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 These equations are of the form

{{MathForm2|(I)|$$\left.\begin{array}{lll} \mathsf{curl}\ H=\frac{\partial D}{\partial t}+s, & & \mathsf{div}\ D=\rho\\ \\\mathsf{curl}\ E=-\frac{\partial B}{\partial t}, & & \mathsf{div}\ B=0\end{array}\right\} $$}}

where the vectors E, H, D, B denote the electric force, magnetic force, electric displacement, and magnetic induction respectively, s denotes the current and ρ the volume density of electricity. The equations differ from those used by Lorentz by the fact that the vector H - [Pw] occurring in Lorentz's equations is replaced here by the vector H. It should be remarked that Frank has obtained Minkowski's equations by a process of averaging in the case of non-magnetic bodies.

We shall suppose that the electric polarisation P and the magnetic polarisation Q are connected with D, E, B, and H by the formulae

$P=D-E,\ Q=B-H.$

The electrodynamical equations (I) can be replaced by the two integral equations

These equations are unaltered in form by a transformation from (x, y, z, t) to (x', y', z', t') if

where θ and φ are constants.

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 The formulae of transformation of the type used by Einstein and Laub in the case of Lorentz's transformation are obtained by putting θ = φ = 1. If we use a spherical wave transformation with positive Jacobian, we can deduce the relation

and this, combined with (V), gives

which enables us to obtain the formulae of transformation of the polarisation vectors.

The constitutive relations are obtained by Einstein and Laub by assuming that all the bodies in the dashed system of coordinates are at rest, and that in this system

This gives a set of constitutive relations for the case in which a system of bodies are moving with constant velocity w.

The constitutive relations that are obtained in this way may be written in the form

{{MathForm2|(IX)|$$\left.\begin{array}{rl} D+[wH]= & \epsilon\{E+[wB]\}\\ \\B-[wE]= & \mu\{H-[wD]\}\\ \\\frac{s_{w}-\left|w\right|\rho}{\sqrt{1-w^{2}}}= & \sigma\{E+[wB]\}_{w}\\ \\s_{\overline{w}}= & \frac{\sigma\{E+[wB]\}_{\overline{w}}}{\sqrt{1-w^{2}}}\end{array}\right\} ,$$}}

where the suffix w denotes that the component in the direction of w, $$\overline{w}$$, a component in a direction perpendicular to w is to be taken.

The first two equations are seen to be invariant for the group of spherical wave transformations when we obtain them in the following way. The expression

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

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text:
User:DPRC3A

DPRC3A2011
DPRC3A2011 was founded by the chairperson in 2011. Initially, the original name was Democratic People's Republic of Class 3A 2011.

title: User:DPRC3A


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Page:BatemanElectrodynamical.djvu/36

 is seen from (1), § 6, to be an invariant. If we multiply this by the invariants

we obtain the invariants

and the constitutive relations are obtained by making the first of these equal to μ times the third, and the second equal to ε times the fourth, where ε and μ are invariants. These, however, are not the only constitutive relations which remain invariant, for we may obtain the two integral invariants

A set of constitutive relations given by two linear relations between

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text: Dictionary of National Biography, 1885-1900/Balfour, Robert (1550?-1625?)


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Page:BatemanElectrodynamical.djvu/37

 these six integral forms of the third order is invariant for the group of spherical wave transformations.

To obtain the other constitutive relations, we construct an integral form of the third order reciprocal to (X) and write it in the form

where $$\rho_0$$ is a quantity which will be determined presently.

Subtracting this from the invariant

we may obtain a set of constitutive relations by identifying the resulting invariant with

$\begin{array}{l} \frac{\sigma\lambda}{\sqrt{1-w^{2}}}\left[\left(E_{x}+w_{y}B_{z}-w_{z}B_{y}\right)dy\ dz\ dt+\left(E_{y}+w_{z}B_{x}-w_{x}B_{z}\right)dz\ dx\ dt\right.\\ \\\qquad\left.+\left(E_{z}+w_{x}B_{y}-w_{y}B_{x}\right)dx\ dy\ dt-\left(E_{x}w_{x}+E_{y}w_{y}-E_{z}w_{z}\right)dx\ dy\ dz\right].\end{array}$|undefined

If we multiply the first coefficient in this invariant by $$w_x$$, the second by $$w_y$$, the third by $$w_z$$, the fourth by 1, and add, the result is zero. The same must hold in the case of the invariant to which it is equated; therefore

$s_{x}w_{x}+s_{y}w_{y}+s_{z}w_{z}-\rho-\frac{\rho_{0}}{1-w^{2}}\left[w_{x}^{2}+w_{y}^{2}+w_{z}^{2}-1\right]=0$|undefined

or

$\rho=\rho_{0}+(sw).$

Hence we have the constitutive relations

{{center|$$s-\frac{\rho-(sw)}{1-w^{2}}w=\frac{\sigma\lambda}{\sqrt{1-w^{2}}}[E+[wB]\},$$}}

which agree with those obtained by Minkowski, Einstein and Laub, in the case when λ = 1.

We shall now show that it is possible to construct a set of constitutive relations which are invariant for a much wider class of transformations.

Let the transformation be biuniform within a certain domain of values of (x, y, z, t), and such that the bilinear form

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 is an invariant. When we put $$dx=\delta x,\dots$$ this implies that a certain quadratic form is an invariant.

Let us suppose that the constitutive relations connecting $$B_{x},B_{y},B_{z},E_{x},E_{y},E_{z}$$ with $$H_{x},H_{y},H_{z},D_{x},D_{y},D_{z}$$ are given by the circumstance that the invariant reciprocal to

$D_{x}dy\ dz+D_{y}dz\ dx+D_{z}dx\ dy-H_{x}dx\ dt-H_{y}dy\ dt-H_{z}dz\ dt$

is an invariant multiple of

$B_{x}dy\ dz+B_{y}dz\ dx+B_{z}dx\ dy+E_{x}dx\ dt+E_{y}dy\ dt+E_{z}dz\ dt.$

This assumption preserves the analogy with the electron equations where the two fundamental integral invariants of the second order are reciprocals with regard to the quadratic form

$\lambda^{2}\left[dx^{2}+dy^{2}+dz^{2}-dt^{2}\right].$

In the present case the relations between the two sets of vectors are of the type

{{MathForm2|(2)|$$\left.\begin{array}{rl} \kappa\sqrt{\Delta}B_{x}= & -\left(BC-F^{2}\right)H_{x}-(FG-CH)H_{y}-(HF-BG)H_{z}\\ & +(HW-VG)D_{x}+(BW-VF)D_{y}+(FW-CV)D_{z}\\ \\\kappa\sqrt{\Delta}E_{x}= & -\left(HW-VG\right)H_{x}-(GU-AW)H_{y}-(AV-HU)H_{z}\\ & +(AD-U^{2})D_{x}+(HD-UV)D_{y}+(GD-UW)D_{z}\\ \\\frac{1}{\kappa}\sqrt{\Delta}D_{x}= & \left(BC-F^{2}\right)E_{x}+(FG-CH)E_{y}+(HF-BG)E_{z}\\ & +(HW-VG)B_{x}+(BW-VF)B_{y}+(FW-CV)B_{z}\\ \\-\frac{1}{\kappa}\sqrt{\Delta}H_{x}= & \left(HW-VG\right)E_{x}+(GU-AW)E_{y}+(AV-HU)E_{z}\\ & +(AD-U^{2})B_{x}+(HD-UV)B_{y}+(GD-UW)B_{z}\end{array}\right\} $$}}

where Δ denotes the determinant

$\left

To obtain the other constitutive relations we start with the assumption that there is an integral invariant of the type

$\theta\left(w{}_{x}dy\ dz\ dt+w{}_{y}dz\ dx\ dt+w{}_{z}dx\ dy\ dt-dx\ dy\ dz\right)$

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 From this we may obtain the reciprocal invariant

$v_{x}dx+v_{y}dy+v_{z}dz+v_{t}dt,$

where

{{MathForm2|(3)|$$\left.\begin{array}{l} \sqrt{\Delta}v_{x}=\theta\left(Aw_{x}+Hw_{y}+Gw_{z}+U\right)\\ \sqrt{\Delta}v_{y}=\theta\left(Hw_{x}+Bw_{y}+Fw_{z}+V\right)\\ \sqrt{\Delta}v_{z}=\theta\left(Gw_{x}+Fw_{y}+Cw_{z}+W\right)\\ \sqrt{\Delta}v_{t}=\theta\left(Uw_{x}+Vw_{y}+Ww_{z}+D\right)\end{array}\right\} $$}}

Multiplying these and rejecting the invariant factor $$\sqrt{\Delta}dx\ dy\ dz\ dt$$, we obtain the invariant

Multiplying

$D_{x}dy\ dz+D_{y}dz\ dx+D_{z}dx\ dy+H_{x}dx\ dt-H_{y}dy\ dt-H_{z}dz\ dt$

by

$v_{x}dx+v_{y}dy+v_{z}dz+v_{t}dt,$

we obtain the invariant

We now assume that

$\begin{array}{l} s_{x}dy\ dz\ dt+s_{y}dz\ dx\ dt+s_{z}dx\ dy\ dz-\rho dx\ dy\ dz\\ \qquad-\theta\left[w_{x}dy\ dz\ dt+w_{y}dz\ dx\ dt+w_{z}dx\ dy\ dt-dx\ dy\ dz\right]\end{array}$

is an invariant multiple of this invariant. This gives the relation

$s_{x}v_{x}+s_{y}v_{y}+s_{z}v_{z}+\rho v_{t}-\theta\left[v_{x}w_{x}+v_{y}w_{y}+v_{z}w_{z}+v_{t}\right]=0,$

or

The constitutive relations are of the type

{{MathForm2|(7)|$$\left.\begin{array}{l} s_{x}-\theta w_{x}=\sigma\left(v_{t}D_{z}-v_{y}H_{z}+v_{z}H_{y}\right)\\ s_{y}-\theta w_{y}=\sigma\left(v_{t}D_{y}-v_{z}H_{x}+v_{x}H_{z}\right)\\ s_{z}-\theta w_{z}=\sigma\left(v_{t}D_{s}-v_{x}H_{y}+v_{y}H_{x}\right)\end{array}\right\},$$}}

and can be expressed in terms of E and B by means of the relations connecting these quantities with D and H.

