138 Prof. Gauss on a new general Principle of Mechanics. 



a brilliant manner, has not deemed it useless to give more de- 

 finiteness and generality to Maupertuis's principle of least 

 effect; and indeed this principle may sometimes be applied 

 with great advantage*. 



The peculiar characteristic of the principle of virtual ve- 

 locities is, that it contains a general formula for solving all 

 problems of statics, and is thus the representative of all other 

 principles of the kind ; but its title to the honour of represen- 

 tation is not so clear as to be self-evident by the mere enun- 

 ciation of it. In this respect the principle which I am going 

 to propose appears to me to deserve the preference ; it has 

 besides a second advantage, viz. that of embracing in a per- 

 fectly equal manner the law of motion as well as of rest. It 

 is perfectly natural that in the gradual advancement of science, 

 and in the acquirement of it, the easy parts should come in 

 before the more difficult ones, the simple before the more com- 

 plicated, the particular before the more general ; but, at the 

 same time, the mind, once arrived at the higher station, en- 

 deavours to reverse this order, and thus views the theory of 

 statics as a particular case only of mechanics. Even the 

 above-mentioned geometrician recommends the principle of 

 least effect, on account of its embracing the theories of equili- 

 brium and of motion at the same time, if the former be so ex- 

 pressed that the living forces should be a minimum in either 

 case. This remark is however more a play upon the word 

 than truth, as the minimum takes place in both cases in very 

 different respects. 



The new principle is as follows : 



The motion of a system of material points connected to- 

 gether in any manner whatsoever, whose motions are modified 

 by any external restraints whatsoever, proceeds in every in- 

 stance in the greatest possible accordance with free motion, or 

 under the least possible constraint ; the measure of the con- 

 straint which the whole system suffers in every particle of 

 time being considered equal to the sum of the products of the 



* I beg however to remark, that the manner in which another great 

 geometrician has endeavoured to prove Huyghens's law of the extraor- 

 dinary refraction of light in crystals having double refraction, by means of 

 the law of least effect, does not appear satisfactory to me. The admissibility 

 of this principle is indeed essentially dependent on the preservation of 

 living forces, according to which the velocities of the moving material 

 points are determined by their places only, without being influenced by 

 the direction of the motion, as is assumed in the theory above alluded to. 

 It appears to me that on the supposition of emanation of light, all at- 

 tempts to connect the phenomena of double refraction with the general 

 laws of dynamics must prove fruitless, so long as the particles of light are 

 considered as points. 



square 



