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N order to attain the greatest possible clearness, let us return to our example of the railway carriage supposed to be travelling uniformly. We call its motion a uniform translation (‘‘uniform” because it is of constant velocity and direction, ‘‘translation” because although the carriage changes its position relative to the embankment yet it does not rotate in so doing). Let us imagine a raven flying through the air in such a manner that its motion, as observed from the embankment, is uniform and in a straight line. If we were to observe the flying raven from the moving railway carriage, we should find that the motion of the raven would be one of different velocity and direction, but that it would still be uniform and in a straight line. Expressed in an abstract manner we may say: If a mass m is moving uniformly in a straight line with respect to a co-ordinate system K, then it will also be moving uniformly and in a straight line relative to a second co-ordinate system Kʹ, provided that

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 the latter is executing a uniform translatory motion with respect to K. In accordance with the discussion contained in the preceding section, it follows that:

If K is a Galileian co-ordinate system, then every other co-ordinate system Kʹ is a Galileian one, when, in relation to K, it is in a condition of uniform motion of translation. Relative to Kʹ the mechanical laws of Galilei-Newton hold good exactly as they do with respect to K.

We advance a step farther in our generalisation when we express the tenet thus: If, relative to K, Kʹ is a uniformly moving co-ordinate system devoid of rotation, then natural phenomena run their course with respect to Kʹ according to exactly the same general laws as with respect to K. This statement is called the principle of relativity (in the restricted sense).

As long as one was convinced that all natural phenomena were capable of representation with the help of classical mechanics, there was no need to doubt the validity of this principle of relativity. But in view of the more recent development of electrodynamics and optics it became more and more evident that classical mechanics affords an insufficient foundation for the physical description of all natural phenomena. At this juncture the question of the validity of the principle of relativity became ripe for discussion, and it did not appear

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 impossible that the answer to this question might be in the negative.

Nevertheless, there are two general facts which at the outset speak very much in favour of the validity of the principle of relativity. Even though classical mechanics does not supply us with a sufficiently broad basis for the theoretical presentation of all physical phenomena, still we must grant it a considerable measure of “truth,” since it supplies us with the actual motions of the heavenly bodies with a delicacy of detail little short of wonderful. The principle of relativity must therefore apply with great accuracy in the domain of mechanics. But that a principle of such broad generality should hold with such exactness in one domain of phenomena, and yet should be invalid for another, is a priori not very probable.

We now proceed to the second argument, to which, moreover, we shall return later. If the principle of relativity (in the restricted sense) does not hold, then the Galileian co-ordinate systems K, Kʹ, Kʹʹ, etc., which are moving uniformly relative to each other, will not be equivalent for the description of natural phenomena. In this case we should be constrained to believe that natural laws are capable of being formulated in a particularly simple manner, and of course only on condition that, from amongst all possible Galileian

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 co-ordinate systems, we should have chosen one (K₀) of a particular state of motion as our body of reference. We should then be justified (because of its merits for the description of natural phenomena) in calling this system “absolutely at rest,” and all other Galileian systems K “in motion.” If, for instance, our embankment were the system K₀, then our railway carriage would be a system K, relative to which less simple laws would hold than with respect to K₀. This diminished simplicity would be due to the fact that.the carriage K would be in motion (i.e. “really’’) with respect to K₀. In the general laws of nature which have been formulated with reference to K, the magnitude and direction of the velocity of the carriage would necessarily play a part. We should expect, for instance, that the note emitted by an organ-pipe placed with its axis parallel to the direction of travel would be different from that emitted if the axis of the pipe were placed perpendicular to this direction. Now in virtue of its motion in an orbit round the sun, our earth is comparable with a railway carriage travelling with a velocity of about 30 kilometres per second. If the principle of relativity were not valid we should therefore expect that the direction of motion of the earth at any moment would enter into the laws of nature, and also that physical systems in their behaviour would be dependent on the orientation in space

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 with respect to the earth. For owing to the alteration in direction of the velocity of revolution of the earth in the course of a year, the earth cannot be at rest relative to the hypothetical system K₀ throughout the whole year. However, the most careful observations have never revealed such anisotropic properties in terrestrial physical space, i.e. a physical non-equivalence of different directions. This is a very powerful argument in favour of the principle of relativity.

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ET us suppose our old friend the railway carriage to be travelling along the rails with a constant velocity $$v$$, and that a man traverses the length of the carriage in the direction of travel with a velocity $$w$$. How quickly, or, in other words, with what velocity $$W$$ does the man advance relative to the embankment during the process? The only possible answer seems to result from the following consideration: If the man were to stand still for a second, he would advance relative to the embankment through a distance $$v$$ equal numerically to the velocity of the carriage. As a consequence of his walking, however, he traverses an additional distance $$w$$ relative to the carriage, and hence also relative to the embankment, in this second, the distance w being numerically equal to the velocity with which he is walking. Thus in total he covers the distance $$W = v + w$$ relative to the embankment in the second considered. We shall see later that this result, which expresses the theorem of the addi-

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 tion of velocities employed in classical mechanics, cannot be maintained; in other words, the law that we have just written down does not hold in reality. For the time being, however, we shall assume its correctness.

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HERE is hardly a simpler law in physics than that according to which light is propagated in empty space. Every child at school knows, or believes he knows, that this propagation takes place in straight lines with a velocity $$c = 300,000\ \mathrm{ km./sec.}$$ At all events we know with great exactness that this velocity is the same for all colours, because if this were not the case, the minimum of emission would not be observed simultaneously for different colours during the eclipse of a fixed star by its dark neighbour. By means of similar considerations based on observations of double stars, the Dutch astronomer De Sitter was also able to show that the velocity of propagation of light cannot depend on the velocity of motion of the body emitting the light. The assumption that this velocity of propagation is dependent on the direction ‘‘in space” is in itself improbable.

In short, let us assume that the simple law of the constancy of the velocity of light $$c$$ (in vacuum)

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 is justifiably believed by the child at school. Who would imagine that this simple law has plunged the conscientiously thoughtful physicist into the greatest intellectual difficulties? Let us consider how these difficulties arise.

Of course we must refer the process of the propagation of light (and indeed every other process) to a rigid reference-body (co-ordinate system). As such a system let us again choose our embankment. We shall imagine the air above it to have been removed. If a ray of light be sent along the embankment, we see from the above that the tip of the ray will be transmitted with the velocity $$c$$ relative to the embankment. Now let us suppose that our railway carriage is again travelling along the railway lines with the velocity $$v$$, and that its direction is the same as that of the ray of light, but its velocity of course much less. Let us inquire about the velocity of propagation of the ray of light relative to the carriage. It is obvious that we can here apply the consideration of the previous section, since the ray of light plays the part of the man walking along relatively to the carriage. The velocity $$W$$ of the man relative to the embankment is here replaced by the velocity of light relative to the embankment. $$w$$ is the required velocity of light with respect to the carriage, and we have

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 The velocity of propagation of a ray of light relative to the carriage thus comes out smaller than $$c$$.

But this result comes into conflict with the principle of relativity set forth in Section V. For, like every other general law of nature, the law of the transmission of light in vacuo must, according to the principle of relativity, be the same for the railway carriage as reference-body as when the rails are the body of reference. But, from our above consideration, this would appear to be impossible. If every ray of light is propagated relative to the embankment with the velocity $$c$$, then for this reason it would appear that another law of propagation of light must necessarily hold with respect to the carriage—a result contradictory to the principle of relativity.

In view of this dilemma there appears to be nothing else for it than to abandon either the principle of relativity or the simple law of the propagation of light in vacuo. Those of you who have carefully followed the preceding discussion are almost sure to expect that we should retain the principle of relativity, which appeals so convincingly to the intellect because it is so natural and simple. The law of the propagation of light in vacuo would then have to be replaced by a more complicated law conformable to the principle of relativity. The development of theoretical

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 physics shows, however, that we cannot pursue this course. The epoch-making theoretical investigations of H. A. Lorentz on the electrodynamical and optical phenomena connected with moving bodies show that experience in this domain leads conclusively to a theory of electromagnetic phenomena, of which the law of the constancy of the velocity of light in vacuo is a necessary consequence. Prominent theoretical physicists were therefore more inclined to reject the principle of relativity, in spite of the fact that no empirical data had been found which were contradictory to this principle.

At this juncture the theory of relativity entered the arena. As a result of an analysis of the physical conceptions of time and space, it became evident that in reality there is not the least incompatibility between the principle of relativity and the law of propagation of light, and that by systematically holding fast to both these laws a logically rigid theory could be arrived at. This theory has been called the special theory of relativity to distinguish it from the extended theory, with which we shall deal later. In the following pages we shall present the fundamental ideas of the special theory of relativity.

