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 CHRISTIAN SOCIOLOGY.

INTRODUCTION.

I. term Christian Sociology is unfortunate in certain of its applications. The names of many sciences may be used in two ways: (1) they may indicate the method by which results are obtained, and (2) they may indicate the formulation of such results. Thus history may be a method science or it may be a descriptive science. In the former case it would be absurd to unite with it any word having a moral content. A method of investigation may be ill or well fitted to produce the best results, but ethically it can be neither good nor bad. The same is perhaps even clearer of such objective sciences as chemistry and geology. To speak of a Christian method of sociological investigation is quite as impossible. The investigation of social forces and results, the discovery of the true nature of society, can no more have an ethical—still less religious—character than the study of a crystal or a chemical compound.

But in the other sense in which the name of a science is used, no such criticism can hold. The moment an investigator attempts to formulate his results in propositions, that moment he injects into them his own characteristics. While the method of investigation may be morally neutral, the statement and the application of its results may be largely tinged with ethics. This is less obvious in the case of physical sciences, but admittedly true of the social. Thus in a true sense there may be a Christian view of history, and, so to speak, a Christian history. This is even more obvious in the case of philosophy. In this sense of the formulation and application of results derived by Christian students, sociology may be said to be Christian.

It is, however, not altogether clear that such a terminology


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 ENGLISH AND AMERICAN CHRISTIAN SOCIALISM: AN ESTIMATE.

To what extent and in what particulars have the agitations of the English and American Christian socialists for improved social conditions been vitiated by defective social ideals? term "Christian Socialism" is of vague import, both as to doctrine and as to the personnel of its adherents. The term was first adopted in its English application by Frederick Denison Maurice to denote the doctrines of the group of social reformers led by himself. The leading spirits of this group were Maurice, Kingsley, Hughes, Neal, Ludlow and others; but though the term had a more definite implication than at any time since, even then its application was quite vague. The movement originated with the Owens communism on the one hand and with the Chartist agitation on the other. From the latter it derived its occasion, from the former its method. A formal organization was entered into and publications established: at first Politics for the People, and later The Christian Socialist. From lack of support neither continued long.

More recently the movement has revived under the name of the "Christian Social Union." The most flourishing society publishes a quarterly magazine, The Economic Review. Other less important publications are issued on both sides of the Atlantic. This movement finds its occasion in present social problems and is an attempt at a solution through the efforts of the church. Both of these formal organizations have been in the main identified with the established church, or rather with the adherents of this church; though there are numerous other writers and workers of other denominations who are frequently termed Christian socialists, for their aims are similar.

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388 On the bearing of the Principle of Relativity on Gravitational Astronomy. By W. de Sitter, Assoc. R.A.S.

1. The principle of relativity, first developed in connection with the electromagnetic theory of light, has in recent years been more and more considered as of universal application, and the claim has been made that the whole of our physical sciences should be framed in conformity with it. In this paper are considered some of the results of introducing the principle in the laws of planetary motion. Poincaré has made the remark that some of the difficulties of the problem of three bodies are due to the fact that in the undisturbed motion the nodes and perihelia are fixed. Now, with a law of attraction which is in conformity with the principle of relativity, the perihelion has a motion even in the problem of two bodies, and it is probable that such questions as the existence of periodic solutions and the convergence of series entirely change their aspect. In the present paper, however, these interesting mathematical questions are not touched upon, and I consider the problem exclusively from the point of view of the practical astronomer, investigating only such effects as may be expected to yield the possibility of an empirical verification of the principle.

All natural phenomena are described in terms of four variable quantities; three "coordinates" $$x, y, z,$$ and the "time" $$t$$. If we introduce other variables $$x', y', z', t',$$ the formulæ describing any event will generally be altered. Also the physical laws, which are differential equations defining $$x, y, z,$$ as functions of $$t$$ and certain constants, are in general altered by a change of the system of reference. Physical science has, however, been so built up that there are certain transformations which leave the form of the equations unaltered. In the classical, or Newtonian, mechanics these are all orthogonal transformations of the three coordinates $$x, y, z,$$ combined with an arbitrary uniform velocity of these axes and an arbitrary change of the units of length and time.

The principle of relativity can be enunciated as the postulate

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Mar. 1911. that the transformations, with respect to which the laws of nature shall be invariant, are "Lorentz-transformations." A Lorentz-transformation is defined by a modulus $$q$$ and an axis. Taking the latter as the axis of $$x$$, the transformation-formulæ are—

where $$c$$ is a universal constant, which, according to the electromagnetic theory, is equal to the velocity of light in free space. In Newtonian mechanics the value of this constant is $$c = \infty$$. Putting, then, $$q = v/c$$, so that $$q = 0$$, the Lorentz-transformation degenerates into a "Newton-transformation,"—

To both Lorentz- and Newton-transformations may be added an arbitrary orthogonal transformation of coordinates.

The physical meaning of the principle has been very clearly explained in these pages by Messrs. Plummer and Whittaker, and need not be repeated here. The mathematical formulæ are all that is required for our purpose.

The literature of the subject is very extensive, and it is hardly possible for an outsider to be even superficially acquainted with it. Also I do not claim originality for any of the formulæ or results given below. The starting-point of my investigations has been the papers by Poincaré and Minkowski. The manner in which the equations of motion are derived below is entirely derived from the last section of Poincaré’s paper. I also owe much to conversations with and advice from my colleague Professor Lorentz.

2. Let there be two systems of reference:— the "general" system $$(x', y', z', t')$$, and the "special" system $$(x, y, z, t)$$.

The first is an absolutely arbitrary system of reference. The

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390 three variables $$x', y', z'$$ define what Newton would call absolute space, and $$t'$$ corresponds to absolute time.

The second is a system of reference of which the origin and the direction of the axes are chosen according to the needs of the problem in hand. The transformation from $$x, y, z, t$$ to $$x', y', z', t',$$ or inversely, is a Lorentz-transformation.

The chief consequence of the principle of relativity is that it is impossible to observe any but relative motions. The "general" system only differs from any other possible system in that no convention is made as to its origin or the direction of its axes. It is thus not possible, from the point of view of the principle of relativity, to speak of "absolute" velocity or position otherwise than as velocity or position relative to any, not specified, "general" system of reference. If the word "absolute" is used in this sense, it is unobjectionable, but unnecessary. The laws of nature must, of course, be primarily framed with respect to the general system of reference. This does not mean that they assert anything about "absolute" motion or "absolute" time, but only that they must be so built up as to be true in whatever system of reference we choose to use.

We have thus to consider two problems:—

(a) What is the law of force that must replace Newton’s law, and what is the motion of a planet under this law? So far as this differs from ordinary Keplerian motion, we shall have to consider the question whether the differences are large enough to be verified by observation.

(b) A motion being given in any "special" system, how is it expressed in the "general" system, or in any other special system? This only involves the working out of the formulæ of transformation for the required cases.

A third question then arises, viz. whether the "astronomical system," i.e. the coordinates and the time actually used by practical astronomers, coincides or not with any "special" system as defined above. This question is practically not affected by the introduction of the principle of relativity, and we need refer to it only very briefly.

3. I will now begin by stating the necessary formulæ for a Lorentz-transformation in the form which I find most convenient for my purpose. Very probably most of them have already been published elsewhere in the same form, but I found it easier to work them out for myself than to search for them in an unfamiliar literature.

The formulæ become more symmetrical if the unit of time is so chosen that $$c=1$$. From an astronomical point of view, however, it is more convenient to retain the ordinary unit of time. Both advantages are combined by using $$ct$$ as variable instead of $$t$$. Derivatives with respect to $$ct$$ are denoted by Greek letters, thus—

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Rh by the Government on aborigines was covered by an annual vote amounting in 1878 to £5,254. This was expended partly on grants in money and goods to four mission stations. The fifth, Poonindie, at Port Lincoln, which has a reserve of 15,000 acres attached to it, received nothing. The others which received various sums were Point Pierce, Yorke's Peninsula, with 12,800 acres of land; Point Macleay, Lake Alexandrina, with 4,498 acres; Kopperamanna, Far North, with 64,000 acres; and Hermansburgh, Finke River, N.T., with 576,000 acres. Besides these there are fifty depôts, distributed through the districts, at which rations, clothing, medical comforts, &c., are distributed to the sick and infirm aborigines, and boats, netting, tools, &c., to the men. All this is done within the vote mentioned, assisted by contributions from the religious congregations—apparently chiefly Lutheran—which have engaged in the mission work. Individual instances of progress are reported by the sub-protector which are astonishing to those who know the natives. One aboriginal had obtained a four years' lease of a farm of 160 acres. He is "an industrious intelligent man, has saved money, and now possesses stock and farm implements, keeps a bank account, and has made several improvements on his farm." Similar leases were about to issue to four other natives, "one of whom recently married a European woman."

The general report for each year contains special reports from the mission stations and other agencies. Taking the latest, that for 1879, we find that the superintendent of Kopperamanna reports that in his district the natives during the year had been well off. On the mission station were sixteen buildings, 5000 sheep, 45 head of cattle, 40 horses, and 850 goats. There had been an average attendance at school during the year of about twenty-five children, who seemed particularly fond of arithmetic. The country was not very suitable for agriculture, but the natives were employed in shepherding, fencing, building, &c., and hunting wild dogs, having secured 235 dingo scalps during the year. The missionaries have taken the trouble to learn the aboriginal tongue, which helps them with the natives, who are, of course, under no restraint, coming and going as they please, and therefore only to be kept by moral influence. As an instance of the difficulties in the way of raising the condition of the race, we quote the remark of the superintendent, "They all, with few exceptions, suffer from syphilis."