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 With these constitutive relations the equations of electrodynamics are invariant for a very large class of space time transformations. The relations simplify considerably when the quadratic form is of a simple type.

The vanishing of the quadratic form may be supposed to represent the condition that two neighbouring particles are in a position to act on one another.

We shall now verify that in a particular case the constitutive relations obtained in this way agree with the ones obtained by Minkowski, Einstein, and Laub.

Starting with a system at rest, we assume that the invariant quadratic form is

This gives

and if we take

the relations (2) take the form

Now make the Lorentzian transformation

the quadratic form then becomes

We again have $$\Delta=-\epsilon\mu$$, and the relations (2) take the form

$$\begin{array}{l} B_{x}=\mu H_{x},\\ \\B_{y}=\frac{\epsilon\mu-u^{2}}{\epsilon\left(1-u^{2}\right)}H_{y}+u\frac{\epsilon\mu-1}{\epsilon\left(1-u^{2}\right)}D_{z},\\ \\B_{z}=\frac{\epsilon\mu-u^{2}}{\epsilon\left(1-u^{2}\right)}H_{z}-u\frac{\epsilon\mu-1}{\epsilon\left(1-u^{2}\right)}D_{y},\\ \\E_{x}=\frac{1}{\epsilon}D_{x},\\ \\E_{y}=\frac{1-u^{2}\epsilon\mu}{\epsilon\left(1-u^{2}\right)}D_{y}+u\frac{\epsilon\mu-1}{\epsilon\left(1-u^{2}\right)}H_{z},\\ \\E_{z}=\frac{1-u^{2}\epsilon\mu}{\epsilon\left(1-u^{2}\right)}D_{z}-u\frac{\epsilon\mu-1}{\epsilon\left(1-u^{2}\right)}H_{y}.\end{array}$$

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 These are equivalent to the relations

$\begin{array}{rl} B_{x}= & \mu H_{x},\\ B_{y}+\mu E_{z}= & \mu\left[H_{y}+uD_{z}\right],\\ B_{z}-uE_{y}= & \mu\left[H_{z}-uD_{y}\right],\\ E_{x}= & \epsilon^{-1}D_{x},\\ E_{y}-uB_{z}= & \epsilon^{-1}\left[D_{y}-uH_{z}\right],\\ E_{z}+uB_{y}= & \epsilon^{-1}\left[D_{y}+uH_{y}\right],\end{array}$

obtained by Minkowski, Einstein, and Laub.

It is also easy to verify that the constitutive relations (7) take the form

$\frac{s_{x}-u\rho}{\sqrt{1-u^{2}}}=\sigma E_{x},\ s_{y}=\sigma\frac{E_{y}-uB_{z}}{\sqrt{1-u^{2}}},\ s_{z}=\sigma\frac{E_{z}-uB_{y}}{\sqrt{1-u^{2}}},$|undefined

given by Minkowski, Einstein, and Laub.

We have thus shown that the scheme of constitutive relations indicated by the invariance of a quadratic form agrees with the known scheme of relations in particular cases, and is invariant for any relevant space time transformation which is biuniform in a certain domain.

These relations are not the most general possible, and so the configuration and state of motion under consideration is of a special type, but the relations are sufficiently general for most ordinary purposes.

[Note added October 8th, 1909.]

Spherical wave transformations are not the only ones which can be used to transform problems occurring in the theory of electrons, for there are large classes of transformations which can be applied to particular problems, but cannot be applied to an arbitrary problem. The equations of transformation in this case involve the magnitudes of the electric and magnetic forces occurring in the particular problem.

Let us suppose that the electrodynamical field in a particular problem is of such a nature that the components $$\left(E_{x},E_{y},E_{z}\right),\ \left(H_{x},H_{y},H_{z}\right),$$ of the electric and magnetic forces are connected by the relations

and let $$\left(s_{x},s_{y},s_{z}\right)$$ be the components of Poynting's vector.

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 Then, if $$a_{x},a_{y},a_{z},a,s$$ are five functions of x, y, z, t satisfying the relations

a transformation of coordinates for which

$\begin{array}{r} dx^{2}+dy^{2}+dz^{2}-dt^{2}+\left(a_{x}dx+a_{y}dy+a_{z}dz-a\ dt\right)\left(s_{x}dx+s_{y}dy+s_{z}dz-s\ dt\right)\\ =\lambda\left(dx'^{2}+dy'^{2}+dz'^{2}-dt'^{2}\right),\end{array}$

λ being a function of x', y', z', t', is in general suitable for the transformation of the problem in question. The above equation implies that, if the velocity of radiation is represented by unity in the first system of coordinates, it is also represented by unity in the second system.

[March 15th, 1910.—

The relation $$a_{x}s_{x}+a_{y}s_{y}+a_{z}s_{z}=as$$ can be omitted.]

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text: Dictionary of National Biography, 1885-1900/Balfour, Robert (d.1663)


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Page:Feilberg.djvu/17

Rh at being so easily forgiven, chatting merrily. When out some distance, Mr. ——— quietly remarked, "I am going to shoot you, Toby." The black turned round smiling, thinking this was some joke, and saw Mr. ——— coolly pulling out his revolver. The wretched boy, in an agony of sudden fear, crouched on his saddle, putting out his hands and shrieking, "Baal shoot—baal shoot!" when his master sent a bullet crashing through his brain. The two whites then returned leading the riderless horse. This fact was much discussed in the neighborhood of ——— Downs, as it was well known. Some people approved of the action, as being the best way of "putting the fear of God in the blacks," and preventing them from at any future time doing mischief; but the majority, though quite admitting the right of Mr. ——— to deal as he liked with a "nigger," were of opinion that it was rather a dirty transaction. The Kanaka who was the aggrieved party was genuinely horror struck when he heard of the affair—but then he was only a South Sea Island savage.

On ——— Downs station there was a tribe of blacks who were quiet and quite harmless. But, in a large tract of desert country to the north of it, there was another tribe hostile to them, and to the whites. These "myalls" occasionally made a raid on ——— Downs, and plundered huts, &c., but the station blacks, who feared and disliked them, were always ready to warn the whites of their coming. After one of their raids, the superintendent sent for the native police. Sub-inspector ——— arrived with his troopers, and started out for the scene of the depredation. A young gentleman who was on the station acquiring "colonial experience" thought he would like to add to it by accompanying the police on an expedition which appeared to him, naturally enough, as a legitimate act of war. The party started, and they got on the tracks of the "myalls"—tracks which the troopers could follow as easily as an ordinary white man can follow a beaten road. The track led out into the desert, an uncomfortable region of sand and spinifex, where water was doubtful, and little food could be got for the police horses. Still, if the blacks who had made the raid were to be punished, it would be necessary to follow them there. The track led through a spur of a low precipitous range of hills, containing rock-surrounded pockets, from which escape would be difficult to any human beings penned up in them. Near one of these places the party espied a small troop of blacks, and to the astonishment of the new chum, who recognised them as belonging to the station tribe, and quite innocent of any outrage, the officer gave the word to the troopers to run them in to the pocket. They succeeded in penning up a small group of defenceless creatures who were shouting appeals for mercy to the sub-inspector by name. The new chum, who had in his astonishment followed the example of the others and dismounted, cried out to the sub-inspector, "Why, Mr. ———, these are our blacks." The answer he got was an angry "Stoop down, d——n you," for he was in the range of the sub-inspector, who was anxious to try the quality of a new sporting rifle he had purchased, and was taking deliberate aim at a wretched creature who was making frantic attempts to escape by clambering up the naked rock. The inspector's rifle was a good one, and his target was soon writhing in his death agony on the sand. The troopers "got" two more of the little group; the rest escaped. Then they returned home. They had done the work for which the State paid them—they had shot some blacks. To be sure they had not gone near the real offender, and they had exasperated a friendly tribe, but that is a matter with which we, their employers, do not concern ourselves.

On ——— Downs Station the blacks were "troublesome." How they became so does not concern this particular narrative, but they had taken some sheep. The native police were not available, but the partners who owned and managed the station got a trusted man and a neighbor who was willing to help them, and they started out to look for the offenders. They were fortunate enough to come across a mob of blacks away from the scrub, just before evening. The affair was quite a successful one. The blacks were paralysed with fear; some took to trees, some lay down to await their fate, others attempted to fly. Men on good stock-horses, quick to turn and pursue a quarry, armed with revolvers, can "get" a good many under these circumstances. They rode down the flying ones, and then returned quietly to practice shooting on the blacks perched in the trees. Altogether they managed to dispose of twenty-two, and then they camped at a neighboring waterhole, had their supper, and slept as men sleep who have done a good day's work. In the morning they saddled up to go home, but one of the number, a prudent one, remarked, "We ought to see that we have made an end of those ——." Accordingly he went carefully over the scene. Most of the blacks were stone dead; some were groaning in their last agonies; a few who had not been mortally wounded seemed to be reviving. Blacks have a wonderful capacity for enduring severe wounds and recovering from

title: Page:Feilberg.djvu/17


text: Dictionary of National Biography, 1885-1900/Balfour, Robert (d.1757)


text: Index:BatemanTime.djvu

title: Index:BatemanTime.djvu


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Rh

Received May 3rd, 1910.

1. During recent years mathematicians and philosophers have been much occupied in analysing the fundamental conceptions on which the different sciences are based, with the result that many things which were formerly regarded as quite simple and axiomatic can no longer be regarded as such. The tendency has, of course, been to make definitions as precise as possible, and to make descriptions of phenomena approximate to reality as we know it, and not to a preconceived idea of what the description ought to be.

Many difficulties arise, however, in a careful examination of the fundamental concepts of any science, and this is soon found to be the case when we commence to examine the ideas of space and time which are fundamental in all physical and metaphysical enquiries.

