BOOK VI 



MECHANICS. 



CHAPTER III. 

 PRINCIPLES AXD PROBLEMS. 



Significance of Analytical Mechanics. 



IN the text, page 372, I have stated that Lagrange, near the end of 

 his life, expressed his sorrow that the methods of approximation 

 employed in Physical Astronomy rested on arbitrary processes, and 

 not on any insight into the results of mechanical action. From the 

 recent biography of Gauss, the greatest physical mathematician of 

 modern times, we learn that he congratulated himself on having es- 

 caped this error. He remarked 1 that many of the most celebrated 

 mathematicians, Euler very often, Lagrange sometimes, had trusted too 

 much to the symbolical calculation of their problems, and would not 

 have been able to give an account of the meaning of each successive 

 step of their investigation. He said that he himself, on the other hand, 

 could assert that at every step which he took, he always had the aim 

 and purpose of his operations before his eyes Avithout ever turning 

 aside from the way. The same, he remarked, might be said of Newton. 



Engineering Mechanics. 



The principles of the science of Mechanics were discovered by ob- 

 servations made upon bodies within the reach of men ; as we have 

 seen in speaking of the discoveries of Stevinus, Galileo, and others, up 

 to the time of Newton. And when there arose the controversy about 

 vis viva (Chap. v. Sect. 2 of this Book) ; namely, whether the " liv- 

 ; ng force" of a body is measured by the product of the weight into the 



1 Gauss, Zum Geddchtniss, wn IF. Sartorius v. Wallershausen, p. SO. 