The Hermansburgh station, on he Finke River, in the Central Territory, is especially interesting to Queenslanders, as it is situated in country similar to our own Western interior. It has been lately established, and there also the missionaries have learned the aboriginal dialect. They have on the station 2530 sheep, 100 goats, 32 head of cattle, and 52 horses. From a special report made on this mission by the station-master at the telegraph station, Alice Springs, we learn that substantial buildings, yards and woolshed, have been erected, and a large paddock fenced in. Attempts were being made at cultivation with promise of success, and the missionaries proposed to lay down next year (1880) 100 acres in grain. The natives come and go, and are shy and retiring. The station-master reports of the missionaries that "they have had, and will still have, a certain amount of uphill work, but in the end will, I think, be successful." The neighboring squatters speak "in most praiseworthy terms" of the mission station. The report ends by an admission on the part of the writer that he has been most favorably impressed by the mission station, "and erroneuoserroneous [sic] opinions previously entertained are entirely removed."

No special remarks need be made on the Point Macleay and Point Pierce institutions, but Poonindie deserves special mention. At this place some of the natives appear to be really rising into civilised beings. One—a half-caste—is mentioned who does nearly all the painting, glazing, and carpentering of the institution, and who made a neat little boat in his spare time out of a few boards he bought in Port Lincoln. The average number resident has been from sixty-four to eighty-four, although a number of others come and go. They work well, and the produce of their labor supports the whole institution very comfortably. They are taught in the school, doctored by a skilful medical man, who visits the place once a week. They must have decidedly a good time of it, as besides cricket and bagatelle, of which they are fond, and out-door sports, there is a weekly dance in the school-room "in which nearly all, young and old, take part; and were it not for the rather heavy boots and bare feet of some, their graceful manner and movement would surprise many of those of our own people who delight in the 'light fantastic toe.'"

We have no space for further extracts from these interesting documents. The Souh Australian Government, unlike our own, recognises that it owes a duty to the aborigines, and very effectively discharges it, without any very great cost to the Treasury. No Queenslander will require that we should point the contrast between the

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Mar. 1911. Further, we put

The modulus of the transformation is $$q$$. We also introduce $$q_{1}=1-\sqrt{1-q^{2}}$$. If $$q$$ is a small quantity of the first order, then $$q_1$$ is of the second order. The cosines of the angles which the axis of the transformation makes with the axes of $$x, y, z$$ are denoted by $$\alpha, \beta, \gamma,$$ so that $$\alpha^2 + \beta^2 + \gamma^2 = 1$$.

The transformation-formulæ are then—

We find easily

and similarly for $$\eta'$$ and $$\zeta'$$.

Further,

In these formulæ $$r_q$$ and $$\phi_q$$ are the projections of $$\rho$$ and $$\phi$$ on the axis of transformation:—

If we put

we can easily verify that the transformation-formulas for $$(\xi), (\eta), (\zeta), (\kappa)$$ are the same as those for $$x, y, z, t$$, viz.—

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392 The invariants of the transformation are all of the form—,

where $$x_{1},\ y_{1},\ z_{1},\ ct_{1}$$, or $$x_{2},\ y_{2},\ z_{2},\ ct_{2},$$ may be replaced by any set of quantities, which are transformed by the same formulæ, such as $$(\xi), (\eta), (\zeta), (\kappa),$$ etc.

The equation

is thus not altered by the transformation. If now we define a new variable $$c\tau$$ by the equations

this variable is the same function of $$x', y', z', t'$$ as of $$x, y, z, t,$$ and is consequently independent of the system of reference. We have, of course,

The variable $$\tau$$ is called by Minkowski the "Eigenzeit" of the point whose coordinates are $$x, y, z,$$ which may be translated by "proper-time". In many problems it is more convenient as an independent variable than $$t$$.

Every point has thus its own proper-time, which is independent of the system of reference, but depends on the state of motion of the point and on its previous history. The proper-time of a point rigidly connected with the axes of the system of reference ($$x, y, z, t$$) is $$t$$ itself. As a convenient abbreviation, we may speak of "heliocentric time," "geocentric time," etc., meaning the proper-time of the Sun, the Earth, etc.

4. A set of values of $$m, x, y, z, t,$$ defining the position of a particle of mass $$m$$ in the system of reference ($$x, y, z, t$$), may be called an "event." Two events are called simultaneous if their values of $$t$$ are the same. Two events which are simultaneous in one system ($$x, y, z, t$$) are in general not simultaneous in another system ($$x', y', z', t'$$). And, within certain restrictions, which are of no importance for our purpose, a system can always be found in which two arbitrarily given events are simultaneous.

We have

where

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Mar. 1911. Thus, if we wish the two events to be simultaneous with respect to the time $$t',$$ or $$t'_{1}=t'_{2}$$, we have

Denoting the coordinates of simultaneous events by non-italic letters, we find thus—

or, remarking that $$q_{1}-q^{2}=-q_{1}\sqrt{1-q^{2}},$$

and similarly for the other coordinates.

We find easily, denoting the distance between simultaneous positions by $$\boldsymbol{r}$$:—

Therefore (6) can be written—

5. If we consider the action on $$m_1$$ at time $$t_1$$ of a force emanating from $$m_2$$ at time $$t_2$$, we will suppose—

The expression

is of the general form (4), and is thus an invariant of the transformation. We have thus also $$c\left(t'_{1}-t'_{2}\right)=\Delta'$$. The equation (8) states that the force is propagated through space with the velocity of light. This is, of course, an arbitrary assumption, which is not a necessary consequence of the principle of relativity. The velocity of propagation might be defined by any invariant of the transformation containing $$c\left(t_{1}-t_{2}\right)$$, put equal to zero. But it is a natural assumption, and the most simple which can be made.

Denoting now the simultaneous relative coordinates by letters of another type, $$\boldsymbol{x, y, z}$$, we have, for time $$t_{1}$$,

where

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394 The values of $$\xi_2$$ and the higher differential coefficients must be taken for the time $$t_2$$, defined by (8). We consider $$1/c$$ as a small quantity of the first order, and we wish our formulæ to be exact to the second order inclusive.

We find easily

where

$$\epsilon_1$$ and $$\epsilon_2$$ are of the first order, $$\chi_2$$ is of the second order.

In the equations of motion there appear the invariants—

To express these in simultaneous relative coordinates we have—

6. The equations of motion can be given in three forms:—

and similarly for the other coordinates.

$$\mathrm{X}$$ is the force according to the ordinary definition, or "Newtonian" force; $$(\mathrm{X})$$ is called the "Minkowskian" force. The mass $$m$$ is a constant.

Differentiating the formula $$(\kappa)^{2}=1+(\phi)^{2}$$, we derive a fourth equation analogous to (11) or (12), viz.:

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Page:American Journal of Sociology Volume 1.djvu/91

 THE CIVIC FEDERATION OF CHICAGO.

A STUDY IN SOCIAL DYNAMICS.

descriptions by old residents may be trusted, the most prominent element in the population of Chicago, previous to the period of the World's Fair, had been a constellation of groups, made up of intense individualists. The members of each group had calculated and coöperated with a chief view to each man's main chance, yet under restrictions which instinct and experience of business necessity had declared to be expedient. Floating in and out among these charmed circles of cooperators was a great multitude, whom no man could number, of unattached outsiders, all bent on the same purpose of personal profit. To both classes corporate municipal action was an affair of so small proportionate moment that it fell into comparative indifference and neglect. The only efficient municipal consciousness was among the people who saw in administrative machinery a means of getting gain which they could not win in competition with merchants and manufacturers and operators in real estate. How far the concentration of effort to get the World's Fair for Chicago resulted in changes which require modification of this description, it would be impossible to say and futile to inquire. Undoubtedly there was enlargement of view and increase of sympathy from that cooperation, which prepared the way for a kind of patriotic action that had been unknown before.

Since the autumn of 1893 a civic revival has occurred in Chicago, the evidences of which are familiar to all her citizens. These acts of civic patriotism are by no means, as will appear later, the work of a single organization. The Civic Federation


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Mar. 1911. or

where

Minkowski gives the name "kinetic energy" to the quantity

The equation (12′) thus turns out to be the equation of energy,

If we use Minkowskian velocities and forces, and put

we find similarly from (11′)

The law of the force must be such that the form of the equations of motion is not changed by a Lorentz-transformation. Therefore

must be transformed by the same formulæ as

or, in other words, $$\mathrm{(X), (Y), (Z)}$$ must be linear functions of

the coefficients being invariants of the transformation.

For zero velocities the equations of Newtonian mechanics must be reproduced, therefore the coordinates can only enter by their differences $$x_{1}-x_{2}$$, etc.

Introducing further the condition that the resulting equations must not contain the velocities in the first degree, and certain other simplifications, Poincaré is led to take (l.c., page 174)—

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396 Similarly we have for the force acting on $$m_2$$ from $$m_1$$,

We will now introduce simultaneous coordinates. Let these be for time $$t$$—

In the equations of motion of $$m_1$$, i.e. in the expression (14), we must use the coordinates and velocities of $$m_2$$ for the time $$t_2$$ defined by

and we have

In (15) we must use the coordinates and velocities of $$m_1$$ for the time $$t_1$$ defined by

and we have

Further, we have for use in (14)—

and in (15)—

The expression for $$\mathrm C$$ is the same in both cases.

We find then,

This form of the equations is not unique. We can multiply by any power of $$\mathrm C$$, or make more complicated alterations, for which the reader is referred to Poincaré.

Multiplying by $$\mathrm C$$ we get—

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Mar. 1911.

