Feb. 20, 1890] 



NATURE 



!8i 



of the m + I equations, thereby obtained an identity which is 

 fundamental in the subject. This identity involves those sym- 

 metric functions which are here termed fundamental, and marks 

 the starting-point of the present investigation. 



In particular, three distinct laws of symmetry are established, 

 large generalizations of those established by the author in the 

 American J ottrnal of Mathematics (vol. xi.). Of these the first 

 two are of fundamental importance, and are examined in detail. 

 A leading idea in these theorems, as in the whole investiga- 

 tion, is the " separation" of a partition ; the separation bearing 

 the same relation to the partition as the partition to the number 

 or collection of numbers. 



In conclusion, the memoir consolidates and largely generalizes 

 the author's recent researches alluded to above. 



February 13. — " On the Unit of Length of a Standard Scale 

 by Sir George Shuckburgh, appertaining to the Royal Society." 

 By General J. T. Walker, K.E., F.R.S. 



In the determinations of the length of the seconds pendulum, 

 which were made in London by Kater and at Greenwich by 

 Sabine, and are described in the Philosophical Transactions 

 for 1818, 1829, and 1831, the distance between the upper and 

 lower edges of the pendulum was measured off on a standard 

 scale which had been constructed by Sir George Shuckburgh. 

 The scale had not yet been compared with any of the modern 

 standard scales, but it had been preserved with much care with 

 the instruments appertaining to the Royal Society. 



In the autumn of 1888, M. le Commandant Defforges, an 

 officer of the French Geodetic Survey, came to England to 

 take a share in operations for the determination of the difference 

 in longitude between Greenwich and Paris, and also to determine 

 the length of a French seconds pendulum at Greenwich, He 

 kindly undertook to comply with a suggestion which was made 

 to him by me, to compare the portion of Shuckburgh's scale 

 which had been employed by Kater and Sabine with one of the 

 standard metre bars of the International Bureau of Weights and 

 Measures in Paris. The Council of the Royal Society assented, 

 and the scale was sent across to Paris and brought back again by 

 special agent. 



The details and results of the comparison are given in a 

 special account by Commandant Defforges, from which it will 

 be seen that the scale was compared with the French metrical 

 brass scale, N, at the temperature of 48° 7 F., at which the dis- 

 tance between Kater and Sabine's divisions, o and 39 '4, of the 

 Shuckburgh scale was found equal to I '0006245 metre. On 

 reducing to the temperature of 62° F., which was employed by 

 Kater and Sabine, this distance becomes i '0007619 metre, which 

 is equivalent to 39*400428 inches if we adopt the relation 

 I metre — 39 '370432 inches, which was determined by Colonel 

 Clarke, C.B., of the Ordnance Survey, and is given in his 

 valuable work on the comparisons of standards of length. 

 Thus the actual length of the space o to 39*4 on the Shuckburgh 

 scale may be regarded with some probability as differing by not 

 more than about 0*0004 inch, or, say, the 100,000th part, from 

 the quantity which the scale indicates. 



Physical Society, February 7. — Annual General Meeting. 

 — Prof. Reinold, F. R.S., President, in the chair. — The reports 

 of the Council and of the Treasurer were read and adopted. 

 The former stated that there had been a very satisfactory increase 

 in the number of members during the year. The number now 

 exceeds 360, of whom 80 are Fellows of the Royal Society. 

 During the year the Council had proposed to change the time of 

 meeting of the Society from Saturday afternoon to Friday 

 evening. The change was adopted by the members by a vote of 

 129 to 30, and had resulted in a larger attendance at the meetings. 

 During the year the second part of vol. i. of the translations of 

 important foreign memoirs had been issued to the members, and 

 it was hoped that a third part would be published early in 

 the present session. The Council had to regret the loss by death 

 of three well-known members — ^James P. Joule, Warren de la 

 Rue, and Father Perry. A valuable collection of books had 

 been given the Society by the Royal Astronomical Society. 

 From the Treasurer's report, it appeared that the balance of the 

 Society had been increased by ;^I20 during the year. Prof. 

 Hittorf, of MUnster, was, at the recommendation of the Council, 

 elected an honorary member of the Society. The result of the 

 new election of officers was declared as follows : — President : 

 Prof. W. E. Ayrton, F.R.S. ; Vice-Presidents : Dr. E. Atkin- 

 son, Walter Baily, Shelford Bidwell, F.R.S, and Prof. S. P. 