In the case of time, for instance, it is found that we have to examine the connection between time as it is known to us by the mind's experience, i.e., psychological time, and time as it is measured by the course of physical phenomena, i.e., physical time.

With regard to psychological time, it has been contested that it is purely qualitative, in other words that we are quite unable to decide intuitively whether two intervals of time are equal or not. This means that June 15th, 1910.

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 there is no fixed method by which two sequences of events may be compared in the mind. The comparisons which actually occur give a qualitative description of events, inasmuch as the sequence of processes is generally unaltered in direct perception and in memory, but the lack of a standard set of units invariably connected with the method of comparison, prevents the description from being a true quantitative one.

This being the case, we are met with a fundamental difficulty when we try to analyse the idea of simultaneity as presented to us by the mind.

If we could represent an event by a point on a line, the idea of simultaneity would be quite simple, for two events could be regarded as simultaneous when their representative points were coincident. In reality such a representation is not valid, there is no sensation of such a simple nature that it can be represented by a point on a line. If we adopt a representation by means of an interval on a line, we obtain what is probably a truer representation of an event as regards its duration; but if we suppose that two events are simultaneous when their representative intervals have a common part, it is clear that two events which are simultaneous with the same event would not necessarily be simultaneous with one another.

It will be realised after a little thought that we can only obtain a satisfactory definition of simultaneity by introducing the idea of the measurement of time; we are thus obliged to consider the physical aspect of time in order to understand the idea of simultaneity.

An observer provided with an instrument for measuring time, such as a clock or a pendulum, can attach a definite number to each event that occurs. In some cases he may find it difficult to decide as to which of two

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 consecutive numbers should be attached to an event; but we shall suppose that he has a consistent method of avoiding the difficulty, as, for example, by always choosing the larger number of the two.

A satisfactory definition of simultaneity for two events which happen in the immediate vicinity of the observer can be given as soon as events are numbered, for we can say that two events are simultaneous when their corresponding numbers are equal. The actual enumeration may depend upon the personal equation of the observer, but discrepancies may be eliminated as soon as a method of comparing the observations of different observers has been adopted.

We now require a method of comparison by means of which we can decide whether the observations of time made by two different observers are equivalent or not. The criterion of equivalence must be such that if the observations of A are equivalent to those of B, and also to those of C, then the observations of B and C are equivalent to one another.

It is clear that if two observers are situated at different points of space a comparison of observations can only be made by means of something which travels from one to the other, and for the sake of simplicity it is convenient to choose something which can be supposed to travel in a straight line with constant velocity. It should be remarked, however, that these terms have no meaning until time and distance have been defined.

It is by no means obvious that a universal method of comparing observations can be found which will lead to consistent results, for this presupposes the existence of a universal time, an entity which has sometimes been regarded as the psychological time of an infinite mind governing the whole of the universe. The latter point of

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text: Dictionary of National Biography, 1885-1900/Balfour, William (d.1660)


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 view is really not sound, because the universal time we are endeavouring to define is essentially quantitative in character. The best way of establishing the existence of a consistent method of comparison is to give an example of one, and so we shall consider Galileo's method of light signals, which was used in a first but unsuccessful attempt to measure the velocity of light.

The way in which this method is applied is as follows. An observer situated at a point A observes at time t an event which has taken place at another point B. If τ is the time which light takes to travel from B to A, the universal time to be associated with the event at B according to A's measurements is $$t-\tau$$. As soon as A has observed the event he makes a signal, and it is clear that by a series of signals the two measures of an interval of time may be compared.

By means of this rule the clocks belonging to a number of observers $$A_{1}, A_{2},\dots$$ can be regulated in a consistent manner, provided light always takes the same time to travel from an observer $$A_r$$ to an observer $$A_s$$.

Let us suppose that a large number of observers $$A_r$$ find that their observations of one another's experiences give a consistent universal time as far as they are concerned; they can then regard themselves as being at constant distances from one another, the distance between two observers $$A_{r}, A_{s}$$, being defined as $$C\tau_{rs}$$, where $$\tau_{rs}$$ is the time light takes to travel from $$A_r$$ to $$A_s$$, and C is a constant called the velocity of light.

These observers may then form a standard system for the measurement of time and distances at other points of space. The measurements of four standard observers should suffice to determine the position and time of any

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Rh occurrence, if space is of three dimensions. If there are more than four observers in the standard system the relations between all the different observations of an event will depend upon the nature of space, and will take a comparatively simple form if the space is Euclidean.

If the position and time associated with an object B is always determined from measurements by a number of standard observers $$A_{1},\dots A_{r}$$, so that a consistent universal time exists for each point of space, the following conclusion may be deduced by elementary geometry for Euclidean space:

If two observers B and C are at rest or in motion relative to the standard system, and their velocities are less than that of light, there is only one instant at which B is able to observe an instantaneous event experienced by C, but if one of the observers is moving with a velocity greater than that of light this is not necessarily the case; in fact it may happen that B sees two or more pictures of the same event.

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6 In order that Galileo's method of comparing times at different points of space may be suitable for a sober world, it seems necessary to suppose that a body cannot move with a velocity greater than that of light, and it may be of interest to remark that this view is supported by modern electrical theories.

Now let us suppose that a second system of observers, $$B_{1}, B_{2}, \dots B_{n}$$, find that their observations are in agreement, and so can regard themselves as a standard system. It may happen that according to their measurements the first system of observers $$A_{1}, A_{2}, \dots A_{n}$$ are in motion, and then it is easy to see that the specifications of position and time as made by the A's and the B's will not agree.

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Rh For instance, if two observers $$A_{r}, A_{s}$$ pass an observer B at different times, their distance apart as measured by B is zero, while measured from A's point of view it is not.

The relation between the two sets of measurements may be obtained by taking into account the fact that the analytical conditions that an observer P should be able at time $$t_1$$ to observe an event which happened at another point Q at time $$t_2$$, ought to be of the same form in the two systems of coordinates.

If $$\left(x_{1},y_{1},z_{1}\right),$$ $$\left(x_{2},y_{2},z_{2}\right)$$ are the coordinates of P and Q, we have, in the first place, the necessary conditions

$$\left(x_{1}-x_{2}\right)^{2}+\left(y_{1}-y_{2}\right)^{2}+\left(z_{1}-z_{2}\right)^{2}=c^{2}\left(t_{1}-t_{2}\right)^{2}\ t_{1}>t_{2}.$$

These conditions, combined with the kinematical character of the motion of the B's relative to the A's, are

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8 practically sufficient to determine the relation between the two systems of measurement in certain cases, as, for instance, when the B's are moving with a uniform velocity relative to the A's.

It is found that in the case of uniform relative motion the units of length and time in the two systems are different, and that two events occurring at different points of space may appear to be simultaneous according to measurements made by the A's, and not appear to be simultaneous according to measurements made by the B's. Also, the shape of a body is theoretically different according to the two series of measurements, but the difference is so very slight as to be unnoticeable.

The fact that the electromagnetic equations have the same form in the two systems of coordinates, indicates, that as far as our observations of electromagnetic phenomena are concerned, a uniform motion of a system of observers would remain undetected. This, of course, is in accordance with the view that position and motion are purely relative, and that the term absolute motion is meaningless.

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Rh A. Einstein has developed this theory of relativity starting with the fundamental idea of the constancy of the velocity of light, and has thus been able to present us with a new kinematics which is apparently more consistent with the modern theories of electrodynamics than the approximate kinematics to which we are accustomed. Some of the most interesting results of the theory are that the resultant of two velocities, both of which are less than that of light, is always a velocity less than that of light; the resultant of two velocities one of which is equal to that of light is a velocity equal to that of light; the resultant of two velocities equal to that of light but of opposite directions is indeterminate, and may have any value less than or equal to that of light.

This theory of relativity is not based simply on theoretical considerations; it has received considerable support from some very delicate experiments. It was first put forward in an approximate form by Lorentz and Larmor, following a suggestion made by FitzGerald , to explain the negative results of the Michelson-Morley experiment. It was then found that it provided an ample explanation of a number of other negative results concerning the effect of the motion of the Earth on double refraction, the rotation of the plane of polarisation , the resistance of a piece of metal , and other physical phenomena. Also, the theoretical formula

title: Page:BatemanTime.djvu/9


text:
Page:BatemanTime.djvu/10

10 deduced for the transverse mass of a moving electron is in fairly good agreement with the results of Kaufmann's experiments, and has been verified very closely in a recent experiment made by Bucherer.

At present the theory is being widely used as a working hypothesis, and is of great theoretical importance, as it enables us to pass from the known analytical specification of a phenomenon for a medium at rest to the corresponding case of a medium in motion. It has been used in this way by the late Hermann Minkowski to obtain a scheme of electromagnetic relations for ponderable bodies in uniform motion, and has been shown by Planck and von Mosengeil to provide a very useful method of studying the properties of radiation in a cavity in a moving body.

With regard to the ideas of time that have arisen in connection with the theory, it may be mentioned that two new terms have been introduced. The term local time is used by Lorentz to denote time as it is measured by a set of observers who are moving uniformly in a straight line relative to a standard set of observers. The relation between the local time and the standard time is a reciprocal one, the local time for one set of observers being the standard time for the other set, and vice-versa.

A second term, used by Minkowski, is Eigenzeit or the "proper time." It is defined for each particle and may be regarded as the age of a particle. As a particle moves from one point to another, the increase of age depends upon the increase of the standard time, and also upon the velocity of the particle. If the particle is moving

title: Page:BatemanTime.djvu/10


text:
Page:BatemanTime.djvu/11

Rh uniformly, the increase in age is equal to the increase in local time. The advantage of using the age of a particle in forming the equations of motion is that there is a gain in simplicity. The analytical methods based upon the use of the age of a particle may be compared with Lagrange's method of dealing with problems in hydrodynamics, while the methods based on the use of a standard time may be compared with the Eulerian method.

When a particle is moving in an arbitrary manner it is by no means certain that its age can be derived from a knowledge of an initial position and the position at a given time. It is to be expected, in fact, that the age of the particle will depend upon the path from one point to the other, and also upon the rates at which it describes different parts of the path.

