also to be found in 's paper in which it is remarked that the quantity in question may be regarded as the measure of the curvature of the four-dimensional extension to which (1) relates. Here we have to speak only of the interpretation of this quantity. To find this the following geometrical considerations may be used.

Let $$PQ$$ and $$PR$$ be two line-elements starting from a point $$P$$ of the field-figure, $$QR$$ the line-element joining the extremities $$Q$$ and $$R$$. If then the lengths of these elements in natural measure are

$PQ=ds',\ PR=ds'',\ QR=ds $

we define the angle $$(s',s'') $$ between $$PQ$$ and $$PR$$ by the well known trigonometric formula

from which one can derive

By means of this formula we are able to determine the angle between any two intersecting lines. Of course the two other angles of the triangle $$PQR$$ can be calculated in the same way.

Now two cases must be distinguished.

a. The plane of the triangle $$PQR$$ cuts the conjugate indicatrix, but not the indicatrix itself. Then the three sides have positive imaginary values. Moreover each of them proves to be smaller than

title: Page:LorentzGravitation1916.djvu/6


text: Page:Wittgenstein - Tractatus Logico-Philosophicus, 1922.djvu/28


text:
Page:LorentzGravitation1916.djvu/7

 the sum of the others, from which one finds that the angles have real values and that their sum is $$\pi $$.

b. The plane PQR cuts both the indicatrix and the conjugate indicatrix. In this case different positions of the triangle are still possible. We can however confine ourselves to triangles the three sides of which are real. These are really possible, for in the plane of a hyperbola we can draw triangles the sides of which are parallel to radius-vectors drawn from the centre to points of the curve (and not of the conjugate hyperbola).

By a closer consideration of the triangles now in question it is found however that by the choice of our "natural" units one side is necessarily longer than the sum of the other two. Formula (4) then shows that the cosines of the angles are real quantities, greater than 1 in absolute value, two of them being positive, and the third negative. We must therefore ascribe to the angles imaginary or complex values. If for $$p>+1 $$ we put

$\arccos p=i\log\left(p+\sqrt{p^{2}-1}\right) $

and

$\arccos(-p)=\pi-\arccos p $

we find for the three angles expressions of the form

$i\alpha,\ i\beta $ and $\pi-i(\alpha+\beta) $

so that the sum is again $$\pi $$.

From the cosine calculated by (4) or (5) the sine can be derived by means of the formula

$\sin\varphi=\sqrt{1-\cos^{2}\varphi} $

where for the case $$\cos^{2}\varphi>1 $$ we can confine ourselves to the value

$\sin\varphi=i\sqrt{\cos^{2}\varphi-1} $

with the positive sign.

It deserves special notice that two conjugate radius-vectors of the indicatrix and the conjugate indicatrix are perpendicular to each other and that a deformation of the field-figure does not change the angle between two intersecting lines determined according to our definitions.

§ 8. Before proceeding further we must now indicate the natural units (§ 5) for two-, three-, or four-dimensional extensions in the field-figure. Like the unit of length, these are defined for each point separately, so that the numerical value of a finite extension is found by dividing it into infinitely small parts.

A two-dimensional extension cuts the conjugate indicatrix in an ellipse, or the indicatrix itself and the conjugate indicatrix in two

title: Page:LorentzGravitation1916.djvu/7


text:
Page:LorentzGravitation1916.djvu/8

 conjugate hyperbolae. In both cases we derive our unit from the area of a parallelogram described on conjugate radius-vectors.

A three-dimensional extension cuts the conjugate indicatrix in an ellipsoid, or the indicatrix and its conjugate in two conjugate hyperboloids. Now our unit will be derived from the volume of a parallelepiped described on three conjugate radius-vectors.

In a similar way the magnitude of four-dimensional extensions will be determined by comparison with a parallelepiped the edges of which are four conjugate radius-vectors of the indicatrix and the conjugate indicatrix.

It must here be kept in mind that, according to well known theorems, the area of the parallelogram and the volume of the parallelepipeds in question are independent of the special choice of the conjugate radius-vectors.

We shall further specify the units in such a way (comp. § 5) that the numerical magnitude of a parallelogram or a parallelepiped described on conjugate radius-vectors is found by multiplying the numbers by which the edges are expressed in natural measure.

From what has been said it follows that the area of the parallelogram described on two line-elements is given by the product of the lengths of these elements and the sine of the enclosed angle. Similarly the area of an infinitely small triangle is determined by half the product of two sides and the sine of the angle between them.

We need hardly add that the numerical value of any two-, three- or four-dimensional domain expressed in natural measure is not changed by a deformation of the field-figure.

§ 9. Let, at any point $$P$$ of the field-figure, 1, 2, 3, 4 be four arbitrarily chosen conjugate radius-vectors of the indicatrix. Two of these determine an infinitely small part $$V$$ of a two-dimensional extension. We may prolong this part to finite distances from $$P$$ by drawing from this point geodetic lines whose initial directions lie in the plane $$V$$. In this way we obtain six two-dimensional extensions (1,2), (2,3), (3,1), (1,4), (2,4) and (3,4). Let us now consider in one of these e. g. ($$a, b$$) an infinitesimal triangle near the point $$P$$, the sides of which are geodetic lines (viz. geodetic lines in ($$a, b$$)). If in calculating the angles of this triangle we go to quantities of the second order with respect to the sides and to the distances from $$P$$, the sum $$s$$ of the angles proves to have no longer the value $$\pi$$ (comp. § 7). The "excess" $$e=s-\pi $$ is proportional to the area $$\Delta $$ of the triangle, independently of the length of the sides, of their ratios and of the position of the triangle in the extension ($$a, b$$). For the three extensions

title: Page:LorentzGravitation1916.djvu/8


text:
Page:LorentzGravitation1916.djvu/9

 (1,2) (2,3), (3,1), which do not intersect the indicatrix itself but the conjugate indicatrix, this proposition follows from a well-known theorem of in the theory of curvature of surfaces; for the other three (1,4), (2,4), (3,4), which cut the indicatrix itself, the proof can be given by direct calculation. The considerations necessary for this, and some other calculations with which we shall be concerned further on will be communicated in a later paper.

In considering the three last-mentioned extensions I have confined myself to triangles with real sides (§ 7, b).

The quotient

$\frac{e}{\Delta}=K_{ab} $

is now for each extension a definite number, which we may consider as a measure of the curvature of the two-dimensional extension ($$a, b$$); the sum $$K$$ of the six numbers $$K_{ab} $$ may be called the curvature of the field-figure at the point $$P$$ in question. This quantity is the same that has been introduced by ; this results from the calculation of its value, which at the same time shows $$K$$ to be independent of the special choice of the directions 1, 2, 3, 4 introduced in the beginning of this §.

The numbers $$K_{ab} $$ all real and have a meaning that can be indicated without the introduction of coordinates; moreover their sum $$K$$ is not changed by a deformation of the field-figure.

If now $$d\Omega $$ is an element of the four-dimensional extension of the field-figure, expressed in natural measure, the part of the principal function belonging to the gravitation field is

where the integration is extended to the domain considered (§ 6) while $$\varkappa $$ is the gravitation constant. $$H_{3} $$ too is not changed by a deformation of the field-figure.

The factor $$i$$ has been introduced in order to obtain a real value for $$H_3$$, the element $$d\Omega $$ being represented in natural measure by a negative imaginary number (§ 8).

§ 10. What we have to say of the electromagnetic field must be preceded by some considerations belonging to what may be called the "vector theory" of the field-figure.

A line-element $$PQ$$, taken in a definite, direction (indicated by the order of the letters), may be called a vector. Such vectors can be compounded or decomposed by means of parallelograms or parallelepipeds. Especially, when coordinates $$x_{1},\dots x_{4} $$ have been chosen,

title: Page:LorentzGravitation1916.djvu/9


text:
Page:LorentzGravitation1916.djvu/10

 a vector may be resolved into four components which have the directions of the coordinates, viz. such directions that a shift along the first e.g. changes $$x_{1} $$, while $$x_{2},x_{3},x_{4} $$ remain constant. The four components in question are determined by the differentials $$dx_{1},\dots dx_{4} $$ corresponding to $$PQ$$. We shall say that by these they are expressed in "$$x$$-measure". Their values in natural measure are found by multiplying $$dx_{1},\dots dx_{4} $$ by certain factors. If we keep in mind that the radius-vectors of the e conjugate indicatrix and the indicatrix in the directions of the axes are expressed in "$$x$$ measure" by

$\frac{\epsilon}{\sqrt{-g_{11}}},\ \frac{\epsilon}{\sqrt{-g_{22}}},\ \frac{\epsilon}{\sqrt{-g_{33}}},\ \frac{\epsilon}{\sqrt{g_{44}}}, $|undefined

and in natural units by

$i\epsilon,\ i\epsilon,\ i\epsilon,\ \epsilon $

we find for the reducing factors

In the language of vector-analysis the vector obtained by the composition of two or more vectors is also called the sum of these vectors.

We shall also speak of finite vectors, i.e. of directed quantities which can be represented on an infinitely reduced scale by line-elements in the field-figure. If $$\omega$$ is the constant "reduction factor" chosen for this purpose, a vector $$\mathrm{A} $$ will be represented by a line-element $$\omega\mathrm{A} $$, the direction of which is also ascribed to $$\omega\mathrm{A} $$. It will now be evident that two finite vectors, as well as two infinitely small ones, determine an infinitesimal two dimensional extension and that finite vectors can be compounded and resolved by means of parallelograms and parallelepipeds. Also that we may speak of the "magnitude" of such figures, that e.g. the rule given in § 8 applies to the parallelogram described on two vectors.

The components of a vector in the directions of the coordinates expressed in $$x$$-measure will be called $$X_{1},X_{2},X_{3},X_{4} $$. This means that $$\omega X_{1},\dots\omega X_{4} $$ are equal to the differentials $$dx_{1},\dots dx_{4} $$ corresponding to the infinitely small vector $$\omega\mathrm{A} $$.

