872 



SCIENCE. 



[N. S. Vol. XX. Xo. 521. 



. logues of Lagrange's equations, indispens- 

 able matrix of all mechanics. 



While admiring these bold works, we 

 fear lest the authors have neglected certain 

 hidden masses, as Helmholtz and Hertz 

 would have said. But although that may 

 happen, there is in these doctrines a curious 

 application of mathematics, which, at least 

 in well-circumscribed cases, has already 

 rendered great services. 



I have terminated, messieurs, this sum- 

 mary history of some of the applications 

 of analysis, with the reflections which it 

 has at moments suggested to me. 



It is far from being complete; thus I 

 have omitted to speak of the calculus of 

 probabilities, which demands so much 

 subtlety of mind, and of which Pascal re- 

 fused to explain the niceties to the chevalier 

 de Mere because he was not a geometer. 



Its practical utility is of the first rank, 

 its theoretic interest has always been great ; 

 it is further augmented to-day, thanks to 

 the importance taken by the researches 

 that Maxwell called statistical and which 

 tend to envisage mechanics under a wholly 

 new light. 



I hope, however, to have shown, in this 

 sketch, the origin and the reason of the 

 bonds so profound which unite analysis to 

 geometry and physics, more generally to 

 every science bearing on quantities numer- 

 ically measurable. 



The reciprocal influence of analysis and 

 physical theories has been in this regard 

 particularly instructive. 



What does the future reserve 1 



Problems more difficult, corresponding to 

 an approximation of higher order, will 

 introduce complications which we can only 

 vaguely forecast, in speaking, as I have 

 .iust done, of functional equations replacing 

 systematically our actual differential equa- 

 tions, or further of integrations of equa- 

 tions infinite in number with an infinity of 

 unknown functions. But CA'en though that 



happens, mathematical analysis will always 

 remain that language which, according to 

 the mot of Fourier, has no symbols to ex- 

 press confused notions, a language endowed 

 with an admirable power of transforma-' 

 tion and capable of condensing in its for- 

 mulas a number immense of results. 



Emile Picard. 



PRESENT PROBLEMS OF METEOROLOGY.* 

 Never in the history of the science have 

 so many problems presented themselves for 

 solution as at the present time. Numerous 

 a priori theories require demonstration 

 and, in fact, the whole structure of meteor- 

 ology, which has been erected on hypoth- 

 eses, needs to be strengthened or rebuilt 

 by experimental evidence. Until recently 

 the observations have been carried on at 

 the very bottom of the atmosphere and 

 our predecessors have been compared justly 

 to shell-fish groping about the abysses of 

 the ocean floor to which they are confined. 

 Probably meteorology had its origin in 

 a crude system of weather predictions, 

 based on signs in the heavens, and it did not 

 become a science until the invention of the 

 principal meteorological instruments in 

 the seventeenth century made possible the 

 study of climatology by the collection of 

 exact and comparable observations at many 

 places on the globe. These data, owing 

 to extensive operations of the meteorolog- 

 ical services in the different countries, are 

 now tolerably complete, there being com- 

 paratively small portions of the land-sur- 

 face, at least, for which the climatic ele- 

 ments are not fairly well known, the gaps 

 that remain to be filled lying chiefly on the 

 Antarctic continent and in the interior of 

 Africa. 



Although it is about fifty years ago since 

 the first observations, made synchronously 



* Address at St. Louis to the Section of Cos- 

 mieal Physics of the International Congress of 

 Arts and Science. 