There is, at present, considerable uncertainty with regard to the exact laws of the kinematics and dynamics of a body whose motion is not uniform. Systems of non-Newtonian mechanics and kinematics of a rigid electron have been based upon the theory of relativity for the case of uniform motion, but they can hardly be regarded as satisfactory, and difficulties arise as soon as a uniform motion of rotation about an axis is considered.

If mechanics is to be based on the science of electromagnetism, we must make a complete study of the transformations connected with the fundamental equations of electromagnetism.

Now the general problem of determining the transformations which leave the electrodynamical equations unaltered in form, may be partially solved by simply paying attention to the conditions which must be satisfied

title: Page:BatemanTime.djvu/11


text: Dictionary of National Biography, 1885-1900/Balfour, William (1785-1838)


text:
Page:BatemanTime.djvu/12

12 in order that an observer P who is at a point $$\left(x_{1},y_{1},z_{1}\right)$$ at time $$t_1$$ may be in a position to record the effect of a disturbance which issued from a point $$\left(x_{2},y_{2},z_{2}\right)$$ at time $$t_2$$.

It should be remarked that the conditions given above with regard to the possibility of P seeing Q at the given times are necessary, but not sufficient. This accounts for the fact that the transformations for which the condition

$$\left(x_{1}-x_{2}\right)^{2}+\left(y_{1}-y_{2}\right)^{2}+\left(z_{1}-z_{2}\right)^{2}=c^{2}\left(t_{1}-t_{2}\right)^{2}$$

is invariant are limited to a certain group.

It is clear that P is able to see Q if there is a flow of energy from P to Q. If $$\left(s_{x},s_{y},s_{z}\right)$$ denotes the direction in which energy is flowing from Q at time $$t_2$$, and we regard the differences $$x_{1}-x_{2}$$, etc., as small, so that

$$x_{1}-x_{2}=dx,\ y_{1}-y_{2}=dy,\ z_{1}-z_{2}=dz,\ t_{1}-t_{2}=dt$$

we may consider transformations such that the equations

are invariant. Since the flow of energy depends upon the state of the electromagnetic field, the formulæ of transformation will depend upon the character of the electromagnetic field, but it can be shown that if the above equations are invariant, the fundamental equations which describe the sequence of electromagnetic disturbances are also invariant. The description of any series of phenomena is thus qualitatively the same in the two series of coordinates.

It is interesting to compare the result just obtained with some ideas with regard to the way in which experience is interpreted by the mind.

If we suppose that some physical process taking place

title: Page:BatemanTime.djvu/12


text:
Page:BatemanTime.djvu/13

Rh in the brain is the physical adjunct of a sensation in the mind, such as visual perception, we may regard the mind's interpretation of the sensation as a transformation of the actual physical process as it would be described by external observers if observed directly by them.

If now the exact nature of this transformation depends upon the physical process taking place as in the case of the transformations just considered, but at the same time leaves invariant the fundamental laws on which a description of the process depends, the description of the process by means of the transformation will be a correct qualitative description but will not be a true quantitative one, since the transformation varies for each independent event and so there are no fixed units of measurement. It is possible that when the mind is concentrated on a subject the type of transformation is practically constant, and so our interpretations of sensations become clearer as they become more of a quantitative nature, but it is dangerous to speculate and so I shall leave the subject at this point.

title: Page:BatemanTime.djvu/13


text: 1911 Encyclopædia Britannica/Diamantina

title: 1911 Encyclopædia Britannica/Diamantina


text: Index:BatemanGeneral.djvu

title: Index:BatemanGeneral.djvu


text:
Page:BatemanGeneral.djvu/1

,—

HE appearance of Dr. Silberstein's recent article on "General Relativity without the Equivalence Hypothesis" encourages me to restate my own views on the subject. I am perhaps entitled to do this as my work on the subject of General Relativity was published before that of Einstein and Kottler, and appears to have been overlooked by recent writers. In 1909 I proposed a scheme of electromagnetic equations which are covariant for all transformations of co-ordinates which are biuniform in the domain we are interested in. These equations were similar to Maxwell's equations, except that the familiar relations B = μH, D = kE of Maxwell's theory were replaced by more

title: Page:BatemanGeneral.djvu/1


text:
Page:BatemanGeneral.djvu/2

 general equations, which implied that two fundamental integral forms were reciprocals with regard to a quadratic differential form

$$\sum\sum g_{m,n}dx_{m}dx_{n}$$

which was assumed to be invariant for all transformations of co-ordinates. The coefficients of the quadratic form were regarded as characteristics of the medium supporting the electromagnetic field and of the motion of the medium and its parts. The vanishing of the quadratic form was regarded as the condition that two neighbouring particles should be in positions such that a disturbance starting from one at the associated time should arrive at the other at its associated time.

The idea that the coefficients of the quadratic form might be considered as characteristics of the mind interpreting the phenomena was also entertained, and it was suggested that a correspondence or transformation of co-ordinates might be considered as a crude mathematical symbol for a mind.

The phenomena here considered were those occurring in the brain and body; and although the correspondence by which the universe is reconstructed, so to speak, may be totally different from the type contemplated here, yet it was thought that some of the general conclusions might still be valid if a transformation of co-ordinates was adopted as a working model of the correspondence. It was thought, for instance, that there was an analogy between the relativity principle that the earth's motion in space cannot be detected from experiments with terrestrial objects: and the interesting fact that we are unaware of the flow of blood and other processes taking place in our own bodies so long as they take place in the normal way. It was thought that the

title: Page:BatemanGeneral.djvu/2


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Page:BatemanGeneral.djvu/3

Rh correspondence by which the elementary processes in the brain are interpreted may be adjusted in such a way that some of the changes are obscured.

Again, if we assume that the nature of an electromagnetic field depends on the type of fundamental quadratic form which determines the constitutive relations, and thus depends indirectly on a transformation which filters the coefficients of this quadratic form, this dependence may be a symbol for the relation between physical and mental phenomena instead of giving the influence of gravitation on light as in Einstein's theory.

Einstein and others have attempted to formulate a set of equations of motion which will cover all physical phenomena; but the present writer does not feel inclined to accept them as final, because in his opinion the true equations of motion should be capable of accounting for the phenomena of life, which after all are the most important physical phenomena.

To make my position more definite, let us consider one of the methods by which the equations of motion of an electron are obtained in the usual electromagnetic theory. The principle is adopted that at each instant the integral over the electron of the total force on each element must be zero. Now before this principle can be used to write down the equations of motion we must know the design of the electron, and we must know the way in which the motions of the different elements are co-ordinated. This co-ordination or organization of the motions of the elements may be represented mathematically by a sequence of infinitesimal transformations, by which some of the features of the design are preserved. The design of the electron and the co-ordinated motion of its parts may, perhaps, be specified by a quadratic differential form in four variables, which determines a mapping of the interior of the electron on the interior of a stationary sphere; but I doubt if this is sufficiently general. A knowledge of this quadratic differential form is necessary then before we can write down the equations of motion of the electron as a whole. What we usually regard as the equations of motion of matter need then to be supplemented by geometrical conditions which specify the design and organization of each elementary portion of matter. Furthermore, when this design and organization is assumed to be known, the ordinary equations of motion may be regarded as a consequence of the electromagnetic laws and the above-mentioned principle.

It must be confessed, however, that this principle does not

title: Page:BatemanGeneral.djvu/3


text:
Page:BatemanGeneral.djvu/4

 seem satisfactory for a fundamental principle, and is probably a consequence of some deep underlying principles which are the true equations of motion. These new principles should indicate the reason for a similarity of design of the different electrons. One of the fundamental facts of life is that a good design is copied, and that there is a certain characteristic of the design of an object and its surrounding medium, depending perhaps on the closeness of fit of an imperfect correspondence, which determines the extent to which the design of the object is copied and preserved in the surrounding medium. This may be called the value of the design in relation to the medium, and it is a quantity which I feel must be taken into account in the true equations of motion, and a number assigned to it at each instant. As an example of standardization, the Ford motor-car is not in it with the electron; and, according to the above view, we must regard the design of the electron as one of very great value in relation to the surrounding medium.

Returning to our generalized scheme of electromagnetic equations, and looking at matters from the point of view of physical optics, it may be remarked that the scheme of constitutive relations mentioned above is not sufficiently general to cover the case of a doubly-refracting crystalline medium. To remedy this defect we may use a biquadratic integral form instead of a quadratic differential form to specify the constitutive relations. The vanishing of the biquadratic integral form may perhaps be regarded as the condition for action of a moving curve on a particle, a type of condition that seems natural if we regard moving Faraday tubes as fundamental. With this generalized theory it is possible for the elementary wave surface in a medium to be a general Kummer surface, a surface of which Fresnel's wave surface is a particular case. It is doubtful whether this generalized theory is sufficiently general for all purposes, and the above example is given just to emphasize that the absolute calculus of Ricci and Levi Civita can be used to develop a theory of generalized relativity on many lines in addition to that adopted by Einstein.

Going back to the case in which a quadratic form is sufficient to determine the optical properties of a medium, we may remark that if Einstein's idea of the gravitational equations is accepted, it is still by no means certain that his

title: Page:BatemanGeneral.djvu/4


text:
Page:BatemanGeneral.djvu/5

Rh quadratic form from which the gravitational equations are derived is the same as the quadratic form which determines the optical properties of the medium. Indeed, the example which I considered on p. 262 of my first paper would seem to indicate that this was not the case. It should be mentioned that in the first seven equations in this example there is a misprint, $$\epsilon\mu$$ should be replaced by $$(\epsilon\mu)^{-1}$$. On the above view Einstein's idea of an influence of gravitation on light is simply an hypothesis, but a very interesting and reasonable one. It may be remarked, however, that in the theory of surfaces there are two fundamental quadratic forms, and we may perhaps expect something similar in general relativity.

