538 MEMOIR OF KIRCHIIOFF. 



the end of his course what circuiustaiices spoke against his hypothesis 

 and, in this way, demolished before the eyes of the students the whole 

 structure, is to be accounted for by his idea of the scope and the limits 

 of the investigation and interpretation of nature. 



On such occasions, I must confess, 1 asked myself many a time, 

 "What for? Why develop a theory that leads to contradiction with 

 experiment? Is the probing- of nature, for Kirclihoft", only the greatest 

 and the most interesting exercise m calculation ?" 



In answer to such doubts 1 shall adduce his own words in his discourse 

 delivered in 1865, as rector of Heidelberg University "on the scope of 

 the natural S(;ieuces." He says there: "There is a science called me- 

 chanics, whose object is to determine the motion of bodies when the 

 causes that occasion them are known, - - - Mechanics is a twin sis 

 ter of geometry; both sciences are applications of pure mathematics; 

 the propositions of both, as to their certainty, stand on the same level ; 

 we have just as much right to ascribe absolute certainty to mechanical 

 theorems as to geometrical/' And further : " If we were acquainted 

 with all the forces of nature and knew what is the state of matter at a 

 certain moment of time, we should be able to deduce by means of me- 

 chanics its state at every subsequent moment, and to deduce how the 

 various natural phenomena follow and accompany each other. The 

 highest goal the natural sciences must strive to attain is the realization 

 of the just mentioned suppostion, - - - viz, the reduction of all 

 natural phenomena to mechanics. We shall never attain the goal of the 

 natural sciences, but even the fact that it is recognized as such offers ji. 

 certain satisfaction, and in approximating to it lies the highest pleasure 

 to be derived from the study of natural phenomena." 



I must mention besides the famous words with which Kirchhoff com- 

 mences his Mechanics, published in 1875 : " Mechanics is the science 

 of motion ; its object may be stated to be to describe in the most com 

 jylete and sinqjle way the motion that takes place in nature." TLe dil- 

 ference between the first and the last definition of mechanics is worthy^ 

 of notice. At the former time, and before the large public, Kirchhoff 

 spoke of causes of motion. Now, and in a strictly mathematical book, 

 the word and the notion of cause do not appear. The interpretation 

 of nature is given up ; the only thing looked for is the simplest possible 

 description of nature. These introductory words of his Mechanics, 

 and their working out in the book itself are the most consequent, far- 

 reaching expression of Kirchhoff's way of looking at nature. He 

 makes no hypothesis as to the possibility of arriving at a knowledge of 

 things in themselves. He wants only to portray tlie i)henomena in a 

 logically certain form. In relation to the sensible world (according to 

 Kant) we havelogical (that is to say,a^non) certainty only of the propo- 

 sitions of geometry and mechanics, the last distinguished from the first 

 on account of their requiring, besides the three dimensions of space, the 

 fourth one, time, and the notion of a mobile matter. With these three 