If we want to know the components of $$\mathrm{A} $$ in natural units we must multiply $$X_{1},\dots X_{4} $$ by the factors (7).

§ 11. Two vectors $$\mathrm{A}$$ and $$\mathrm{B}$$ starting from a point $$P$$ of the field-figure and lying in a plane $$V$$, determine what we shall call a rotation $$\mathrm{R}$$ in that plane. We ascribe to it the direction indicated by the order $$\mathrm{AB}$$ and a value given by the parallelogram described on

title: Page:LorentzGravitation1916.djvu/10


text:
Page:LorentzGravitation1916.djvu/11

 $$\mathrm{A}$$ and $$\mathrm{B}$$ and expressed in natural measure. This involves that the same rotation may be represented in many different ways by two vectors in the plane $$V$$.

For the rotation $$\mathrm{R}$$ we shall also use the symbol $$[\mathrm{A\cdot B]} $$.

By the vector product $$[\mathrm{A\cdot B\cdot C]} $$ of three vectors $$\mathrm{A,B,C} $$ at a point of the field-figure and not lying in one plane we shall understand a vector $$\mathrm{D}$$ the direction of which is conjugate with each of the three vectors (and therefore with the three-dimensional extension $$\mathrm{A,B,C} $$), the direction of $$\mathrm{D}$$ corresponding to those of $$\mathrm{A,B} $$ and $$\mathrm{C}$$ in a way presently to be indicated, while the magnitude of $$\mathrm{D}$$, expressed in natural measure, is equal to that of the parallelepiped described on $$\mathrm{A}$$, $$\mathrm{B}$$ and $$\mathrm{C}$$ and expressed in the same measure. This definition involves that the value is ascribed to the vector product of three vectors lying in one and the same plane.

A further statement about the direction of $$\mathrm{D}$$ is necessary because two opposite directions are conjugate with $$\mathrm{A,B,C} $$. For one set of three directions $$\mathrm{A_{0},B_{0},C_{0}} $$ we shall choose arbitrarily which of its two conjugate directions will be said to correspond to it. If this is the direction $$\mathrm{D}_{0} $$, then the direction $$\mathrm{D}$$ corresponding to $$\mathrm{A,B,C} $$ will be determined by the rule that $$\mathrm{D}_{0} $$, passes into $$\mathrm{D}$$ by a gradual passage of the first three vectors from $$\mathrm{A_{0},B_{0},C_{0}} $$ into $$\mathrm{A,B,C} $$, this latter passage being effected in such a way that during the change the vectors never come to lie in one plane.

The vector product $$[\mathrm{A\cdot B\cdot C]} $$ takes the opposite direction when one of the vectors is reversed as well as when two of them are interchanged. We must therefore always attend to the order of the symbols in $$[\mathrm{A\cdot B\cdot C]} $$.

The vector product possesses the distributive property with respect to each of the three vectors, so that e.g. if $$\mathrm{A}_{1} $$ and $$\mathrm{A}_{2} $$ are vectors,

$\left[\left(\mathrm{A}_{1}+\mathrm{A}_{2}\right)\cdot\mathrm{B\cdot C}\right]=\mathrm{\left[A_{1}\cdot B\cdot C\right]+\left[A_{2}\cdot B\cdot C\right]} $

From this we can infer that $$[\mathrm{A\cdot B\cdot C]} $$ depends only on $$\mathrm{C}$$ and the rotation $$\mathrm{R}$$ determined by $$\mathrm{A}$$ and $$\mathrm{B}$$. For this reason we write for the vector product also $$[\mathrm{R\cdot C]} $$; in calculating it we are free to replace the rotation $$\mathrm{R}$$ by any two vectors by means of which it can be represented.

If $$\mathrm{R}$$, $$\mathrm{R}_{1}$$ and $$\mathrm{R}_{2}$$ are rotations in the same plane, such that the value and direction of $$\mathrm{R}$$ are found by adding $$\mathrm{R}_{1}$$ and $$\mathrm{R}_{2}$$ algebraically, we have, in virtue of the distributive property

$[\mathrm{R_{1}\cdot C]}+[\mathrm{R_{2}\cdot C]}=[\mathrm{R\cdot C]} $

title: Page:LorentzGravitation1916.djvu/11


text:
Page:LorentzGravitation1916.djvu/12

 § 12. In what precedes we were concerned with the volumes of parallelepipeds expressed in natural units. When we have introduced coordinates $$x_{1},\dots x_{4} $$ we may also express these volumes in the "$$x$$-units" corresponding to the coordinates chosen.

Let us consider e.g. the three-dimensional extension $$x_{4}=const. $$, which cuts the conjugate indicatrix in the ellipsoid

$g_{11}x_{1}^{2}+g_{22}x_{2}^{2}+g_{33}x_{3}^{2}+2g_{12}x_{1}x_{2}+2g_{23}x_{2}x_{3}+2g_{31}x_{3}x_{1}=-\epsilon^{2} $

If we agree that in $$x$$-measure spaces in this extension will be represented by positive numbers and that a parallelepiped with the positive edges $$dx_{1},dx_{2},dx_{3} $$ will have the volume $$dx_{1}\ dx_{2}\ dx_{3} $$, we find for that of the parallelepiped on three conjugate radius-vectors

$\frac{\epsilon^{3}}{\sqrt{-G_{44}}} $|undefined

where it has been taken into consideration that $$G_{44} $$ is negative.

The volume of the same parallelepiped being expressed in natural measure by — $$-i\epsilon^{3} $$ (§ 8), we have to multiply by

if we want to pass from the expression in $$x$$-measure to that in natural measure.

For the extension $$\left(x_{2},x_{3},x_{4}\right) $$, i.e. $$x_{1}=0 $$ the corresponding factor is

§ 13. In the theory of electromagnetic phenomena we are concerned in the first place with the electric charge and the convection current. So far as these quantities belong to a definite element $$d\Omega $$ of the field-figure they may be combined into

$\mathrm{q}d\Omega $

where $$\mathrm{q} $$ is a vector which we may call the current vector. When it is resolved into four components having the directions of the axes, the first three components determine the convection current, while the fourth component gives the density of the electric charge.

As to the electric and the magnetic force, these two taken together can be represented at each point of the field-figure by two rotations

$\mathrm{R}_{e} $ and $\mathrm{R}_{h} $

in definite, mutually conjugate two-dimensional extensions. These quantities are closely connected with the current vector, for after having introduced coordinates $$x_{1},\dots x_{4} $$ we have for each closed surface $$\sigma $$ the vector equation

title: Page:LorentzGravitation1916.djvu/12


text:
Page:LorentzGravitation1916.djvu/13

where the second integral has to be taken over the domain $$\Omega $$ enclosed by $$\sigma $$. On the left hand side $$d\sigma $$ represents a three-dimensional surface-element expressed in natural units and $$\mathrm{N} $$ a vector of the magnitude 1 in natural measure conjugate with or perpendicular to that element (§ 7) and directed towards the outside of the domain $$\Omega $$. The index $$x$$ shows that the vector $$\left[\mathrm{R}_{e}\cdot\mathrm{N}\right]+\left[\mathrm{R}_{h}\cdot\mathrm{N}\right] $$ must be expressed in $$x$$-measure. At each point of the surface we must resolve the vector along the four directions of the coordinates, express each component in $$x$$-measure (§10) and finally, after multiplication by $$d\sigma $$, we must add algebraically all $$x_{1} $$-components; similarly all $$x_{2} $$-components and so on.

It must be expressly remarked that if an equation like (10) in which we are concerned with the composition of vectors at different points of the field-figure, shall have a definite meaning we must know which components are to be considered as having the same direction, so that they can be added. This has been determined by the introduction of coordinates.

On the right hand side of the equation the index $$x$$ means that the vector $$\mathrm{q} $$ must be expressed in $$x$$-measure and the factor $$i$$ had to be introduced because $$d\Omega $$ is imaginary.

One can prove that equation (10) is equivalent to the differential equations which in 's theory serve for the same purpose and further that when the equation holds for one choice of coordinates it will also be true for any other choice.

§ 14. The proof for these assertions must be deferred to the second part of this communication. For the present we shall only add that the part of the principal function referring to the electromagnetic field is given by

$H_{2}=i\int\frac{1}{2}\left(\mathrm{R}_{e}^{2}+\mathrm{R}_{h}^{2}\right)d\Omega $

where $$\mathrm{R}_{e} $$ and $$\mathrm{R}_{h} $$ are, expressed in natural units, the two rotations that are characteristic of the field. Like the two other parts of the principal function, $$H_{2} $$ is not changed by a deformation of the field-figure. In this statement it is to be understood that the parallelograms by which $$\mathrm{R}_{e} $$ and $$\mathrm{R}_{h} $$ are represented take part in the deformation.

Some remarks on the way in which, starting from the principal function, we may obtain the fundamental equations of the theory

title: Page:LorentzGravitation1916.djvu/13


text:
Page:LorentzGravitation1916.djvu/14

 must also be deferred. I shall conclude now by remarking that, as an immediate consequence of 's principle, the world-line of a material point which is acted on only by a given gravitation field, will be a geodetic line, and that the equations which determine the gravitation field caused by material and electromagnetic systems will be found by the consideration of infinitely small variations of the indicatrices, by which the numerical values of all quantities that are measured by means of these surfaces will be changed.

(Communicated in the meeting of March 25, 1916).

§ 15. In the first part of this communication the connexion between the electric and the magnetic force on one hand and the charge and the convection current on the other was expressed by the equation

which has been discussed in § 13. It will now be shown that this formula is equivalent to the differential equations by which the connexion in question is expressed in the theory of. For this purpose some further geometrical considerations must first be developed. They refer to the special case that the quantities $$g_{ab} $$, have the same values at every point of the field-figure.

If this condition is fulfilled, considerations which generally may be applied to infinitesimal extensions only are valid for finite extensions too.

