286 REPORT— 1897. 



formations gained a clearer insight into the properties of the f^-functions 

 of two variables. See Liouville (' Compt. Rendus,' 1851) ; and Hermite, 

 (Crelle, bd. xxxii. pp. 176 and 277). 



(48) As those mathematicians whose works were mentioned in arts. 

 1-11 laid the foundation for the investigations of Jacobi and Abel, so 

 may we also regard the works that have been reviewed up to the present 

 time as introductory to the works of Weierstrass and Riemann. 



The theory of Abelian functions has been so generalised, so widened, 

 by these mathematicians and their followers that we may make the same 

 remark concerning it as Jacobi (in a letter to Crelle, ' Crelle's Journ.' 

 bd. iii. p. 310) made regarding the elliptic functions : 'You see that the 

 theory is a vast subject of research, which in the course of its development 

 embraces almost all algebra, the theory of definite integrals and the 

 science of numbers.' 



As suggested in the introduction, an account of the works of Weier- 

 strass, Riemann, Clebsch, and later writers cannot be given in this report 

 owing to the lack of space required for such a statement. To leave the 

 woi'k thus unfinished would cause tlie author much regret ; however, there 

 has just appeared the admirable treatise of Mr. H. F. Baker on ' Abel's 

 Theorem and the Allied Theory,' in which the discoveries of the mathe- 

 maticians just mentioned and the development of the theory of Abelian 

 functions are treated in a very comprehensive and elegant manner. 



In conclusion, the author takes much pleasure in referring to this book, 

 at the beginning of which we are taught that no better guide can be found 

 to the analytical developments of pure mathematics than a study of the 

 theory of Abelian functions. 



The Action of Light vpon Dyed Colours. — Rejjort of the Committee, 

 consisting of Professor T. E. Thorpe (Chairman), Professor J. J. 

 Hummel (Secretary), Dr. W. N. Perkin, Professor W. J. Russell, 

 Captain Abney, Professor W, Stroud, and Professor R. Meldola. 

 (Drawn vp by the Secretary.) 



During the past year (1896-97) the work of this Committee has beca 

 continued as usual, and a large number of wool and silk patterns, dyed 

 with various natural and artificial brown and black colouring matters, have 

 been examined with respect to their power of resisting the fading action 

 •of light. 



The Committee regret to state, however, that at this meeting of the 

 Association they are unable to give an account of the results obtained, 

 since at the earlier date this year at which Reports of Committees had to 

 be sent to the Organising Committees the dyed patterns were still under 

 exposure to light, so that the Report could not be prepared. It will be 

 presented, however, at the next meeting of the Association. The Com- 

 mittee ask for reappointment, and for a grant of 81. to carry on the 

 work. 



