TRANSACTIONS OF SECTION A. 521 



and botany, illustrated by experiments. On account of these lectures the 

 Society had to fight an action-at-law, and although the case was won, its slender 

 resources were crippled for many years. In 18:^7 Benjamin Gompertz, F.R.S., 

 succeeded to the presidency on the death of the Rev. George Paroissen. From the 

 year 1830 onwards the membership gradually declined and the financial outlook 

 became serious. In 1843 there was a crisis ; the Society left Crispin Street for 

 cheaper rooms at 9 Devonshire Street, Bishopsgate Street, and finally, in 1845, 

 after a futile negotiation with the London Institution, it was taken over by the 

 Royal Astronomical Society, which had been founded in 1821. The library and 

 documents were accepted and the few surviving members were made life members 

 of the Astronomical Society without payment. So perished this curious old insti- 

 tution ; it had amassed a really valuable library, containing books on all branches 

 of science. The Astronomical Society has retained the greater part, but some have 

 found their way to the libraries of the Chemical and other societies. An inspec- 

 tion of the documents establishes that it was mainly a society devoted to physics, 

 chemistry and natural history. It had an extensive museum of curiosities and 

 specimens of natural history, presented by individual members, which seems to 

 have disappeared when the rooms in Crispin Street were vacated. It seems a pity 

 that more eflbrt was not made to keep the old institution alive. The fact is that 

 at that date the Royal Society had no sympathy with special societies and did all 

 in its power to discourage them. The Astronomical Society was only formed in 

 1821 in the teeth of the opposition of the Royal Society. 



Reverting now to the date 1845, it may be said that from this period to 

 1866 much good work emanated from this country, but no Mathematical 

 Society existed in London. At the latter date the present Society was formed, 

 with De Morgan as its first President. Gompertz was an original member, 

 and the only person who belonged to both the old and new societies. The 

 thirty-three volumes of proceedings that have appeared give a fair indication 

 of the nature of the mathematical work that has issued from the pens of our 

 countrymen. All will admit that it is the duty of anyone engaged in a particular 

 line of research to keep himself abreast of discoveries, inventions, methods, and 

 ideas, which are being brought forward in that line in his own and other coun- 

 tries. In pure science this is easier of accomplishment by the individual worker 

 than in the case of applied science. In pure mathematics the stately edifice of the 

 Theory of Functions has, during the latter part of the century which has expired, 

 been slowly rising from its foundations on the continent of Europe. It had reached 

 a considerable height and presented an imposing appearance before it attracted 

 more than superficial notice in this country and in America. It is satisfactory to 

 note that during recent years much of the leeway has been made up. English- 

 speaking mathematicians have introduced the first notions into elementary text- 

 books ; they have written advanced treatises on the whole subject ; they have 

 encouraged the younger men to attend courses of lectures in foreign universities ; 

 so that to-day the best students in our universities can attend courses at home 

 given by competent persons, and have the opportunity of acquiring adequate know- 

 ledge, and of themselves contributing to the general advance. The Theory of 

 Functions, being concerned with the functions that satisfy differential equations, 

 has attracted particularly the attention of those whose bent seemed to be towards 

 applied mathematics and mathematical physics, and there is no doubt, in analogy 

 with the work of Poincare in celestial dynamics, those sciences will ultimately 

 derive great benefit from the new study. If, on the other hand, one were asked 

 to specify a department of pure mathematics which has been treated somewhat 

 coldly in this country during the last quarter of the last century, one could point 

 to geometry in general, and to pure geometry, descriptive geometry, and the 

 theory of surfaces in particular. This maj' doubtless be explained by the cir- 

 cumstance that, at the present time, the theory of differential equations and the 

 problems that present themselves in their discussion are of such commanding 

 importance from the point of view of the general advance of mathematical science 

 that those subjects naturally prove to be most attractive. 



As regards organisation and co-operation ip jnathematics, Germany, I believe, 