§ 16. The factor required, in the measurement of four-dimensional domains, for the passage from $$x$$-units to natural units has now the same value at every point of the field-figure. Similarly, when any one-, two- or three-dimensional extension in the field-figure that is determined by linear equations ("linear extensions") is considered, the factor by means of which the said passage may be effected for parts of that extension, will be the same for all those parts. Moreover the factor in question will be the same for two "parallel" extensions of this kind, i.e. for two extensions the determining equations of which can be written in such a way that the coefficients of $$x_{1},\dots x_{4} $$ are the same in them.

title: Page:LorentzGravitation1916.djvu/14


text:
Page:Weird Tales volume 28 number 03.djvu/49

  "The priestess led the rigid little creature forward under the fabulous tree."

VER time-ruined Illar the searching planes swooped and circled. Northwest Smith, peering up at them with a steel-pale stare from the shelter of a half-collapsed temple, thought of vultures wheeling above carrion. All day long now they had been raking these ruins for him. Presently, he knew, thirst would begin to parch his throat and hunger to gnaw at him. There was neither food nor water in these ancient Martian ruins, and he knew {{right|{{sm|315|offset=2em}}


text:
Page:The Corsair (Byron).djvu/107

Rh On Conrad's stricken soul exhaustion prest, And stupor almost lull'd it into rest; So feeble now—his mother's softness crept To those wild eyes, which like an infant's wept: It was the very weakness of his brain, Which thus confess'd without relieving pain. None saw his trickling tears—perchance, if seen, That useless flood of grief had never been: Nor long they flowed—he dried them to depart, In helpless—hopeless—brokenness of heart: The sun goes forth—but Conrad's day is dim— And the night cometh—ne'er to pass from him— There is no darkness like the cloud of mind, On Grief's vain eye—the blindest of the blind! Which may not—dare not see—but turns aside To blackest shade—nor will endure a guide!

His heart was form'd for softness—warp'd to wrong— Betray'd too early, and beguil'd too long; Each feeling pure—as falls the dropping dew Within the grot; like that had harden'd too;—

title: Page:The Corsair (Byron).djvu/107


text:
Page:Weird Tales volume 28 number 03.djvu/50

516 that it could be only a matter of time before the urgencies of his own body would drive him out to signal those wheeling Patrol ships and trade his hard-won liberty for food and drink. He crouched lower under the shadow of the temple arch and cursed the accuracy of the Patrol gunner whose flame-blast had caught his dodging ship just at the edge of Illar's ruins.

Presently it occurred to him that in most Martian temples of the ancient days an ornamental well had stood in the outer court for the benefit of wayfarers. Of course all water in it would be a million years dry now, but for lack of anything better to do he rose from his seat at the edge of the collapsed central dome and made his cautious way by still intact corridors toward the front of the temple. He paused in a tangle of wreckage at the courtyard's edge and looked out across the sun-drenched expanse of pavement toward that ornate well that once had served travelers who passed by here in the days when Mars was a green planet.

It was an unusually elaborate well, and amazingly well preserved. Its rim had been inlaid with a mosaic pattern whose symbolism must once have borne deep meaning, and above it in a great fan of time-defying bronze an elaborate grille-work portrayed the inevitable tree-of-life pattern which so often appears in the symbolism of the three worlds. Smith looked at it a bit incredulously from his shelter, it was so miraculously preserved amidst all this chaos of broken stone, casting a delicate tracery of shadow on the sunny pavement as perfectly as it must have done a million years ago when dusty travelers paused here to drink. He could picture them filing in at noontime through the great gates that

The vision vanished abruptly as his questing eyes made the circle of the ruined walls. There had been no gate. He could not find a trace of it anywhere around the outer wall of the court. The only entrance here, as nearly as he could tell from the foundations that remained, had been the door in whose ruins he now stood. Queer. This must have been a private court, then, its great grille-crowned well reserved for the use of the priests. Or wait—had there not been a priest-king Illar after whom the city was named? A wizard-king, so legend said, who ruled temple as well as palace with an iron hand. This elaborately patterned well, of material royal enough to withstand the weight of ages, might well have been sacrosanct for the use of that long-dead monarch. It might

Across the sun-bright pavement swept the shadow of a plant. Smith dodged back into deeper hiding while the ship circled low over the courtyard. And it was then, as he crouched against a crumbled wall and waited, motionless, for the danger to pass, that he became aware for the first time of a sound that startled him so he could scarcely credit his ears—a recurrent sound, choked and sorrowful—the sound of a woman sobbing.

The incongruity of it made him forgetful for a moment of the peril hovering overhead in the sun-hot outdoors. The dimness of the temple ruins became a living and vital place for that moment, throbbing with the sound of tears. He looked about half in incredulity, wondering if hunger and thirst were playing tricks on him already, or if these broken halls might be haunted by a million-years-old sorrow that wept along die corridors to drive its hearers mad. There were tales of such haunters in some of Mars' older ruins. The hair prickled faintly at the back of his neck as he laid a hand on the butt of his force-gun and commenced


text:
Page:Wittgenstein - Tractatus Logico-Philosophicus, 1922.djvu/37

Rh Just as we cannot think of spatial objects at all apart from space, or temporal objects apart from time, so we cannot think of any object apart from the possibility of its connexion with other things.

If I can think of an object in the context of an atomic fact, I cannot think of it apart from the possibility of this context.

The thing is independent, in so far as it can occur in all possible circumstances, but this form of independence is a form of connexion with the atomic fact, a form of dependence. (It is impossible for words to occur in two different ways, alone and in the proposition.)

If I know an object, then I also know all the possibilities of its occurrence in atomic facts.

(Every such possibility must lie in the nature of the object.)

A new possibility cannot subsequently be found.

In order to know an object, I must know not its external but all its internal qualities.

If all objects are given, then thereby are all possible atomic facts also given.

Every thing is, as it were, in a space of possible atomic facts. I can think of this space as empty, but not of the thing without the space.

A spatial object must lie in infinite space. (A point in space is an argument place.)

A speck in a visual field need not be red, but it must have a colour; it has, so to speak, a colour space round it. A tone must have a

Rh


text:
Page:Wittgenstein - Tractatus Logico-Philosophicus, 1922.djvu/39

Rh pitch, the object of the sense of touch a hardness, etc.

Objects contain the possibility of all states of affairs.

The possibility of its occurrence in atomic facts is the form of the object.

The object is simple.

Every statement about complexes can be analysed into a statement about their constituent parts, and into those propositions which completely describe the complexes.

Objects form the substance of the world. Therefore they cannot be compound.

If the world had no substance, then whether a proposition had sense would depend on whether another proposition was true.

It would then be impossible to form a picture of the world (true or false).

It is clear that however different from the real one an imagined world may be, it must have something—a form—in common with the real world.

This fixed form consists of the objects.

The substance of the world can only determine a form and not any material properties. For these are first presented by the propositions—first formed by the configuration of the objects.

Roughly speaking: objects are colourless.

Two objects of the same logical form are—apart from their external properties—only differentiated from one another in that they are different.

Either a thing has properties which no other has, and then one can distinguish it straight away from the others by a description and refer to it; or, on the other hand, there are several things which have the totality of their properties in Rh


text:
Page:Wittgenstein - Tractatus Logico-Philosophicus, 1922.djvu/41

Rh common, and then it is quite impossible to point to any one of them.

For if a thing is not distinguished by anything, I cannot distinguish it—for otherwise it would be distinguished.

Substance is what exists independently of what is the case.

It is form and content.

Space, time and colour (colouredness) are forms of objects.

Only if there are objects can there be a fixed form of the world.

The fixed, the existent and the object are one.

The object is the fixed, the existent; the configuration is the changing, the variable.

The configuration of the objects forms the atomic fact.

In the atomic fact objects hang one in another, like the links of a chain.

In the atomic fact the objects are combined in a definite way.

The way in which objects hang together in the atomic fact is the structure of the atomic fact.

The form is the possibility of the structure.

The structure of the fact consists of the structures of the atomic facts.

The totality of existent atomic facts is the world.

The totality of existent atomic facts also determines which atomic facts do not exist.

The existence and non-existence of atomic facts is the reality.

(The existence of atomic facts we also call a positive fact, their non-existence a negative fact.)

Atomic facts are independent of one another. Rh


text:
Page:Weird Tales volume 28 number 03.djvu/51

Rh a cautious prowl toward the source of the muffled noise.

Presently he caught a flash of white, luminous in the gloom of these ruined walls, and went forward with soundless steps, eyes narrowed in the effort to make out what manner of creature this might be that wept alone in time- forgotten ruins. It was a woman. Or it had the dim outlines of a woman, huddled against an angle of fallen walls and veiled in a fabulous shower of long dark hair. But there was something uncannily odd about her. He could not focus his pale stare upon her outlines. She was scarcely more than a luminous blot of whiteness in the gloom, shimmering with a look of unreality which the sound of her sobs denied.

EFORE he could make up his mind just what to do, something must have warned the weeping girl that she was no longer alone, for the sound of her tears checked suddenly and she lifted her head, turning to him a face no more distinguishable than her body's outlines. He made no effort to resolve the blurred features into visibility, for out of that luminous mask burned two eyes that caught his with an almost perceptible impact and gripped them in a stare from which he could not have turned if he would.

They were the most amazing eyes he had ever met, colored like moonstone, milkily translucent, so that they looked almost blind. And that magnetic stare held him motionless. In the instant that she gripped him with that fixed, moonstone look he felt oddly as if a tangible bond were taut between them.

Then she spoke, and he wondered if his mind, after all, had begun to give way in the haunted loneliness of dead Illar; for though the words she spoke fell upon his ears in a gibberish of meaningless sounds, yet in his brain a message formed with a clarity that far transcended the halting communication of words. And her milkily colored eyes bored into his with a fierce intensity.

"I'm lost—I'm lost——" wailed the voice in his brain.

