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 themselves 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 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 [Greek: d]. 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., as so many real moving forces of (for a time) unknown magnitude, will always help us out of any dynamical scrape we may get into. Laplace, page 20, Mec. Cel. art. 7, is a little obscure here, and in deriving his equation (_f_) a page of explanation would be well bestowed. One thing let me recommend, if you use as principles either this, or that of virtual velocities, or any other, state them broadly and in general terms.... You will think me, I fear, a rough critic, but I think of Horace's _good critic_, Fiet Aristarchus: nec dicet, cur ego amicum Offendam in nugis? Hae nugae seria ducent In mala, and what we can both now laugh at, and you may, if you like, burn as nonsense (I mean these remarks), would come with a very different kind of force from some sneering reviewer in the plenitude of his triumph at the detection of a slip of the pen or one of those little inaccuracies which _humana parum cavit natura_.... Very faithfully yours, J. HERSCHEL. * * * * * [About the same time my father received a letter from Dr. Whewell, afterwards Master of Trinity College, Cambridge, dated 2nd November, 1831, in which he says:--]