This last form (II.) is preferred by Lorentz (l.c., p. 1239), because the corresponding Newtonian force, $$\mathrm{X}_{i}=(\mathrm{X})_{i}\sqrt{1-\phi_{i}^{2}}$$, does not contain the velocity of $$m_i$$. (I.) is the law adopted by Minkowski, presumably because it gives the simplest result for a planet of infinitesimal mass.

As has already been remarked, the values of $$\xi_{2},\ \eta_{2},\ \zeta_{2},$$ in $$(\mathrm{X})_1$$, and those of $$\xi_{1},\ \eta_{1},\ \zeta_{1},$$ in $$(\mathrm{X})_2$$ differ from the values at the time $$t$$ for which the simultaneous coordinates are taken. If we are content to neglect third orders, however, we can assume all velocities to correspond to the time $$t$$. If the motion were quasi-stationary, i.e. if the accelerations could be neglected, the velocities would be constant, and also $$\delta x_2$$ and $$\delta x_1$$ would disappear. The equations (16) and (17) would in that case be rigorous.

7. We will first consider the law (I.). Introducing the developments of $$\mathrm{B}_1$$ and $$\mathrm{A}_2$$ we find—

We thus have by (13)—

Now we have, to second orders,—

Further, if we put

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398 we find

In these equations the system of reference is arbitrary. We can always, by a Lorentz-transformation, make the velocity of any point equal to zero. If there were a point in the system having no acceleration, like the centre of gravity in Newtonian mechanics, the equations could be simplified by taking that point as origin of the system of reference. Now the integrals of the motion of the centre of gravity do not exist in this simple form under the new law, but it is still possible to find a point without acceleration. The centre of gravity has the coordinates $$x_{0},\ y_{0}\ z_{0}$$, defined by—

We have thus

If we denote relative velocities by letters without index, thus—

We have

We find at once from (20)—

The right-hand member is of the second order, and is thus the same for the laws I. and II. In it we can, for the relative coordinates and velocities, use their values in ordinary Keplerian motion. If then we take the orbital plane for the plane of ($$x, y$$) and the axis of $$x$$ through the perihelion, the equations (21) become—

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Mar. 1911. The coefficients $$\mathrm{P, Q, R, P', Q', R'}$$ are periodic functions of $$t$$ devoid of constant terms. Consequently $$c\xi_{0},\ c\eta_{0}$$ are also periodic, and $$c\zeta_{0}$$ is constant. The point the components of whose velocity id are the non-periodic parts of $$c\xi_{0},\ c\eta_{0},\ c\zeta_{0}$$ therefore has no acceleration. If we perform a Lorentz-transformation to a new system having this point as its origin, then the mean values of $$\xi_{0},\ \eta_{0}$$ and $$\zeta_{0}$$ are zero. Thus, if we neglect the periodic terms (which are, moreover, of the second order, and would introduce into (20) only terms of the fourth order, and those multiplied by $$\mu'$$), we have—

By subtracting the second equation (20) from the first we find then—

where

If the mass of the planet is neglected we have $$\mu'=0$$, and we find—

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400 Comparing (13) and (11) we find that (23) is equivalent to

This is the equation given by Minkowski (l.c., p. 110). It could, of course, have been derived by taking $$\mu = 0$$ from the beginning. In that case the acceleration of $$m_2$$ is zero, and we can take $$m_2$$ as the origin of our system of reference. Then $$\xi_{2}=\eta_{2}=\zeta_{2}=0$$, $$\mathrm{B}_{1}=\boldsymbol{r},\ \mathrm{x}_{1}=\boldsymbol{x}$$, and (24) is derived at once from (14).

In (24) $$\tau$$ is the proper-time of the planet, or planeto-centric time; in (23) $$t$$ is the time of the system of reference, which has been chosen with its origin in the mean position of the centre of gravity. Practically $$t$$ will coincide with the proper-time of the Sun, or heliocentric time.

The equations for the other two coordinates are, of course, quite similar.

The equations for the law II. are derived from those for the law I. by multiplying the right-hand members by $$\mathrm C$$. Introducing the relative velocities we find, neglecting fourth orders,

The only difference between the laws II. and I. is therefore that in (22) and (23,) the term $${\boldsymbol x\phi}^{2}$$ is changed to $$\tfrac{1}{2}{\boldsymbol x\phi}^{2}$$. The simple form (24) is no longer possible with the law II. We have, however, in accordance with (12), for this law—

The only previous investigations on the same subject which have come to my knowledge, beyond the quoted papers of Poincaré and Minkowski, are those by Mr. Wilkens ("Zur Elektronentheorie," V.J.S. 1904, p. 209) and by Mr. Wacker ("Ueber Gravitation und Elektromagnetismus," Inaugural Dissertation. (Tübingen), 1909). Mr. Wilkens finds secular terms in all elements. Some of these have amounts which could not long remain undetected. Thus, e.g., his secular perturbation of the mean distance corresponds, for the Earth, to a shortening of the year by 19 seconds per century. His formulæ, however, are not in conformity with the principle of relativity, and his results are not confirmed here.

Mr. Wacker gives the equations (25). His equations are thus in conformity with the principle of relativity, and he adopts the law II., and neglects the mass of the planet.

8. The equation (24) is the ordinary equation of Keplerian motion. Consequently, if we neglect the mass of the planet and

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Mar. 1911. use planeto-centric time, the motion is Keplerian. Thus, e.g., the integrals of areas are

Or, introducing heliocentric time, to second orders—

In (22), on the other hand, it is not advantageous to introduce the proper-time of one of the bodies, since we should thereby lose the symmetry gained by the introduction of relative velocities and coordinates. In the second-order terms We can introduce the ordinary Keplerian motion. We find then, taking the orbital plane for plane of ($$x, y$$), for the two laws equally—

where

and v is the true anomaly.

Similarly we find for the vis-viva integral from (24)—

or in heliocentric time—

From (22), on the other hand, we find—

For the law II. we must add to (28) and (29) the term—

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402 The equation (28) can then also be written in the form given by Wacker (l.c., page 55),

 * $$\mathrm{E}=\frac{k^{2}\mathrm{M}}{r}+\text{const.},$$

where

9. The equations (24) of course give, taking the orbital plane as plane of ($$x, y$$),—

where

To introduce heliocentric time we have

therefore

or if we put

we have

Consequently for the law I. the coordinates of a planet of infinitesimal mass are expressed by the ordinary formulæ (30) of elliptical motion, but to express the excentric anomaly in heliocentric time we must in the equation of Kepler (33) use a slightly different excentricity, and also Kepler’s third law is no longer quite exact. The deviations from pure Keplerian motion are periodic and have $$\lambda^{2}$$ as a factor. Taking the semi-major axis of the Earth’s orbit as unit of length, the value of $$\lambda^{2}$$ is

All these periodic terms are thus entirely insensible. The length of the year appears to be different when measured in

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Mar. 1911. geocentric or in heliocentric time. This, of course, is a purely formal change of unit, and has nothing to do with the number of days in the year.

The difference between heliocentric and geocentric time, apart from this change of unit, is purely periodic. We find

which is the formula given by Minkowski, l.c., page 111. The value of the coefficient of $$\sin u$$ is, for the Earth, $$0^{\mathrm{s}}.00083$$.

10. For the integration of the equations (22), or the corresponding equations for the law II., the easiest way seems to be to use the Keplerian motion as a first approximation, and to compute "perturbations" by the method of variation of elements, introducing the radial, transversal, and orthogonal perturbing forces. Taking the orbital plane for plane of ($$x, y$$), these forces are found to be

where

In the perturbing forces we can use the undisturbed or Keplerian motion. We find, then, taking the axis of $$x$$ towards the (unperturbed) perihelion,—

In the well-known equations for the variation of elements, we introduce as independent variable, instead of the time, either the excentric or the true anomaly, or the radius-vector, by—

30

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404 With the true anomaly as independent variable, the equations are then—

We find the following "perturbations":—

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 The periodic terms, all of which have very short periods, can be entirely neglected. For the law I. we find that there are no secular terms not multiplied by $$\mu'$$, which is in accordance with what was found above. The terms which have $$\mu'$$ as a factor also give nothing secular in $$\delta a$$ or $$\delta e$$. In $$\delta\varpi$$ we have—

For the law II. we find this same term, but also a secular term not multiplied by $$\mu$$, viz.—

With the law II. we have thus a secular motion of the perihelia, even for a planet of infinitesimal mass. The motion in one century is—

The effect of the secular terms in $$\delta\epsilon_1$$ is, of course, only to make the observed mean motion disagree with the value derived from Kepler's third law. As we have no sufficiently accurate means of independently determining the mean distances, this can never be detected.

The formulæ (35) are valid for all excentricities, and can thus also be used for comets. The perturbations in $$\delta\varpi$$ remain of the same order as for planets. Those in $$\delta e$$ and $$\delta\epsilon_1$$ become zero for a parabola. Only the perturbation in $$\delta a$$ would appear to become very large at perihelion. We have, however,

from which we find, for both laws,

which does remain small for $$e = 1$$.

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Page:American Journal of Sociology Volume 1.djvu/116

 SEMINAR NOTES.

developments in systematic sociology are evidences of a change of front in general philosophy. Men have everywhere and always differed in opinion about the intrinsic and the mediate value of all things. Especially has the question been discussed in connection with music, sculpture, painting, poetry, science—Is it valuable chiefly for its own sake, or chiefly for its utilitarian services? Without prying into the psychology of the change, we note the fact that men are more generally content than ever before to adjourn this attempt at giving an absolute position in the scale of values to the different objects of human interest; and we are able to say of each object of knowledge—it is worth attention both for its own intrinsic importance and for its value as a fragment of all useful knowledge. In other words, we no longer take either horn of the dilemma, but we regard all knowable truths both as ends and as means; as the goal of one stage of knowledge and as the points of departure for another stage.