A rush of sudden tears brimmed the compelling eyes, veiling their brilliance. And he was free again with that clouding of the moonstone surfaces. Her voice wailed, but the words were meaningless and no knowledge formed in his brain to match them. Stiffly he stepped back a pace and looked down at her, a feeling of helpless incredulity rising within him. For he still could not focus directly upon the shining whiteness of her, and nothing save those moonstone eyes were clear to him.

The girl sprang to her feet and rose on tiptoe, gripping his shoulders with urgent hands. Again the blind intensity of her eyes took hold of his, with a force almost as tangible as the clutch of her hands; again that stream of intelligence poured into his brain, strongly, pleadingly.

"Please, please take me back! I'm so frightened—I can't find my way—oh, please!"

He blinked down at her, his dazed mind gradually realizing the basic facts of what was happening, Obviously her milky, unseeing eyes held a magnetic power that carried her thoughts to him without the need of a common speech. And they were the eyes of a powerful mind, the outlets from which a stream of fierce energy poured into his brain. Yet the words they conveyed were the words of a terrified and helpless girl. A strong sense of wariness was rising in him as he considered the incongruity of speech and power, both of which were beating upon him more urgently with every breath. The mind of a forceful and


text:
Page:Weird Tales volume 28 number 03.djvu/52

318 strong-willed woman, carrying the sobs of a frightened girl. There was no sincerity in it.

"Please, please!" cried her impatience in his brain. "Help me! Guide me back!"

"Back where?" he heard his own voice asking.

"The Tree!" wailed that queer speech in his brain, while gibberish was all his ears heard and the moonstone stare transfixed him strongly. "The Tree of Life! Oh, take me back to the shadow of the Tree!"

A vision of the grille-ornamented well leaped into his memory. It was the only tree symbol he could think of just then. But what possible connection could there be between the well and the lost girl—if she was lost? Another wail in that unknown tongue, another anguished shake of his shoulders, brought a sudden resolution into his groping mind. There could be no harm in leading her back to the well, to whose grille she must surely be referring. And strong curiosity was growing in his mind. Much more than met the eye was concealed in this queer incident. And a wild guess had flashed through his mind that perhaps she might have come from some subterranean world into which the well descended. It would explain her luminous pallor, if not her blurriness; and, too, her eyes did not seem to function in the light. There was a much more incredible explanation of her presence, but he was not to know it for a few minutes yet.

"Come along," he said, taking the clutching hands gently from his shoulders. "I'll lead you to the well."

She sighed in a deep gust of relief and dropped her compelling eyes from his, murmuring in that strange, gabbling tongue what must have been thanks. He took her by the hand and turned toward the ruined archway of the door.

Against his fingers her flesh was cool and firm. To the touch she was tangible, but even thus near, his eyes refused to focus upon the cloudy opacity of her body, the dark blur of her streaming hair. Nothing but those burning, blinded eyes were strong enough to pierce the veil that parted them.

She stumbled along at his side over the rough floor of the temple, saying nothing more, panting with eagerness to return to her incomprehensible "tree." How much of that eagerness was assumed Smith still could not be quite sure. When they reached the door he halted her for a moment, scanning the sky for danger. Apparently the ships had finished with this quarter of the city, for he could see two or three of them half a mile away, hovering low over Illar's northern section. He could risk it without much peril. He led the girl cautiously out into the sun-hot court.

HE could not have known by sight that they neared the well, but when they were within twenty paces of it she flung up her blurred head suddenly and tugged at his hand. It was she who led him that last stretch which parted the two from the well. In the sun the shadow tracery of the grille's symbolic pattern lay vividly outlined on the ground. The girl gave a little gasp of delight. She dropped his hand and ran forward three short steps, and plunged into the very center of that shadowy pattern on the ground. And what happened then was too incredible to believe.

The pattern ran over her like a garment, curving to the curve of her body in the way all shadows do. But as she stood there striped and laced with the darkness of it, there came a queer shifting in the lines of black tracery, a subtle, inexplicable movement to one side. And with that motion she vanished. It was exactly as if that shifting had moved her out of


text:
Page:Weird Tales volume 28 number 03.djvu/56

322 with the disappearance of the priestess' white-glowing figure. Head down, paying little heed to where he was going, he went on over the flowery sward.

An odd sense of voids about him startled Smith at last out of his lethargic plodding. He lifted his head. He stood just at the edge of a line of trees, dim and indistinct in the unchanging twilight. Beyond them—he came to himself with a jerk and stared incredulously. Beyond them the grass ran down to nothingness, merging by imperceptible degrees into a streaked and arching void—not the sort of emptiness into which a material body could fall, but a solid nothing, curving up toward the dark zenith as the inside of a sphere curves. No physical thing could have entered there. It was too utterly void, an inviolable emptiness which no force could invade.

He stared up along the inward arch of that curving, impassable wall. Here, then, was the edge of the queer land Illar had wrested out of space itself. This arch must be the curving of solid space which had been bent awry to enclose the magical land. There was no escape this way. He could not even bring himself to approach any nearer to that streaked and arching blank. He could not have said why, but it woke in him an inner disquiet so strong that after a moment's staring he turned his eyes away.

Presently he shrugged and set off along the inside of the line of trees which parted him from the space-wall. Perhaps there might be a break somewhere. It was a forlorn hope, but the best that offered. Wearily he stumbled on over the flowery grass.

How long he had gone on along that almost imperceptibly curving line of border he could not have said, but after a timeless interval of gray solitude he gradually became aware that a tiny rustling and whispering among the leaves had been growing louder by degrees for some time. He looked up. In and out among the trees which bordered that solid wall of nothingness little, indistinguishable figures were flitting. The tree-men had returned. Queerly grateful for their presence, he went on a bit more cheerfully, paying no heed to their timid dartings to and fro, for Smith was wise in the ways of wild life.

Presently, when they saw how little heed he paid them, they began to grow bolder, their whispers louder. And among those rustling voices he thought he was beginning to catch threads of familiarity. Now and again a word reached his ears that he seemed to recognize, lost amidst the gibberish of their speech. He kept his head down and his hands quiet, plodding along with a cunning stillness that began to bear results.

From the corner of his eye he could see that a little dark tree-man had darted out from cover and paused midway between bush and tree to inspect the queer, tall stranger. Nothing happened to this daring venturer, and soon another risked a pause in the open to stare at the quiet walker among the trees. In a little while a small crowd of the tree-people was moving slowly parallel with his course, staring with all the avid curiosity of wild things at Smith's plodding figure. And among them the rustling whispers grew louder.

Presently the ground dipped down into a little hollow ringed with trees. It was a bit darker here than it had been on the higher level, and as he went down the slope of its side he saw that among the underbrush which filled it were cunningly hidden huts twined together out of the living bushes. Obviously the hollow was a tiny village where the tree-folk dwelt.

He was surer of this when they began to grow bolder as he went down into the dimness of the place. The whispers


text:
Page:Weird Tales volume 28 number 03.djvu/55

Rh "Then what becomes, afterward, of the men Thag desires?" he pursued.

"You must ask Thag that."

She turned her eyes away as she spoke, snapping the mental bond that had flowed between them with a suddenness that left Smith dizzy. He went on at her side more slowly, pulling back a little on the tug of her fingers. By degrees the sense of dreaminess was fading, and alarm began to stir in the deeps of his mind. After all, there was no reason why he need let this blank-eyed priestess lead him up to the very maw of her god. She had lured him into this land by what he knew now to have been a trick; might she not have worse tricks than that in store for him?

She held him, after all, by nothing stronger than the clasp of her fingers, if he could keep his eyes turned from hers. Therein lay her real power, but he could fight it if he chose. And he began to hear more clearly than ever the queer note of warning in the rustling whispers of the tree-folk who still fluttered in and out of sight among the leaves. The twilight place had taken on menace and evil. Suddenly he made up his mind. He stopped, breaking the clasp of the girl's hand.

"I'm not going," he said.

She swung round in a sweep of richly tinted hair, words jetting from her in a gush of incoherence. But he dared not meet her eyes, and they conveyed no meaning to him. Resolutely he turned away, ignoring her voice, and set out to retrace the way they had come. She called after him once, in a high, clear voice that somehow held a note as warning as that in the rustling voices of the tree-people, but he kept on doggedly, not looking back. She laughed then, sweetly and scornfully, a laugh that echoed uneasily in his mind long after the sound of it had died upon the twilit air.

After a while he glanced back over one shoulder, half expecting to see the luminous dazzle of her body still glowing in the dim glade where he had left her; but the blurred tapestry-landscape was quite empty.

He went on in the midst of a silence so deep it hurt his ears, and in a solitude unhaunted even by the shy presences of the tree-folk. They had vanished with the fire-bright girl, and the whole twilight land was empty save for himself. He plodded on across the dark grass, crushing the upturned flower-faces under his boots and asking himself wearily if he could be mad. There seemed little other explanation for this hushed and tapestried solitude that had swallowed him up. In that thunderous quiet, in that deathly solitude, he went on.

HEN he had walked for what seemed to him much longer than it should have taken to reach his starting-point, and still no sign of an exit appeared, he began to wonder if there were any way out of the gray land of Thag. For the first time he realized that he had come through no tangible gateway. He had only stepped out of a shadow, and—now that he thought of it—there were no shadows here. The grayness swallowed everything up, leaving the landscape oddly flat, like a badly drawn picture. He looked about helplessly, quite lost now and not sure in what direction he should be facing, for there was nothing here by which to know directions. The trees and shrubs and the starry grass still stretched about him, uncertainly outlined in that changeless dusk. They seemed to go on for ever.

But he plodded ahead, unwilling to stop because of a queer tension in the air, somehow as if all the blurred trees and shrubs were waiting in breathless anticipation, centering upon his stumbling figure. But all trace of animate life had W. T.—5


text:
Page:Weird Tales volume 28 number 03.djvu/54

320 about them in the thick, confusing gloom of the place. He could see only a little distance through that dim air. It was as if they walked a strip of tapestried twilight in some unlighted dream. And the girl, with her lovely, luminous body and richly colored robe of hair was like a woman in a tapestry too, unreal and magical.

