53 . Mr. Spottiswoode — Equations of Rotation [1863, 



ragged) fall of tlie atmospheric pressure, which reached its minimum about 

 4^ 45m p -jyj^ There was then a very abrupt and nearly perpendicular rise 

 of about five hundredths of an inch of pressure, or rather less, after which 

 the rise still went on, but only more gradually. 



Through the kindness of the Kev. R. Main, of the Radcliffe Observa- 

 tory, I have been favoured with a copy of the trace afforded by the Oxford 

 barograph during this squall, in which there appears a very sudden rise of 

 nearly the same extent as that at Kew, but which took place about four 

 o'clock, and therefore, as on the previous occasion, somewhat sooner than 

 at Kew. This change of pressure at Oxford was accompanied by a very 

 rapid fall of temperature of about 8° Fahr. 



The minimum atmospheric pressure at Kew was 29*52 inches, while at 

 Oxford it was 29 '28 inches. 



It will be seen from the Plate that at Kew the electricity of the air fell 

 rapidly from positive to negative about 4^ 30°" p.m., and afterwards fluctu- 

 ated a good deal, remaining, however, generally negative until S'' 22"^. p.m., 

 when it rose rapidly to positive. 



"We see also from the Plate that there was an increase in the average 

 velocity of the wind at Kew during the continuance of this squall. To 

 conclude, it would appear that in these two squalls there was in both 

 cases an exceedingly rapid rise of the barometer from its minimum both at 

 Oxford and at Kew, this taking place somewhat sooner at the former 

 place than at the latter ; and that in both cases the air at Kew remained 

 negatively electrified during the continuance of the squall, while the 

 average velocity of the wind was also somewhat increased. 



. The Society then adjourned over the Christmas recess to Thursday 

 January 7, 1864. 



'^On the Equations of Rotation of a Solid Body about a Pixed 

 Point.^^ By William Spottiswoode, M.A., P.R.S., &c. Received 

 March 21, 1863.* 



In treating the equations of rotation of a solid body about a fixed point, 

 it is usual to employ the principal axes of the body as the moving system 

 of coordinates. Cases, however, occur in which it is advisable to employ 

 other systems ; and the object of the present paper is to develope the funda- 

 mental formulae of transformation and integration for any system. Adopt- 

 ing the usual notation in all respects, excepting a change of sign in the 

 quantities F, G, H, which will facilitate transformations hereafter to be 

 made, let 



— F = 2m2/^, — G=Sm^x, —ll = ^mxy \ 



* Read April 16, 1863 : see abstract, vol. xii. p. 523. 