With regard to possible extensions of the idea of relativity it may be worth while to consider transformations analogous to the contact transformations of dynamics in which the co-ordinates x, y, z, t and the component velocities u, v, w correspond to a new set $$\left(x_{1}y_{1}z_{1}t_{1}u_{1}v_{1}w_{1}\right)$$ in such a way that the differential equations

are a consequence of the equations

This may be secured by making a single quadratic form, such as

$$\begin{array}{cc} \left(dx^{2}+dy^{2}+dz^{2}-c^{2}dt^{2}\right)\left(c^{2}-u^{2}-v^{2}-w^{2}\right)\\ +\left(c^{2}dt-udx-vdy-wdz\right)^{2}, & \left(c^{2}>u^{2}+v^{2}+w^{2}\right)\end{array}$$

an invariant. Various other quadratic forms consisting of sums of squares may, of course, be adopted instead.

H..

Throop College.
 * Pasandena, Cal.
 * Aug. 10th, 1918.

title: Page:BatemanGeneral.djvu/5


text: 1911 Encyclopædia Britannica/Diamante, Juan Bautista


text: 1911 Encyclopædia Britannica/Diamante, Fra


text:
Page:Poems, Volume 1, Coates, 1916.djvu/57

BEAUTY! vision of forgotten gladness!

Fulfillment of a dream that ne'er betrays!

O miracle of hope, and balm of sadness!

Creative ecstasy and fount of praise!

I lay upon the ground and gave no token,

I hid my face mid sodden leaves and sere,

My languid pulses chill, my spirit broken,—

I knew not, O divine one! you were near;

For snows and frosts of winter, new-departed,

Still held my will in thrall and weighed me down;

And I forgot—forlorn and heavy-hearted—

Your promise, goddess of the violet crown!

But soft as music in remembrance sighing,

You fanned me with your wooing breath, and I

Who shed no tears when lone I seemed and dying

Wept at your touch, and knew I should not die.


text:
Page:Feilberg.djvu/18

Rh the effects of them. Mr. ——, knowing this, carefully finished each one of the groaning wretches who looked as if he might revive. Those that were evidently dying he left alone. And, as revolver cartridges cost money, he economically battered in their temples with one of the blacks' clubs that had been left on the field of battle (?).—Queenslander, May 15, 1880.

II.

squatter, taking his wife out to his station, had in his household two blacks, husband and wife. The wife, a young girl, came from New South Wales, and having been brought up from childhood among white people could speak no other language than English, and had in all respects the habits of an English girl of the lower classes. She was an excellent servant, could sew neatly and well, cooked fairly, and was neat and clean in her person and habits. Her "benjeman," Starlight, was also a civilised black, spoke English well and correctly, was a good stockman, and very handy with horses. The pair were hired at fair wages, and made as good use of their money as any of the white employés on the station. After serving the squatter who took them out west for a while, Starlight and his wife signed an agreement with one of his neighbors for, we believe, an advanced rate of wages. Their new employer was unmarried, and a number of young men were about the station. Polly, the black girl, was a source of great amusement to the whole crowd. She had no objection to flirtation, and probably enjoyed the evident jealousy of her "benjeman." For, strange as it must appear to some supporters of our present system of dealing with them, it is nevertheless a fact that the blacks are very much like the rest of us, and have the audacity to cherish similar sentiments. One evening Starlight returned home in the dusk from a hard day's work, and he heard cries coming from an outbuilding belonging to the head station. The cries were those of his wife—or "gin" we shall call her. He forgot that being a black he ought not to be a man, and hastened to the spot. There he saw one of the young overseers engaged in what, if she had been a white girl, would have been called a criminal assault on Polly. Still forgetting himself, he threw himself upon the white overseer and grappled with him. They struggled and fell. Starlight reaching his hand out seized a shear blade lying on the ground, and scored his antagonist's shoulder. It was a flesh wound, but the black, the moment he had inflicted it knew what his fate would be, and let go his grip of the overseer, who cried out, "I am stabbed," to the group of men who, attracted by the noise, hurried to the spot. Starlight slipped away from them in the gathering darkness, and escaped into the thick growing timber. A council of war at the head-station came to the conclusion that a black who had, under any provocation, raised his hand against a white ought not to live. They accordingly offered the half-wild blacks camped at the head station a reward for his capture. This the savages readily agreed to effect, for they knew he was unarmed: and being a stranger to them they had no pity for him. Accordingly they went away next day, and returned triumphantly. They did not bring Starlight, but they had caught him. Finding, however, some difficulty in bringing in their prisoner, they had hamstrung him, and he was then lying at the disposal of the whites, if they chose to go to the spot. However, the people of the station were spared the trouble of finishing their work. Sub-inspector ——— and his troopers arrived that afternoon, and on being informed of the circumstances he very obligingly sent a couple of the "boys" with their rifles, who, being led to the spot by the station blacks, ended Starlight's agony by blowing out his brains. The wounded overseer was well in a week.

It is wonderful what vitality the blacks possess. Mr. X., superintendent of ——— Downs, was riding with his storekeeper over an almost unused end of the run—poor country, with spinifex growing on it. Suddenly he espied the tracks of a blackfellow. There were some "myalls" in the ranges not far distant, but they had committed no outrage of any kind, and this was probably the track of one. Soon Mr. X's quick eyes espied a black in the long spinifex, endeavouring to pass himself off for a blackened stump—a manoeuvre often more successful than those who have not seen it practised would believe. "Ha, ha! there he is," he laughed, as he rode towards the object. It was an old grizzled black, bent with growing infirmity, and he had a nulla in his hand. The poor old creature held out his hands deprecatingly, and jabbered in his fear. Mr. X. motioned him to run, which, after a moment's hesitation, he did. The superintendent was a sportsman, and did not care about shooting his game sitting. As the old black ran, he followed, putting his horse into an easy canter, and tried a snap shot with his revolver. The ball evidently pierced the old man's back, as the bright red blood began to flow. He stopped and turned again, begging for life with beseeching gesture. Mr. X., who had reined up his horse, again

title: Page:Feilberg.djvu/18


text: Dictionary of National Biography, 1885-1900/Balguy, John


text:
Page:EB1911 - Volume 08.djvu/9

 * }

title: Page:EB1911 - Volume 08.djvu/9


text:
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x

 * }

title: Page:EB1911 - Volume 08.djvu/10


text:
Executive Order 10655

By virtue of the authority vested in me as President of the United States, and in order to provide for the fullest development and coordination of the aviation policies and activities of Federal agencies, it is ordered as follows:

, January 28, 1956.

title: Executive Order 10655


text: Talk:Executive Order 10655

title: Talk:Executive Order 10655


text:
Portal:Geology

General

 * Portal:Chicago Field Museum of Natural History
 * Portal:Geological Society of London
 * The Grand Cañon of the Colorado, 1902 by John Muir
 * Transactions of the Geological Society by the Geological Society of London:
 * Volume 1
 * Volume 2
 * Volume 3
 * Volume 4
 * Geological Evidences of the Antiquity of Man
 * Geology and Mineralogy considered with reference to Natural Theology
 * Glossary of Geological and other Scientific terms used in Principles of Geology
 * Journal Of William Ellis
 * Student's Elements of Geology
 * A Treatise on Geology
 * Bulletin of the Department of Geology, Volume 12

Eras

 * Portal:Cenozoic
 * Portal:Mesozoic
 * Portal:Paleozoic

Regional

 * The Past and Future of Niagara as it appeared in the September 1872 Popular Science Monthly
 * Ups and Downs of the Long Island Coast as it appeared in the February 1877 Popular Science Monthly
 * The Geological History of New York Island and Harbor as it appeared in the October 1878 Popular Science Monthly
 * The Origin of Upland Lakes as it appeared in the April 1879 Popular Science Monthly
 * The Parallel Roads of Glen Roy as it appeared in the January 1877 Popular Science Monthly
 * Artesian Wells and the Great Sahara as it appeared in the February 1880 Popular Science Monthly
 * Vibration of Rocks in Patapsco Valley, Maryland as it appeared in the February 1882 Popular Science Monthly
 * The Colorado Desert as it appeared in the January 1882 Popular Science Monthly
 * Subterranean Streams in South Carolina as it appeared in the June 1876 Popular Science Monthly
 * The Geological Distribution of North American Forests as it appeared in the August 1883 Popular Science Monthly
 * Recent Geological Changes in Western Michigan as it appeared in the April 1884 Popular Science Monthly
 * The Loess-Deposits of Northern China as it appeared in the December 1883 Popular Science Monthly
 * The Salt-Deposits of Western New York as it appeared in the August 1884 Popular Science Monthly
 * Nature and Origin of the Drift-Deposits of the Northwest I as it appeared in the June 1873 Popular Science Monthly
 * Nature and Origin of the Drift-Deposits of the Northwest II as it appeared in the July 1873 Popular Science Monthly
 * Some Observations on Niagara as it appeared in the June 1873 Popular Science Monthly
 * State Geological Surveys as it appeared in the June 1873 Popular Science Monthly
 * Physical Features of the Colorado Valley II as it appeared in the September 1875 Popular Science Monthly
 * North America in the Ice Period as it appeared in the December 1881 Popular Science Monthly
 * The New York Geological Survey as it appeared in the April 1883 Popular Science Monthly
 * A sketch of the physical structure of Australia, so far as it is at present known (1850) by Joseph Beete Jukes

Articles

 * Popular Geology as it appeared in the September 1872 Popular Science Monthly
 * Geology and History as it appeared in the August 1880 Popular Science Monthly
 * Some Unsolved Problems in Geology I as it appeared in the October 1883 Popular Science Monthly
 * Some Unsolved Problems in Geology II as it appeared in the November 1883 Popular Science Monthly
 * Accoutrement of a Field-Geologist as it appeared in the April 1877 Popular Science Monthly
 * Studies in Experimental Geology as it appeared in the June 1880 Popular Science Monthly

Rocks and Minerals
Rocks are mixtures or aggregates; minerals are pure chemical compounds
 * Portal:Mineralogy, the study of minerals
 * Portal:Petrology, the study of rocks

Paleontology

 * Portal:Paleontology, the study of prehistoric life
 * Portal:Dinosaurs
 * Portal:Eurypterids
 * Portal:Paleontology in the United States

