404 



NATURE fl- 



\Sept. 9, 1875 



REPORTS. 



Report of the Committee on Mathematical Tables.— The portion 

 of the report that had been prepared by Prof. Cayley during the 

 year contained a rhumS of works and memoirs on the theory of 

 numbers. The publication of the elliptic function tables had, 

 under the direction of Mr. J. W. L. Glaisher, proceeded during 

 the year, and the first sixty-four pages of the table, printed from 

 the stereotype plates, were exhibited to the Section. It was 

 expected that the whole table would be printed by the next 

 meeting. Mr. Glaisher stated that considerable additions had 

 been received from mathematicians relating to the report on 

 general tables, and that it was probable a supplementary report 

 on this subject might be presented at the next meeting of the 

 Association. 



Hyperelliptic Functions. ^"bUx. W. H. L. Russell stated the 

 contents of the portion of his report that he had written in the 

 year, and which related chiefly to memoirs of Weierstrass. His 

 report would be completed in two more parts. 



Report of the Committee on Mathematical Printing, by Mr. W. 

 Spottiswoode. — At the Belfast meeting the committee, consisting 

 of Mr. Spottiswoode, Professors Stokes, Cayley, Clifford, and 

 Mr. J. W. L. Glaisher, was appointed to report on mathematical 

 notation and printing, with the view of leading mathematicians 

 to prefer in optional cases such forms as are more easily put into 

 type, and of promoting uniformity of notation. The report 

 related wholly to printing, and contained a list of forms having 

 the same signification, the o ne requ iring "justification," and the 

 other not (such as ex. gr. \/a + x, and \J{a + x)) There were 

 also attached diagrams showing the mechanical operation of 

 setting up mathematical expressions in type, so that when there 

 were two forms equally satisfactory from the mathematical point 

 of view, writers might choose the one that would give the printer 

 less trouble ; as everything that tended to cheapen mathematical 

 printing tended to the spread of the science. With regard to 

 notation, the committee had thought it better not to report, feel- 

 ing that in presence of the differences of opinion that must exist, 

 it would be desirable that the matter should be discussed by a 

 larger committee. The committee was reappointed to report on 

 mathematical notation, with the addition of Sir Wm. Thomson, 

 Professors H. J. S. Smith and Henrici, and Lord Rayleigh. 



Report of the Committee on Tides, by Sir William Thomson. — 

 He remarked that tides rise and fall in a series of harmonic vibra- 

 tions, like the various tones in music, some tidal waves being due 

 to the moon, others to the sun, others to meteorological causes. 

 Even the overtones in music — so thoroughly studied by Helm- 

 holtz — were represented in the tidal waves. The committee had 

 been engaged upon tides ioralongtime, and had shown theGovern- 

 ment, harbour authorities, and others interested, the way to con- 

 tinue the work, but it could do so itself no longer, for he believed 

 that day to be the last of the existence of the committee. The 

 calculations connected with tidal observations were of a laborious 

 nature. Col. Walker, of the Trigonometrical Survey of India, 

 had helped the committee very much by printing the forms re- 

 quired for the calculations. Col. Walker had also had a series 

 of tidal observations made in the Indian seas, and might possibly 

 send the results home to have the calculations made from them. 

 The Indian Government would probably have further obfcrva- 

 lions made, especially in an important new harbour they were 

 constructing at Madras. A great mass of other observations was 

 accumulating. Mr. H. C. Russell, the Government astronomer 

 at Sydney, had made several years' tidal observations, but had been 

 obliged to stop them on account of the cessation of the grant for 

 the work, but he hoped that the duty would be undertaken once 

 more j as yet, the committee had no reductions whatever of tidal 

 observations in the southern hemisphere, and knew nothing 

 about the tides there. He had been promised a long series of 

 observations, extending over eighteen years, from Brest, and he 

 had applied for a series of eighteen years' observations from 

 Toulon ; so that he expected to obtain some information about 

 tides on the French coast. The Tidal Committee had had some 

 assistance from the Royal Society, which had given it a grant of 

 100/. to carry on tidal calculations. It had thus ascertained that 

 the tides in Erebus Bay were connected with the Atlantic and 

 not with the Pacific. Sir William Thomson then exhibited to 

 the meeting and described his tide-gauge and tide-calculating 

 machine, the latter being an improvement on that first described 

 at Brighton and shown at Bradford two years ago. Although 

 the old committee on tides ceased to exist at this meeting, a new 

 one was appointed, consisting of Sir W. Thomson, Prof. J. C. 

 Adams, Rear- Admiral Richards, General Strachey, [Mr. W. 



