Vlll 



limits of the instrumental powers ; Kirchhoff's eyes suffered in con- 

 sequence, and he had to leave the completion of the map to 

 K. Hofmann. 



Soon after the mathematical development by Clansius and Sir 

 William Thomson of the mechanical theory of heat, Kirchhoff was the 

 first to carry the application of that fruitful theory into the domain 

 of Chemical Physics. The thermal phenomena connected with the 

 absorption of gases and the dissolution of salts in liquids as well 

 as their relationship with the vapour- pressures of the solvent, were 

 treated in two papers of great interest and importance. 



A few words must be said on Kirchhoff's papers on elasticity. 



There are few problems which have occupied so many eminent 

 mathematicians, and our author's investigations contributed very 

 materially to the progress of that important branch of theoretical 

 physics. Before Kirchhoff's time Sophia Germain had made an 

 attempt which was only partially successful to establish the equations 

 which regulate the vibrations of thin plates. Poisson had gone a 

 good deal further, especially as regards the treatment of rectangular 

 plates. Kirchhoff points out that Poisson's boundary conditions 

 cannot in general be satisfied, and deduces from the general theory 

 of elasticity a solution which can be applied to circular plates. With 

 the help of measurements made by M. Strehlke, the theoretical 

 results were checked and verified by experiment. In some later 

 papers the elastic deformations of rods were treated in a more general 

 way than had previously been done, and especially in 1879 the 

 solution of the problem was extended to prismatic and conical rods. 



The science of hydrodynamics also is indebted to Kirchhoff for 

 several beautiful investigations, amongst which special attention may 

 be drawn to the paper " Zur Theorie freier Fliissigkeitsstrahlen," and 

 to one in which it is shown that two rigid rings in a fluid moving 

 irrotationally exert apparent forces on each other which are identical 

 with those which the rings would show if electric currents were to 

 circulate round them. 



Kirchhoff's papers have been collected into a volume of moderate 

 size. He has also published a series of lectures on mechanics, in 

 which we are especially struck with the precision with which the 

 subject is treated, and with the way all metaphysical difficulties in 

 the first definitions are avoided. " For this reason," he says in the 

 introduction, " I take it to be the object of mechanics to describe 

 the phenomena of nature, to describe them completely and in the 

 simplest manner. I mean that it will be our task to state what 

 the phenomena are, but not to find out the causes." None of those 

 who have attended Kirchhoff's lectures on mathematical physics 

 are ever likely to forget them. Each lecture was complete in 

 itself, and the student felt on leaving the room that he had learnt 