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IGHTNING has struck the rails on our railway embankment at two places $$A$$ and $$B$$ far distant from each other. I make the additional assertion that these two lightning flashes occurred simultaneously. If I ask you whether there is sense in this statement, you will answer my question with a decided “Yes.” But if I now approach you with the request to explain to me the sense of the statement more precisely, you find after some consideration that the answer to this question is not so easy as it appears at first sight.

After some time perhaps the following answer would occur to you: “The significance of the statement is clear in itself and needs no further explanation; of course it would require some consideration if I were to be commissioned to determine by observations whether in the actual case the two events took place simultaneously or not.” I cannot be satisfied with this answer for the following reason. Supposing that as a result of ingenious considerations an able meteorologist were to dis-

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 cover that the lightning must always strike the places $$A$$ and $$B$$ simultaneously, then we should be faced with the task of testing whether or not this theoretical result is in accordance with the reality. We encounter the same difficulty with all physical statements in which the conception “simultaneous” plays a part. The concept does not exist for the physicist until he has the possibility of discovering whether or not it is fulfilled in an actual case. We thus require a definition of simultaneity such that this definition supplies us with the method by means of which, in the present case, he can decide by experiment whether or not both the lightning strokes occurred simultaneously. As long as this requirement is not satisfied, I allow myself to be deceived as a physicist (and of course the same applies if I am not a physicist), when I imagine that I am able to attach a meaning to the statement of simultaneity. (I would ask the reader not to proceed farther until he is fully convinced on this point.)

After thinking the matter over for some time you then offer the following suggestion with which to test simultaneity. By measuring along the rails, the connecting line $$AB$$ should be measured up and an observer placed at the mid-point $$M$$ of the distance $$AB$$. This observer should be supplied with an arrangement (e.g. two mirrors inclined at 90°) which allows him visually to ob-

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 serve both places $$A$$ and $$B$$ at the same time. If the observer perceives the two flashes of lightning at the same time, then they are simultaneous.

I am very pleased with this suggestion, but for all that I cannot regard the matter as quite settled, because I feel constrained to raise the following objection: “Your definition would certainly be right, if I only knew that the light by means of which the observer at $$M$$ perceives the lightning flashes travels along the length $$A \longrightarrow M$$ with the same velocity as along the length $$B \longrightarrow M$$. But an examination of this supposition would only be possible if we already had at our disposal the means of measuring time. It would thus appear as though we were moving here in a logical circle.”

After further consideration you cast a somewhat disdainful glance at me—and rightly so—and you declare: “I maintain my previous definition nevertheless, because in reality it assumes absolutely nothing about light. There is only one demand to be made of the definition of simultaneity, namely, that in every real case it must supply us with an empirical decision as to whether or not the conception that has to be defined is fulfilled. That my definition satisfies this demand is indisputable. That light requires the same time to traverse the path $$A \longrightarrow M$$ as for the path $$B \longrightarrow M$$ is in reality neither a supposition nor a hypothesis about the physical nature of light,

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 but a stipulation which I can make of my own freewill in order to arrive at a definition of simultaneity.”

It is clear that this definition can be used to give an exact meaning not only to two events, but to as many events as we care to choose, and independently of the positions of the scenes of the events with respect to the body of reference (here the railway embankment). We are thus led also to a definition of “time” in physics. For this purpose we suppose that clocks of identical construction are placed at the points $$A$$, $$B$$ and $$C$$ of the railway line (co-ordinate system), and that they are set in such a manner that the positions of their pointers are simultaneously (in the above sense) the same. Under these conditions we understand by the “time” of an event the reading (position of the hands) of that one of these clocks which is in the immediate vicinity (in space) of the event. In this manner a time-value is associated with every event which is essentially capable of observation.

This stipulation contains a further physical

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 hypothesis, the validity of which will hardly be doubted without empirical evidence to the contrary. It has been assumed that all these clocks go at the same rate if they are of identical construction. Stated more exactly: When two clocks arranged at rest in different places of a reference-body are set in such a manner that a particular position of the pointers of the one clock is simultaneous (in the above sense) with the same position of the pointers of the other clock, then identical “settings” are always simultaneous (in the sense of the above definition).

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P to now our considerations have been referred to a particular body of reference, which we have styled a “railway embankment.” We suppose a very long train travelling along the rails with the constant velocity $$v$$ and in the direction indicated in Fig. 1. People travelling in this train will with advantage use the train as a rigid reference-body (co-ordinate system); they regard all events in reference to

the train. Then every event which takes place along the line also takes place at a particular point of the train. Also the definition of simultaneity can be given relative to the train in exactly the same way as with respect to the embankment. As a natural consequence, however, the following question arises:

Are two events (e.g. the two strokes of lightning $$A$$ and $$B$$) which are simultaneous with reference to

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 the railway embankment also simultaneous relatively to the train? We shall show directly that the answer must be in the negative.

When we say that the lightning strokes $$A$$ and $$B$$ are simultaneous with respect to the embankment, we mean: the rays of light emitted at the places $$A$$ and $$B$$, where the lightning occurs, meet each other at the mid-point $$M$$ of the length $$A \longrightarrow B$$ of the embankment. But the events $$A$$ and $$B$$ also correspond to positions $$A$$ and $$B$$ on the train. Let $$M'$$ be the mid-point of the distance $$A \longrightarrow B$$ on the travelling train. Just when the flashes of lightning occur, this point $$M'$$ naturally coincides with the point $$M$$, but it moves towards the right in the diagram with the velocity $$v$$ of the train. If an observer sitting in the position $$M'$$ in the train did not possess this velocity, then he would remain permanently at $$M$$, and the light rays emitted by the flashes of lightning $$A$$ and $$B$$ would reach him simultaneously, i.e. they would meet just where he is situated. Now in reality (considered with reference to the railway embankment) he is hastening towards the beam of light coming from $$B$$, whilst he is riding on ahead of the beam of light coming from $$A$$. Hence the observer will see the beam of light emitted from $$B$$ earlier than he will see that emitted from $$A$$. Observers who take the railway train as their reference-body

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 must therefore come to the conclusion that the lightning flash $$B$$ took place earlier than the lightning flash $$A$$. We thus arrive at the important result:

Events which are simultaneous with reference to the embankment are not simultaneous with respect to the train, and vice versa (relativity of simultaneity). Every reference-body (co-ordinate system) has its own particular time; unless we are told the reference-body to which the statement of time refers, there is no meaning in a statement of the time of an event.

Now before the advent of the theory of relativity it had always tacitly been assumed in physics that the statement of time had an absolute significance, i.e. that it is independent of the state of motion of the body of reference. But we have just seen that this assumption is incompatible with the most natural definition of simultaneity; if we discard this assumption, then the conflict between the law of the propagation of light in vacuo and the principle of relativity (developed in Section VII) disappears.

We were led to that conflict by the considerations of Section VI, which are now no longer tenable. In that section we concluded that the man in the carriage, who traverses the distance $$w$$ per second relative to the carriage, traverses the same distance also with respect to the embank-

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 ment in each second of time. But, according to the foregoing considerations, the time required by a particular occurrence with respect to the carriage must not be considered equal to the duration of the same occurrence as judged from the embankment (as reference-body). Hence it cannot be contended that the man in walking travels the distance $$w$$ relative to the railway line in a time which is equal to one second as judged from the embankment.

Moreover, the considerations of Section VI are based on yet a second assumption, which, in the light of a strict consideration, appears to be arbitrary, although it was always tacitly made even before the introduction of the theory of relativity.

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Rh dern Greenlanders, as they entertain no Correpondence with thoe Parts; either being hindered by the Ice, which renders them altogether inacceible; or ele for fear the Inhabitants of that Country might kill and devour them; for they repreent them as a cruel, barbarous and inhuman Nation, that detroy and eat all Foreigners that fall into their Hands. Yet this notwithtanding, if we may believe the Relation of thoe Adventurers, who have coated a great Part of the Eatern Shore; there is no other fort of Inhabitants found on this, than on the Wetern Side. But how it comes to pas, that the Eatern Ditrict, which was o well ettled with Norway and Iceland Colonies, that it contained 12 large Parihes, and 190 Villages, beides one Bihop's See and two Convents, and flourihed till the Year 1540; at lat has been detroyed and laid wate, is what I can't conceive. That ome are of Opinion, that the black Plague, o call'd, which ravaged the Northern Countries in the Year 1348, alo reach'd Greenland, and made its Havock among its Rh

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ET us consider two particular points on the train travelling along the embankment with the velocity $$v$$, and inquire as to their distance apart. We already know that it is necessary to have a body of reference for the measurement of a distance, with respect to which body the distance can be measured up. It is the simplest plan to use the train itself as the reference-body (co-ordinate system). An observer in the train measures the interval by marking off his measuring-rod in a straight line (e.g. along the floor of the carriage) as many times as is necessary to take him from the one marked point to the other. Then the number which tells us how often the rod has to be laid down is the required distance.

