May 1 8^ 1916] 



NATURE 



253 



missions granted to other graduates and students is 

 273. Honours and distinctions conferred include one 

 Companionship of the Bath, one Victoria Cross, thirty 

 Military Crosses, and seventy-eight Mentions in 

 Despatches. Eighty-nine members of the contingent 

 have fallen in the war. Returns received already from 

 schools and institutions of the University show that 

 upwards of 600 members of the staffs, and more than 

 6000 of their present and former students, have gone 

 to the war. During the year the number of. these 

 who have given their lives has been 226. A large 

 number of professors, demonstrators, and others, both 

 teachers and students, are engaged in assisting the 

 national authorities as chemists, physicists, engineers, 

 and otherwise. 



Oxford. — The statute providing that original ex- 

 perimental investigation shall be a necessary' condition 

 for obtaining a class in the honour school of chem- 

 istry passed Convocation on May 16 without a division. 

 This marks an important new departure in the regula- 

 tion of chemical work at Oxford. It is hoped in many 

 quarters that the principle thus established may be 

 widely extended, so as to affect other scientific sub- 

 jects besides chemistrj'. 



The Halley Lecture for igi6 will be delivered in 

 the Hall of Queen's College at 8.30 p.m. on Satur- 

 day, May 20, by Dr. G. W. Walker, late fellow of 

 Trinity College, Cambridge. His subject is "The 

 Measurement of Earthquakes." 



Sheffield. — Under the will of the late Mr. W. 

 Edgar Allen, for many years chairman of Messrs. 

 Edgar Allen and Company, Ltd., Imperial Steel 

 Works, Sheffield, the sum of 32,000?. has just been 

 paid to the University. Mr. Edgar Allen left estate 

 of the gross value of 271,068/., of which the net per- 

 sonalty was sworn at 251,792/. Among the numerous 

 legacies for Sheffield institutions was the whole of 

 his books for the University library, of which Mr. 

 Allen was the donor. He also appointed the Univer- 

 sity one of the residuary legatees. Two-fifths of the 

 residue of the property was to go to the University 

 of Sheffield, one-fifth to Dr. Bamardo's Homes for 

 general purposes, one-fifth to the Church Army for 

 general purposes, and one-fifth to the Salvation Army 

 for general purposes. 



The 32,000/. mentioned is part of the residue of the 

 estate, though when the distribution is completed the 

 University will most likely receive further substantial 

 proof of the late Mr. Allen's thoughtful generosity. 

 The sum of 5000/. is intended by the will for the 

 Applied Science Department of the University, and 

 the balance is to go to University scholarships, half 

 of the sum to be reserved for the sons of working- 

 men. 



Sir Joseph Jonas, chairman of the Applied Science 

 Committee, who has been a generous supporter of the 

 Universit}' from the time of its inception, was a close 

 friend of the late Mr. Allen, and he agreed to giye 

 5000J. to the Applied Science Department, and this, 

 with the sum left bv Mr. Allen — 10,000/. in all — will 

 be devoted to- the provision of materials-testing labora- 

 tories for the department, to be known respectively 

 as "The Edgar Allen Physical Testing Laboratory" 

 and. "The Jonas Mechanical Testing- Laboratory'." 

 In regard to anv further amount which mav still be 

 received under Mr. Allen's will, this sum will be set 

 aside for the provision of further scholarships. 



Summer evening classes began at the Manchester 

 Municipal School of Technology- on May 15. From 

 the prospectus, a copy of which has been received, 

 we find that classes at low fees have been arranged 

 in numerous branches of mechanical, electrical, muni- 



NO. 2429, VOL. 97] 



cipal, and sanitary engineering, chemical technology, 

 mining, the textile industries, and in some depart- 

 ments of pure science. That Manchester students are 

 willing to devote themselves to evening study during 

 the summer months is a satisfactory indication of 

 their earnest intention to qualify themselves to take 

 a worthy part in the international industrial competi- 

 tion of the future. 



SOCIETIES AND ACADEMIES. 

 London. 

 Royal Society, May 11. — Sir J. J. Thomson, presi- 

 dent, in the chair. — Major P. A. Macmahon : Seventh 

 memoir on the partition of numbers. A detailed study 

 of the enumeration of the partitions of multipartite 

 numbers. Whereas a unipartite number m enumer- 

 ates objects of the same species, a multipartite num- 

 ber Wi, nij, wij . . . may be regarded as numbering 

 objects which involve similarities. The problem is 

 the partition of a multipartite, or dividing up into sets 

 of objects a given assemblage of objects, the division 

 being subject to various governing conditions. The 

 author showed long ago that the solution is implicitly 

 contained in the algebra of s3Tnmetric functions. The 

 difficulty has been in the evaluation of numerical co- 

 efficients which arise in the development of the sym- 

 metric function which presents itself as the solution 

 for a particularly specified problem of partition. The 

 discovery of the paper is principally that there exists, 

 a set of symmetric functions, Q„ O,, — Qj...such 

 that the effect of any one of the operations upon the 

 product Qi^, O2*"-, . . . Qi^' ... is merely to multiply it by 

 an easily ascertainable integer, combined with the 

 circumstance that the symmetric fvmction operand can 

 be expanded in terms of such products. The result is 

 that laws are obtained. It is established that under 

 any given conditions enumeration in regard to a uni- 

 partite number tn, is given by the expression 

 Xag + fibg + vCf . . . wherein X , /t, v, . . . are constants. 

 Then the enumeration in regard to a multipartite 

 number mi, nij, . . - m, is given by 



AttiOj . . . ag+fihjhj . . . bg + vCiC, . . . Cg+ 



It is therefore only necessary to obtain the unipartite 

 solution in the form above given, when the multi- 

 partite solution at once follows. The set of functions 

 Q can be modified to meet any specified conditions of 

 partition. The complete solution of the problem of 

 multipartite partition has thus been reached. — Lord 

 Rayleigh : Legendre's function P„(^) when n is great 

 and 6 has any value. As is well known, an approxi- 

 mate formula for Legendre's function P„(fl), when n 

 is very large, was given by Laplace. The subject has 

 been treated with great generality by Hobson, who 

 has developed the complete series proceeding by de- 

 scending powers of n, not only for P,^, but also for 

 the "associated functions." The generality arrived at 

 by Hobson requires the use of advanced mathematical 

 methods. A simpler derivation, sufficient for prac- 

 tical purposes and more within the reach of physicists 

 with a smaller mathematical equipment, may be use- 

 ful. It had, indeed, been worked out independently. 

 The series, of which Laplace's expression constitutes 

 the first term, is arithmetically useful only when n6 is 

 at least moderately large. On the other hand, when 

 ,6 is small, P„ tends to identify itself with the Bessel"'s 

 function, J<,(r»^), as was first remarked by Mehler. 

 A further development of this approximation is here 

 proposed. Finally, a comparison of the results of the 

 two methods of approximation with the numbers cal- 

 culated by A. Lodge for »i = 2o is exhibited. — Prof. A. 

 Dendy : The occurrence of gelatinous spicules and their 

 mode of origin in a new genus of siliceous sponges. 



