say a very rough idea, because the actual state of motion in a ring vortex or a Hill's vortex is not quite so simple as the analogy might lead one to think. 1 Now a compound vortex atom of this kind is just what we want to produce rotation of the plane of polarisation of light. The light passing through such a vortex has the direction of vibration twisted in the wave front. In ordinary matter no such rotation is produced, because the various atoms are indifferently directed, and they neutralise each other's effects. Let, however, a magnetic field be produced, and they will range themselves so that, on the average, the primary circulations through the apertures will point in the direction of the field. Consequently the average direction of the secondary spin will be in planes perpendicular to this, and will rotate the plane of polarisation of any light whose wave front passes them. The rotation is produced only on the light which is transmitted through the vortex. The rotation observed is a resultant effect. In fact it is clear that in the case of refraction the optical media belong to the type in which every portion transmits the light, and not to the type in which refraction is produced by opaque bodies embedded in the ether. The atoms are only opaque if they contain vacuous cores. The question of the grip of the particles on the ether does not enter, but difference of quality-showing itself in refraction and dispersion is due to difference in average rotational quasi-elasticity produced by the atomic circulations, and possibly absorption is due to precessional and nutational motion set up by the secondary spins. These, however, are perhaps rather vague speculations. Instead of attempting to invent ethers, to deduce their properties from their specifications, and then seeing whether they fit in with experience, we may begin half way. We may assume different forms for the function giving the energy of the medium when disturbed, apply general dynamical methods, and distinguish between those which are capable of explaining the phenomena we are investigating and those which are not. Invention is then called upon to devise a medium for which the desired energy-function is appropriate. This was the method applied by MacCullagh to the luminiferous ether. He obtained an algebraical form of the energy function which completely satisfied the conditions for a luminiferous ether; its essential property being that the energy depended only on the rotational displacements of its small parts. He was unable, however, to picture a stable material medium which would possess this property. We recognise now that such a medium is possible if the rotational rigidity is produced by intrinsic motions in the small parts of the medium of a gyrostatic nature. In a most masterly manner Larmor has recently investigated by general dynamical methods the possibility of explaining electric and magnetic phenomena by means of the same energy function. Electric lines of force are rotational filaments in the ether,3 similar in fact to those I suggested at Bath, whilst a magnetic field consists of a flow of the ether. The same difficulty in accounting for electro-dynamic induction arises, but the general form of the equations for the electro-dynamic and magnetic fields are the same as those generally received. 2 Towards the end of this paper he is led to postulate a theory of electrons whose convection through the ether constitutes an electric current. Two rotating round each other are supposed to produce the same effect as a vortex ring. The mass of ordinary matter is attributed to the electric inertia of these electrons. The electron itself is a centre or nucleus of rotational strain. If I express a doubt as to the possibility of the existence of these nuclei as specified, I do so with great diffidence. 1 'Primary' refers to the motion as usually understood; 'secondary,' to the superposed, as explained above. 2 'A Dynamical Theory of the Electric and Luminiferous Medium,' Phil. Trans.,1894. 3 The necessity that the filaments shall be in pairs does not seem to be recognised. This is, however, essential. Moreover, if the complementary circulations of the filaments between (say) a plate condenser be placed otherwhere than in the same region, the filaments between the plates must rotate as a whole; that is, an electric field would always be combined with a magnetic one. It would appear that the same results would flow if two particles oppositely electrified―i.e. joined by two complementary filaments, as already described-were to rotate round each other. Whether they can or cannot exist, however, the general results of the investigation are not affected. Since this paper was published Larmor has read a second one on the same subject before the Royal Society, developing further his theory of the electron. The publication of this will be awaited with interest. It is impossible in an address such as this to go seriatim into the numerous points which he takes up and illuminates, because the mathematical treatment of the general question does not lend itself easily to oral exposition even to an audience composed of professed mathematicians. There is no doubt but that this paper has put the theory of a rotationally elastic ether-and with it that of a fluid vortex ether on a sounder basis, and will lead to its discussion and elucidation by a wider circle of investigators. One further class of physical phenomena yet remains, viz., those of gravitation. The ether must be capable of transmitting gravitational forces as well as electric and optical effects. Does the rotational ether give any promise of doing this? No satisfactory explanation of gravitation on any theory has yet been offered. Perhaps the least unsatisfactory is that depending on the vortex atom theory of matter, which attributes it to pulsations of hollow vortex atoms. But this necessitates that they should all pulsate with the same period and in the same phase. It is very difficult to conceive how this can happen, unless, as Larmor suggests, all matter is built up of constant elements like his electrons, whose periods are necessarily all alike. It is possible that the vortex cell theory of the ether, of which I have already spoken, may suffice to explain gravitation also. The cells, besides their rotational rigidity, have, in addition, as we saw, a peculiar elasticity of form. To get an idea of how this theory may account for weight, let us suppose the simplest case where all the cells are exactly alike, and the medium is in equilibrium. Now suppose one of the cells begins to grow. It forces the medium away on all sides; the cells will be distorted in some definite way, and a strain set up. Further, this strain will be transmitted from the centre, so that the total