It is a different matter when the distance has to be judged from the railway line. Here the following method suggests itself. If we call $$A'$$ and $$B'$$ the two points on the train whose distance apart is required, then both of these points are

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 moving with the velocity $$v$$ along the embankment. In the first place we require to determine the points $$A$$ and $$B$$ of the embankment which are just being passed by the two points $$A'$$ and $$B'$$ at a particular time $$t$$—judged from the embankment. These points $$A$$ and $$B$$ of the embankment can be determined by applying the definition of time given in Section VIII. The distance between these points $$A$$ and $$B$$ is then measured by repeated application of the measuring-rod along the embankment.

A priori it is by no means certain that this last measurement will supply us with the same result as the first. Thus the length of the train as measured from the embankment may be different from that obtained by measuring in the train itself. This circumstance leads us to a second objection which must be raised against the apparently obvious consideration of Section VI. Namely, if the man in the carriage covers the distance $$w$$ in a unit of time—measured from the train,—then this distance—as measured from the embankment—is not necessarily also equal to $$w$$.

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HE results of the last three sections show that the apparent incompatibility of the law of propagation of light with the principle of relativity (Section VII) has been derived by means of a consideration which borrowed two unjustifiable hypotheses from classical mechanics; these are as follows:

(1) The time-interval (time) between two events is independent of the condition of motion of the body of reference.

(2) The space-interval (distance) between two points of a rigid body is independent of the condition of motion of the body of reference.

If we drop these hypotheses, then the dilemma of Section VII disappears, because the theorem of the addition of velocities derived in Section VI becomes invalid. The possibility presents itself that the law of the propagation of light in vacuo may be compatible with the principle of relativity, and the question arises: How have we to modify the considerations of Section VI in order to remove

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 the apparent disagreement between these two fundamental results of experience? This question leads to a general one. In the discussion of Section VI we have to do with places and times relative both to the train and to the embankment. How are we to find the place and time of an event in relation to the train, when we know the place and time of the event with respect to the railway embankment? Is there a thinkable answer to this question of such a nature that the law of transmission of light in vacuo does not contradict the principle of relativity? In other words: Can we conceive of a relation between place and time of the individual events relative to both reference-bodies, such that every ray of light possesses the velocity of transmission $$c$$ relative to the embankment and relative to the train? This question leads to a quite definite positive answer, and to a perfectly definite transformation law for the spacetime magnitudes of an event when changing over from one body of reference to another.

Before we deal with this, we shall introduce the following incidental consideration. Up to the present we have only considered events taking place along the embankment, which had mathematically to assume the function of a straight line. In the manner indicated in Section II we can imagine this reference-body supplemented laterally and in a vertical direction by means of a

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 framework of rods, so that an event which takes place anywhere can be localised with reference to this framework. Similarly, we can imagine the train travelling with the velocity $$v$$ to be continued across the whole of space, so that every event, no matter how far off it may be, could also be localised with respect to the second framework. Without committing any fundamental error, we can disregard the fact that in reality these frameworks would continually interfere with each other, owing to the impenetrability of solid bodies. In every such framework we imagine three surfaces perpendicular to each other marked out, and designated as ‘‘co-ordinate planes” (‘‘co-ordinate system”). A co-ordinate system $$K$$ then corresponds to the embankment, and a co-ordinate system $$K'$$ to the train. An event, wherever it may have taken place, would be fixed in space with respect to $$K$$ by the three perpendiculars $$x$$, $$y$$, $$z$$ on the co-ordinate planes, and with regard to time by a time-value $$t$$. Relative to $$K'$$, the same event would be fixed in respect of space and time by corresponding values $$x'$$, $$y'$$, $$z'$$, $$t'$$, which of course are not identical with $$x$$, $$y$$, $$z$$, $$t$$. It has already been set forth in detail how these magnitudes are to be regarded as results of physical measurements.

Obviously our problem can be exactly formulated in the following manner. What are the

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 values $$x'$$, $$y'$$, $$z'$$, $$t'$$ of an event with respect to $$K'$$, when the magnitudes $$x$$, $$y$$, $$z$$, $$t$$, of the same event with respect to $$K$$ are given? The relations must be so chosen that the law of the transmission of light in vacuo is satisfied for one and the same ray of light (and of course for every ray) with respect to $$K$$ and $$K'$$. For the relative orientation in space of the co-ordinate systems indicated in the diagram (Fig. 2), this problem is solved by means of the equations:

$$\begin{align} x' & = \frac{x - vt}{\sqrt{1 - \frac{v^2}{c^2}}} \\ y' & = y \\ z' & = z \\ t' & = \frac{t - \frac{v}{c^2} \cdot x}{\sqrt{1 - \frac{v^2}{c^2}}} \end{align}$$

This system of equations is known as the “Lorentz transformation.”

If in place of the law of transmission of light we had taken as our basis the tacit assumptions of the older mechanics as to the absolute character

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 of times and lengths, then instead of the above we should have obtained the following equations:

$$\begin{align} x' & = x - vt \\ y' & = y \\ z' & = z \\ t' & = t \end{align}$$

This system of equations is often termed the “Galilei transformation.” The Galilei transformation can be obtained from the Lorentz transformation by substituting an infinitely large value for the velocity of light $$c$$ in the latter transformation.

Aided by the following illustration, we can readily see that, in accordance with the Lorentz transformation, the law of the transmission of light in vacuo is satisfied both for the reference-body $$K$$ and for the reference-body $$K'$$. A light-signal is sent along the positive x-axis, and this light-stimulus advances in accordance with the equation

i.e. with the velocity $$c$$. According to the equations of the Lorentz transformation, this simple relation between $$x$$ and $$t$$ involves a relation between $$x'$$ and $$t'$$. In point of fact, if we substitute for $$x$$ the value $$ct$$ in the first and fourth equations of the Lorentz transformation, we obtain:

$$\begin{align} x' & = \frac{(c - v)t}{\sqrt{1 - \frac{v^2}{c^2}}} \\ t' & = \frac{\left ( 1 - \frac{v}{c} \right ) t}{\sqrt{1 - \frac{v^2}{c^2}}} \end{align}$$

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from which, by division, the expression

immediately follows. If referred to the system $$K'$$, the propagation of light takes place according to this equation. We thus see that the velocity of transmission relative to the reference-body $$K'$$ is also equal to $$c$$. The same result is obtained for rays of light advancing in any other direction whatsoever. Of course this is not surprising, since the equations of the Lorentz transformation were derived conformably to this point of view.

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PLACE a metre-rod in the $$x'$$-axis of $$K'$$ in such a manner that one end (the beginning) coincides with the point $$x' = 0$$, whilst the other end (the end of the rod) coincides with the point $$x' = 1$$. What is the length of the metre-rod relatively to the system $$K$$? In order to learn this, we need only ask where the beginning of the rod and the end of the rod lie with respect to $$K$$ at a particular time $$t$$ of the system $$K$$. By means of the first equation of the Lorentz transformation the values of these two points at the time $$t = 0$$ can be shown to be

$$\begin{align} x_{\mathrm{(beginning\ of\ rod)}} & = 0 \cdot \sqrt{1 - \frac{v^2}{c^2}} \\ x_{\mathrm{(end\ of\ rod)}} & = 1 \cdot \sqrt{1 - \frac{v^2}{c^2}}\mathrm{,} \end{align}$$

the distance between the points being $$\sqrt{1 - \frac{v^2}{c^2}}$$.

But the metre-rod is moving with the velocity $$v$$ relative to $$K$$. It therefore follows that the length of a rigid metre-rod moving in the direction of its length with a velocity $$v$$ is $$\sqrt{1 - \tfrac{v^2}{c^2}}$$ of a metre. The rigid rod is thus shorter when in motion than

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 when at rest, and the more quickly it is moving, the shorter is the rod. For the velocity $$v = c$$ we should have $$\sqrt{1 - \tfrac{v^2}{c^2}} = 0$$, and for still greater velocities the square-root becomes imaginary. From this we conclude that in the theory of relativity the velocity $$c$$ plays the part of a limiting velocity, which can neither be reached nor exceeded by any real body.

Of course this feature of the velocity $$c$$ as a limiting velocity also clearly follows from the equations of the Lorentz transformation, for these become meaningless if we choose values of $$v$$ greater than $$c$$.

If, on the contrary, we had considered a metre-rod at rest in the $$x$$-axis with respect to $$K$$, then we should have found that the length of the rod as judged from $$K'$$ would have been $$\sqrt{1 - \tfrac{v^2}{c^2}}$$; this is quite in accordance with the principle of relativity which forms the basis of our considerations.