Parkes, Col. Walker, Prof. Guthrie, Mr. J. W. L. Glaisher, 

 Mr. John Exley, Mr. J. N. Shoolbred, and Mr. J. R. Napier, 

 and the sum of 200/. was granted to them for completing and 

 setting up in I^ondon, where it may be available for use, Sir 

 William Thomson's tide- calculating machine. It was suggested 

 that perhaps the machine might be placed at South Kensington. 



Report of the Committee on Wave Numbers. — Portions of a letter 

 were read from Mr. G. Johnstone Stoney relating to the work done 

 in the year. At the Belfast meeting it was arranged that Mr. 

 Stoney should interpolate Kirchhoff's lines into the table of wave 

 numbers of the solar spectrum which Mr. Burton had prepared 

 for the committee. When this was attempted, however, it was 

 found that there were points requiring personal explanations from 

 Mr, Burton, who was absent at Rodriguez on the Transit of 

 Venus expedition, and the delay so occasioned had prevented any 

 portion of the table being as yet printed. About thirty-four 

 folios in manuscript, forming about two-thirds of the whole, were 

 complete and were exhibited to the section, 

 -■'^n interim Report of the Committee for testing experimentally 

 Ohm's Law, by Prof. Clerk-Maxwell, was read. It stated that 

 he had had two compound resistance coils constructed by 

 Warden and Co., one containing five equal, or nearly equal, 

 coils of thirty ohms each, and the other two similar coils of 

 thirty ohms, and by means of these he had devised a satisfactory- 

 test of Ohm's Law which could be worked to about TFurtr' 

 Nothing had, however, been done as yet. It was mentioned 

 that Mr. Chrystal had compared the resistances of the standard 

 coils belonging to the Association, and now in the Cavendish/^ 

 Laboratory at Cambridge. / 



Prof. Thorpe presented a preliminary Report of the Committee 

 appointed for the purpose of determining the specific volumes of 

 liquids. It gave a resume of experiments upon certain liquids 

 and gases, experiments made with a view of following up the 

 work of Hermann Kopp, to whom almost all our knowledge of 

 the subject is due, and further to arrive at definite conclusions 

 with reference to the laws laid down by Kopp. 



Prof. Corfield, on reading the Report of the Srwaqe Committee, 

 observed that want of funds during the past year had prevented 

 them from employing a sufficient amount of labour to obtain 

 many useful results, but he was happy to state that the prospect 

 for the ensuing year was brighter, as they had had a very liberal 

 offer of pecuniary assistance. The observations which have been 

 made on the Sewage Farm (situated near Romford) go to show 

 that the weight of the crops removed from the land has increased 

 each year. The great thing required is to make a comparison 

 between the nitrogen taken up by the crops and the effluent 

 nitrogen, and in order to accomplish this with accuracy it was 

 necessary that the experiments should be constantly repeated, 

 and should extend over a considerable number of years. 



Report of Committee for considerifig the desirability of establishing 

 a close time for the Protection of Indigenous Animals. — This 

 report expressed regret that it had been found impossible to in- 

 troduce the desired measure into Parliament this year in time 

 to allow of its being carried; but Mr. Henry Chaplin, M. P. for 

 that part of the Atlantic Doldrums which lies in the track of 

 Mid- Lincolnshire, holds out the hope that he will bring forward 

 such a measure early next session. The committee continue to 

 receive assurances of the efficient working of the Sea Birds' Per- 

 servation Act of 1869. 



The report (unfortunately the last) of the Sub-Wealden Ex- 

 ploration states that the new bore-hole has failed to penetrate to 

 the Paleozoic rocks. The small diameter prevents tubing, and 

 the sides now appear to be too friable to preserve verlicality. 

 Cessation of the work is hourly expected. The most note- 

 worthy result of this heroic but unsuccessful investigation is the 

 great thickness of the Kimmeridge clay, which, as was predicted 

 by Mr. Searles Wood, considerably exceeds the estimate of the 

 Sub-Wealden Boring Committee. 



SECTIONAL PROCEEDINGS 

 SECTION A— Mathematics and Physics 

 Dr. J. Janssen made four communications to the Section, the 

 first of which related to the eclipse of April 1875, as observed 

 at Bangchalio (Siam). He used a special telescope for the study 

 of the corona. The results were — I. The establishing that the 

 line 1474 is infinitely more pronounced in the corona than in the 

 protuberances. This line seems even to stop abruptly at the 

 edge of the protuberances without penetrating them. The light, 

 then, which gives the line 1474 belongs entirely to the corona. 

 This observation is one of the strongest proofs which can be 



