118 HISTORY OF MECHANICS. 



tated by a constant series of undulations, produced 

 by the solar and lunar forces. The difficulty of 

 such an investigation may be judged of from this, 

 that Laplace, in order to carry it on, is obliged to 

 assume a mechanical proposition, unproved, and 

 only conjectured to be true; namely 13 , that, "in a 

 system of bodies acted upon by forces which are 

 periodical, the state of the system is periodical like 

 the forces." Even with this assumption, various 

 other arbitrary processes are requisite; and it ap- 

 pears still very doubtful whether Laplace's theory is 

 either a better mechanical solution of the problem, 

 or a nearer approximation to the laws of the phe- 

 nomena, than that obtained by D. Bernoulli, follow- 

 ing the views of Newton. 



In most cases, the solutions of problems of 

 hydrodynamics are not satisfactorily confirmed by 

 the results of observation. Poisson and Cauchy 

 have prosecuted the subject of waves, and have 

 deduced very curious conclusions by a very recon- 

 dite and profound analysis. The assumptions of the 

 mathematician here do not represent the conditions 

 of nature ; the rules of theory, therefore, are not a 

 good standard to which we may refer the aberra- 

 tions of particular cases; and the laws which we 

 obtain from experiment are very imperfectly illus- 

 trated by a priori calculation. The case of this 

 department of knowledge, Hydrodynamics, is very 

 peculiar ; we have reached the highest point of the 

 13 Mtc. C'd. t. ii. p. 218. 