A priori it is quite clear that we must be able to learn something about the physical behaviour of measuring-rods and clocks from the equations of transformation, for the magnitudes $$x$$, $$y$$, $$z$$, $$t$$, are nothing more nor less than the results of measurements obtainable by means of measuring-rods and clocks. If we had based our considerations on the Galilei transformation we should not have obtained a contraction of the rod as a consequence of its motion.

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 facts as they are, but rather according to the names by which they are called. The current estimate of Rabbinic Literature is a case in point. With the label Rabbinic later ages inherited from former ages a certain distorted view of the literature so designated. To this day, and even among scholars that approach its investigation with unprejudiced minds, the opinion prevails that it is purely a learned product. And yet the truth is that the most prominent feature of Rabbinic Literature is its popular character.

The school and the home are not mutually opposed to each other in the conception of the Jews. They study in their homes, and they live in their schools. Likewise there is no distinct class of scholars among them, a class that withdraws itself from participation in the affairs of practical life. Even in the domain of the Halakah, the Rabbis were not so much occupied with theoretic principles of law as with the concrete phenomena of daily existence. These they sought to grasp and shape. And what is true of the Halakah is true with greater emphasis of the Haggadah, which is popular in the double sense of appealing to the people and being produced in the main by the people. To speak of the Haggadah of the Tannaim and Amoraim is as far from fact as to speak of the legends of Shakespear and Scott. The ancient authors and their modern brethren of the guild alike elaborate legendary material which they found at hand.

It has been held by some that the Haggadah contains no popular legends, that it is wholly a factitious, academic product. A cursory glance at the pseudepigraphic literature of the Jews, which is older than the Haggadah literature by several centuries, shows how untenable this


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 Let us now consider a seconds-clock which is permanently situated at the origin $$(x' = 0)$$ of $$K'$$. $$t' = 0$$ and $$t' = 1$$ are two successive ticks of this clock. The first and fourth equations of the Lorentz transformation give for these two ticks:

and

$$t = \frac{1}{\sqrt{1 - \frac{v^2}{c^2}}}$$

As judged from $$K$$, the clock is moving with the velocity $$v$$; as judged from this reference-body, the time which elapses between two strokes of the clock is not one second, but $$\frac{1}{\sqrt{1 - \frac{v^2}{c^2}}}$$ seconds, i.e. a somewhat larger time. As a consequence of its motion the clock goes more slowly than when at rest. Here also the velocity $$c$$ plays the part of an unattainable limiting velocity.

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OW in practice we can move clocks and measuring-rods only with velocities that are small compared with the velocity of light; hence we shall hardly be able to compare the results of the previous section directly with the reality. But, on the other hand, these results must strike you as being very singular, and for that reason I shall now draw another conclusion from the theory, one which can easily be derived from the foregoing considerations, and which has been most elegantly confirmed by experiment.

In Section VI we derived the theorem of the addition of velocities in one direction in the form which also results from the hypotheses of classical mechanics. This theorem can also be deduced readily from the Galilei transformation (Section XI). In place of the man walking inside the carriage, we introduce a point moving relatively to the co-ordinate system $$K'$$ in accordance with the equation

By means of the first and fourth equations of the

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 Galilei transformation we can express $$x'$$ and $$t'$$ in terms of $$x$$ and $$t$$, and we then obtain

This equation expresses nothing else than the law of motion of the point with reference to the system $$K$$ (of the man with reference to the embankment). We denote this velocity by the symbol $$W$$, and we then obtain, as in Section VI,

But we can carry out this consideration just as well on the basis of the theory of relativity. In the equation

we must then express $$x'$$ and $$t'$$ in terms of $$x$$and $$t$$, making use of the first and fourth equations of the Lorentz transformation. Instead of the equation (A) we then obtain the equation

which corresponds to the theorem of addition for velocities in one direction according to the theory of relativity. The question now arises as to which of these two theorems is the better in accord with experience. On this point we are enlightened by a most important experiment which the brilliant physicist Fizeau performed more than half a century ago, and which has been repeated since

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 then by some of the best experimental physicists, so that there can be no doubt about its result. The experiment is concerned with the following question. Light travels in a motionless liquid with a particular velocity $$w$$. How quickly does it travel in the direction of the arrow in the tube $$T$$ (see the accompanying diagram, Fig. 3) when the liquid above mentioned is flowing through the tube with a velocity $$v$$?

In accordance with the principle of relativity we shall certainly have to take for granted that the propagation of light always takes place with the same velocity $$w$$ with respect to the liquid, whether the latter is in motion with reference to other bodies or not. The velocity of light relative to the liquid and the velocity of the latter relative to the tube are thus known, and we require the velocity of light relative to the tube.

It is clear that we have the problem of Section VI again before us. The tube plays the part of

the railway embankment or of the co-ordinate system $$K$$, the liquid plays the part of the carriage or of the co-ordinate system $$K'$$, and finally, the light plays the part of the man walking along the carriage, or of the moving point in the present

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 section. If we denote the velocity of the light relative to the tube by $$W$$, then this is given by the equation (A) or (B), according as the Galilei transformation or the Lorentz transformation corresponds to the facts. Experiment decides in favour of equation (B) derived from the theory of relativity, and the agreement is, indeed, very exact. According to recent and most excellent measurements by Zeeman, the influence of the velocity of flow $$v$$ on the propagation of light is represented by formula (B) to within one per cent.

Nevertheless we must now draw attention to the fact that a theory of this phenomenon was given by H. A. Lorentz long before the statement of the theory of relativity. This theory was of a purely electrodynamical nature, and was obtained by the use of particular hypotheses as to the electromagnetic structure of matter. This circumstance, however, does not in the least diminish the conclusiveness of the experiment as a crucial test in favour of the theory of relativity, for the

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 electrodynamics of Maxwell-Lorentz, on which the original theory was based, in no way opposes the theory of relativity. Rather has the latter been developed from electrodynamics as an astoundingly simple combination and generalisation of the hypotheses, formerly independent of each other, on which electrodynamics was built.

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text: Author:John Neilson (d. 1819)

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UR train of thought in the foregoing pages can be epitomised in the following manner.

Experience has led to the conviction that, on the one hand, the principle of relativity holds true, and that on the other hand the velocity of transmission of light in vacuo has to be considered equal to a constant $$c$$. By uniting these two postulates we obtained the law of transformation for the rectangular co-ordinates $$x$$, $$y$$, $$z$$ and the time $$t$$ of the events which constitute the processes of nature. In this connection we did not obtain the Galilei transformation, but, differing from classical mechanics, the Lorentz transformation.

The law of transmission of light, the acceptance of which is justified by our actual knowledge, played an important part in this process of thought. Once in possession of the Lorentz transformation, however, we can combine this with the principle of relativity, and sum up the theory thus:

Every general law of nature must be so constituted that it is transformed into a law of exactly the same form when, instead of the space

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 time variables $$x$$, $$y$$, $$z$$, $$t$$ of the original co-ordinate system $$K$$, we introduce new space-time variables $$x'$$, $$y'$$, $$z'$$, of a co-ordinate system $$K'$$. In this connection the relation between the ordinary and the accented magnitudes is given by the Lorentz transformation. Or, in brief: General laws of nature are co-variant with respect to Lorentz transformations.

This is a definite mathematical condition that the theory of relativity demands of a natural law, and in virtue of this, the theory becomes a valuable heuristic aid in the search for general laws of nature. Ifa general law of nature were to be found which did not satisfy this condition, then at least one of the two fundamental assumptions of the theory would have been disproved. Let us now examine what general results the latter theory has hitherto evinced.

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T is clear from our previous considerations that the (special) theory of relativity has grown out of electrodynamics and optics. In these fields it has not appreciably altered the predictions of theory, but it has considerably simplified the theoretical structure, i.e. the derivation of laws, and—what is incomparably more important—it has considerably reduced the number of independent hypotheses forming the basis of theory. The special theory of relativity has rendered the Maxwell-Lorentz theory so plausible, that the latter would have been generally accepted by physicists even if experiment had decided less unequivocally in its favour.