Hydrology and Oceanography

 * Geysers and How They are Explained as it appeared in the February 1878 Popular Science Monthly
 * A Visit to the New Zealand Geysers as it appeared in the July 1879 Popular Science Monthly
 * Why Do Springs and Wells Overflow? I as it appeared in the November 1879 Popular Science Monthly
 * The Mineral Springs of Saratoga as it appeared in the May 1881 Popular Science Monthly
 * River and Lake Terraces as it appeared in the April 1873 Popular Science Monthly
 * The Mechanics of Intermittent Springs as it appeared in the July 1882 Popular Science Monthly
 * On the Formation of Lakes as it appeared in the September 1876 Popular Science Monthly
 * The World's Geyser-Regions as it appeared in the August 1884 Popular Science Monthly
 * The Hydraulics of Great Rivers as it appeared in the July 1874 Popular Science Monthly
 * Water-Supply of Islands as it appeared in the February 1875 Popular Science Monthly

Vulcanology

 * (1757)
 * Vesuvius as it appeared in the June 1872 Popular Science Monthly
 * Fouque's Santorin and its Eruptions as it appeared in the August 1880 Popular Science Monthly
 * The Origin and Structure of Volcanic Cones I as it appeared in the April 1881 Popular Science Monthly
 * The Origin and Structure of Volcanic Cones II as it appeared in the May 1881 Popular Science Monthly
 * A New Theory of Volcanoes as it appeared in the December 1872 Popular Science Monthly
 * Volcanic Products as it appeared in the January 1882 Popular Science Monthly
 * Volcanoes, their Action and Distribution as it appeared in the November 1881 Popular Science Monthly
 * The Volcanic Eruption of Krakatau as it appeared in the July 1884 Popular Science Monthly
 * by Capt. W. J. Watson

Seismology

 * Measurement of Earthquake-Waves as it appeared in the September 1872 Popular Science Monthly
 * The Causes of Earthquakes as it appeared in the February 1884 Popular Science Monthly
 * Ischia and its Earthquakes as it appeared in the November 1883 Popular Science Monthly
 * Earthquakes and their Causes as it appeared in the October 1875 Popular Science Monthly
 * Earthquake-Phenomena as it appeared in the March 1873 Popular Science Monthly
 * San Francisco Earthquake & Fire: April 18, 1906, a 1906 anonymous black-and-white documentary silent short film
 * San Francisco Earthquake & Fire: April 18, 1906, a 1906 anonymous black-and-white documentary silent short film

Structural geology
Structural geology is the study of the three-dimensional distribution of rock units with respect to their deformational histories. The primary goal of structural geology is to use measurements of present-day rock geometries to uncover information about the history of deformation (strain) in the rocks, and ultimately, to understand the stress field that resulted in the observed strain and geometries. This understanding of the dynamics of the stress field can be linked to important events in the regional geologic past; a common goal is to understand the structural evolution of a particular area with respect to regionally widespread patterns of rock deformation (e.g., mountain building, rifting) due to plate tectonics.

 * The Formation of Mountains as it appeared in the February 1879 Popular Science Monthly
 * The Interior of the Earth I as it appeared in the July 1880 Popular Science Monthly
 * The Interior of the Earth II as it appeared in the August 1880 Popular Science Monthly
 * The Primeval American Continent as it appeared in the June 1881 Popular Science Monthly
 * Old Continents as it appeared in the September 1873 Popular Science Monthly

Stratigraphy
Stratigraphy, a branch of geology, studies rock layers and layering (stratification). It is primarily used in the study of sedimentary and layered volcanic rocks. Stratigraphy includes two related subfields: lithologic or lithostratigraphy and biologic stratigraphy or biostratigraphy.

 * Proclamation 6920, 18 September 1996 by Bill Clinton regarding the Grand Staircase-Escalante National Monument: "The monument is a geologic treasure of clearly exposed stratigraphy and structures"

Geologists

 * Louis Agassiz
 * Robert Bakewell
 * Walter A. Bell
 * Henry Grey Bennet
 * Jean-François Berger
 * Edward Bogg
 * John Casper Branner
 * Richard Bright
 * George Bryce
 * William Buckland
 * Thomas Chrowder Chamberlin
 * rank Wigglesworth Clarke
 * Grenville Arthur James Cole
 * Arthur Philemon Coleman
 * John Josias Conybeare
 * William Daniel Conybeare
 * George Cumberland
 * Charles Robert Darwin
 * William Morris Davis
 * William Boyd Dawkins
 * Henry Thomas De la Beche
 * ens Esmark
 * Hugh Falconer
 * William Henry Fitton
 * Lazarus Fletcher
 * John Smith Flett
 * Edward Forbes
 * Archibald Geikie
 * Walcot Gibson
 * Davies Gilbert
 * Grove Karl Gilbert
 * illiam Hall Gilby
 * William Gregor
 * John Hailstone
 * Richard Hennah
 * Wheelton Hind
 * Leonard Horner
 * John Allen Howe
 * James Furman Kemp
 * John Kidd
 * Cargill Gilston Knott
 * Charles Konig
 * Philip Lake
 * Lawrence Lambe
 * Charles Lapworth
 * Joseph Le Conte
 * John Lhotsky
 * Richard Lydekker
 * Charles Lyell
 * John MacCulloch
 * Frederick James Hamilton Merrill
 * Ludwig Meyn
 * John Milne
 * John Muir
 * Henry Smith Munroe
 * Roderick Impey Murchison
 * Nicholas Nugent
 * Kenneth Oakley
 * Henry Fairfield Osborn
 * James Parkinson
 * John Phillips
 * William Phillips
 * John Wesley Powell
 * Frederick William Rudler
 * Gunnar Säve-Söderbergh
 * George Julius Poulett Scrope
 * Albert Charles Seward
 * Webb John Seymour
 * Nathaniel Shaler
 * Henry Clifton Sorby
 * Leonard James Spencer
 * Henry Steinhauer
 * Paweł Edmund Strzelecki
 * Thomas Stewart Traill
 * Alfred Tylor
 * Henry Warburton
 * Lester Frank Ward
 * George Robert Waterhouse
 * Thomas Webster
 * Charles Abiathar White
 * Alice Wilson
 * Nathaniel John Winch
 * Alexander Winchell
 * William Withering
 * Horace Bolingbroke Woodward

title: Portal:Geology


text:
Witchcraft Act 1735

 An Act to repeal the statute made in the first year of the reign of King James the First, intitutled, An Act against conjuration, witchcraft, and dealing with evil and wicked spirits, except so much thereof as repeals an Act of the fifth year of the reign of Queen Elizabeth , Against conjurations, inchantments and witchcrafts, and to repeal, an Act passed in the parliament of Scotland in the ninth parliament of Queen Mary, intituled , Anentis witchcrafts, and for punishing such persons as pretend to exercise or use any kind of witchcraft, sorcery, inchantment, or conjuration.

Be it enacted by the King's most Excellent Majesty, by and with the Advice and Consent of the Lords Spiritual and Temporal, and Commons, in this present Parliament assembled, and by the Authority of the same, That the Statute made in the First Year of the Reign of King James the First, intituled, An Act against Conjuration, Witchcaft, and dealing with evil and wicked Spirits, shall, from the Twenty-fourth Day of June next, be repealed and utterly void, and of none effect (except so much thereof as repeals the Statute made in the Fifth Year of the Reign of Queen Elizabeth intituled, An Act against Conjurations, Inchantments, and Witchcrafts ).

Ⅱ. And be it further enacted by the Authority aforesaid, That from and after the said Twenty-fourth Day of June, the Act passed in the Parliament of Scotland , in the Ninth Parliament of Queen Mary , intituled, Anentis Witchcrafts , shall be, and is hereby repealed.

Ⅲ. And be it further enacted, That from and after the said Twenty-fourth Day of June, no Prosecution, Suit, or Proceeding, shall be commenced or carried on against any Person or Persons for Witchcraft, Sorcery, Inchantment, or Conjuration, or for charging another with any such Offence, in any Court whatsoever in Great Britain.

Ⅳ. And for the more effectual preventing and punishing of any Pretences to such Arts or Powers as are before mentioned, whereby ignorant Persons are frequently deluded and defrauded; be it further enacted by the Authority aforesaid, That if any Person shall, from and after the said Twenty-fourth Day of June, pretend to exercise or use any kind of Witchcraft, Sorcery, Inchantment, or Conjuration, or undertake to tell Fortunes, or pretend, from his or her Skill or Knowledge in any occult or crafty Science, to discover where or in what manner any Goods or Chattels, supposed to have been stolen or lost, may be found, every Person, so offending, being thereof lawfully convicted on Indictment or Information in that part of Great Britain called England , or on Indictment or Libel in that part of Great Britain called Scotland , shall, for every such Offence, suffer Imprisonment by the Space of one whole Year without Bail or Mainprize, and once in every Quarter of the said Year, in some Market Town of the proper County, upon the Market Day, there stand openly on the Pillory by the Space of One Hour, and also shall (if the Court by which such Judgement shall be given shall think fit) be obliged to give Sureties for his or her good Behaviour, in such Sum, and for such Time, as the said Court shall judge proper according to the Circumstances of the Offence, and in such case shall be further imprisoned until such Sureties be given.

title: Witchcraft Act 1735


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 of Norman, French, and later literary and scientific additions from classical and other sources, while the present-day “dialects” preserve, in inflections, pronunciation and particular words, traces of the original variety of the language not incorporated in the standard language of the country. See the various articles on languages (,, &c.).