The civilization in which our own lot is cast has without formal or very distinctly conscious action adopted as a last applicable standard for measuring the worth of all knowledge the visible service of that knowledge to man. In other words we are all in a real sense utilitarians. Scholars of a certain type zealously cultivate the tradition that all truths are uniformly important. This tradition is as false as the vulgar version of our democratic doctrine, "all men are born free and equal." All truths are not equally important. On the contrary they vary in importance in direct ratio with their bearing upon human weal. This is not to imply that the ratio may always or often be precisely determined. It will doubtless never be possible to apply this standard so that we may catalogue all sciences and all truths organized by sciences in the exact order of their utility. The impossibility of making exact application of the principle does not vacate the principle itself. The principle is at all events applicable in a certain approximate way.


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1922 Encyclopædia Britannica/Moltke, Helmuth von

MOLTKE, HELMUTH VON (1848-1916), Prussian general, chief of the German general staff at the outbreak of the World War, was born at Gersdorf in Mecklenburg on May 23 1848, and was the nephew of the great Moltke. From 1902 to 1904 he was in command of the 1st Div. of the Guards Corps with the rank of lieutenant-general. In 1906 he was appointed chief of the general staff of the army. He was responsible for the general conduct of the German operations at the beginning of the World War and is now known to have been acting upon the plan for the invasion of the north-east of France and a rapid advance upon Paris which had been drawn up by his great predecessor, Gen. von Schlieffen. In important particulars, however, he appears to have deviated from Schlieffen's plan, and in particular to have failed to concentrate sufficient force in the blow which was delivered on the north-east. He has likewise been charged with having failed to coordinate the positions of the German forces on the eve of the battle of the Marne, and having allowed to be issued confusing orders which contributed to the German defeat in that decisive battle. About the same time his health had become seriously impaired, and on Oct. 25 1914 he was relieved of his post and was succeeded by Gen. von Falkenhayn. He was entrusted in Berlin with the office of chief of the home substitute for the general staff (Der stellvertretende Generalstab), which had the task of organizing and forwarding the reserves and of controlling the Territorial army corps, corresponding to those at the front. General von Moltke died suddenly at a celebration in the Reichstag building on June 18 1916. He left memoirs entitled Die “Schuld” am Kriege, which up to 1921 had not yet been published.


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406 The two laws I. and II. are the only ones that have been actually proposed, but we can, without violating the principle of relativity, multiply the forces by any power of $$\mathrm{C}$$, and consequently any (positive or negative or even fractional) multiple of the quantities (37) will be in agreement with that principle.

11. The final result by the method of the preceding article must, for the law I. and for $$\mu=0$$, of course be the same as that derived in article 9, and contained in the formulæ (30), (32), (33). We have, since $$\varpi_{0}=0$$,—

where $$\delta a, \delta e, e \delta\varpi, \delta\epsilon_{1}$$ must be collected from (35), taking the values for $$S_1 + S_2 + T_1$$, and

On the other hand, from article 9, we have—

where

and we have put

By equating the values of $$\delta x$$ and $$\delta y$$ given by (38) and (39) we must then find for $$\Delta a$$ and $$\Delta e$$ constant values. To the first power of $$e$$ I find—

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Mar. 1911. 12. In the motion of the Moon we have first the same terms as in the planetary motion, but $$\mathrm{M}$$ in the expression for $$\lambda^2$$ is now the sum of the masses of the Earth and Moon. The motion of the perigee in one century for the law II. is found from (36)—

But, in addition to this, the disturbing force of the Sun is changed. To find the effect of this, we must use the first equation of (20), first taking for $$m_1$$ the Moon and for $$m_2$$ the Sun, and then for $$m_1$$ the Earth and for $$m_2$$ the Sun. The difference of the two equations thus derived—without the first term, which gives the ordinary Newtonian perturbation—will furnish the new terms in the acceleration of the Moon with respect to the Earth.

We can neglect the masses of the Moon and the Earth, and the acceleration of the Sun. Then, if we take the origin of the system of reference in the Sun, we find for the additional terms—

where the suffix 1 refers to the Moon and 2 to the Earth, and where

and $$m$$ is the Sun's mass. For the law II. the terms involving $$\phi_{1}^{2}$$ and $$\phi_{2}^{2}$$ are halved.

A development in series cannot be avoided. We will retain only the terms of the first order in the parallax, and in the inclination and excentricities, and of these only those which can give secular perturbations, i.e. which do not contain the Sun's longitude. I find—

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408 The second lines must be halved for law II. We have put—

$\begin{align}&\lambda'=\frac{k\sqrt{\mathrm{M}}}{c},\quad \mathrm{M} = \text{mass of Earth + Moon,}\\ &\nu = n'/c,\quad n' = \text{mean motion of Sun.}\\ &l = \text{the Moon's mean anomaly.}\end{align}$|undefined

I find then for the two laws—

There are no secular perturbations in $$a$$, $$e$$, and $$i$$. In the other elements we find—

The numerical values for one century are—

These quantities are too small to be detected from observation. Even the value of $$\delta\varpi$$ for law I. is well within the limits of uncertainty of the observed value.

13. We are thus left with the motion of the perihelion of Mercury as the only effect which reaches an appreciable amount. Unfortunately this same motion presents the well-known excess of observation on theory, which has been explained by Seeliger by the attraction of the masses forming the zodiacal light. Until

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Mar. 1911. we have some independent means of accurately determining this mass — which seems a very remote possibility indeed — any motion of the perihelion of Mercury within reasonable limits can be so explained. It will be remarked that the value (37) of $$e\delta\varpi$$ for Mercury is only little larger than the part of the motion (1″.203), which Seeliger explains by a rotation of the astronomical system of coordinates with respect to the "inertial system," i.e. the system to which the equations of motion are referred. If this rotation were rejected, and the term (37) were added, most of Seeliger's residuals would be very little changed. There would then be appreciable residuals only for the nodes of Mercury and Venus, and the perihelion of Mars. The node of Venus could be put right by increasing the density of Seeliger's second ellipsoid to about three times the value adopted by Seeliger (which would still leave it less than 1/2000 of that of the inner ellipsoid). Seeliger's rotation is practically determined from the motions of the node of Mercury and the perihelion of Mars, the excesses of which over their theoretical values, as determined by Newcomb, are 1.2 and 2.1 times their respective probable errors. If the density of the second ellipsoid were so determined as to represent the node of Venus exactly, the residual in the perihelion of Mars would be reduced to 1.6 times its p.e. The other residuals would not be much affected, and the representation would thus be on the whole very satisfactory.

14. We now come to the effect of a Lorentz-transformation on the elements of the orbit. First consider the orbital plane. In the system ($$x, y, z, t$$), of which the origin is in the Sun, or in the mean centre of gravity if the mass of the planet is not negligible, this plane is—

We must transform to simultaneous coordinates by (6) or (7). Since $$x_{2}=y_{2}=z_{2}=0$$ and $$\xi_{2}=\eta_{2}=\zeta_{2}=0$$ we have $$\Delta_{q}=r_{q},\ x_{1}-x_{2}=x,$$ etc. The transformed plane is thus—

or

where

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 Rh Thus, whatever may be the scientific value of a circumstantial account of the spot which we call the north pole, it will in all probability be a value incalculably inferior to that of a discovery which would inaugurate the era of complete combustion of fuel and of abated smoke nuisance in Chicago. Again, we cannot imagine a discovery in the historical portion of linguistic science that would equal Jenner's invention of vaccination in value to the human race. A final demonstration and formulation of the precise method of evolution up to date would be immeasurably inferior in value to such projection of the process of evolution into the future that the present generation of men would be enabled and induced to secure for the next generation a single step of advancement toward the ultimate realization of maximum welfare. In general, no truth held apart from other truths and unrelated to them is as valuable as any truth brought into connection with the other truths with which it belongs.

Sociology has been promoted by increased attention to the fact that all knowledge is mediate. No knowledge is self-sufficient. Each kind of knowledge plays its rôle, but its value is the value of the service which it renders in the economy of human existence. It is therefore principal or subordinate—primary or secondary—essential or incidental—but never absolute. Knowledge ranks with knowledge according to the part which each species of knowledge performs in procuring life larger in any dimension, or richer in any quality. That knowledge is of capital value which contributes to the intensifying or harmonizing of human life in its essential elements.

It would be a most unscholarly procedure to enter upon an argument to prove that one science, or one branch of knowledge is worthy and another unworthy of human pursuit. No detail of knowledge distinct enough to present unsolved problems to the human mind is too insignificant for the scholar's attention, so long as the problem remains unsolved. Every science may therefore make incalculably valuable contributions to the final art of life, provided that the results of each science are brought into correlation with the results of all the rest. The perception to which attention is called is not that one science deserves more sincere respect than another, but that all kinds of knowledge belong together at last, and that they can attain their proper dignity


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410 The orbit thus remains fixed and plane after the transformation. Since

we find easily

If $$\mathrm{L}$$ and $$\mathrm{B}$$ are the longitude and latitude of the positive half of the axis of the transformation we have—

If the plane to be transformed is the plane of ($$x, y$$) itself, we have in the system ($$x, y, z, t$$) $$i_{0}=0$$. The transformed position of the plane is then defined by

or

Let the plane of ($$x, y$$) be the ecliptic, and consider another plane of which the inclination and node in the system ($$x, y, z, t$$) are $$i$$ and $$\Omega$$. In the system ($$x', y', z', t'$$) its inclination and node on the plane of ($$x', y'$$) are $$i + di$$ and $$\Omega + d\Omega$$, as given by the formulæ (40). Let its inclination on the transformed ecliptic be $$i + \Delta i, \Omega + \Delta \Omega$$. Taking unity for the denominator of $$\tan i'_0$$ in (41) we find easily—

or

If the transformed plane be the equator, we have—

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Mar. 1911. where $$p$$ is the constant of general precession in longitude. We have thus—

If we take for the axis of the transformation the direction of the Sun’s motion relatively to the fixed stars, and for $$q$$ the velocity of this motion, divided by the velocity of light, so that in the system ($$x', y', z', t')$$ the mean velocity of the stars is zero, we have—

We find—

This is, on the basis of the principle of relativity, the theoretical difference between the constant of procession as determined from the fixed stars (system $$x', y', z', t'$$) and from the motions in the solar system (system $$x, y, z, t$$).