amount across any concentric sphere will be the same. Stresses will therefore be set up in the whole medium. If a second cell begins to grow at another place it will produce also a state of strain, the total strain depending on the presence of both. The stresses called into play in the medium will produce a stress between the bodies, but it is questionable whether it would be inversely as the square of the distance. Whether it would be an attraction or repulsion can only be determined by mathematical investigation. The problem is quite determinate, though probably a very difficult one, and would be of mathematical interest quite apart from its physical importance. Since apparently the phenomena of gravitation have no direct interaction with those of light and electricity, whilst the mind rejects the possibility of two different media occupying the same space, we seem driven to look for it in an independent structure of the same medium. Such a structure is already to our hands, with its effects waiting to be determined. It may well be that it may prove to be the cause we are seeking. The rapid survey I have attempted to make is no doubt a medley of suppositions and inferences combined with some sound deductions. This is the necessary consequence of a prospecting survey in a region whose surface has been merely scratched by pioneers. My object has been to show that this theory of an ether, based on a primitive perfect fluid, is one which shows very promising signs of being able to explain the various physical phenomena of our material universe. Probably, nay certainly, the explanations suggested are not all the true ones. Some will have to be given up, others modified with further knowledge. We cannot proceed to particularise in our secondary hypotheses until we know more about the properties of such media as we have been considering. Every special problem solved in vortex motion puts us in a position to form clearer ideas of what can and what cannot happen. The whole question of vortex aggregates and their interactions is 1 On the Problem of Two Pulsating Spheres in a Fluid,' Proc. Camb. Phil. Soc., iii. p. 283. practically untouched, and a rich field is open for mathematical investigation in this portion only of the subject. In all cases, whether a fluid ether is an actual fact or not, the results obtained will be of special interest as types of fluid motion. It is at present a subject in which the mathematicians must lead the attack. I shall have attained my object in choosing this subject for my address, if by it I can induce some of our younger mathematicians to take it up, and work out its details. The following Papers and Report were read :- 1. On the Reichsanstalt, Charlottenburg, Berlin. The original idea of this establishment emanated from von Helmholtz and Werner von Siemens. The site at Charlottenburg, about 11 acres, was given by Dr. Werner von Siemens, and he contributed 250,000 marks (12,0007.) in aid of the building. Thereupon the German Government undertook the construction of the building and its endowment. The design of the buildings and the working arrangements were planned by von Helmholtz, who was appointed its first director. One portion of the establishment is complete and in operation. The buildings for the other portion are still in course of erection. The scientific work of the second portion is meanwhile being partially carried on in the Royal Technical High School, situated at Charlottenburg. As the establishment is thus still far from complete, the cost of the building and equipment, and of the annual expenditure for maintenance, cannot be given. The object of the establishment may be defined to be the development of pure scientific research, and the promotion of new applications of science for industrial purposes.' The establishment consists of two divisions. The first is charged with pure research, and is at the present time engaged in various thermal, optical, and electrical and other physical investigations. The reports on many branches of work which have been done in this establishment are appended to the paper. The second branch is employed in delicate operations of standardising and testing to assist the wants of outside research students, and to facilitate applications of science to industries. As, for instance, comparison with standards of the dilatation of metals, of electrical resistances, of electric and other forms of light, of lenses, of pressure gauges, of recording instruments, thermometers, pyrometers, and tuning-forks, experiments on the qualities of glass, examination of oil-testing apparatus, viscosity of glycerine, &c. The plans exhibited give a general idea of the size of the establishment, which stands in its own grounds, of which the space not covered by buildings is laid out in gardens. The principal building is occupied by the first division; it faces the northwest, and stands at some distance back from the road. This building is about 100 feet long and 85 feet deep. It has three floors of laboratories, and a basement which stands on a mass of cement concrete 2 metres thick, so as to protect the apparatus from vibration; but notwithstanding every precaution, the passing of heavy waggons in the road occasions some movement. An electric tramway is talked of. If this be constructed, serious injury will result to the institution. In this building there are thirty separate apartments devoted to laboratories, in addition to the several official rooms required for the director and staff, and there is also in the building a large and excellent library of works on pure and applied science. To the south of this, and parallel to it, is the building for the second division. This building is nearly 200 feet long, and there are two wings, each of which projects to the south to a distance of nearly 95 feet. This building also is three storeys in height. In the second division there are about forty-one or forty-two apartments devoted to laboratories, in addition to a considerable number of rooms required for the director, the clerks, and the staff, and for a small library. Towards the front on the eastern side, but nearer the road, is the director's house. On the western side is a house which affords apartments for two of the assistants, and a meeting room for the Board of Management and subsidiary clerks' offices. Behind the latter building, on the west side, are placed the engine house, and rooms for dynamos and storage batteries, as well as laboratories for operations in which the use of cold air is required. These are in course of construction. These buildings are equally convenient for the supply of power to both divisions. Two important questions for a department of pure research are: first, the management and the arrangements for regulating