302 NOTES. 



Mr. Eyley's statement of the principle is this : After the 

 enunciation given in page 38, line 21, "it would have re- 

 " mained at rest," add, "Since these last forces mutually 

 " destroy each other, and that the forces actually impressed 

 " were compounded of them and of those (usually called 

 " effective} which act in the direction the bodies really move 

 " in, so that the force originally applied (usually called the 

 " impressed force) is the result of these two forces, it follows 

 " that the effective forces would, if they acted in the contrary 

 " direction, exactly balance the impressed forces." He adds, 

 that problems of dynamics are thus reduced to a general 

 equation of equilibrium, and become statical. 



Dr. Booth thus states it : Since the impressed forces result 

 in the effective forces, their differences or the lost forces must 

 l>e zero or equilibrate each other. 



An excellent geometrician has observed, that " the prin- 

 " ciple applies equally to the most elementary and the most 

 " difficult problems ; to the motion of a body down an inclined 

 " plane and the vibration of a simple pendulum, or to the 

 " theory of the radiation of heat and the vibrations of a chord 

 " two subjects of insuperable difficulty, to which D'Alembert 

 " applied his new method of partial differences as well as his 

 " principle, and which became remarkable in his hands, not 

 " only for the solutions which he obtained, but also for the 

 " manner of them." It was indeed his singular good fortune, 

 by the further improvement of the calculus, to overcome the 

 analytical difficulties into which the fecundity of his dy- 

 namical principle had led him. 



NOTE IV. 



There is not given among these Tracts the two papers on 

 Light and Colours, inserted in the Phil. Trans, for 1796 and 

 1797, because objections have been made to the principal 

 doctrines there maintained, upon the different inflexibility of 

 the rays as supposed to be indicated in the colours which 

 appear in the spectra made by reflexion from striated surfaces. 