15. If we take the orbital plane in the system ($$x, y, z, t$$) as the plane of ($$x, y$$), and choose the axis of $$x$$ perpendicular to the axis of the transformation, we have—

and the formulæ for transformation to simultaneous relative coordinates in the system ($$x', y', z', t'$$) become—

The problem is now, if $$x, y$$ are given as functions of $$t$$, to find the expression of $$x',y',z'$$ as functions of $$t'$$. Knowing that the orbit remains plane, we can eliminate $$z'$$ by combining with our Lorentz-transformation a rotation round the axis of $$x'$$ by an angle given by—

from which

The new plane of $$x'_{1},\ y'_{1}$$ is thus the transformed orbital plane, and we have—

If, to take a simple example, the orbit in ($$x, y, z, t$$) were a circle—

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412 we find

or putting

we have

If the orbit in ($$x, y, z, t$$) is a "perturbed" ellipse, the formulæ of transformation are more complicated, but the differences between the real motion and pure elliptic motion remain of the second order and periodic in terms of $$t',$$ if they were so in terms of $$t$$.

16. One of the consequences of the principle of relativity is that it must be impossible by observations on bodies belonging to one and the same system to detect a motion of the whole system. Suppose in the system of reference ($$x, y, z, t$$) the Sun to be at rest, and a planet to describe a circle with uniform velocity. This, of course, is a dynamically possible state of motion under the new law as well as under the old. In the system ($$x', y', z', t'$$) derived from ($$x, y, z, t$$) by a Lorentz-transformation with the axis ($$\alpha, \beta, \gamma$$) and the modulus $$q$$, the Sun and the planet have a common velocity $$-cq$$ in the direction ($$\alpha, \beta, \gamma$$), and the relative orbit is no longer circular, but is defined by (43). Let, again, the orbital plane be chosen as plane of ($$x, y$$) in the first system of reference, and let the axis of $$x$$ be perpendicular to the axis of the transformation. The observer belonging to the system has no means of ascertaining the position of the plane of ($$x', y'$$), he can only observe the plane of the orbit, i.e. the plane of $$\left(x'_{1},\ y'_{1}\right)$$. To him the velocity of the Sun is thus in the direction ($$\alpha', \beta', \gamma'$$), where—

or

Let the observer be on the Sun, and let a signal be sent him, from the planet every time when this latter crosses the axis of $$y$$.

In the system ($$x, y, z, t$$) the intervals between these crossings are equal, and also the times required by the signal to reach the observer are equal: he will observe signals at equal intervals.

In the system ($$x', y', z', t'$$) the intervals between the crossings are unequal, and the aberration-times are unequal, and these two effects must cancel each other.

The times of crossing are—

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Mar. 1911. or

The intervals are therefore—

or

Let the aberration-time be called $$b/c$$. We find easily—

the upper sign being taken for the crossings through the positive axis of $$y$$ (first and third epoch), and the lower sign for those in which $$y$$ is negative (middle epoch). We find then—

The corrections to be applied to the true intervals to derive the observed intervals are—

The observed intervals are thus seen to be equal, as in the system ($$x, y, z, t$$).

Dr. C. V. Burton, following an idea of Maxwell, has proposed to determine the velocity of the solar system "with respect to the aether" from observations of eclipses of Jupiter’s satellites. Apart from the complications introduced by the excentricities and inclinations, and by the observer being on the Earth instead of on the Sun, his method is to determine $$\beta q$$ from the observed inequality in the intervals. If the principle of relativity be true, the result must necessarily be nil. The method could thus be used to verify the principle of relativity.

Mathematically speaking, the dynamical aspect of the principle is not directly concerned in this verification. The observable effect would be nil whatever the motions of the observer and the signaller, which are subjected to the same Lorentz-transformation, may be, even if they were dynamically impossible, so long as the principle is true for the geometrical relations of time, space, and

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414 rays of light. But in practice the coordinates are always derived from the integration of equations of motion, and they could not be transformed by a Lorentz-transformation unless the right-hand members of these equations of motion satisfy the conditions imposed by the principle of relativity.

If we take for $$cq$$ the Sun’s velocity relative to the fixed stars, the effect to be expected, in case the principle of relativity were not true, would be equivalent to an inequality in the time of eclipse of $$0^{\mathrm{s}}.10$$ with a period of 12 years, corresponding to

in the longitudes of the four satellites. Our observations, as well as our knowledge of the principal constants of the theory, must become many times more accurate than they are now, before it will be possible to detect the existence of an inequality of this amount.

17. The velocity of the solar system relatively to the fixed stars, on the other hand, is the same in any system of reference. If in the system ($$x', y', z', t'$$) in which the Sun has the velocity $$-cq$$, the star has no velocity ($$\xi'_{\star}=\eta'_{\star}=\xi'_{\star}=0$$), then, transforming back to the system ($$x, y, z, t$$), in which the Sun has no velocity, we find for the star the velocity $$\xi_{\star}=\alpha cq,\ \eta_{\star}=\beta cq,\ \zeta_{\star}=\gamma cq,$$ (neglecting terms of the second order).

If in the system ($$z', y', z', t'$$) two groups of stars have any systematic motion relatively to each other, or all stars have a systematic motion relatively to the axes of reference, the same will be the case in the system ($$x, y, z, t$$), apart from small changes (of the second order) in the constants defining the direction of motion relatively to the ecliptic, which are, however, of no importance, as they are constant corrections to quantities whose values must be derived from observation. If no such systematic motion exists in ($$x', y', z', t'$$), neither does it exist in ($$x, y, z, t$$).

This brings us to the question of the astronomical system of coordinates. Let this be ($$\mathrm{x, y, z, t}$$). The observations are referred to a system of axes $$\mathrm{x', y', z'}$$, which is the system of the fundamental catalogue. This system is reduced to ($$\mathrm{x, y, z}$$) by a rotation—

where $$p$$ is the constant of precession. This constant is so determined that the fixed stars shall have no systematic rotation with respect to the system ($$\mathrm{x, y, z}$$), and the assumption is then made that ($$\mathrm{x, y, z}$$) coincides with ($$x, y, z$$), the system to which the equations of motion are referred. Whether this is so or not can only be decided by comparison with the motions in the solar

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Mar. 1911. system. The problem has been exhaustively treated by Anding (Encyclopädie der Math. Wissensch., vi., 2, page 3) and Seeliger ("Ueber die sogenannte absolute Bewegung," Münchener Sitzungsber., 1906, page 85) and others. Since the nodes are fixed under the new law, and also the perihelia are practically fixed, with the exception of Mercury (for which see art. 13), and the correction (42) to the constant of precession is insensible, the problem is not changed in aspect by the introduction of the principle of relativity, and we need not further refer to it here.

18. Astronomical time is defined by the rotation of the Earth, and is measured by the hour-angle of the axis of $$x$$. Such deviations from uniformity as are derived from the action of known causes—which are, however, negligible, and remain negligible under the new law—are allowed for, and the thus corrected rotation is supposed to be uniform. Now a motion which is in a system ($$x, y, z, t$$) described by the formulæ of uniform rotation, is no longer so described in another system ($$x', y', z', t'$$). The definition of astronomical time would thus be dependent on the system of reference.

But the axis of $$x$$ cannot be observed. Time is determined by the observation of the hour-angles of stars. In the new system ($$x', y', z', t'$$) the direction in which we see the stars is also changed, and a compensation is effected.

Determinations of time are made at intervals, and are used to regulate the clock. Equal intervals on the clock are then supposed to be equal intervals of "time." The construction of the clock depends on the laws of the simple pendulum, which swings under the action of gravitation. We would thus be led to identify astronomical time with the proper-time of the pendulum-bob. Instead of this we can, of course, take the proper-time of the transit-room, or of the centre of the Earth. In this time as variable the motion of the Earth, adopting the law I. and neglecting its mass, is strictly Keplerian. But if we wish to consider the whole solar system, it is better to introduce heliocentric (or "barocentric") time. The difference has been found to be insensible [equation (34)]. The whole question of the definition of astronomical time is thus only of academic interest. So far as the interpretation of observations is concerned, we can identify astronomical time with the variable $$t$$ of any system of reference we wish to use.

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1922 Encyclopædia Britannica/Montessori System

MONTESSORI SYSTEM. — In connexion with the theory of education, one of the chief points of new interest during 1910-21 was the attention aroused by Dr. Maria Montessori's work. It is hardly too much to say that, since Froebel, no such stimulus has been given to a revolution in the elements of educational method as her success, from 1907 onwards, with the Case dei Bambini in Rome; and the Montessori system has given a new direction to ideas upon child education.

