384 
Proceedings of the Royal Society 
from the adoption of early harps or other stringed instruments of 
a limited construction. 
Scotch airs were often imitated by introducing a particular 
accentuation, called the Scottish “snap,” as in the Vauxhall air, 
’Twas within a mile of Edinburgh Town.” 
He expressed an opinion that many airs were common to Scot- 
land and the North of England, and he denied that Scotch airs 
were always sombre, as had sometimes been alleged. 
Airs illustrating the views above stated were played by Mr 
Bridgman in a manner of which it may be allowable to say that it 
gave great satisfaction to the audience. 
2. On the Motion of Free Solids through a Liquid. 
By Sir William Thomson. 
This paper commences with the following extract from the 
author’s private journal, of date January 6, 1858 : — 
“ Let IT, 1 L, iPT, be rectangular components of an impul- 
“ sive force and an impulsive couple applied to a solid of invariable 
“ shape, with or without inertia of its own, in a perfect liquid, 
11 and let u, v, w, «r, p , <r, be the components of linear and angular 
“ velocity generated. Then, if the vis viva* (twice the mechanical 
“ value) of the whole motion be, as it cannot but be, given by the 
“ expression 
“ Q = \u, u\v? + [v, v\v 0 - + .... + 2 [v,u\vu + 2 \w,il\wu + Z[z?,u~\z<ru + 
“ where = [w, w], [v,v], &c., denote 21 constant co-efficients determin- 
“ able by transcendental analysis from the form of the surface of 
“ the solid, probably involving only elliptic transcendentals when 
“ the surface is ellipsoidal : involving, of course, the moments of 
“ inertia of the solid itself : w r e must have 
[w, u\u + [v, u]v + [w, u\w + [ar, u\vr + [ p , u]p + [(7, u\a- = &C. 
\u, ztju + [v, -&\v + [w, ar]t0 + [ar, ™\sr + [p, isrjp + [cr , a r](7 = 2L, &C. 
“ If now a continuous force X,Y,Z, and a continuous couple 
“ L,M,N, referred to axes fixed in the body, is applied, and if 
“ M &c., denote the impulsive force and couple capable 
“ of generating from rest the motion u , v, w, w, p, <r, which exists 
* Henceforth T, instead of £ Q, is used to denote the “ mechanical value,” 
or, as it is now called, the “ kinetic energy ” of the motion. 