Classical mechanics required to be modified before it could come into line with the demands of the special theory of relativity. For the main part, however, this modification affects only the laws for rapid motions, in which the velocities of matter v are not very small as compared with the velocity of light. We have experience of such rapid motions only in the case of electrons and

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 ions; for other motions the variations from the laws of classical mechanics are too small to make themselves evident in practice. We shall not consider the motion of stars until we come to speak of the general theory of relativity. In accordance with the theory of relativity the kinetic energy of a material point of mass $$m$$ is no longer given by the well-known expression

but by the expression

This expression approaches infinity as the velocity $$v$$ approaches the velocity of light $$c$$. The velocity must therefore always remain less than $$c$$, however great may be the energies used to produce the acceleration. If we develop the expression for the kinetic energy in the form of a series, we obtain

When $$\tfrac{v^2}{c^2}$$ small compared with unity, the third of these terms is always small in comparison with the second, which last is alone considered in classical mechanics. The first term $$mc2$$ does not contain the velocity, and requires no consideration if we

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 are only dealing with the question as to how the energy of a point-mass depends on the velocity. We shall speak of its essential significance later.

The most important result of a general character to which the special theory of relativity has led is concerned with the conception of mass. Before the advent of relativity, physics recognised two conservation laws of fundamental importance, namely, the law of the conservation of energy and the law of the conservation of mass; these two fundamental laws appeared to be quite independent of each other. By means of the theory of relativity they have been united into one law. We shall now briefly consider how this unification came about, and what meaning is to be attached to it.

The principle of relativity requires that the law of the conservation of energy should hold not only with reference to a co-ordinate system $$K$$, but also with respect to every co-ordinate system $$K'$$ which is in a state of uniform motion of translation relative to $$K$$, or, briefly, relative to every “Galileian” system of co-ordinates. In contrast to classical mechanics, the Lorentz transformation is the deciding factor in the transition from one such system to another.

By means of comparatively simple considerations we are led to draw the following conclusion from these premises, in conjunction with the

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 fundamental equations of the electrodynamics of Maxwell: A body moving with the velocity $$v$$, which absorbs an amount of energy $$E_0$$ in the form of radiation without suffering an alteration in velocity in the process, has, as a consequence, its energy increased by an amount

In consideration of the expression given above for the kinetic energy of the body, the required energy of the body comes out to be

Thus the body has the same energy as a body of mass $$\left ( m + \tfrac{E_0}{c^2} \right )$$ moving with the velocity $$v$$. Hence we can say: If a body takes up an amount of energy $$E_0$$, then its inertial mass increases by an amount $$\tfrac{E_0}{c^2}$$; the inertial mass of a body is not a constant, but varies according to the change in the energy of the body. The inertial mass of a system of bodies can even be regarded as a measure

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 of its energy. The law of the conservation of the mass of a system becomes identical with the law of the conservation of energy, and is only valid provided that the system neither takes up nor sends out energy. Writing the expression for the energy in the form

we see that the term $$mc^2$$, which has hitherto attracted our attention, is nothing else than the energy possessed by the body before it absorbed the energy $$E_0$$. A direct comparison of this relation with experiment is not possible at the present time, owing to the fact that the changes in energy $$E_0$$, to which we can subject a system are not large enough to make themselves perceptible as a change in the inertial mass of the system. $$\tfrac{E_0}{c^2}$$is too small in comparison with the mass $$m$$, which was present before the alteration of the energy. It is owing to this circumstance that classical mechanics was able to establish successfully the conservation of mass as a law of independent validity.

Let me add a final remark of a fundamental nature. The success of the Faraday-Maxwell

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 interpretation of electromagnetic action at a distance resulted in physicists becoming convinced that there are no such things as instantaneous actions at a distance (not involving an intermediary medium) of the type of Newton’s law of gravitation. According to the theory of relativity, action at a distance with the velocity of light always takes the place of instantaneous action at a distance or of action at a distance with an infinite velocity of transmission. This is connected with the fact that the velocity $$c$$ plays a fundamental rôle in this theory. In Part II we shall see in what way this result becomes modified in the general theory of relativity.

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O what extent is the special theory of relativity supported by experience? This question is not easily answered for the reason already mentioned in connection with the fundamental experiment of Fizeau. The special theory of relativity has crystallised out from the Maxwell-Lorentz theory of electromagnetic phenomena. Thus all facts of experience which support the electromagnetic theory also support the theory of relativity. As being of particular importance, I mention here the fact that the theory of relativity enables us to predict the effects produced on the light reaching us from the fixed stars. These results are obtained in an exceedingly simple manner, and the effects indicated, which are due to the relative motion of the earth with reference to those fixed stars, are found to be in accord with experience. We refer to the yearly movement of the apparent position of the fixed stars resulting from the motion of the earth round the sun (aberration), and to the influence of the radial

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 components of the relative motions of the fixed stars with respect to the earth on the colour of the light reaching us from them. The latter effect manifests itself in a slight displacement of the spectral lines of the light transmitted to us from a fixed star, as compared with the position of the same spectral lines when they are produced by a terrestrial source of light ( principle). The experimental arguments in favour of the Maxwell-Lorentz theory, which are at the same time arguments in favour of the theory of relativity, are too numerous to be set forth here. In reality they limit the theoretical possibilities to such an extent, that no other theory than that of Maxwell and Lorentz has been able to hold its own when tested by experience.

But there are two classes of experimental facts hitherto obtained which can be represented in the Maxwell-Lorentz theory only by the introduction of an auxiliary hypothesis, which in itself—i.e. without making use of the theory of relativity—appears extraneous.

It is known that cathode rays and the so-called $$\beta$$-rays emitted by radioactive substances consist of negatively electrified particles (electrons) of very small inertia and large velocity. By examining the deflection of these rays under the influence of electric and magnetic fields, we can study the law of motion of these particles very exactly.

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 In the theoretical treatment of these electrons, we are faced with the difficulty that electrodynamic theory of itself is unable to give an account of their nature. For since electrical masses of one sign repel each other, the negative electrical masses constituting the electron would necessarily be scattered under the influence of their mutual repulsions, unless there are forces of another kind operating between them, the nature of which has hitherto remained obscure to us. If we now assume that the relative distances between the electrical masses constituting the electron remain unchanged during the motion of the electron (rigid connection in the sense of classical mechanics), we arrive at a law of motion of the electron which does not agree with experience. Guided by purely formal points of view, H. A. Lorentz was the first to introduce the hypothesis that the particles constituting the electron experience a contraction in the direction of motion in consequence of that motion, the amount of this contraction being proportional to the expression $$\sqrt{1 = \tfrac{v^2}{c^2}}$$. This hypothesis, which is not justifiable by any electrodynamical facts, supplies us then with that particular law of motion which has been confirmed with great precision in recent years.

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 The theory of relativity leads to the same law of motion, without requiring any special hypothesis whatsoever as to the structure and the behaviour of the electron. We arrived at a similar conclusion in Section XIII in connection with the experiment of Fizeau, the result of which is foretold by the theory of relativity without the necessity of drawing on hypotheses as to the physical nature of the liquid.

The second class of facts to which we have alluded has reference to the question whether or not the motion of the earth in space can be made perceptible in terrestrial experiments. We have already remarked in Section V that all attempts of this nature led to a negative result. Before the theory of relativity was put forward, it was dificult to become reconciled to this negative result, for reasons now to be discussed. The inherited prejudices about time and space did not allow any doubt to arise as to the prime importance of the Galilei transformation for changing over from one body of reference to another. Now assuming that the Maxwell-Lorentz equations hold for a reference-body $$K$$, we then find that they do not hold for a reference-body $$K'$$ moving uniformly with respect to $$K$$, if we assume that the relations of the Galileian transformation exist between the co-ordinates of $$K$$ and $$K'$$. It thus appears that of all Galileian co-ordinate

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 systems one ($$K$$) corresponding to a particular state of motion is physically unique. This result was interpreted physically by regarding $$K$$ as at rest with respect to a hypothetical æther of space. On the other hand, all co-ordinate systems $$K'$$ moving relatively to $$K$$ were to be regarded as in motion with respect to the æther. To this motion of $$K'$$ against the æther (“æther-drift” relative to $$K'$$) were assigned the more complicated laws which were supposed to hold relative to $$K'$$. Strictly speaking, such an æther-drift ought also to be assumed relative to the earth, and for a long time the efforts of physicists were devoted to attempts to detect the existence of an æther-drift at the earth’s surface.