Maria Montessori (b. 1870) came to the study of educational theory after a thorough training in practical medicine. She was the first woman to whom (in 1894) the university of Rome gave the degree of M.D., and as assistant doctor in the “psychiatry” clinic at the university she had become specially interested in the question of the treatment of the feeble-minded. At the Pedagogic Congress at Turin in 1898 she gave an address on this subject, which led the Italian Minister of Education, Signor Barcelli, to ask her to give a series of lectures to teachers in Rome; the result was the foundation of a new school for feeble-minded children, the Scuola Ortofrenica, of which she was made directress. Her ideas as to the proper way of awakening a defective intelligence had been founded on a study of what Dr. Itard, physician to the Institution for the Deaf and Dumb in Paris, had attempted early in the 19th century in the case of the much-discussed “Wild Boy of Aveyron,” and particularly of the later work of Edouard Séguin (1812-88), author of the Traitement des idiots (1846), who opened in 1839 the first school for idiots in France, and who in 1850 made his home in America and there did so much for the education of defective children. In carrying on Séguin's principles at the Scuola Ortofrenica for the two years that she was directress, Dr. Montessori had such remarkable success that it was borne in upon her that something must be wrong with the methods of education ordinarily applied to normal children. Idiots sent to her from the asylums were being taught to read and write so that they passed just as good examinations as pupils of the same age in the public schools; and, as she says, “while everyone was admiring the progress of my idiots, I was wondering what could keep the normal children on so low a plane.” The reason, in her opinion, was clear; the children from the asylums, under her treatment, had been helped in their psychic development, while the normal children, taught by ordinary methods, were retarded. If the same methods were applied to good material that were successful with bad, much better results ought to be attainable; and she determined to investigate the whole subject afresh.

In 1900 she left the Scuola Ortofrenica, and turned her attention definitely away from the question of the feeble-minded to that of the normal child mind and its development. She returned to the university of Rome as a student of philosophy, and devoted herself to experimental psychology, then in its infancy at the Italian universities, at the same time making a prolonged and careful study of the actual practice of teaching at the primary schools. The result of several years of child study and practical pedagogy was to establish her conviction that the master principle in any proper system is “self-education” — that the work of mental growth must be done by the child itself, according to its own initiative and inclination, not in mechanical obedience to dogmatic dictation from a teacher; and she set herself to devise new methods for making the child-mind shape its own channels instead of the teacher telling the pupil what to do.

After six or seven years of inquiry and study a unique opportunity arose in Rome for putting her theories into practice. During the building “boom” at the end of the 1880's, a whole new quarter of apartment houses had been run up by speculators outside the Porta San Lorenzo. It was from the first a complete fiasco, the houses failing altogether to attract the superior class of tenants for which they were intended; and the district gradually developed into the worst of slums, the flats being farmed out room by room to the poorest families, so that at last a serious condition of insanitary overcrowding had resulted, which seriously engaged the attention of social reformers. In order to remedy this evil, an association was started on philanthropic lines, the Instituto Romano di Bene Stabili, with Signor Edoardo Talamo as director-general. It bought up a large part of the San Lorenzo quarter, and reorganized it in 1906 in separate and convenient working-class tenements, with proper air-space, prizes being instituted for the best-kept dwellings. A novel point of the scheme was the provision of infant schools (Case dei Bambini) for the children of each block, the supervision of which was entrusted to Dr. Montessori, the first of these being opened in Jan. 1907. These “houses of childhood” for children between three and seven were themselves a very interesting social experiment apart from the new methods of teaching which Dr. Montessori introduced. They provided a creche and something more, taking the children off their mothers' hands during working hours. Each school had a directress living in the block which it served and in touch with the parents, who could at any time come and see how the children were getting on; it was thus part of the home life.

The Montessori system of education was first put in practice in these tenement schools, under teachers following Dr. Montessori's methods. Its fundamental aim and object is self-education by the pupils themselves. There are no time-tables, no set lessons, no classes. There are no rewards or punishments of the ordinary kind. The pleasure of succeeding and getting things right is the only incentive. “Each child is doing what, for the time being, pleases him best. When he is admitted to the school he sees small groups of children playing at various ‘games,’ and he joins the group which happens to take his fancy. Then and there his education begins. All kinds of interesting ‘occupations’ are going on, and wherever he goes he will get help and guidance from the teachers. If he gets tired of playing at this thing he goes off and plays at that. But he is never idle, for whatever he does interests him. The children are provided with light and comfortable chairs, which are easily moved about. There are also rugs laid on the floor for them to sit, kneel or recline upon, should they prefer those attitudes. Low and light tables are provided in abundance, but there is also plenty of open floor-space, and many of the ‘occupations’ are carried on on the floor” (Holmes). An extensive variety of apparatus, elaborately devised by Dr. Montessori, is provided for the educational games by which the children are stimulated to acquire knowledge; and this “didactic material” constitutes a distinctive part of the originality of the system.

The first stage is to develop the senses of touch, sight and hearing; this is done both by games of various sorts and by guiding the attention systematically to the association of things, names and ideas. When a child washes his hands, for instance,

he is given first cold and then hot water, and led to observe and understand the difference; the distinction of rough and smooth is emphasized by the provision of different qualities of cards for fingering and sorting. In each case the teacher gets the child to know the word, “hot,” “cold,” “rough,” “smooth,” and thus the knowledge of language is extended in all directions (“high,” “low,” “thick,” “thin,” “round,” “oval,” etc.) before any question of writing or reading arises. Ideas of form and colour are given precision by games with blocks, cylinders, etc., of varying sizes, to be fitted into frames, or with shades of silk to be arranged to match; touch is practised by playing the games blindfold; the sense of hearing is developed by the “silence” lesson, and by the use of small cylindrical boxes containing stones, sands and different substances to be rattled by the children, who arrange them in order of intensity of sound and so forth. Skill and neatness in the use of the fingers and movement of limbs are stimulated partly by the mobility of the light furniture, which the children learn to rearrange for their own comfort, and partly by games at tying and untying, hooks and eyes, dressing and undressing, waiting on one another at table, washing up, and so on. Many of these occupations are preliminary to writing and reading, and lead naturally up to both.

Writing comes essentially before reading, on the Montessori system, in any proper sense of “reading.” Emery-paper letters gummed on cards are provided, with which the child is familiarized by games of hide and seek, etc., so that, without any active teaching of the alphabet, he not only knows them by sight and by name, but also by feeling. He learns how to imitate them, partly by a touch game of passing the fingers over the paper letter, thus making the actual motion of writing, and partly by playing at pencilling and colouring with specially devised cards on which an outline is given. The child thus learns to write before he knows that “writing” is what he is learning; the sounds and shapes of the letter being known it is a natural transition to build up the letters and their sounds into words.

The next thing is for the child to “read” — not merely to re-translate into sound a word he has translated into symbol, which goes with the acquisition of “writing,” but to extract a previously unknown idea from written or printed symbols of the same sort not put together by himself. It is found, however, that, at any rate in so easy and phonetically spelt a language as Italian, this is very quickly learnt. Numbers of words, already well known to the children, are written on cards, and various games are played in identifying them with their objects; and from single words the children pass to phrases and sentences, the teacher writing on the blackboard, for instance, questions or orders which form part of a game. Arithmetic is similarly introduced to the children's minds by the employment of counting games, in which an apparatus of striped poles, counters, etc., is used. The whole curriculum is devised for the content and happy employment of the natural energies of the child, who is left free to respond to his own impulses, under the influence of “didactic material,” rather than under the discipline of a teacher.

After 1912 the diffusion of Dr. Montessori's educational influence was rapid and widespread. Following close upon the interest which had already been aroused in Italy and America, Dr. Montessori, in response to urgent requests from educational enthusiasts all over the world, began a series of international training courses for teachers. These courses were held in Rome in 1913 and 1914. In subsequent years Dr. Montessori held training courses in Barcelona and in several cities of the United States, two international courses having been held in London in 1919 and 1921. To these training courses came not only class teachers of the particular country, but persons eminent in the educational field from all over the world. During this later period two of the most notable features in connexion with the Montessori movement were the appearance of Dr. Montessori's new books, The Advanced Montessori Method and The Didactic Material for the Education of Children from 7 to 11 years. The first volume gives a clear and complete exposition of the scientific researches which led to the establishment of the fundamental psychological and physiological principles upon which Dr.

Montessori bases her method of auto-education, and the second volume fully describes in detail the educational material for the older children. The form of the advanced apparatus is such that the children who have passed beyond infant school age are provided with material which continues to perfect the muscular control achieved in a previous stage, while at the same time the way in which the material is used tends to strengthen those attributes of character which are the tests of educational values. By means of the objects provided for the child between the ages of 7 and 11 he becomes possessed of considerable mental acquirements, notably in the comprehensive intellectual fields of mathematics and language. The arrangements of artistically coloured beads which are used by the child for his progress in arithmetic, the ingenious geometrical forms which render geometry no longer a tedious abstraction, but a fascinating reality, the system of small attractive cards handled by the children in their study of grammar, all form a far more potent incentive to work and persistent effort than any exhortation or command of the teacher.

“Montessori Societies” have, since 1912, come into existence in London, New York, and elsewhere, for dissemination of the ideas of the system and promoting its training courses.

(Author:Hugh Chisholm)


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BY A. A. MICHELSON

According to the undulatory theory of light the velocity of light is independent of the velocity of the source, and of the velocity of a mirror at which it is reflected.

According to the emission theory the resultant velocity from a moving source is increased by the component of the velocity of the source. But it appears that different forms of emission theory require different results on reflection from a moving mirror. If the light corpuscles are reflected as projectiles from an elastic wall, then the velocity of light should be increased by twice the component of the velocity of the mirror.

The following arrangement was devised for the purpose of deciding the question experimentally.