After a while, when he had become a little adjusted to the queerness of the whole scene, he began to notice furtive movements in the shrubs and trees they passed. Things flickered too swiftly for him to catch their outlines, but from the tail of his eye he was aware of motion, and somehow of eyes that watched. That sensation was a familiar one to him, and he kept an uneasy gaze on those shiftings in the shrubbery as they went on. Presently he caught a watcher in full view between bush and tree, and saw that it was a man, a little, furtive, dark-skinned man who dodged hastily back into cover again before Smith's eyes could do more than take in the fact of his existence.

After that he knew what to expect and could make them out more easily: little, darting people with big eyes that shone with a queer, sorrowful darkness from their small, frightened faces as they scuttled through the bushes, dodging always just out of plain sight among the leaves. He could hear the soft rustle of their passage, and once or twice when they passed near a clump of shrubbery he thought he caught the echo of little whispering calls, gentle as the rustle of leaves and somehow full of a strange warning note so clear that he caught it even amid the murmur of their speech. Warning calls, and little furtive hiders in the leaves, and a landscape of tapestried blurting carpeted with Botticelli flower-strewn sward. It was all a dream. He felt quite sure of that.

T was a long while before curiosity awakened in him sufficiently to make him break the stillness. But at last he asked dreamily.

"Where are we going?"

The girl seemed to understand that without the necessity of the bond her hypnotic eyes made, for she turned and caught his eyes in a white stare and answered.

"To Thag. Thag desires you."

"What is Thag?"

In answer to that she launched without preliminary upon a little singsong monolog of explanation whose stereotyped formula made him faintly uneasy with the thought that it must have been made very often to attain the status of a set speech; made to many men, perhaps, whom Thag had desired. And what became of them afterward? he wondered. But the girl was speaking.

"Many ages ago there dwelt in Illar the great King Illar for whom the city was named. He was a magician of mighty power, but not mighty enough to fulfill all his ambitions. So by his arts he called up out of darkness the being known as Thag, and with him struck a bargain. By that bargain Thag was to give of his limitless power, serving Illar all the days of Illar's life, and in return the king was to create a land for Thag's dwelling-place and people it with slaves and furnish a priestess to tend Thag's needs. This is that land. I am that priestess, the latest of a long line of women born to serve Thag. The tree-people are his—his lesser servants.

"I have spoken softly so that the tree-people do not hear, for to them Thag is the center and focus of creation, the end and beginning of all life. But to you I have told the truth."

"But what does Thag want of me?"

"It is not for Thag's servants to question Thag." W.T.—4


text:
Page:Weird Tales volume 28 number 03.djvu/53

Rh one world into another. Stupidly Smith stared at the spot from which she had disappeared.

Then several things happened almost simultaneously. The zoom of a plane broke suddenly into the quiet, a black shadow dipped low over the rooftops, and Smith, too late, realized that he stood defenseless in full view of the searching ships. There was only one way out, and that was too fantastic to put faith in, but he had no time to hesitate. With one leap he plunged full into the midst of the shadow of the tree of life.

Its tracery flowed round him, molding its pattern to his body. And outside the boundaries everything executed a queer little sidewise dip and slipped in the most extraordinary manner, like an optical illusion, into quite another scene. There was no intervention of blankness. It was as if he looked through the bars of a grille upon a picture which without warning slipped sidewise, while between the bars appeared another scene, a curious, dim landscape, gray as if with the twilight of early evening. The air had an oddly thickened look, through which he saw the quiet trees and the flower-spangled grass of the place with a queer, unreal blending, like the landscape in a tapestry, all its outlines blurred.

In the midst of this tapestried twilight the burning whiteness of the girl he had followed blazed like a flame. She had paused a few steps away and stood waiting, apparently quite sure that he would come after. He grinned a little to himself as he realized it, knowing that curiosity must almost certainly have driven him in her wake even if the necessity for shelter had not compelled his following. She was clearly visible now, in this thickened dimness—visible, and very lovely, and a little unreal. She shone with a burning clarity, the only vivid thing in the whole twilit world. Eyes upon that blazing whiteness, Smith stepped forward, scarcely realizing that he had moved.

Slowly he crossed the dark grass toward her. That grass was soft underfoot, and thick with small, low-blooming flowers of a shining pallor. Botticelli painted such spangled swards for the feet of his angels. Upon it the girl's bare feet gleamed whiter than the blossoms. She wore no garment but the royal mantle of her hair, sweeping about her in a cloak of shining darkness that had a queer, unreal tinge of purple in that low light. It brushed her ankles in its fabulous length. From the hood of it she watched Smith coming toward her, a smile on her pale mouth and a light blazing in the deeps of her moonstone eyes. She was not blind now, nor frightened. She stretched out her hand to him confidently.

"It is my turn now to lead you," she smiled. As before, the words were gibberish, but the penetrating stare of those strange white eyes gave them a meaning in the depths of his brain.

Automatically his hand went out to hers. He was a little dazed, and her eyes were very compelling. Her fingers twined in his and she set off over the flowery grass, pulling him beside her. He did not ask where they were going. Lost in the dreamy spell of the still, gray, enchanted place, he felt no need for words. He was beginning to see more clearly in the odd, blurring twilight that ran the outlines of things together in that queer, tapestried manner. And he puzzled in a futile, muddled way as he went on over what sort of land he had come into. Overhead was darkness, paling into twilight near the ground, so that when he looked up he was staring into bottomless deeps of starless night.

Trees and flowering shrubs and the flower-starred grass stretched emptily


text:
Page:Weird Tales volume 28 number 03.djvu/68

By ROBERT E. HOWARD

One of the strangest stories ever written—the tale of a barbarian adventurer, a woman pirate, and a weird roofed city inhabited by the most peculiar race of men ever spawned

The Story Thus Far

ONAN the Cimmerian, and Valeria, a woman pirate, having deserted from a mercenary army on the Stygian-Darfar border, came, after many days' flight, to a vast forest far to the south. There their horses were slain and devoured by a dragon, which Conan managed to kill with a poisoned spear. In a plain surrounded by the forest, they came upon a fantastic city called Xuchotl, a series of halls and chambers built all under one roof, floored with a lambent red stone and illuminated by means of skylights and green fire-jewels. At first it appeared to be deserted, but later they discovered it to be inhabited by a tribe of mongrel Stygians called Tlazitlans, who were divided into rival clans known as Tecuhltli and Xotalancas.

Valeria saved the life of a Tecuhltli named Techotl, and with him they fled to the castle of Tecuhltli near the western gate of the city, pursued by the Xotalancas, who dwelt by the eastern gate. Tecuhltli was ruled over by Prince Olmec and Princess Tascela, who displayed a sinister interest in Valeria. Olmec told the adventurers that half a century ago a tribe of Tlazitlans had fled southward from the Stygians, and fought their way through the dragon—haunted forest and found the city, then occupied by a degenerate race which had once been powerful magicians. The Tlazitlans had destroyed them and settled in the city, ruled by the brothers Tecuhltli and Xotalanc, and by; an evil ancient named Tolkemec.

A quarrel over a woman had split the tribe into three clans, of which that of Tolkemec had been utterly destroyed twelve years before, Tolkemec escaping, supposedly dying, from the dungeon where he was thrown. Fear of the dragons in the forest kept the people imprisoned in the city, while the feud reduced the tribe to a handful on each side.

Red nails driven in an ebon column denoted the number of Xotalancas slain in the feud. Olmec persuaded Conan and Valeria to remain and fight for his clan as mercenaries. They were shown to separate chambers, and Valeria awoke during the night to find Yasala, Tascela's maid, trying to drug her with the black lotus. She tried to make the girl explain her actions, but Yasala, fleeing from her, ran down a stair leading to the catacombs beneath the city, into which old Tolkemec had dragged his broken body twelve years before. Valeria heard her scream down in the darkness, and heard an inhuman, high-pitched tittering. Returning to her chamber she secured her garments and weapons, meaning to urge Conan to join her in flight from the city she had begun to fear. But just as she started for his chamber she heard a sudden clamor of yells and the clash of swords.

The story continues:

334


text:
Page:Weird Tales volume 28 number 03.djvu/69

Rh

WO warriors lounged in the guardroom on the floor known as the Tier of the Eagle. Their attitude was casual, though habitually alert. An attack on the great bronze door from without was always a possibility, but for many years no such assault had been attempted on either side.

"The strangers are strong allies," said one. "Olmec will move against the enemy tomorrow, I believe."

He spoke as a soldier in a war might have spoken. In the miniature world of Xuchotl each handful of feudists was an army, and the empty halls between the castles was the country over which they campaigned.

The other meditated for a space.

"Suppose with their aid we destroy Xotalanc," he said. "What then, Xatmec?"

"Why," returned Xatmec, "we will drive red nails for them all. The captives we will burn and flay and quarter."  "Even as he shifted, he hurled the knife." "But afterward?" pursued the other. "After we have slain them all? Will it


text:
Page:Wittgenstein - Tractatus Logico-Philosophicus, 1922.djvu/43

Rh From the existence or non-existence of an atomic fact we cannot infer the existence or non-existence of another.

The total reality is the world.

We make to ourselves pictures of facts.

The picture presents the facts in logical space, the existence and non-existence of atomic facts.

The picture is a model of reality.

To the objects correspond in the picture the elements of the picture.

The elements of the picture stand, in the picture, for the objects.

The picture consists in the fact that its elements are combined with one another in a definite way.

The picture is a fact.

That the elements of the picture are combined with one another in a definite way, represents that the things are so combined with one another.

This connexion of the elements of the picture is called its structure, and the possibility of this structure is called the form of representation of the picture.

The form of representation is the possibility that the things are combined with one another as are the elements of the picture.

Thus the picture is linked with reality; it reaches up to it.

It is like a scale applied to reality.

Only the outermost points of the dividing lines touch the object to be measured.

According to this view the representing relation which makes it a picture, also belongs to the picture.

The representing relation consists of the co-ordinations of the elements of the picture and the things.