 DIALECTIC, or (from Gr. , discourse, debate;  , sc.  , the art of debate), a logical term, generally used in common parlance in a contemptuous sense for verbal or purely abstract disputation devoid of practical value. According to Aristotle, Zeno of Elea “invented” dialectic, the art of disputation by question and answer, while Plato developed it metaphysically in connexion with his doctrine of “Ideas” as the art of analysing ideas in themselves and in relation to the ultimate idea of the Good (Repub. vii.). The special function of the so-called “Socratic dialectic” was to show the inadequacy of popular beliefs. Aristotle himself used “dialectic,” as opposed to “science,” for that department of mental activity which examines the presuppositions lying at the back of all the particular sciences. Each particular science has its own subject matter and special principles  ) on which the superstructure of its special discoveries is based. The Aristotelian dialectic, however, deals with the universal laws  ) of reasoning, which can be applied to the particular arguments of all the sciences. The sciences, for example, all seek to define their own species; dialectic, on the other hand, sets forth the conditions which all definitions must satisfy whatever their subject matter. Again, the sciences all seek to educe general laws; dialectic investigates the nature of such laws, and the kind and degree of necessity to which they can attain. To this general subject matter Aristotle gives the name “Topics” , loci, communes loci). “Dialectic” in this sense is the equivalent of “logic.” Aristotle also uses the term for the science of probable reasoning as opposed to demonstrative reasoning ( ). The Stoics divided  (logic) into rhetoric and dialectic, and from their time till the end of the middle ages dialectic was either synonymous with, or a part of, logic.

In modern philosophy the word has received certain special meanings. In Kantian terminology Dialektik is the name of that portion of the Kritik d. reinen Vernunft in which Kant discusses the impossibility of applying to “things-in-themselves” the principles which are found to govern phenomena. In the system of Hegel the word resumes its original Socratic sense, as the name of that intellectual process whereby the inadequacy of popular conceptions is exposed. Throughout its history, therefore, “dialectic” has been connected with that which is remote from, or alien to, unsystematic thought, with the a priori, or transcendental, rather than with the facts of common experience and material things.

 DIALLAGE, an important mineral of the pyroxene group, distinguished by its thin foliated structure and bronzy lustre. The chemical composition is the same as diopside, Ca Mg (SiO3)2, but it sometimes contains the molecules (Mg, Fe″) (Al, Fe‴)2 SiO6 and Na Fe‴ (SiO3)2, in addition, when it approaches to augite in composition. Diallage is in fact an altered form of these varieties of pyroxene; the particular kind of alteration which they have undergone being known as “schillerization.” This, as described by Prof. J. W. Judd, consists in the development of a fine lamellar structure or parting due to secondary twinning and the separation of secondary products along these and other planes of chemical weakness (“solution planes”) in the crystal. The secondary products consist of mixtures of various hydrated oxides—opal, göthite, limonite, &c.—and appear as microscopic inclusions filling or partly filling cavities, which have definite outlines with respect to the enclosing crystal and are known as negative crystals. It is to the reflection and interference of light from these minute inclusions that the peculiar bronzy sheen or “schiller” of the mineral is due. The most pronounced lamination is that parallel to the orthopinacoid; another, less distinct, is parallel to the basal plane, and a third parallel to the plane of symmetry; these planes of secondary parting are in addition to the ordinary prismatic cleavage of all pyroxenes. Frequently the material is interlaminated with a rhombic pyroxene (bronzite) or with an amphibole (smaragdite or uralite), the latter being an alteration product of the diallage.

Diallage is usually greyish-green or dark green, sometimes brown, in colour, and has a pearly to metallic lustre or schiller on the laminated surfaces. The hardness is 4, and the specific gravity 3·2 to 3·35. It does not occur in distinct crystals with definite outlines, but only as lamellar masses in deep-seated igneous rocks, principally gabbro, of which it is an essential constituent. It occurs also in some peridotites and serpentines, and rarely in volcanic rocks (basalt) and crystalline schists. Masses of considerable size are found in the coarse-grained gabbros of the Island of Skye, Le Prese near Bornio in Valtellina, Lombardy, Prato near Florence, and many other localities.

The name diallage, from diallage, “difference,” in allusion to the dissimilar cleavages and planes of fracture, as originally applied by R. J. Haüy in 1801, included other minerals (the orthorhombic pyroxenes hypersthene, bronzite and bastite, and the smaragdite variety of hornblende) which exhibit the same peculiarities of schiller structure; it is now limited to the monoclinic pyroxenes with this structure. Like the minerals of similar appearance just mentioned, it is sometimes cut and polished for ornamental purposes.

 DIALOGUE, properly the conversation between two or more persons, reported in writing, a form of literature invented by the Greeks for purposes of rhetorical entertainment and instruction, and scarcely modified since the days of its invention. A dialogue is in reality a little drama without a theatre, and with scarcely any change of scene. It should be illuminated with those qualities which La Fontaine applauded in the dialogue of Plato, namely vivacity, fidelity of tone, and accuracy in the opposition of opinions. It has always been a favourite with those writers who have something to censure or to impart, but who love to stand outside the pulpit, and to encourage others to pursue a train of thought which the author does not seem to do more than indicate. The dialogue is so spontaneous a mode of expressing and noting down the undulations of human thought that it almost escapes analysis. All that is recorded, in any literature, of what pretend to be the actual words spoken by living or imaginary people is of the nature of dialogue. One branch of letters, the drama, is entirely founded upon it. But in its technical sense the word is used to describe what the Greek philosophers invented, and what the noblest of them lifted to the extreme refinement of an art.

The systematic use of dialogue as an independent literary form is commonly supposed to have been introduced by Plato, whose earliest experiment in it is believed to survive in the Laches. The Platonic dialogue, however, was founded on the mime, which had been cultivated half a century earlier by the Sicilian poets, Sophron and Epicharmus. The works of these writers, which Plato admired and imitated, are lost, but it is believed that they were little plays, usually with only two performers. The recently discovered mimes of Herodas (Herondas) give us some idea of their scope. Plato further simplified the form, and reduced it to pure argumentative conversation, while leaving intact the amusing element of character-drawing. He must have begun this about the year 405, and by 399 he had brought the dialogue to its highest perfection, especially in the cycle directly inspired by the death of Socrates. All his philosophical writings, except the Apology, are cast in this form. As the greatest of all masters of Greek prose style, Plato lifted his favourite instrument, the dialogue, to its highest splendour, and to this day he remains by far its most distinguished proficient. In the 2nd century Lucian of Samosata achieved a brilliant success with his ironic dialogues “Of the Gods,” “Of the Dead,” “Of Love” and “Of the Courtesans.” In some of them he attacks superstition and philosophical error with the sharpness of his wit; in others he merely paints scenes of modern life. The title of Lucian’s most famous collection was borrowed in the 17th century by two French writers of eminence, each of whom prepared Dialogues des morts. These were Fontenelle (1683) and Fénelon (1712). In English non-dramatic literature the dialogue had not been extensively<section end="Dialogue" />

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103 sons with the hatred and curses of North America. Indeed, my Lords, we are treating posterity very scurvily. We have mortgaged all the lands; we have cut down all the oaks; we are now trampling down the fences, rooting up the seedlings and saplings, and mining all the resources of another age. We shall send the next generation into the world, like the wretched heir of a worthless father, without money, credit, or friends; with a stripped, encumbered, and perhaps untenanted estate.

Having spoke so largely against the principles of the Bill, it is hardly necessary to enter into the merits of it. I shall only observe, that even if we had the consent of the People to alter their Government, it would be unwise to make such alterations as these. To give the appointment of the Governor and Council to the Crown, and the disposal of all places, even of the Judges, and with a power of removing them, to the Governor, is evidently calculated with a view to form a strong party in our favour. This I know has been done in other Colonies; but still this is opening a source of perpetual discord, where it is our interest always to agree. If we mean any thing by this establishment, it is to support the Governor and the Council against the People, i. e. to quarrel with our friends, that we may please their servants. This scheme of governing them by a party is not wisely imagined, it is much too premature, and at all events, must turn to our disadvantage. If it fails, it will only make us contemptible; if it succeeds, it will make us odious. It is our interest to take very little part in their domestic administration of Government, but purely to watch over them for their good. We never gained so much by North America as when we let them govern themselves, and were content to trade with them and to protect them. One would think, my Lords, there was some statute law, prohibiting us, under the severest penalties, to profit by experience.

My Lords, I have ventured to lay my thoughts before you, on the greatest national concern that ever came under your deliberation, with as much honesty as you will meet with from abler men, and with a melancholy assurance, that not a word of it will be regarded. And yet, my Lords, with your permission, I will waste one short argument more on the same cause, one that I own I am fond of, and which contains in it, what, I think, must affect every generous mind. My Lords, I look upon North America as the only great nursery of freemen now left upon the face of the earth. We have seen the liberties of Poland and Sweden swept away, in the course of one year, by treachery and usurpation. The free towns in Germany are like so many dying sparks, that go out one after another, and which must all be soon extinguished under the destructive greatness of their neighbours. Holland is little more than a great trading company, with luxurious manners, and an exhausted revenue; with little strength and with less spirit. Switzerland alone is free and happy within the narrow enclosure of its rocks and vallies. As for the state of this country, my Lords, I can only refer myself to your own secret thoughts. I am disposed to think and hope the best of Public Liberty. Were I to describe her, according to my own ideas at present, I should say that she has a sickly countenance, but I trust she has a strong constitution.

But whatever may be our future fate, the greatest glory that attends this country, a greater than any other nation ever acquired, is to have formed and nursed up to such a state of happiness, those Colonies whom we are now so eager to butcher. We ought to cherish them as the immortal monuments of our public justice and wisdom: as the heirs of our better days, of our old arts and manners, and of our expiring national virtues. What work of art, or power, or public utility, has ever equalled the glory of having peopled a continent without guilt or bloodshed, with a multitude of free and happy commonwealths; to have given them the best arts of life and Government, and to have suffered them under the shelter of our authority, to acquire in peace the skill to use them. In comparison of this, the policy of governing; by influence, and even the pride of war and victory, are dishonest tricks and poor contemptible pageantry.

We seem not to be sensible of the high and important trust which Providence has committed to our charge. The most precious remains of civil liberty, that the world can now boast of, are lodged in our hands; and God forbid that we should violate so sacred a deposit. By enslaving your Colonies, you not only ruin the peace, the commerce, and the fortunes of both countries, but you extinguish the fairest hopes, shut up the last asylum of mankind. I think, my Lords, without being weakly superstitious, that a good man may hope that heaven will take part against the execution of a plan which seems big, not only with mischief, but impiety.