. 1.—Diagram of apparatus

Light from a source at S falls on a lightly silvered mirror A. The reflected pencil goes to a revolving mirror D, thence to the concave mirror E, to the second mirror C revolving about the same axis O, whence it proceeds to the plane mirror B and is reflected back to A. The transmitted pencil pursues the same path in the

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 opposite direction, returning via DA to the starting-point, where it meets the first pencil, producing interference fringes which are observed by means of a telescope with micrometer eyepiece.

According to the undulatory theory the velocity of light is unaffected by the velocity of the mirror while the emission theory requires that

$\bar{V}=V+rv$

where $$\bar{V}$$ is the velocity of light after reflection, V the velocity before reflection and v the component of the velocity of the mirror in the direction of the reflected pencil, and r = 2 according to the elastic impact theory; while r = 1 if the mirror surface acts as a new source.

The time occupied by the pencil DEC is

$T_{1}=\frac{2(D+d)}{V_{1}}$|undefined

while that taken by the pencil CED is

$T_{2}=\frac{2(D-d)}{V_{2}}$|undefined

where D is the distance OE, d = distance the revolving mirror moves while light passes over DEC, and V1 the resultant velocity of the first pencil, V2 that of the second.

The difference in time is therefore

$T_{1}-T_{2}=2\left[\frac{D+d}{V+rv}-\frac{D-d}{V-rv}\right]$

But

$\frac{d}{2D}=\frac{v}{V}$

whence

$T_{1}-T_{2}=4\frac{D}{V}(2-r)\frac{v}{V}.$

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 The corresponding displacement of the interference fringes is

$\Delta=\frac{V\left(T_{1}-T_{2}\right)}{\lambda}=4\frac{D}{\lambda}(2-r)\frac{v}{V}$

The experiment was tried under the following conditions.

The revolving mirrors were mounted on the shaft of an electric motor the speed of which (measured by a speed counter) could be varied from zero to 1800 revolutions per minute. The distance between centers of the mirrors was l = 26.5 cm; the distance OE was 608 cm. The light of the carbon arc (in one experiment, sunlight) was filtered through a gelatine film transmitting light of mean wave-length λ = 0μ.60.

The formula for the displacement,

$\Delta=8\pi n\frac{l}{\lambda}\frac{D}{V}$ if n is turns per sec.

or

$\Delta=\frac{8}{60}\pi N\frac{l}{\lambda}\frac{D}{V}$ if N is turns per min.

gives with these data and r = 0 a displacement of 3.76 fringes for 1000 revolutions per minute.

Following is a table of results of observations reduced to this speed.

It appears therefore that within the limit of error of experiment (say 2 per cent) the velocity of a moving mirror is without influence on the velocity of light reflected from its surface.

Assuming that the effect is actually nil, this interference method may be used to measure the velocity of light with an order of accuracy equal to that of the improved Foucault method or of the "combination" method proposed in an article in the ''Phil. Mag.'',

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 March 1902. Any one of these three methods is capable of furnishing results of the order of accuracy of one part in one hundred thousand; and differential measurements (e.g., with the light of the

two limbs of the sun) can be obtained with a still higher degree of precision; and thus the effect of a moving source on the velocity of light could be determined.

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the Physikalische Zeitschrift a method is proposed by W. Wien for deciding the important question of the trainement of the æther by the earth in its motion through space, by measuring the velocity of light in one direction—that is, without reflecting it back from the distant station.

The essentials in the proposed method are two Foucault mirrors, or two Fizeau wheels (one at each station) revolving at the same speed. The control for this synchronism is to be furnished by the "Konstanz des hindurchgehendes Lichtes oder in bekannten stroboskopischen Methoden."

The flaw in the proposed method—as was pointed out by Simon Newcomb as long ago as 1880—lies in the fact that the effect which it is proposed to measure is exactly the same as the effect on the light which is to furnish the test of synchronism.

In November 1887 I proposed a method differing in no essential respect from the foregoing, except that the control of synchronism was to be furnished by electrical methods. This was before the celebrated work of Hertz showed that electrical impulses differed in no essential from light. This identity constitutes the same objection to this plan.

The possibility of a mechanical method of control was pointed out in a paper on the "Velocity of Light," in the Philosophical Magazine, March 1902. This is based on some experiments made in 1899, which showed that the vibrations of a timing-fork could be transmitted over a mile of piano-wire with but little diminution of amplitude.

Suppose it were possible to transmit two pencils of light in opposite directions around the earth parallel to the equator, returning the pencils to the starting-point. If the rotation of the earth does not entrain the æther, it is clear that one of the two pencils will be accelerated and the other retarded (relatively to the observing apparatus) by a quantity proportional to the velocity of the earth's surface, and to the length of the parallel of latitude at the place; so that a

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Rh measurement of the difference of time required for the two pencils to traverse the circuit would furnish a quantitative test of the entrainement.

But it is not necessary that the path should encircle the globe, for there would still be a difference in time for any position of the circuit.

This difference is given by the formula

$$\mathrm{T}=\frac{2}{\mathrm{V}^{2}}\int v\ \cos\ \theta\ ds$$

where $$\mathrm{V}$$ is the velocity of light, $$v$$ the velocity of the earth's surface at the element of path $$ds$$, and $$\theta$$ the angle between $$v$$ and $$ds$$.

If the circuit be horizontal, and $$x$$ and $$y$$ denote distances east and west and north and south respectively, and $$\phi$$ the latitude of the origin, and $$\mathrm{R}$$ the radius of the earth, then for small values of $$y/\mathrm{R}$$ we have approximately

$$\mathrm{T}=\frac{2v_{0}}{\mathrm{V}^{2}}\int\left(\cos\phi-\frac{y}{\mathrm{R}}\sin\phi\right)dx.$$

The integral being taken round the circuit the first, term vanishes, and if $$\mathrm{A}={\textstyle\int} ydx=$$ area of the circuit,

$$T=\frac{2v_{0}\mathrm{A}}{\mathrm{V}^{2}\mathrm{R}}\sin\phi.$$

The corresponding difference of path for equal times expressed in light-waves of length $$\lambda$$ is

$$\Delta=\frac{2v_{0}\mathrm{A}}{\mathrm{VR}\lambda}\sin\phi.$$

Thus, for latitude 45° $$\sin\phi=\sqrt{1/2},\ \frac{v_{0}}{\mathrm{R}}=\frac{2\pi}{\mathrm{T}}$$; the velocity of light is $$3\times10^{8}$$ in the same units, and the length of a light-wave is $$5\times10^{-7}$$: which approximate values substituted in the preceding formula give

$$\Delta=7\times10^{-7}\mathrm{A}.$$

Thus if the circuit be one kilometre square

$$\Delta=0.7.$$

The system of interference-fringes produced by the superposition of the two pencils—one of which has traversed the circuit clockwise, and the other counterclockwise—would be shifted through seven-tenths of the distance between the fringes, in the direction corresponding to a retardation of Phil. Mag. S. 6. Vol. 8. No. 48. Dec. 1904.

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718 the clockwise pencil, if the experiment were tried in the Northern hemisphere.

The observation of interference-fringes produced by pencils which traversed a path 60 x 20 metres presented so little difficulty, that it seems quite feasible to proceed to much greater distances.

In the case considered, the length of the path would be four kilometres. If this length were doubled the area enclosed would be quadrupled and the expected displacement would be 2.8 fringes.

A difficulty in the measurement of this displacement lies in the fact that it cannot be reversed (as was the case in the experiment where the entire apparatus was rotated). A fiducial mark is, however, furnished by the image produced by one of the two pencils.

Thus let light, starting from a slit and rendered parallel by a collimator, fall on a glass plate the upper half of which is heavily silvered while the lower half is clear or lightly silvered.

The light transmitted by the lower half is reflected round the circuit, returning to the glass plate through which it passes to the observing telescope—while the reflected part traverses the, circuit in the opposite sense, returning to the glass plate where it is reflected to the observing telescope, interfering with the former pencil.

Observing by reflexion from the upper half, the image of the slit is seen, and the cross-hair of the eyepiece is made to divide this image symmetrically. The upper half is now covered and the lower half clear.

The system of interference-fringes should have its central or achromatic fringe bisected by the cross-hair if the æther rotates with the earth. If the æther does not partake of the earth's motion of rotation, the central fringe will be displaced from the cross-hair by the amount calculated from the formula.

A control is furnished by introducing another pair of mirrors in the path so as to make the area of the circuit so much smaller that the displacement would be negligible.

The attempt to apply the same principle to the revolution of the earth about the sun is less promising. The formula for the displacement from noon to midnight is in this case

$\Delta=\frac{4\mathrm{A}v}{\lambda \mathrm{RV}}\sin\phi\ \cos\delta,$|undefined

where $$\mathrm{A}, \lambda, \phi$$ and $$\mathrm{V}$$ have the same meaning as before, and

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Rh $$v$$ is the velocity of the earth in its orbit, $$\mathrm R$$ the radius of earth's orbit, and $$\delta$$ the sun's declination.

If $$\mathrm A$$=10×10 kilometres,

$$\begin{alignat}{3} v / \mathrm{V} =&\ 10^{-4}, & \mathrm{R} =&\ 1.5 \times 10^{11}, & \lambda =&\ 5 \times 10^{-7} \\ \sin \phi =&\ 0.7, & \quad\cos \delta =&\ 1, & \text{then }\Delta =&\ 0.37 \end{alignat}$$

To obtain this displacement would require a circuit 40 kilometres in length.

