478 



NA TURE 



[September 12, 1901 



ages we note Fresnel, Bessel, Cauchy, Chasles, Lame, Mcibius, 

 V. Staudt and Steiner on the Continent, and Babbage, Peacock, 

 John Herschel, Henry Parr Hamilton and (leorge Green in this 

 country. It was not, indeed, till about 1845, '^'^ ^ little later, 

 that we could point to the great names of William Rowan 

 Hamilton, MacCullagh, Adams, Boole, Salmon, Stokes, 

 Sylvester, Cayley, William Thomson, H. J. S. Smith and 

 Clerk Maxwell as adequate representatives of mathematical 

 science. It is worthy of note that this date, 1845, marks also 

 the year of the dissolution of a very interesting society, the 

 Mathematical Society of Spitalfields ; and I would like to pause 

 a moment, and, if I may say so. rescue it from the oblivion 

 which seems to threaten it. In iSoi it was already a venerable 

 institution, having been founded by Joseph Middleton, a writer 

 of mathematical text-books, in 1717.' The members of the 

 Society at the beginning were for the most part silk-weavers of 

 French extraction ; it was little more than a working man's 

 club, at which questions of mathematics and natural philosophy 

 were discussed every Saturday evening. The number of mem- 

 bers was limited to the " square of seven," but later it was 

 increased to the "square of eight," and later still to the "square 

 of nine." In 1725 the place of meeting was changed from the 

 Monmouth's Head to the White Horse in Wheeler Street, and 

 in 1735 to the Ben Jonson's Head in Pelham Street. The sub- 

 scription was six-and-sixpence a quarter, or sixpence a week, 

 and entrance was gained by production of a metal ticket, which 

 had the proposition of Pythagoras engraved on one side and a 

 sighted quadrant with level on the other. The funds, largely 

 augmented by an elaborate system of fines, were chiefly used 

 for the purchase of books and philosophical apparatus. A 

 president, treasurer, inspector of instruments, and secretary 

 were appointed annually, and there were, besides, four stewards, 

 six auditors and six trustees. By the constitution of the Society 

 it was the duty of every member, if he were asked any mathe- 

 matical or philosophical question by another member, to instruct 

 him to the best of his ability. It was the custom for each 

 member in rotation to lecture or perform experiments on 

 each evening of meeting. There was a fine of half-a-crown 

 for introducing controverted points of divinity or politics. 

 The members dined together twice annually, viz. on the 

 second Friday in January in London in commemoration 

 of the birth of Sir Isaac Newton (this feast frequently took 

 place at the Black Swan, Brown's Lane, Spitalfields), and on the 

 second Friday in July " at a convenient distance in the country 

 in commemoration of the birth of the founder." The second 

 dinner frequently fell through because >the members could not 

 agree as to the locality. It was found necessary to introduce a 

 rule fining members sixpence for letting oft" fireworks in the place 

 of meeting. Every member present was entitled to a pint of 

 beer at the common expense, and, further, every live members 

 were entitled to call for a quart for consumption at the meeting. 

 Such were some of the quaint regulations lin force when about 

 the year 1750 the Society moved to larger apartments in Crispin 

 Street, where it remained without interruption till 1843. It 

 appears from the old minute books that about the year 1750 the 

 Society absorbed a small mathematical society iwhich used to 

 meet at the Black Swan, Brown's Lane, above mentioned, and 

 that in 17S3 an ancient historical society was also incorporated 

 with it. By the year 1800 the class of the members had become 

 improved, and we find some well-known names, such as 

 Dolland, Simpson, Saunderson, Crossley, Paroissen and Gom- 

 pertz. At the time lectures were given in all branches of 

 science by the members in the Society's rooms, which 

 on these occasions were open to the public on payment of one 

 shiUing. The arrangements for the Jsession 1822-23 included 

 lectures in mechanics, hydrostatics and hydraulics, pneumatics, 

 optics, astronomy, chemistry, electricity, galvanism, magnetism 

 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 1827 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 Devon- 

 shire Street, Bishopsgate Street, and finally, in 1845, after a 



1 Its first place of meeting was the Monmouth's Head.;Monmouth Street, 

 Spitalfields. This street ha^ long disappeared. From a map of London of 

 1746 it appears to have run parallel to the present Brick Lane and to have 

 orresponded to the present Wilks Street. 



NO. 1663, VOL. 64] 



futile negotiation with the London Institution, it was taken 

 over by the Royal Astronomical Society, which had been 

 founded in 1S21. 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 institution ; 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 in- 

 spection 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 disap- 

 peared when the rooms in Crispin Street were vacated. It 

 seems a pity that more eft^ort 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 182 1 in the teeth of the opposition of the Royal Society. 



Reverting now to the date 1845, ■' '"^V be said that from this 

 period to i865 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 any one 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 countries. In pure science this is easier of accom- 

 plishment 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 countryjand 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 op- 

 portunity of acquiring adequate knowledge, and of themselves 

 contributing to the general advance. The Theory of Functions, 

 being concerned with the functions that satisfy diff"erential equa- 

 tions, 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 mathe- 

 matics 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 may doubtless be 

 explained by the circumstance 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 cooperation in mathematics, 

 Germany, I beHeve, stands first. The custom of offering prizes 

 for the solutions of definite problems which are necessary to the 

 general advance obtains more in Germany and in France than 

 here, where, I believe, the Adams Prize stands alone. The idea 

 has an indirect value in pointing out some of the more pressing 

 desiderata to young and enthusiastic students, and a direct im- 

 portance in frequently, as it proves, producing remarkable 

 dissertations on the proposed questions. The field is so vast 

 that any comprehensive scheme of cooperation is scarcely 

 possible, though much more might be done with advantage. 



If we turn our eyes to the world of astronomy we find there 

 a grand scheme of cooperation which other departments may 

 indeed envy. The gravitation formula has been recognised from 

 the time of Newton as ruling the dynamics of the heavens, and 

 the exact agreement of the facts derived from observation with 