These co-ordinations are as it were the feelers of Rh


text:
Page:Wittgenstein - Tractatus Logico-Philosophicus, 1922.djvu/45

Rh its elements with which the picture touches reality.

In order to be a picture a fact must have something in common with what it pictures.

In the picture and the pictured there must be something identical in order that the one can be a picture of the other at all.

What the picture must have in common with reality in order to be able to represent it after its manner—rightly or falsely—is its form of representation.

The picture can represent every reality whose form it has.

The spatial picture, everything spatial, the coloured, everything coloured, etc.

The picture, however, cannot represent its form of representation; it shows it forth.

The picture represents its object from without (its standpoint is its form of representation), therefore the picture represents its object rightly or falsely.

But the picture cannot place itself outside of its form of representation.

What every picture, of whatever form, must have in common with reality in order to be able to represent it at all—rightly or falsely—is the logical form, that is, the form of reality.

If the form of representation is the logical form, then the picture is called a logical picture.

Every picture is also a logical picture. (On the other hand, for example, not every picture is spatial.)

The logical picture can depict the world.

The picture has the logical form of representation in common with what it pictures.

The picture depicts reality by representing a possibility of the existence and non-existence of atomic facts. Rh


text:
Page:Wittgenstein - Tractatus Logico-Philosophicus, 1922.djvu/47

Rh The picture represents a possible state of affairs in logical space.

The picture contains the possibility of the state of affairs which it represents.

The picture agrees with reality or not; it is right or wrong, true or false.

The picture represents what it represents, independently of its truth or falsehood, through the form of representation.

What the picture represents is its sense.

In the agreement or disagreement of its sense with reality, its truth or falsity consists.

In order to discover whether the picture is true or false we must compare it with reality.

It cannot be discovered from the picture alone whether it is true or false.

There is no picture which is a priori true.

The logical picture of the facts is the thought.

“An atomic fact is thinkable”—means: we can imagine it.

The totality of true thoughts is a picture of the world.

The thought contains the possibility of the state of affairs which it thinks.

What is thinkable is also possible.

We cannot think anything unlogical, for otherwise we should have to think unlogically.

It used to be said that God could create everything, except what was contrary to the laws of logic. The truth is, we could not say of an “unlogical” world how it would look.

To present in language anything which “contradicts logic” is as impossible as in geometry to present by its co-ordinates a figure which contradicts the laws of space; or to give Rh


text:
Page:Wittgenstein - Tractatus Logico-Philosophicus, 1922.djvu/49

Rh the co-ordinates of a point which does not exist.

We could present spatially an atomic fact which contradicted the laws of physics, but not one which contradicted the laws of geometry.

An a priori true thought would be one whose possibility guaranteed its truth.

Only if we could know a priori that a thought is true if its truth was to be recognized from the thought itself (without an object of comparison).

In the proposition the thought is expressed perceptibly through the senses.

We use the sensibly perceptible sign (sound or written sign, etc.) of the proposition as a projection of the possible state of affairs.

The method of projection is the thinking of the sense of the proposition.

The sign through which we express the thought I call the propositional sign. And the proposition is the propositional sign in its projective relation to the world.

To the proposition belongs everything which belongs to the projection; but not what is projected.

Therefore the possibility of what is projected but not this itself.

In the proposition, therefore, its sense is not yet contained, but the possibility of expressing it.

(“The content of the proposition” means the content of the significant proposition.)

In the proposition the form of its sense is contained, but not its content.

The propositional sign consists in the fact that its elements, the words, are combined in it in a definite way.

The propositional sign is a fact.

The proposition is not a mixture of words Rh


text:
Page:Wittgenstein - Tractatus Logico-Philosophicus, 1922.djvu/51

Rh (just as the musical theme is not a mixture of tones).

The proposition is articulate.

Only facts can express a sense, a class of names cannot.

That the propositional sign is a fact is concealed by the ordinary form of expression, written or printed.

(For in the printed proposition, for example, the sign of a proposition does not appear essentially different from a word. Thus it was possible for Frege to call the proposition a compounded name.)

The essential nature of the propositional sign becomes very clear when we imagine it made up of spatial objects (such as tables, chairs, books) instead of written signs.

The mutual spatial position of these things then expresses the sense of the proposition.

We must not say, “The complex sign ‘aRb’ says ‘a stands in relation R to b’”; but we must say, “That ‘a’ stands in a certain relation to ‘b’ says that aRb”.

States of affairs can be described but not named.

(Names resemble points; propositions resemble arrows, they have sense.)

In propositions thoughts can be so expressed that to the objects of the thoughts correspond the elements of the propositional sign.

These elements I call “simple signs” and the proposition “completely analysed”.

The simple signs employed in propositions are called names.

The name means the object. The object is its meaning. (“A” is the same sign as “A”.)

To the configuration of the simple signs in the Rh


text:
Page:Wittgenstein - Tractatus Logico-Philosophicus, 1922.djvu/53

Rh propositional sign corresponds the configuration of the objects in the state of affairs.

In the proposition the name represents the object.

Objects I can only name. Signs represent them. I can only speak of them. I cannot assert them. A proposition can only say how a thing is, not what it is.

The postulate of the possibility of the simple signs is the postulate of the determinateness of the sense.

A proposition about a complex stands in internal relation to the proposition about its constituent part.

A complex can only be given by its description, and this will either be right or wrong. The proposition in which there is mention of a complex, if this does not exist, becomes not nonsense but simply false.

That a propositional element signifies a complex can be seen from an indeterminateness in the propositions in which it occurs. We know that everything is not yet determined by this proposition. (The notation for generality contains a prototype.)

The combination of the symbols of a complex in a simple symbol can be expressed by a definition.

There is one and only one complete analysis of the proposition.

The proposition expresses what it expresses in a definite and clearly specifiable way: the proposition is articulate.

The name cannot be analysed further by any definition. It is a primitive sign.

Every defined sign signifies via those signs by which it is defined, and the definitions show the way.

Two signs, one a primitive sign, and one defined by primitive signs, cannot signify in the Rh


text:
Page:Wittgenstein - Tractatus Logico-Philosophicus, 1922.djvu/55

Rh same way. Names cannot be taken to pieces by definition (nor any sign which alone and independently has a meaning).

What does not get expressed in the sign is shown by its application. What the signs conceal, their application declares.

The meanings of primitive signs can be explained by elucidations. Elucidations are propositions which contain the primitive signs. They can, therefore, only be understood when the meanings of these signs are already known.

Only the proposition has sense; only in the context of a proposition has a name meaning.

Every part of a proposition which characterizes its sense I call an expression (a symbol).

(The proposition itself is an expression.)

Expressions are everything—essential for the sense of the proposition—that propositions can have in common with one another.

An expression characterizes a form and a content.

An expression presupposes the forms of all propositions in which it can occur. It is the common characteristic mark of a class of propositions.

It is therefore represented by the general form of the propositions which it characterizes.

And in this form the expression is constant and everything else variable.

An expression is thus presented by a variable, whose values are the propositions which contain the expression.

(In the limiting case the variable becomes constant, the expression a proposition.)

I call such a variable a “propositional variable”.

An expression has meaning only in a proposition. Every variable can be conceived as a propositional variable. Rh


text: Author:Horatio Gates Jones

title: Author:Horatio Gates Jones


text:
Page:Wittgenstein - Tractatus Logico-Philosophicus, 1922.djvu/57

Rh (Including the variable name.)

If we change a constituent part of a proposition into a variable, there is a class of propositions which are all the values of the resulting variable proposition. This class in general still depends on what, by arbitrary agreement, we mean by parts of that proposition. But if we change all those signs, whose meaning was arbitrarily determined, into variables, there always remains such a class. But this is now no longer dependent on any agreement; it depends only on the nature of the proposition. It corresponds to a logical form, to a logical prototype.

What values the propositional variable can assume is determined.

The determination of the values is the variable.

The determination of the values of the propositional variable is done by indicating the propositions whose common mark the variable is.

The determination is a description of these propositions.

The determination will therefore deal only with symbols not with their meaning.

And only this is essential to the determination, that it is only a description of symbols and asserts nothing about what is symbolized.

The way in which we describe the propositions is not essential.

I conceive the proposition—like Frege and Russell—as a function of the expressions contained in it.

The sign is the part of the symbol perceptible by the senses.

Two different symbols can therefore have the sign (the written sign or the sound sign) in common—they then signify in different ways.


text:
Page:Wittgenstein - Tractatus Logico-Philosophicus, 1922.djvu/59

Rh  It can never indicate the common characteristic of two objects that we symbolize them with the same signs but by different methods of symbolizing. For the sign is arbitrary. We could therefore equally well choose two different signs and where then would be what was common in the symbolization.

In the language of everyday life it very often happens that the same word signifies in two different ways—and therefore belongs to two different symbols—or that two words, which signify in different ways, are apparently applied in the same way in the proposition.

Thus the word "is" appears as the copula, as the sign of equality, and as the expression of existence; "to exist" as an intransitive verb like "to go"; "identical" as an adjective; we speak of something but also of the fact of something happening.

(In the proposition "Green is green"—where the first word is a proper name as the last an adjective—these words have not merely different meanings but they are different symbols.)

Thus there easily arise the most fundamental confusions (of which the whole of philosophy is full).

In order to avoid these errors, we must employ a symbolism which excludes them, by not applying the same sign in different symbols and by not applying signs in the same way which signify in different ways. A symbolism, that is to say, which obeys the rules of logical grammar—of logical syntax.

(The logical symbolism of Frege and Russell is such a language, which, however, does still not exclude all errors.) Rh


text:
Page:Wittgenstein - Tractatus Logico-Philosophicus, 1922.djvu/61

Rh

In order to recognize the symbol in the sign we must consider the significant use.

The sign determines a logical form only together with its logical syntactic application.

If a sign is not necessary then it is meaningless. That is the meaning of Occam’s razor.

(If everything in the symbolism works as though a sign had meaning, then it has meaning.)