Let us be content with the spoils and the destruction of the East. If your Lordships can see no impropriety in it, let the plunderer and the oppressor still go free. But let not the love of liberty be the only crime you think worthy of punishment. I fear we shall soon make it a part of our national character, to ruin every thing that has the misfortune to depend upon us.

No nation has ever before contrived, in so short a space of time, without any war or public calamity (unless unwise measures may be so called) to destroy such ample resources of commerce, wealth, and power, as of late were ours, and which, if they had been rightly improved, might have raised us to a state of more honorable and more permanent greatness than the world has yet seen.

Let me remind the noble Lords in Administration, that before the Stamp Act, they had power sufficient to answer all the just ends of Government, and they were all completely answered. If that is the power they want, though we have lost much of it at present, a few kind words would recover it all.

But if the tendency of this Bill is, as I own it appears to me, to acquire a power of governing them by influence and corruption; in the first place, my Lords, this is not true Government, but a sophisticated kind which counterfeits the appearance, but without the spirit or virtue of the true: and then, as it tends to debase their spirits and corrupt their manners, to destroy all that is great and respectable in so considerable a part of the human species, and by degrees to gather them together with the rest of the world, under the yoke of universal slavery; I think, for these reasons, it is the duty of every wise man, of every honest man, and of every Englishman, by all lawful means, to oppose it.

Whereas by Letters Patent under the great seal of England, made in the third year of the reign of their late Majesties King William and Queen Mary, for uniting, erecting, and incorporating, the several Colonies, Territories, and tracts of land therein mentioned, into one real Province, by the name of Their Majesties Province of the Massachusetts Bay, in New England; whereby it was, amongst other things, ordained and established, that the Governor of the said Province should, from thenceforth, be appointed and commissionated by their Majesties, their heirs and successors; it was, however, granted and ordained, that, from the expiration of the term for and during which the eight and twenty persons named in the said letters patent were appointed to be the first Counsellors or Assistants to the Governor of the said Province for the time being, the aforesaid number of eight and twenty Counsellors or Assistants should yearly, once in every year, for ever thereafter, be, by the General Court or Assembly, newly chosen: and whereas the said method of electing such Counsellors or Assistants, to be vested with the several powers, authorities, and privileges, therein mentioned, although conformable to the practice theretofore used in such of the Colonies thereby united, in which the appointment of the respective Governors had been vested in the General Courts or Assemblies of the said Colonies, hath, by repeated experience, been found to be extremely ill adapted to the plan of Government established in the Province of Massachusetts Bay, by the said letters patent herein-before mentioned, and hath been so far from contributing to the attainment of the good ends and purposes thereby intended and to the promoting of the internal welfare, peace, and good government, of the said Province, or to the maintenance of the just subordination to, and conformity with, the


text: 1911 Encyclopædia Britannica/Diallage

title: 1911 Encyclopædia Britannica/Diallage


text: 1911 Encyclopædia Britannica/Dialect

title: 1911 Encyclopædia Britannica/Dialect


text:
The American Journal of Sociology/Volume 29

Articles

 * .The Natural History of the Newspaper


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 radii FA and GA, draw the two arcs AY and AZ which will limit the hour-lines; for in an observation the bead will always be found between them. The forenoon and afternoon hours may then be marked as indicated in the figure. The dial does not of itself discriminate between forenoon and afternoon; but extraneous circumstances, as, for instance, whether the sun is rising or falling, will settle that point, except when close to noon, where it will always be uncertain.

To rectify the dial (using the old expression, which means to prepare the dial for an observation),—open the small door, by turning it about its hinge, till it stands well out in front. Next, set the thread in the line FG opposite the day of the month, and stretching it over the point A, slide the bead P along till it exactly coincides with A.

To find the hour of the day,—hold the dial in a vertical position in such a way that its plane may pass through the sun. The verticality is ensured by seeing that the bead rests against the card without pressing. Now gradually tilt the dial (without altering its vertical plane), until the central line of sunshine, passing through the open slit of the door, just falls along the sun-line. The hour-line against which the bead P then rests indicates the time.

The sun-line drawn above has always, so far as we know, been used as a shadow-line. The upper edge of the rectangular door was the prolongation of the line, and, the door being opened, the dial was gradually tilted until the shadow cast by the upper edge exactly coincided with it. But this shadow tilts the card one-quarter of a degree more than the sun-line, because it is given by that portion of the sun which just appears above the edge, that is, by the upper limb of the sun, which is one-quarter of a degree higher than the centre. Now, even at some distance from noon, the sun will sometimes take a considerable time to rise one-quarter of a degree, and by so much time will the indication of the dial be in error.

The central line of light which comes through the open slit will be free from this error, because it is given by light from the centre of the sun.

The card-dial deserves to be looked upon as something more than a mere toy. Its ingenuity and scientific accuracy give it an educational value which is not to be measured by the roughness of the results obtained.

The theory of this instrument is as follows:—Let H (fig. 9) be the point of suspension of the plummet at the time of observation, so that the angle DAH is the north declination of the sun,—P, the bead, resting against the hour-line VX. Join CX, then the angle ACX is the hour-angle from noon given by the bead, and we have to prove that this hour-angle is the correct one corresponding to a north latitude DAC, a north declination DAH and an altitude equal to the angle which the sun-line, or its parallel AC, makes with the horizontal. The angle PHQ will be equal to the altitude, if HQ be drawn parallel to DC, for the pair of lines HQ, HP will be respectively at right angles to the sun-line and the horizontal.

Draw PQ and HM parallel to AC, and let them meet DCE in M and N respectively.

Let HP and its equal HA be represented by a. Then the following values will be readily deduced from the figure:—

AD＝a cos decl.  DH＝a sin decl. PQ＝a sin alt. CX＝AC＝AD cos lat.＝a cos decl. cos lat. PN＝CV＝CX cos ACX＝a cos decl. cos lat. cos ACX. NQ＝MH＝DH sin MDH＝sin decl. sin lat. (∴ the angle MDH＝DAC＝latitude.) And since we have, by simple substitution, a sin alt.＝a sin decl. sin lat. + a cos del. cos lat. cos ACX; or, dividing by a throughout,

which equation determines the hour-angle ACX shown by the bead.

To determine the hour-angle of the sun at the same moment, let fig. 10 represent the celestial sphere, HR the horizon, P the pole, Z the zenith and S the sun.

From the spherical triangle PZS, we have cos ZS＝cos PS cos ZP + sin PS sin ZP cos ZPS but ZS＝zenith distance＝90°− altitude ZP＝90°− PR＝90°− latitude PS＝polar distance ＝90°− declination, therefore, by substitution

and ZPS is the hour-angle of the sun.

A comparison of the two formulae (1) and (2) shows that the hour-angle given by the bead will be the same as that given by the sun, and proves the theoretical accuracy of the card-dial. Just at sun-rise or at sun-set the amount of refraction slightly exceeds half a degree. If, then, a little cross m (see fig. 8) be made just below the sun-line, at a distance from it which would subtend half a degree at c, the time of sun-set would be found corrected for refraction, if the central line of light were made to fall on cm.

—The following list includes the principal writers on dialling whose works have come down, to us, and to these we must refer for descriptions of the various constructions, some simple and direct, others fanciful and intricate, which have been at different times employed: Ptolemy, Analemma, restored by Commandine; Vitruvius, Architecture; Sebastian Münster, Horologiographia; Orontius Fineus, De horologiis solaribus; Mutio Oddi da Urbino, Horologi solari; Dryander, De horologiorum compositione; Conrad Gesner, Pandectae; Andreas Schöner, Gnomonicae; F. Commandine, Horologiorum descriptio; Joan. Bapt. Benedictus, De gnomonum usu; Georgius Schomberg, Exegesis fundamentorum gnomonicorum; Joan. Solomon de Caus, Horologes solaires; Joan. Bapt. Trolta, Praxis horologiorum; Desargues, Manière universelle pour poser l'essieu, &c.; Ath. Kircher, Ars magna lucis et Umbrae; Hallum, Explicatio horologii in horto regio Londini; Joan. Mark, Tractatus horologiorum; Clavius, Gnomonices de horologiis. Also among more modern writers, Deschales, Ozanam, Schottus, Wolfius, Picard, Lahire, Walper; in German, Paterson, Michael, Müller; in English, Foster, Wells, Collins, Leadbetter, Jones, Leybourn, Emerson and Ferguson. See also Hans Löschner, Über Sonnenuhren (2nd ed., Graz, 1906).

 DIALECT (from Gr. , conversation, manner of speaking,  , to converse), a particular or characteristic manner of speech, and hence any variety of a language. In its widest sense languages which are branches of a common or parent language may be said to be “dialects” of that language; thus Attic, Ionic, Aeolic and Doric are dialects of Greek, though there may never have at any time been a separate language of which they were variations; so the various Romance languages, Italian, French, Spanish, &c., were dialects of Latin. Again, where there have existed side by side, as in England, various branches of a language, such as the languages of the Angles, the Jutes or the Saxons, and the descendant of one particular language, from many causes, has obtained the predominance, the traces of the other languages remain in the “dialects” of the districts where once the original language prevailed. Thus it may be incorrect, from the historical point of view, to say that “dialect” varieties of a language represent degradations of the standard language. A “literary” accepted language, such as modern English, represents the original language spoken in the Midlands, with accretions

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text: Dictionary of National Biography, 1885-1900/Balguy, Thomas


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HEN through thy arching aisles,

O Nature, I perceive

What brooding stillness fills the lonesome choirs

Where, heaven'd late, thy sweet musicians sung;

What rude benumbing touch

Strips from reluctant boughs

The languid leaves and bares to common view

The sacred nest,—the mute, expressive nest,

Whose state defenseless tells

Of fledgeling treasures flown,—

Then, like the prudent birds, my thoughts take flight,

Winging o'er wintry fields to find the spring.

Somewhere on Earth's cold breast

The dauntless crocus glows,

And fair Narcissus hangs his head and dreams.

There,—laughing, blushing, like a happy bride,