the subjects of research; secondly, the methods of taking stock of the work done in the establishment. In the Reichsanstalt the President is supreme over the staff. The successor to v. Helmholtz is Dr. Kohlrausch. He takes charge of the first division, viz., that of pure research. The Director, Professor Hagen, under him, takes charge of the second division. Each main division is subdivided into separate departments for each branch of research; these are in charge of permanent professors. Each of these has under him the necessary assistants selected for limited periods, and for previous good work in one or other of the universities or scientific schools of Germany. The general supervision is under a Council, consisting of a President of the Council, who is a Privy Councillor, and twenty-four members, including the President and the Director of the Reichsanstalt; of the other members, about ten are professors, or heads of physical or astronomical observatories connected with the principal universities in Germany. Three are selected from leading firms in Germany, representing mechanical, optical, and electric science, and the remainder are principal scientific officials connected with the Departments of War and Marine, from the Royal Observatory at Potsdam, and from the Royal Commission for Weights and Measures. This Council is summoned to meet when required, but it generally meets in the winter, for such time as may be necessary, for examining the research work done in the first division during the previous year, and for laying down the scheme for research for the ensuing year, as well as for suggesting any requisite improvements in the second division. It will be seen that the safeguard for ensuring good research work on subjects of general interest and importance lies first in the judicious selection of the President, Director, and Professors of the Reichsanstalt, and after them in a careful selection of the members of the Board of Management, because they not only arrange the subjects for research, but they also hold an annual stock-taking of work done in the department. Members of the Board of Management, who are appointed from the various scientific establishments all over Germany, are carefully selected, and are remunerated for their services. In this country, whilst the more enlightened of the County Councils are forming polytechnic institutions intended to approximate to the higher grade polytechnics in Germany, we have no Government Department which approximates to the Reichsanstalt. The Standards Department was attached to the Board of Trade in 1878, with the duty of making standards of length, weight, and capacity, and in 1889 it was further empowered to make such new standards for the measurements of electricity, temperature, and gravities as appeared to be of use for trade. This department possesses, moreover, under the Gas Acts, powers as to a standard of light. The object of this department is to meet the requirements of trade. Neither the Nation nor the Government appear to have realised the enormous saving of time and labour which would result from systematic standards for every branch of scientific research, coupled with arrangements for comparison easily accessible to students. There would seem to be some difficulty in altering the functions of the Standards Department so as to combine research with its present duties, nor is it established in a situation where delicate observations could be carried on. The Incorporated Kew Observatory, which is administered by a Committee under the Royal Society, is situated in an almost ideal locality for observations. It already conducts, on a small scale, some experimental work, and it appears to afford a nucleus which might be gradually extended into an establishment analogous to the Reichsanstalt, provided the Government would countenance its extension on its present site, and aid the scheme with a grant of money. Under these circumstances, I would suggest that the Committee of Section A upon National Laboratories-which appears not to have been re-appointed at Oxford-be now renewed with members added from Section B and Section G, and that it be requested to report : (a) Upon the functions which an establishment of this nature should fulfil. ment. The Association would then be in a position to approach the Government with a definite proposal, either for the utilisation of the Incorporated Kew Observatory for the purpose, or for some other plan. 2. On the Teaching of Geometrical Drawing in Schools. The teaching of geometrical drawing in schools is in many respects unsatisfactory. It is at present chiefly regulated by the examinations of the Science and Art Department and those for the entrance into the army. At some schools there are also special classes for those boys who intend to become engineers. The requirements for these are at present quite different. It seems desirable, and not at all difficult, to assimilate the teaching by laying down one rational course, so that all pupils at schools can receive the same instruction, at least in the earlier stages. This should be done first of all without any regard to examinations, the only object being the teaching of the art' of geometrical drawing. The syllabus for any examination should then be drawn up in conformity with such a course. To bring this about a committee of the British Association seems to be the most appropriate means. It would be the duty of such a committee to lay down the outlines of the course, and therefore it would be premature to say much about it at present. A few points, however, may here be touched upon. First of all it seems necessary to free the subject, at least at the beginning, from all connection with Euclid and his constructions; in fact, geometrical drawing should be begun long before Euclid is tackled. Euclid only knows two drawing instruments, the straight-edge and the pair of compasses for drawing straight lines and circles. To these should be added at once the set-squares and sooner or later the T-square. The drawing of parallels and perpendiculars should be done by their aid; bisection of lines by their aid and by trial. The first object should be to draw accurately. A great many figures can be drawn, first without circles, where the pupil can judge for himself whether his drawing is accurate. Rules for transforming figures by stretching or by shear may follow, leading to equal and to similar figures. Such a course will be the very best introduction to Euclid, and will form a natural connection between the Kindergarten, which is steadily gaining in importance, and the systematic geometry of Euclid. Solutions of problems which require a knowledge of Euclid should be attempted only when good progress has been made in this art of drawing. |