In logical syntax the meaning of a sign ought never to play a rôle; it must admit of being established without mention being thereby made of the meaning of a sign; it ought to presuppose only the description of the expressions.

From this observation we get a further view—into Russell’s Theory of Types. Russell’s error is shown by the fact that in drawing up his symbolic rules he has to speak about the things his signs mean.

No proposition can say anything about itself, because the propositional sign cannot be contained in itself (that is the “whole theory of types”).

A function cannot be its own argument, because the functional sign already contains the prototype of its own argument and it cannot contain itself.

If, for example, we suppose that the function F(fx) could be its own argument, then there would be a proposition “F(F(fx))”, and in this the outer function F and the inner function F must have different meanings; for the inner has the form ϕ(fx), the outer the form ψ(ϕ(fx)). Common to both functions is only the letter “F”, which by itself signifies nothing.

This is at once clear, if instead of “F(F(u))” we write “(∃ϕ):F(ϕu).ϕu=Fu”.

Herewith Russell’s paradox vanishes. Rh


text:
Page:Wittgenstein - Tractatus Logico-Philosophicus, 1922.djvu/63

Rh

The rules of logical syntax must follow of themselves, if we only know how every single sign signifies.

A proposition possesses essential and accidental features.

Accidental are the features which are due to a particular way of producing the propositional sign. Essential are those which alone enable the proposition to express its sense.

The essential in a proposition is therefore that which is common to all propositions which can express the same sense.

And in the same way in general the essential in a symbol is that which all symbols which can fulfil the same purpose have in common.

One could therefore say the real name is that which all symbols, which signify an object, have in common. It would then follow, step by step, that no sort of composition was essential for a name.

In our notations there is indeed something arbitrary, but this is not arbitrary, namely that if we have determined anything arbitrarily, then something else must be the case. (This results from the essence of the notation.)

A particular method of symbolizing may be unimportant, but it is always important that this is a possible method of symbolizing. And this happens as a rule in philosophy: The single thing proves over and over again to be unimportant, but the possibility of every single thing reveals something about the nature of the world.

Definitions are rules for the translation of one language into another. Every correct symbolism must be translatable into every other according to such rules. It is this which all have in common.

What signifies in the symbol is what is common to all those symbols by which it can


text:
Page:Weird Tales volume 28 number 03.djvu/70

336 not seem strange, to have no foes to fight? All my life I have fought and hated the Xotalancas. With the feud ended, what is left?"

Xatmec shrugged his shoulders. His thoughts had never gone beyond the destruction of their foes. They could not go beyond that.

Suddenly both men stiffened at a noise outside the door.

"To the door, Xatmec!" hissed the last speaker. "I shall look through the Eye"

Xatmec, sword in hand, leaned against the bronze door, straining his ear to hear through the metal. His mate looked into the mirror. He started convulsively. Men were clustered thickly outside the door; grim, dark-faced men with swords gripped in their teeth—and their fingers thrust into their ears. One who wore a feathered head-dress had a set of pipes which he set to his lips, and even as the Tecuhltli started to shout a warning, the pipes began to skirl.

The cry died in the guard's throat as the thin, weird piping penetrated the metal door and smote on his ears. Xatmec leaned frozen against the door, as if paralyzed in that position. His face was that of a wooden image, his expression one of horrified listening. The other guard, farther removed from the source of the sound, yet sensed the horror of what was taking place, the grisly threat that lay in that demoniac fifing. He felt the weird strains plucking like unseen fingers at the tissues of his brain, filling him with alien emotions and impulses of madness. But with a soul-tearing effort he broke the spell, and shrieked a warning in a voice he did not recognize as his own.

But even as he cried out, the music changed to an unbearable shrilling that was like a knife in the ear-drums. Xatmec screamed in sudden agony, and all the sanity went out of his face like a flame blown out in a wind. Like a madman he ripped loose the chain, tore open the door and rushed out into the hall, sword lifted before his mate could stop him. A dozen blades struck him down, and over his mangled body the Xotalancas surged into the guardroom, with a long-drawn, blood-mad yell that sent the unwonted echoes reverberating.

His brain reeling from the shock of it all, the remaining guard leaped to meet them with goring spear. The horror of the sorcery he had just witnessed was submerged in the stunning realization that the enemy were in Tecuhltli. And as his spearhead ripped through a dark-skinned belly he knew no more, for a swinging sword crushed his skull, even as wild-eyed warriors came pouring in from the chambers behind the guardroom.

It was the yelling of men and the clanging of steel that brought Conan bounding from his couch, wide awake and broadsword in hand. In an instant he had reached the door and flung it open, and was glaring out into the corridor just as Techotl rushed up it, eyes blazing madly.

"The Xotalancas!" he screamed, in a voice hardly human. "They are within the door!"

Conan ran down the corridor, even as Valeria emerged from her chamber. "What the devil is it?" she called. "Techotl says the Xotalancas are in," he answered hurriedly. "That racket sounds like it."

ITH the Tecuhltli on their heels they burst into the throneroom and were confronted by a scene beyond the most frantic dream of blood and fury. Twenty men and women, their black hair streaming, and the white skulls gleaming on their breasts, were locked in combat with the people of Tecuhltli. The women W. T.— 5


text: Author:Lawrence Barrett

title: Author:Lawrence Barrett


text:
Page:Ruffhead - The Statutes at Large - vol 2.djvu/33

 27. An Aft touching Fines to be levied in the County Palatine of Durham.

28. AnAfl for the Translating of the Bible and the Divine Service into the Welsh Tongue.

29. An Act for the Confirmation of a Subsidy granted by the Clergy.

30. An Act of a Subsidy, and two Fifteens and Tenths granted by the Temporality.

31. An Act of the Queen's Majesty's most Gracious, General and Free Pardon.

S.

Anno quinto Elizabethæ Regimæ.

N Act of Alignment of certain Sums of Money to defray the Charges of the Queen's Majefty's Houshold.

2. An Act for the Confirmation of certain Liberties granted to the City of Exeter.

3. An Act for the Confirmation of Letters Patents granted to the Town of Southampton, touching the bringing in of Malmesies and other sweet Wines by Merchant Strangers.

4. An Act to enable Viscount Byndon and Dame Elizabeth his Wife, to make Leases for three Lives or twenty-one Years.

5. An Act to give Power to the Lord Burgavenny to make Leases for twenty-one Years.

6. An Act to restrain Henry Howard from discontinuing any of his Lands.

7. An Act touching one Annuity granted for the finding of a School at Guilford.

8. An Act for the Recovery and Inning of Plumpsted Marsh, now overflowed with Water.

9. An Act to restore in Blood the Sons and Daughters of the late Lord Huffy.

10. An Aft for the Restitution in Blood of William West, Esquire.

11. An Act for the Restitution in Blood of Sir Peter Carew, Knight.

12. An Act for the Restitution in Blood of Sir Ralph Chamberlayne, Knight, and John Harleston.

13. An Act for the Restitution in Blood of Thomas Gobbam, William Cromer, and others.

14. An Act for the Restitution in Blood of the Heirs of Thomas Isley.

15. An Act for the Restitution in Blood of the Heirs of William Thomas.

16. An Act for the Restitution in Blood of the Heirs of Leonard Diggs.

17. An Act for the Restitution in Blood of the Heirs of Thomas Cranmer, late Archbishop of Canterbury.

18. An Act for the Restitution in Blood of the Heirs of Sir Henry Isley, Knight.

19. An Act for the Restitution in Blood of Edward Turner.

20. An Act to make free Denizens the Children of John Fitzwilliams, James Harvey, and others, born beyond the Seas.

21. An Act to enable William Pope to alien certain Lands to make his Wife a Jointure.

S.

Anno octavo Elizabethæ Regimæ.

N Act declaring the Manner of Making and Consecrating of the Archbishops and Bishops of this Realm, to be good, lawful and perfect.

2. An Act whereby the Defendant may recover his Costs, being wrongfully vexed.

3. An Act against carrying over Sea, Rams, Lambs, and other Sheep alive.

4. An Act to take away the Benefit of Clergy from certain felonious Offenders.

5. An Act for the avoiding of tedious Suits in Civil and Marine Causes

6. An Act touching Clothworkers, and Cloths ready wrought to be shipped over the Sea.

7. An Act touching Drapers, Cottoners and Frizers, in the Town of Shrewsbury.

8. An Act for the Repeal of a Branch of a Statute made the thirty-second of Henry the Eighth, for the Stature of Horses.

9. An Act to repeal a Branch of a Statute made Anno 23 of Henry the Eighth touching the Prices of Barrels and Kilderkins.

10. An Act for Bowyers, and the Prices of Bows.

11. An Act for the true making of Hats and Caps.

12. An Act for Aulnegers Fees in Lancashire, and for Length, Breadth, and Weight of Cottons, Frizes and Rugs.

13. An Act concerning Sea-marks and Mariners.

14. An Act touching transporting of tawed Leather.

15. An Act for Preservation of Grain.

16. An Act that in divers Counties, there shall be but one Sheriff in one County.

17. An Act for Confirmation of a Subsidy granted by the Clergy.

18. An Act of a Fifteen and Tenth, and Subsidy, granted by the Temporalty.

19. An Act of the Queen's Majesty's Free and General Pardon.

20. An Act for repealing a Branch of a Statute made in the 26th of Hen. 8. c. 6. Sect. 12. for Trial of Offences in Wales.

S.

Anno octavo Elizabethæ Regimæ.

N Act for the Incorporation of the Fellowship and Society of English Merchants for the Discovery of new Trades.

2. An Act for Confirmation of the Queen's Highness Letters Patents made for the Hospital of Saint Bartholomew's in Gloucester.

3. An Act for Confirmation of Letters Patents granted to the Merchants Adventurers of the City of Bristow.

4. An Act confirming the Queen's Majesty's Letters Patents, concerning the making of Allum and Copperas within this Realm and other her Highness's Dominions.

