85 
Ordinary Meeting, March 8th, 1881. 
E. W. Binney, F.RS., F.G.S., President, in the Chair. 
“ Additions to the paper ‘On an adaptation of the La- 
grangian form of the Equations of fluid motion’,” by R. F. 
Gwyther, M.A. 
With the permission of the Society I desire to add a few 
results to those which I communicated to the Society in the 
paper mentioned above. I treat these results as additional 
to the paper rather than as a separate communication, 
because the methods are identical with those used before, 
and deal with the general case of fluid motion. I hope in a 
subsequent paper to show how some special cases can be 
treated so as to obtain simpler results, better capable of 
being tested by observation. 
1. If P be any scalar, so that D*P = P - (So- v P) 
Then vD t P= vP- v(So-vP) 
= V P — Vp v P — (S<r v ) V P — (S v P V V * 
V DjP = D i vP-VpVP-(SvPv)<r 
and D*vP= vD*P + Vp vP + (SvPv)ff 
N ow any vector h may be written l v </>i + m v 02 + n V 0 3 
whence by applying the above we get 
= D t l. V (j)i + D t m. v </> 2 + Dp?.. v 03 + Vp£ + (S3 V )<r (1) 
If we put S = a we get the formula of Section II. (2). 
Also if l be written L^- + + N~we get 
H H H 
D«o = D,L.g + U ( M.| + D.N.2 + LD«“ + &o. 
= D t L.g + &c. -(S3v)<r (2) 
because = 4^- 
H d(f> i 
# Notes on some Quaternion transformations. Proc. Lit. & Phil., Yol. XIX. 
Proceedings— Let. & Phil, Soc.— Yol. XX.— No 7,— Session 1880*81* 