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text:
1922 Encyclopædia Britannica/Moody, William Vaughn

MOODY, WILLIAM VAUGHN (1869-1910), American poet and playwright, was born at Spencer, Ind., July 8 1869. He was educated at Harvard (A.B. 1893; A.M. 1894) and was assistant in English there 1894-5. From 1895 to 1907 he was at the university of Chicago as instructor and, after 1901, as assistant professor. He died at Colorado Springs Oct. 17 1910. He was the author of The Masque of Judgment (1900); Poems (1901); The Fire-Bringer (1904, intended as the first member of a trilogy on the Promethean theme, of which The Masque of Judgment, already published, was the second member); The Great Divide (1907) and The Faith Healer (1909). Of these the last two were prose dramas and were very successful on the stage, especially the first. He compiled (with Robert M. Lovett) A First View of English and American Literature (1902), and edited The Complete Poetical Works of John Milton (1899, Cambridge ed.) and (with George Cabot Lodge and John Ellerton Lodge) The Poems of Trumbull Stickney (1905).


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by Albert A. Michelson

To account for the phenomenon of aberration Fresnel supposes the luminiferous ether at rest, the earth moving through this medium without communicating any perceptible part of its motion. On this theory it has been shown that it should be possible to detect a difference of the velocity of light in two directions at right angles. As no such difference was observed, it would seem to follow that Fresnel's hypothesis is incorrect.

Another theory is that of Stokes, in which the aberration is accounted for if the relative velocity of the earth and the ether have a potential. This requirement, however, is inconsistent with the results of the experiment just cited, which indicates that at the earth's surface the relative motion is zero.

In the hope of detecting a relative motion corresponding to a difference of level, the following experiment was undertaken.

I take this opportunity of gratefully acknowledging the faithful and efficient services rendered in the execution of this work by Professor S. W. Stratton and Mr. C. R. Mann.

Light from the source s, a calcium light or an electric arc lamp, separated into two pencils at a plane-parallel glass plate, o, lightly silvered. The two pencils were reflected by double mirrors along the paths oabcoe, and ocbaoe, respectively. The two paths being equal, interference fringes could be observed with the aid of the telescope at e. Fig. 2 shows details of the corner at $$c:pq$$ are plane-parallel glass disks,

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 cemented to the ends of the iron pipes; mn, plane glass plates silvered on front surface, and provided with adjustments in two planes; omnb. the path of the pencil of light. The apparatus was set up in the vertical east and west plane, the light traversing the entire circuit of the Ryerson Laboratory, a path about 200 feet long and 50 feet high.

It was found that under ordinary conditions the temperature disturbances in this length of air made it impossible to measure the position of the fringes; and the difficulty was only slightly remedied by enclosing the whole path of the light in a wooden box. By making this enclosure an iron pipe and exhausting the air to within a hundredth of an atmosphere, it was found possible to measure the position of the central bright fringe to within something like a twentieth of the fringe-width.

A difficulty is encountered in the selection of a fiducial mark. The double image of the source does not remain on the cross hairs of the observing telescope for any great length of time, notwithstanding the precaution of the double reflections at the corners, but by using this double image itself as the fiducial mark, any possible errors due to daily temperature changes, etc., are eliminated. This double image and the interference fringes are not in focus at the same time, but by sacrificing a very

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Rh little in the definition of each, the measurements may be made with very considerable precision.

The observations were taken in the morning, at noon, evening and night; no special care being taken as to the exact hour. The results are summed up in the table containing the observations taken and reduced by Mr. Mann, as follows:—

The micrometer was set on one spot, then on the central fringe, then on the other spot, giving three readings of the micrometer. The first reading was subtracted from the third, giving the distance between the spots in divisions of the micrometer head. The second reading was subtracted from the third, giving the distance of the central fringe from the lower in divisions of the micrometer head. This last remainder was divided by the first, giving the distance n of the central fringe from the lower spot in fractions of the distance between the spots regarded as unity.

Each reading was reduced this way and the mean of ten taken as the result for any given time. The weights p were calculated as usual from the formula: $$p=c/e^2$$.

12 Noon - 11 P. M. = .013

1 fringe = .250     $$\therefore$$ maximum displacement $$\frac{13}{250}=\frac{1}{20}$$ fringe.

The conclusion from these results is that if there is any displacement of the fringes it is less than one-twentieth of a fringe.

If we consider the times occupied by the two pencils in completing

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478 their paths at noon and at midnight (when the horizontal parts of the path are parallel with the earth's motion in its orbit), we find the difference is $$4s\frac{v}{V^{2}}$$ where s is the length of the horizontal part of the path, v the difference of relative velocities above and below, and V the velocity of light. This corresponds to a displacement $$\Delta=4\frac{s}{\lambda}\frac{v}{V}$$ fringes.

If the relative motion be assumed to follow an exponential law it may be represented by

$$v=v_{0}(1-e^{-kh})$$

where $$v_0$$ is the velocity of the earth and h, the height above the surface.

Suppose $$\frac{v_{0}-v}{v}$$ falls to $$\frac{1}{e}$$ of its surface value in one hundred kilometers. Then in fifteen meters, which is the difference of level of the two horizontal pipes

$$v_{0}-v_{1}=.00015\ v_{0}$$.

Substituting this for v in the equation for $$\Delta$$ we have

$$\Delta=.0006\frac{s}{\lambda}\frac{v_{0}}{V}$$.

Putting $$\frac{s}{\lambda}=12\times10^{7}$$ and $$\frac{v_{0}}{V}=10^{-4}$$ we find $$\Delta=7.2$$ fringes.

As the actual displacement was certainly less than a twentieth of a fringe, it would follow that the earth's influence upon the ether extended to distances of the order of the earth's diameter.

Such a conclusion seems so improbable that one is inclined to return to the hypothesis of Fresnel and to try to reconcile in some other way the negative results obtained in the experiment cited in the first paragraph.

The only attempt of this character is due to H. A. Lorentz. It involves the hypothesis that the length of bodies is altered by their motion through the ether.

In any case we are driven to extraordinary conclusions, and the choice lies between these three:—

 * 1) The earth passes through the ether (or rather allows the ether to pass through its entire mass) without appreciable influence.
 * 2) The length of all bodies is altered (equally?) by their motion through the ether.
 * 3) The earth in its motion drags with it the ether even at distances of many thousand kilometers from its surface.

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Rh chronicling. Surely such a tenderly-sensitive journal could not have gone on all these years believing in the existence of these outages, and yet—beyond an occasional leader when hard-up for a subject—never crying out against them. It seems to me very like raking up something startling to pull through a dull time till Parliament commences.

In the name of everything sensible, what good end can be gained by manufacturing sensational stories by the column to prove—what? To prove that here, as in all other new countries, men who are ruffians and bullies naturally gather about our frontiers, where law is lax and restraint almost unknown. No one ever doubted it yet the Queenslander, by its present course, is endeavoring to slander the majority of our outside men for the acts of the minority, and on what authority? Take the very first yarn recounted. A white man, presumedly educated and acquainted with the laws of this country, goes out intending to shoot a quiet black boy, and takes with him another white man as a witness, who might at any time turn Queen's evidence and hang him. If the hero of this story did this he was a lunatic, and was not responsible for his actions; if he didn't, the story is on internal evidence—false. And again, why drag in mock sentiment to bolster up these charges? In the last yarn retailed, capital is made out of the fact that a man despatching some wounded blacks knocked them on the head instead of shooting them. Really it might be from moral obtuseness, but, putting aside the necessity or not of killing these blacks, I cannot see why it was more sinful to knock them on the head than shoot them. A blow from a heavy nulla would be quite as quick and easy a death as a bullet from a pistol; and if pistol cartridges were scarce, as often they are in outside country, it was a very sensible thing to do. I should feel just as much horror if I read that they were shot.

Possibly the Queenslander aims at supplying a want in our Brisbane literature. It aspires to fill the place of the Newgate Calendar or Police Gazette, and is really making a very creditable attempt. I can see how, under its tuition, our youngsters may grow up to emulate the actors in the Queenslander atrocity column, even as the apprentices of old sought to follow in the footsteps of Jack Sheppard and Dick Tarpin, after revelling in an account of their lives. If the Queenslander were honest in its purpose, one or two well-authenticated specimens would serve the end as well as a hundred. We can enjoy a little devilled kidney, or hot curry, but we don't like a surfeit of such dishes. In publishing these hypothetical narratives, duly embroidered for the occasion, the Queenslander violates good taste, and almost common decency. I maintain that half these yarns are fabrications, and that the rest are exaggerated. I never witnessed one such case myself; I never heard but of one in any district I was in, and that rested on poor foundation. I am equally certain that in all parts of this colony men would be found prompt and ready to stop such deeds by force, if necessary. Again, I know and can affirm that black protection is often only another name for immorality, and I would far rather call that man my friend who rigorously, if wrongfully, kept all blacks off his run, and allowed no intercourse with them, than he, who under the excuse of protecting them allowed them in for the sake of picking out the best looking gins in the tribe.

Beyond branding a certain portion of the community as worse than murderers, the Queenslander has as yet left the main question untouched; therefore, beyond putting in this protest, there is nothing I can remark on, and must await further utterances from the oracle. —Queenslander, May 29, 1880.

,—Much has been written on the subject of our treatment of the aboriginal inhabitants of Australia, and many schemes, distinguished for the most part by their absurdity and impracticability, have been put forward with a view to saving the race from utter annihilation.

That the race is doomed is admitted by all who have studied the subject, and those who know the nigger best feel most the impossibility of doing much to ameliorate his condition or protract the existence of his race.

This callousness as a rule arises from no lack of sympathy with the blacks, but from a firm conviction that their stage of civilisation is too many hundred or perhaps thousand years behind our own to allow their race to thrive side by side with ours.

I have not the slightest doubt that there are many to be found in the bush who would willingly contribute towards the support of any project which offers a reasonable chance of ameliorating the condition of the expiring race of men whose brothers

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