5. An Act for the Inning of Plumpsted Marsh being surrounded.

6. An Act for the Assurance of the Countess of Warwick's Jointure.

7. An Act for the Assurance of the Lady Cobham's Jointure.

8. An Act for Assurance of the Jointure of the Lady Mary Stafford Wife of Edward Lord Stafford.

9. An Act to make John Stafford a free Denizen, being born beyond the Seas.

10. An Act to alter the Nature of Gavelkind in the Lands' of Thomas Brown, Esquire.

11. An Act for the Town Clerk of York.

12. An Act for the paving of Kentish-street in Southwark.

13. An Act for the making of Salt within the Queen's Majesty's Dominion's.

14. An Act for keeping a Market upon Thursdays at Battel in the County of Sussex

PUBLICK


text:
Page:Ruffhead - The Statutes at Large - vol 2.djvu/559

A.D. 1558. CAP. X.

A Confirmation of a Subsidy of eight Shillings in the Pound, granted by the Clergy to the King and Queen, to be paid in four Years, EXP.

 CAP. XI. An Act of a Subsidy and one Fifteen, granted by the Temporality. EXP.

At the Parliament begun at Westminster the xxv. Day of January in the first Year of, the Reign of our Sovereign Lady Elizabeth, by the Grace of God, of England, France and Ireland, Queen, Defender of the Faith, &c. And then and there holden, kept and continued until the Dissolution of the same, being the eighth Day of May then next ensuing, were enacted as followeth.

CAP. I.

An Act to restore to the Crown the ancient Jurisdiction over the Estate Ecclesiastical and Spiritual, and abolishing all foreign Powers repugnant to the same.

OST humbly beseech your most excellent Majesty, your faithful and obedient Subjects the Lords Spiritual and Temporal, and the Commons, in this your present Parliament assembled, That where in Time of the Reign of your most dear Father, of worthy Memory, King Henry the Eighth, divers good Laws and Statutes were made and established, as well for the utter Extinguishment and putting away of all usurped and foreign Powers and Authorities out of this your Realm, and other your Highness Dominions and Countries, as also for the restoring and uniting to the Imperial Crown of this Realm, the ancient Jurisdictions, Authorities, Superiorities and Preheminences to the same of Right belonging or appertaining, by Reason whereof we your most humble and obedient Subjects, from the xxv. Year of the Reign of your said dear Father, were continually kept in good Order, and were disburdened of divers great and intolerable Charges and Exactions before that Time unlawfully taken and exacted by such foreign Power and Authority as before that was usurped, until such Time as all the said good Laws and Statutes by one Act of Parliament made in the firsst and second Years of the Reigns of the late King Philip and Queen Mary, your Highness Sister, entituled, An Act repealing all Statutes, Articles and Provisions made against the See Apostolick of Rome since the twentieth Year of King Henry the Eighth, and also for the Establishment of all Spiritual and Ecclesiastical Possessions and Hereditaments conveyed to the Laity, were all clearly repealed and made void, as by the same Act of Repeal more at large doth and may appear; by Reason of which Act of Repeal, your said humble Subjects were eftsoons brought under an usurped foreign Power and Authority, and do yet remain in that Bondage, to the intolerable Charges of your loving Subjects, if some Redress (by the Authority of this your High Court of Parliament, with the Assent of your Highness) be not had and provided:'

II. May it therefore please your Highness, for the repressing of the said usurped foreign Power, and the restoring of the Rights, Jurisdictions and Preheminences appertaining to the Imperial Crown of this your Realm, that it may be enacted by Authority of this present Parliament, That the said Act made in the said first and second Years of the Reigns of the said late King Philip and Queen Mary, and all and every Branches, Clauses and Articles therein contained (other than such Branches, Clauses and Sentences, as hereafter shall be excepted) may from the last Day of this Session of Parliament, by Authority of this present Parliament, be repealed, and shall from thenceforth be utterly void and of none Effect;

III. And that also for the reviving of divers of the said good Laws and Statutes made in the Time of your said dear Father, it may also please your Highness, That one Act and Statute made in the xxiii. Year of the Reign of the said late King Henry the Eighth, intituled, An Act, That no Person shall be cited out of the Diocess wherein he or she dwelleth, except in certain Cases;

IV. And one other Act made in the xxiv. Year of the Reign of the said late King, intituled, An Act, That Appeals in such Cases as hath been used to be pursued to the See of Rome, shall not be from henceforth had no used, but within this Realm;

V. And one other Act made the xxv. Year of the said late King, concerning Restraint of Payment of Annates and First-fruits of Archbishopricks and Bishopricks to the See of Rome;

VI. And one other Act in the said xxv. Year, intituled, An Act concerning the Submission of the Clergy to the King's Majesty;

VII. And also one Act made in the said xxv. Year, intituled, An Act Restraining the Payment of Annates or First-fruits to the Bishop of Rome, and of the Electing and Consecrating of Archbishops and Bishops within this Realm;  VIII. And


text:
Page:Southern Historical Society Papers volume 05.pdf/25

20


text:
Page:Southern Historical Society Papers volume 05.pdf/26

Rh


text:
Page:Southern Historical Society Papers volume 05.pdf/27

22


text:
Page:Southern Historical Society Papers volume 05.pdf/28

Rh


text:
Page:Southern Historical Society Papers volume 05.pdf/29

24


text:
Page:Southern Historical Society Papers volume 05.pdf/30

Rh


text:
Page:Southern Historical Society Papers volume 05.pdf/31

26


text:
Page:Southern Historical Society Papers volume 05.pdf/32

Rh


text:
Page:Atharva-Veda samhita.djvu/346

iv. 15- there be lightnings; let the wind blow; let them extend the sacrifice, being manifoldly let loose; let the herbs become full of delight.

1. The great superintendent of them sees, as it were, from close by; whoever thinks to be going on in secret, all this the gods know.

title: Page:Atharva-Veda samhita.djvu/346


text:
Page:Atharva-Veda samhita.djvu/347

177 2. Whoso stands, goes about, and whoso goes crookedly (vañc), whoso goes about hiddenly, who defiantly (? pratán̄kam)—what two, sitting down together, talk, king Varuṇa, as third, knows that.

3. Both this earth is king Varuṇa's, and yonder great sky with distant margins (-ánta); also the two oceans are Varuṇa's paunches; also in this petty water is he hidden.

4. Also whoso should creep far off beyond the sky, he should not be released from king Varuṇa; from the sky his spies go forth hither; thousand-eyed, they look over the earth.

5. All this king Varuna beholds (vi-cakṣ)—what is between the two firmaments (ródasī), what beyond; numbered of him are the winkings of people; as a gambler the dice, [so] does he fix (? ni-mi) these things.

6. What fetters (pā́ça) of thine, O Varuṇa, seven by seven, stand triply relaxed (vi-si), shining—let them all bind him that speaks untruth; whoso is truth-speaking, let them let him go.

Our sinántu, at beginning of c, is our emendation, obviously necessary; a few mss. (including our Bp.E.H.) have çinántu, and the rest chin- (our P.M. dhin-, doubtless

title: Page:Atharva-Veda samhita.djvu/347


text:
Author:Frederick William Ricord

Works

 * The Kings of Rome, 1856
 * (in part)

title: Author:Frederick William Ricord


text:
Page:Weird Tales volume 28 number 03.djvu/57

Rh shrilled a little, and the boldest among his watchers ran almost at his elbow, twittering their queer, broken speech in hushed syllables whose familiarity still bothered him with its haunting echo of words he knew. When he had reached the center of the hollow he became aware that the little folk had spread out in a ring to surround him. Wherever he looked their small, anxious faces and staring eyes confronted him. He grinned to himself and came to a halt, waiting gravely.

None of them seemed quite brave enough to constitute himself spokesman, but among several a hurried whispering broke out in which he caught the words "Thag'* and "danger" and "beware." He recognized the meaning of these words without placing in his mind their origins in some tongue he knew. He knit his sun-bleached brows and concentrated harder, striving to wrest from that curious, murmuring whisper some, hint of its original root. He had a smattering of more tongues than he could have counted offhand, and it was hard to place these scattered words among any one speech.

But the word "Thag" had a sound like that of the very ancient dryland tongue, which upon Mars is considered at once the oldest and the most uncouth of all the planet's languages. And with that clue to guide him he presently began to catch other syllables which were remotely like syllables from the dryland speech. They were almost unrecognizable, far, far more ancient than the very oldest versions of the tongue he had ever heard repeated, almost primitive in their crudity and simplicity. And for a moment the sheerest awe came over him, as he realized the significance of what he listened to.

HE dryland race today is a handful of semi-brutes, degenerate from the ages of past time when they were a mighty people at the apex of an almost forgotten glory. That day is millions of years gone now, too far in the past to have record save in the vaguest folklore. Yet here was a people who spoke the rudiments of that race's tongue as it must have been spoken in the race's dim beginnings, perhaps a million years earlier even that that immemorial time of their triumph. The reeling of millenniums set Smith's mind awhirl with the effort at compassing their span.

There was another connotation in the speaking of that tongue by these timid bush-dwellers, too. It must mean that the forgotten wizard king, Illar, had peopled his sinister, twilight land with the ancestors of today's dryland dwellers. If they shared the same tongue they must share the same lineage. And humanity's remorseless adaptability had done the rest.

It had been no kinder here than in the outside world, where the ancient plainsmen who had roamed Mars' green prairies had dwindled with their dying plains, degenerating at last into a shrunken, leather-skinned bestiality. For here that same race root had declined into these tiny, slinking creatures with their dusky skins and great, staring eyes and their voices that never rose above a whisper. What tragedies must lie behind that gradual degeneration!

All about him the whispers still ran. He was beginning to suspect that through countless ages of hiding and murmuring those voices must have lost the ability to speak aloud. And he wondered with a little inward chill what terror it was which had transformed a free and fearless people into these tiny wild things whispering in the underbrush.

The little anxious voices had shrilled into vehemence now, all of them chattering together in their queer, soft, rustling whispers. Looking back later upon that timeless space he had passed in the


text: 1911 Encyclopædia Britannica/Lord High Treasurer