Herschefs Advice. 169 



insuperable difficulties; and if I may so express it, a 

 sketchiness of outline (as a painter you will understand 

 my meaning, and what is of more consequence, see how 

 it is to be remedied). 



You have adopted, I see, the principle of virtual velocity, 

 and the principle of d'Alembert, rather as separate and 

 independent principles to be used as instruments of 

 investigation than as convenient theories, flowing them- 

 selves from the general law of force and equilibrium, 

 to be first proved and then remembered as compact 

 statements in a form fit for use. The demonstration of 

 the 1 principle of virtual velocities is so easy and direct 

 in Laplace that I cannot imagine anything capable of 

 rendering it plainer than he has done. But a good deal 

 more explanation of what is virtual velocity, &c., would be 

 advantageous and virtual velocities should be kept quite 

 distinct from the arbitrary variations represented by the 

 sign 8. 



With regard to the principle of d'Alembert take my 

 advice and explode it altogether. It is the most awkward 

 and involved statement of a plain dynamical equation 

 that ever puzzled student. I speak feelingly and with a 

 sense of irritation at the whirls and vortices it used to 

 cause in my poor head when first I entered on this 

 subject in my days of studentship. I know not a single 

 case where its application does not create obscurity nay 

 doubt. Nor can a case ever occur where any such 

 principle is called for. The general law that the change 

 of motion is proportional to the moving force and takes 

 place in its direction, provided we take care always to 

 regard the reaction of curves, surfaces, obstacles, &c., aa 

 so many real moving forces of (for a time) unknown 

 magnitude, will always help us out of any dynamical 