In one of the most notable of these attempts Michelson devised a method which appears as though it must be decisive. Imagine two mirrors so arranged on a rigid body that the reflecting surfaces face each other. A ray of light requires a perfectly definite time $$T$$ to pass from one mirror to the other and back again, if the whole system be at rest with respect to the æther. It is found by calculation, however, that a slightly different time $$T'$$ is required for this process, if the body, together with the mirrors, be moving relatively to the æther. And yet another point: it is shown by calculation that for a given velocity $$v$$ with reference to the æther, this time $$T'$$ is different

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 when the body is moving perpendicularly to the planes of the mirrors from that resulting when the motion is parallel to these planes. Although the estimated difference between these two times is exceedingly small, Michelson and Morley performed an experiment involving interference in which this difference should have been clearly detectable. But the experiment gave a negative result—a fact very perplexing to physicists. Lorentz and FitzGerald rescued the theory from this difficulty by assuming that the motion of the body relative to the ether produces a contraction of the body in the direction of motion, the amount of contraction being just sufficient to compensate for the difference in time mentioned above. Comparison with the discussion in Section XII shows that also from the standpoint of the theory of relativity this solution of the difficulty was the right one. But on the basis of the theory of relativity the method of interpretation is incomparably more satisfactory. According to this theory there is no such thing as a “specially favoured” (unique) co-ordinate system to occasion the introduction of the ether-idea, and hence there can be no ether-drift, nor any experiment with which to demonstrate it. Here the contraction of moving bodies follows from the two fundamental principles of the theory without the introduction of particular hypotheses; and as the

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 prime factor involved in this contraction we find, not the motion in itself, to which we cannot attach any meaning, but the motion with respect to the body of reference chosen in the particular case in point. Thus for a co-ordinate system moving with the earth the mirror system of Michelson and Morley is not shortened, but it is shortened for a co-ordinate system which is at rest relatively to the sun.

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he non-mathematician is seized by a mysterious shuddering when he hears of “four-dimensional” things, by a feeling not unlike that awakened by thoughts of the occult. And yet there is no more common-place statement than that the world in which we live is a four-dimensional space-time continuum.

Space is a three-dimensional continuum. By this we mean that it is possible to describe the position of a point (at rest) by means of three numbers (co-ordinates) $$x$$, $$y$$, $$z$$, and that there is an indefinite number of points in the neighbourhood of this one, the position of which can be described by co-ordinates such as $$x_1$$, $$y_1$$, $$z_1$$, which may be as near as we choose to the respective values of the co-ordinates $$x$$, $$y$$, $$z$$ of the first point. In virtue of the latter property we speak of a “continuum,” and owing to the fact that there are three co-ordinates we speak of it as being “three-dimensional.”

Similarly, the world of physical phenomena which was briefly called “world” by Minkowski

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 is naturally four-dimensional in the space-time sense. For it is composed of individual events, each of which is described by four numbers, namely, three space co-ordinates $$x$$, $$y$$, $$z$$ and a time co-ordinate, the time-value $$t$$. The “world” is in this sense also a continuum; for to every event there are as many ‘‘neighbouring” events (realised or at least thinkable) as we care to choose, the co-ordinates $$x_1$$, $$y_1$$, $$z_1$$, $$t_1$$ of which differ by an indefinitely small amount from those of the event $$x$$, $$y$$, $$z$$, $$t$$ originally considered. That we have not been accustomed to regard the world in this sense as a four-dimensional continuum is due to the fact that in physics, before the advent of the theory of relativity, time played a different and more independent rôle, as compared with the space co-ordinates. It is for this reason that we have been in the habit of treating time as an independent continuum. As a matter of fact, according to classical mechanics, time is absolute, i.e. it is independent of the position and the condition of motion of the system of co-ordinates. We see this expressed in the last equation of the Galileian transformation $$( t' = t )$$.

The four-dimensional mode of consideration of the “world” is natural on the theory of relativity, since according to this theory time is robbed of its independence. This is shown by the fourth equation of the Lorentz transformation:

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Moreover, according to this equation the time difference $$\Delta t'$$ of two events with respect to $$K'$$ does not in general vanish, even when the time difference $$\Delta t$$ of the same events with reference to $$K$$ vanishes. Pure “space-distance” of two events with respect to $$K$$ results in “time-distance” of the same events with respect to $$K'$$. But the discovery of Minkowski, which was of importance for the formal development of the theory of relativity, does not lie here. It is to be found rather in the fact of his recognition that the four-dimensional space-time continuum of the theory of relativity, in its most essential formal properties, shows a pronounced relationship to the three-dimensional continuum of Euclidean geometrical space. In order to give due prominence to this relationship, however, we must replace the usual time co-ordinate $$t$$ by an imaginary magnitude $$\sqrt{-1}$$. $$ct$$ proportional to it. Under these conditions, the natural laws satisfying the demands of the (special) theory of relativity assume mathematical forms, in which the time co-ordinate plays exactly the same rôle as the three space co-ordinates. Formally, these four co-ordinates

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 correspond exactly to the three space co-ordinates in Euclidean geometry. It must be clear even to the non-mathematician that, as a consequence of this purely formal addition to our knowledge, the theory perforce gained clearness in no mean measure.

These inadequate remarks can give the reader only a vague notion of the important idea contributed by Minkowski. Without it the general theory of relativity, of which the fundamental ideas are developed in the following pages, would perhaps have got no farther than its long clothes. Minkowski’s work is doubtless difficult of access to anyone inexperienced in mathematics, but since it is not necessary to have a very exact grasp of this work in order to understand the fundamental ideas of either the special or the general theory of relativity, I shall at present leave it here, and shall revert to it only towards the end of Part II.

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 view is. That the one literature should have drawn from the other is precluded by historical facts. At a very early time the Synagogue disavowed the pseudepigraphic literature, which was the favorite reading matter of the sectaries and the Christians. Nevertheless the inner relation between them is of the closest kind. The only essential difference is that the Midrashic form prevails in the Haggadah, and the parenetic or apocalyptic form in the pseudepigrapha. The common element must therefore depart from the Midrash on the one hand and from parenesis on the other.

Folklore, fairy tales, legends, and all forms of story telling akin to these are comprehended, in the terminology of the post-Biblical literature of the Jews, under the inclusive description Haggadah, a name that can be explained by a circumlocution, but cannot be translated. Whatever it is applied to is thereby characterized first as being derived from the Holy Scriptures, and then as being of the nature of a story. And, in point of fact, this dualism sums up the distinguishing features of Jewish Legend. More than eighteen centuries ago the Jewish historian Josephus observed that "though we be deprived of our wealth, of our cities, or of the other advantages we have, our law continues immortal." The word he meant to use was not law, but Torah, only he could not find an equivalent for it in Greek. A singer of the Synagogue a thousand years after Josephus, who expressed his sentiments in Hebrew, uttered the same thought: "The Holy City and all her daughter cities are violated, they lie in ruins, despoiled of their ornaments, their splendor darkened from sight. Naught is left to us save one eternal treasure alone—the Holy Torah." The sadder the life of


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24 Eatern Colonies, is without [sic]aay Ground or Reaon; becaue the Commerce was carried into Greenland until the Year 1406; and in 1540 that Colony was till ubiting. If therefore this Ditrict be detitute or bereft of its old Inhabitants: 'tis not unlike, they have undergone the ame Fatality as the Wetern ones, being detroyed by the Barbarity of the Savage Schrellingers.

A whole Century paed from the Ceation of all Commerce and Navigation between Norway and Greenland, till new Adventurers began to apply themelves to the Dicovery of the Eatern Ditrict. The firt of thoe who took this Affair to Heart was Erick Walkendorff, of Drontheim, who was reolved, at his own Charge, to fit out Ships for this Purpoe, but was topt in this pious Deign by King Chritian the Second, whoe Digrace he had Chritian the Second, whoe Digrace he had incurr'd. The next was King Frederick the Firt, whoe Mind (as it is reported, was bent upon the aid Expedition, but was never

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 the Jewish people, the more it felt the need of taking refuge in its past. The Scripture, or, to use the Jewish term, the Torah, was the only remnant of its former national independence, and the Torah was the magic means of making a sordid actuality recede before a glorious memory. To the Scripture was assigned the task of supplying nourishment to the mind as well as the soul, to the intellect as well as the imagination, and the result is the Halakah and the Haggadah.

The fancy of the people did not die out in the post-Biblical time, but the bent of its activity was determined by the past. Men craved entertainment in later times as well as in the earlier, only instead of resorting for its subject-matter to what happened under their eyes, they drew from the fountain-head of the past. The events in the ancient history of Israel, which was not only studied, but lived over again daily, stimulated the desire to criticise it. The religious reflections upon nature laid down in the myths of the people, the fairy tales, which have the sole object of pleasing, and the legends, which are the people's verdict upon history—all these were welded into one product. The fancy of the Jewish people was engaged by the past reflected in the Bible, and all its creations wear a Biblical hue for this reason. This explains the peculiar form of the Haggadah.