 Thompson ; Secretaries : Prof. J. Perry and T. H. Blakesley ; 



Treasurer : Prof. A. W. Riicker, F.R.S. ; Demonstrator : C. V, 

 Boys, F.R.S. ; other Members of Council : W. H. Coffin, Sir 

 John Conroy, Bart., Conrad W. Cooke, Major-General Festing, 

 F.R.S., Prof. J. V. Jones, Prof. O. Lodge, F.R.S., Prof. W. 

 Ramsay, F.R.S., W. N. Shaw, II. Tomlinson, F.R.S., and G. 

 M. Whipple. Votes of thanks were then passed (i) to the 

 Lords of the Committee of the Council on Education for the 

 use of the room in which the Society met ; (2) to the auditors, 

 Prof. Minchin and Dr. Fison ; (3) to the President and officers- 

 of the Society for their services during the year. — The meeting 

 was then resolved into an ordinary science meeting. Messrs. E. 

 W. Smith and C. E. Holland were elected members of the 

 Society, and Mr. Sidney Evershed was proposed as a member^ 

 — The paper on galvanometers, by Prof. W. E. Ayrton, F.R.S., 

 Mr. T. Mather, and Dr. W. E. Sumpner, was then resumed by 

 Prof. Ayrton. A long table of numbers accompanying the 

 paper, and representing the result of experiments on many 

 galvanometers, was explained. From this it appeared that 

 galvanometers of the D'Arsonval type were exceedingly efficient 

 in proportion to the amount of wire used in the coils. It was 

 for this reason that voltmeters with strong permanent magnets 

 could be made sensitive even with an exceedingly large external 

 resistance in series so as to diminish the power absorbed by the 

 instrument. The space occupied by the wire was so exeedingly 

 valuable that the extra resistance did not too much diminish the 

 sensibility. The most sensitive galvanometers should therefore 

 be made of the permanent magnet type. If, however, the magnets- 

 were to form part of the moving system, as in most galvano- 

 meters, the experiments showed that instruments of the Rayleigh,. 

 Gray, or Rosenthal type were the best. The coils should be 

 numerous and small, as Mr. Boys had previously shown. As aI^ 

 astatic system of needles sets itself perpendicular to the earth's 

 field, it was recommended that astatic galvanometers should be 

 placed so that the needles pointed east and west. The controlling, 

 magnet would then not need to be turned round as it was raised 

 or lowered. It was recommended to calibrate low-resistance 

 ballistic galvanometers for quantity by measuring the deflection 

 for a known current. This obviates the necessity for large 

 condensers or high potentials. The method, although not new, is 

 not described in text-books. In conclusion. Prof. Ayrton asked 

 for information with regard to microscope galvanometers. 

 C. V. Boys, F.R.S., thought that the factor of merit of galvano- 

 meters should not be given in scale divisions per micro-ampere- 

 under the condition of constant controlling moment. This gave- 

 too great an advantage to instruments of the Gray or Rosenthal* 

 type. Great sensibility could be obtained by diminishing the 

 moment of inertia of the suspended parts, the practical limit 

 being determined by the trouble due to the silk fibre. Spider 

 lines, when used in place of silk fibres, gave better results. It 

 was possible by using a good suspending arrangement to use 

 needles ^" long and a period of 20 seconds, and to gain a 

 sensibility far greater than those indicated in the paper. Ballistic 

 galvanometers should be made with needles as light as possible.. 

 The method proposed, of winding the central part of the coil in 

 the opposite sense to the rest, would probably not be good, owing, 

 to the unevenness of the field produced. The conclusion come 

 to by the author, that D'Arsonval galvanometers of great sensi- 

 bility should be made with small coils placed in a very strong field,, 

 was one he had himself come to, but had finally abandoned owing 

 to difficulties caused by diamagnetism in the copper and to- 

 excessive damping due to Foucault currents. Mr. Swinburne 

 thought that the factor of merit of a galvanometer should be 

 determined differently according as it was to be used for the 

 measurement of current, or quantity, or for null methods merely. 

 He saw no great advantage in making practical instruments 

 proportional. The name D'Arsonval should be dropped, as the 

 instrument denoted by it was invented by Varley years ago. 

 He would like to know the relative sensibility of the telephone 

 and the Lippman galvanometer. Prof. Fitzgerald stated that 

 Lord Rayleigh had shown that the microscope method of 

 observing angular deflections was as sensitive as the ordinary 

 method of mirror and scale, even when only the mirror was used 

 as a pointer, so that if a pointer were attached it would be far 

 more sensitive. The drawback, however, was that it was 

 impossible to distinguish with the microscope between lateral 

 displacements of the needles and the angular motion whose 

 measurement was required. To get over this error it was 

 necessary to read both ends of the pointer, but this was hard 

 to do. Prof. Ayrton replied to the different points raised 

 in the discussion. 