But what is spontaneously brought forth by the people is often preserved only in the form impressed upon it by the feeling and the thought of the poet, or by the speculations of the learned. Also Jewish legends have rarely been transmitted in their original shape. They have been perpetuated in the form of Midrash, that is, Scriptural exegesis. The teachers of the Haggadah, called Rabbanan d'Aggadta in


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Rh never put in Execution. Chritian the Third, (as Lycander relates) ent everal Ships with the ame Deign, but without making any Dicovery. Frederick the IId ucceeded his Royal Father as well in the Government, as in his good Deign about Greenland; on which Errand he ent Mogens Heinon, a renowned Seaman in thoe Days. This Adventurer, after he had gone through many Difficulties and Dangers of Storms and Ice, got Sight of the Land, but could not approach it; whereupon he returned home again, and pretended, that he might have got on Shore, if his Ship had not been top't in the midt of its Coure by ome Loadtone Rocks hidden in the Sea, that he could not proceed, thoough he had a very favourable and trong Gale of Wind, and no Ice to hinder him; which frightened him and made him ail back again to Denmark. But the true Loadtone Rocks, in my Opinion, was the terrible Fright he was in of not getting afe through the dreadful Ice Mountains, which threatened him, or ele the trong Current, which always runs along the States

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 never been so much affected as on hearing Moore sing some of them, particularly "When I first met thee," which, he said, made him shed tears. "But," added he, with a look full of archness,"it was after I had drunk a certain portion of very potent white brandy." As he laid a peculiar stress on the word affected, I smiled, and the sequel of the white brandy made me smile again; he asked me the cause, and I answered that his observation reminded me of the story of a lady offering her condolence to a poor Irishwoman on the death of her child, who stated that she had never been more affected than on the event; the poor woman, knowing the hollowness of the compliment, answered, with all the quickness of her country, "Sure, then, ma'am, that is saying a great deal, for you were always affected." Lord Byron laughed, and said my apropos was very wicked, but I maintained it was very just. He spoke much more warmly of Moore's social attractions as a companion, which he said were unrivalled, than of his merits as a poet.

He offered to be our cicerone in pointing out all the pretty drives and rides about Genoa; recommended riding as the only means of seeing the country, many of the fine points of view being inaccessible, except on horseback; and he praised Genoa on account of the rare advantage


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 the Talmud, were no folklorists, from whom a faithful reproduction of legendary material may be expected. Primarily they were homilists, who used legends for didactic purposes, and their main object was to establish a close connection between the Scripture and the creations of the popular fancy, to give the latter a firm basis and secure a long term of life for them.

One of the most important tasks of the modern investigation of the Haggadah is to make a clean separation between the original elements and the later learned additions. Hardly a beginning has been made in this direction. But as long as the task of distinguishing them has not been accomplished, it is impossible to write out the Biblical legends of the Jews without including the supplemental work of scholars in the products of the popular fancy.

In the present work, "The Legends of the Jews," I have made the first attempt to gather from the original sources all Jewish legends, in so far as they refer to Biblical personages and events, and reproduce them with the greatest attainable completeness and accuracy. I use the expression Jewish, rather than Rabbinic, because the sources from which I have levied contributions are not limited to the Rabbinic literature. As I expect to take occasion elsewhere to enter into a description of the sources in detail, the following data must suffice for the present.

The works of the Talmudic-Midrashic literature are of the first importance. Covering the period from the second to the fourteenth century, they contain the major part of the Jewish legendary material. Akin to this in content if not always in form is that derived from the Targumim, of which


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26 States Promontory, with uch Violence and Rapidity, that it often tops a Ship under full Sail, o that the Ship can make but little or no Way at all againt it. The Caue by others aigned for this trange Effect is the Fih Remora, which the Northlanders call Kracken is nothing but a fabulous Story of the too credulous Antients, and labours under no les Aburdities than the former Opinion, that Rocks of Loadtone, laying on the Bottom of the Sea, can tay the Coure of a Ship that ails on the Surface of it.

In the ame Year that Mogens Heinon went upon the Greenland Dicovery, the Englih Hitories inform us, that Captain Martin Forbiher, an Englihman, was by the glorious Queen Elizabeth ent upon the ame Errand. This Adventurer got Sight of the Land, but being partly hindred by the Ice, which adhered to it, and partly by the Shortnes of the Winter Days (for it was late in the Year) he could not approach it, and o returned to England again. Next Year

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 PLEASE DO NOT REMOVE CARDS OR SLIPS FROM THIS POCKET

UNIVERSITY OF TORONTO LIBRARY

WGMTJND SAMUEL LIBRARY


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Rh Year in the Spring he went upon the ame Expedition with three Ships. After having gone through many great Dangers of the Ice and Storms, he at length reached the Shore, where he found a wild and avage Nation; who, when they aw the Englih coming to them, being frightened, left their Huts, and run away to hide themelves. Some from the highet Rocks, threw themelves into the Sea; whereupon the Englih entered their Huts, where they met with no body but an old Woman, and a young one big with Child, thoe they carried away with them. 'Tis alo reported, that they here found ome Sand, which contained Particles of Gold and Silver, of which they filled 300 Tuns, and brought it home with them to England. As to this Gold and Silver Sand, I can't help quetioning whether they found any uch on the Greenland Sore, in as much as Sir Martin in the ame Strain relates wonderful Things of the Politenes and Civility of a Nation that dwelt in thoe Parts; of which he ays, they were governed by a Prince, whom they

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London, May 10, 1823.

,

E have now the honour, conformably to your desire, to submit for your consideration our observations on the proposed measure of uniting the Legislatures of the Provinces of Upper and Lower Canada; and on the clauses of the Bill for that purpose, as amended by a Committee of the Honourable the House of Commons, and printed by order of that House on the 31st of July last.

For the facility of reference we have annexed to these observations a copy of the Bill, as reprinted in the French and English languages in Lower Canada, and circulated throughout that province, previous to the subscribing the petitions against it.

Before entering into the subject, we have to


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 apologize to you for the delay which has occurred, and for not transmitting these observations till after your reiterated recommendation to that effect.

His Majesty's Government having, at the last session of Parliament, consented to postpone the proposed measure for a time, sufficient to enable His Majesty's subjects in the Canadas to make known their sentiments thereupon; and these, together with the heads of their objections to this measure, being expressed in the following documents, now in the possession of His Majesty's Government, viz.,

 * 1. The Petition of the Inhabitants of Lower Canada.

 * 2. The Petition of the House of Assembly of Lower Canada.

 * 3. The Petition of the Legislative Council of Lower Canada.

We flattered ourselves that it would not be necessary to trouble His Majesty's Government with our observations on a measure, which nine-tenths of the inhabitants, and all Constitutional Authorities of the Colony to which we belong, so earnestly pray His Majesty to avert, "as fraught with much evil." Copies of the aforementioned documents are annexed in an Appendix under the letter A.

We have also the honour to inform you, that we have been intrusted with Petitions against the


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 said measure from three entire districts of Upper Canada, viz.,

 * The Home District,
 * The District of Newcastle,
 * The London District,

And also ten other Petitions from Counties situated in almost every other District of the said Province; subscribed in the whole by eight thousand and ninety-seven persons, chiefly freeholders and qualified voters.

We also beg leave to observe that, although the Legislature of Upper Canada has been moved to give its approbation to the said measure, it has refused to do so; referring to the Petitions of the People, the majority of which are decidedly against the proposed Union. Copies of five of these Petitions, viz.,

 * The Home District,
 * The County of Kent, in the Western District, and
 * The Counties of Stormont and Glengarry, in
 * the Eastern District,

Together with the Resolutions of the Assembly and Legislative Council of that Province, are annexed under the letter B.

From these documents it will appear that no Bill introduced in Parliament relating to the Colonies ever met with a more general opposition,


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 on the part of those immediately concerned in its enactments, than the present. The population of Lower Canada is estimated at 500,000; that of Upper Canada at 120,000. The number of men from sixteen to sixty, in both Provinces, is about 100,000; and of these about 70,000 have actually petitioned against the measure in any shape. If a few individuals have petitioned in its favour, it must be recollected, that no person in either colony ever publicly proposed or supported such a measure, or even perceived the evils which they now pretend to exist, and render this measure necessary, till such time as they had notice of the present Bill being before Parliament. If it has received any countenance from unprejudiced and disinterested persons, permanently connected with the Colonies, it is more owing to its being supposed a Government measure, than from their opinion of its merits. The examination of the signatures to the Petitions of both Provinces will show, that the opposition to the measure is not confined to any one description of subjects, but that it extends to all; and we have the honour to assure you, from our own knowledge and certain information, that by far the greater portion of these Petitioners are independent proprietors of the soil, and that they amount to a great majority of the Electors duly qualified by law in the two Provinces.

Every person in the Canadas readily acknowledges,


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 that it is essential to the connexion and welfare of the British Dominions, that the supreme Legislative Authority should exist at the sent of empire, subject to the restrictions which it has itself imposed; the inhabitants of Lower Canada have supported this authority when every other British Colony in North America was in successful rebellion against it. The distance at which the Colonies are placed deprives them of all direct participation in the representative branch of the supreme Legislature, and the differences between the state of property, of society, and local circumstances, in Great Britain and the Colonies, render it very difficult for a Legislature, solely constituted in the Mother Country three thousand miles distant, to legislate for the internal affairs of the Colonies with advantage. In cases where changes of their established constitutions are contemplated, it surely cannot be expedient to proceed the almost unanimous and humble Petitions of all ranks and descriptions of men in an avowedly loyal colony.

But in such a case it would at least be necessary for those who propose such changes, to show to the Government and Parliament some very strong grounds for interference, founded in actual evils resulting from the existing Constitutions; instead of alleging contemplated advantages, which woeful experience has proved to be seldom realized. It ought, it is presumed, never to be forgotten


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 that the security of the person and property of the subject depends on the established Constitution of a country, and that the very existence of ideas of sudden and important constitutional changes, particularly without the participation, consent, or even knowledge, of those who are to be chiefly affected thereby, is destructive of their quiet and of the general welfare.

The measure proposed by the Bill is nothing less than the annihilation of two local incorporations, established by Act of Parliament, with authority to make by-laws within the limits assigned to them; for the purpose of forming one similar incorporation, the sphere of whose legislation is to extend throughout the whole limits, at present assigned to the two, while for every other purpose of Government the former limits and distinct interests are to remain.

It is obvious that it is essential to the utility of local and subordinate Legislatures, that their limits be not too extensive; the necessity of their establishment, indeed, arises solely from the local circumstances and wants of the place for which they are constituted. Local knowledge is an indispensable qualification of the members of such bodies. The Aldermen and Common Councilmen of London, it is presumed, would form but a very indifferent local Legislature for Dublin, and vice versa; the members of the two corporations,


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 consolidated into one, sometimes assembled in London, sometimes in Dublin, or at any intermediate place, could hardly be expected to do any thing but mischief in their legislative capacity; unless, indeed, they should agree to render their new Act of Incorporation nugatory, by legislating separately for their respective localities.

The settled parts of Upper Canada and Lower Canada, from Chaleurs Bay and Gaspé, to Soult St. Marie, situated between Lakes Superior and Huron, already extend from north-east to south-west upwards of fifteen hundred miles; throughout which the communications are partly by land, partly by water; in boats or upon the ice; on the ground or on the snow, according to the seasons, the time of commencement of which varies between the two extremes fully four months in the year. The communication between Lower Canada and the London and western districts of Upper Canada, is in fact more difficult and uncertain at some seasons, than between Montreal and London.

The Members of the Assemblies generally in the Colonies, can derive no individual advantage from their trust. It is an onerous public duty; and it is well known that there is scarcely an individual to be found in any of the North American Colonies, who is not forced to engage in some industrious pursuit for the support of himself and


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 his family; the Members of the Legislature can, therefore, only attend to their legislative duties, in the winter season, when they have some relaxation from their private occupations. In Upper Canada the winter sets in, and the winter travelling is practicable, a month an half later than in Lower Canada; and there is the same difference in the commencement of the spring or summer. At the time of the falling of the first snows, and the freezing of the rivers in the autumn, and the melting of the snows and breaking up of the ice in the spring, there is in both Provinces a period of near a month when travelling is nearly impracticable. The difference of the seasons, the distance, the difficulties, dangers, and expenses of travelling to the scite of the joint Legislature, at the only season when the people or their representatives can attend to their public concerns, would be such as to leave them only a mockery of the system of government which has hitherto prevailed in the British Colonies; which was solemnly promised to British subjects settling in Canada by His Majesty's Proclamation of the 7th October, 1763; and which they have hitherto though was inviolably guaranteed to them by a solemn act of the British Parliament. Their situation would be the more severely felt, as amidst their sufferings under the evils resulting from such a state of things, they could not fail to observe on their southern frontier,


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 the United States of America, divided in the same extent, into no less than seven states and territories, for the facility of the local legislation and government.

It is not, however, on account of the distance and difference of climate and seasons, that the proposed measure would be destructive of the rights and interests of the subjects in the Canadas. It is well known that the laws which regulate property and civil rights, the customs, manners, religion, and even prejudices prevailing in the two Provinces, are essentially different. The inhabitants of each are strongly attached to all these, and enjoy them under the most solemn guarantees on the part of Great Britain: their respective codes of law could hardly be amalgamated by the wisest, most unprejudiced and enlightened Legislator, without endangering the security of the property which has been acquired under them. Every new law, every amendment of the old, has reference to the existing laws; and would be met as they bore upon either with suspicion and prejudice even in the Legislature, and be decided upon by at least one part of the members, without sufficient knowledge. The members of the two Provinces would in the end probably be compelled to legislate separately, on nearly all matters relating to their respective Provinces. The government and interests of the two Provinces remaining separate, and the colonial


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 expenditure being chiefly for local purposes, it is not likely that the votes of the members of the joint Legislature, whether in Levying or appropriating the supplies, would always be governed by fairness or justice, the population of the two Provinces have unfortunately, in these matters, opposite interests. The inhabitants of Upper Canada, from their distance from the sea, and the want of an external market for their agricultural produce, have, in great measure, ceased to be consumers of the description of goods upon which duties are raised at the port of Quebec: for rum, they have substituted whiskey of their own manufacture; for salt by the St. Lawrence, salt from the United States or from their own salt-works; for teas from England, teas from the United States; and the settlements in Upper Canada, being separated from the American territory only by a navigable river and lakes, smuggling cannot be sufficiently checked. Upper Canada has, therefore, an interest in continuing to raise the supplies upon such articles as are still consumed in Lower Canada, and it is natural that each should wish to have as large a proportion of them appropriated to its own local uses, as can be procured. The distribution of a colonial revenue for local objects, within a very limited extent of territory, is always difficult in a colonial legislature; between two distinct provinces, differing in almost every thing, excepting their common


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 quality of British subjects, justice in this distribution could hardly be expected.

These, Sir, are general objections to the measure proposed. We shall now proceed to consider the enactments, which are intended to give effect to that measure, referring to the copy of the Bill which is annexed.

To the two first our general observations apply. We shall merely remark that the Bill by permitting the Provinces to remain separate as to government and limits, ans divided by Act 31 Geo. III., there can be no diminution of the necessary expenses of the Government; the real expenses would be increased by the additional cost of travelling and correspondence, and the expenses of transmitting laws, documents, evidence, etc. The duties of the local Executives and of the Departments in England corresponding with them, could not be diminished by a mere legislative union.

If local circumstances and institutions permitted a complete re-union of the Provinces, it could only be rendered useful by the seats in the Legislative Council and in the Assembly becoming vacant, and by appointing Legislative Councillors, who would generally attend in their places, who would not be composed almost exclusively of executive Officers, and particularly of the Judges, whose duties,


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 as such, are sufficient in Canada to occupy the whole of their time; by these means the composition of the Legislative Council might be made more corresponding with that of the House of Lords in England, and it would thus be more likely to be on a footing of better understanding wit the Elective Body. The continuing the Members of the Assembly for one year beyond the time for which they were elected by the people, must be an error: for it is not to be supposed, that it was intended to constitute the Representatives of the people of Canada by and Act of the Imperial Parliament of the United Kingdom.

The clauses provide for the representation of the people in the proposed Legislature of the Canadas.

When the existing constitution of these Provinces was established by the Act 31 Geo. II. cap. 31., Fifty Members of Assembly were allowed to Lower Canada, and fifteen to Upper Canada. The former than contained about 200,000 souls; the latter about 25,000, or one eighth of the former. This was also the proportion of duties which the first agreement between the two Provinces allowed to Upper Canada. The representation of Upper Canada was then double that of the lower Province, in proportion to


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 its population; by the operation of the Upper Canada Act, 60 Geo. III., which is confirmed by the 7th clause, the representation of that Province has been increased to Forty, while that of Lower Canada has remained at Fifty, and every attempt to increase it, has been frustrated in the Lower Province. By the operation of the same Upper Canada Act, continued by the said clause, a regular increase of the representation of that Province, proportionate to the population, is provided for, which would soon carry it to an amount equal to that of Lower Canada, unless the Governor chooses to increase the latter to 60; and even with that increase, the representation of Upper Canada would soon be equal to that of Lower Canada, and it is provided by the 9th Clause, that the number of Representatives shall not be altered, should a minority of one-third of the Members present refuse their assent at either the second or third reading of the Bill.

At the time of the Union between Scotland and England, or Great Britain and Ireland, had the population of England been told that Scotland or Ireland, or both together, were to have a number of Members in the House of Commons equal to that of England, and with such a restriction, it is probable that an alarm fully as great as that which this Bill has excited in Lower Canada, would have prevailed in England.

The present population of Upper Canada has been