414 Mr. G. Gore on Chemical Reactions obtained 



and the remark in reference to it is, that if at the given point 

 P we draw, perpendicular to the plane through P and the given 

 line, a distance PK equal to the distance of P from the given 

 line, then the expressions 



y cosy— z cos jS, z cos a— x cos 7, a?cos/3— y cos a, 



which enter into the preceding formula, denote respectively the 

 coordinates of the point K referred to P as origin. 



If the given line instead of passing through the origin pass 

 through the point a? , y , z , then the corresponding expressions 

 are of course 



{y~ Vo) cos 7- {z—z ) cos ft {z-z ) cos a - (x—x ) cos y, 



(a?— a? )cos£ — (y — 2/ )cos7, , ■ 



and if we denote the "six coordinates" of the given line, viz. 



cosa, cos/3, COS7, y cos7— z Q cosfi } ZqCOsol—WqCOSj, x Q cos/3—y cosy, 



*>y 



a , b , c , / , g , h 



respectively (so that af-\-bg-\-ch — 0), then the three expressions 

 become 



cy — bz—f, az—cx—g, bx—ay—h 



respectively. 



It is moreover clear that if the point P be moved to P' by an 

 infinitesimal rotation co about the given line, then P' lies on the 

 line Vk at a distance PP', =co¥k, from the point P, and the dis- 

 placements of P in the directions of the axes are consequently 

 equal to 



co(cy — bz—f), co(az—cx—g), co{bx — ay — h) 



respectively, which is a fundamental formula in the theory of 

 the'infinitesimal rotations of a solid body. 



Cambridge, October 26, 1865. 



LX. On Chemical Reactions obtained by employing Anhydrous 

 Liquids as Solvents. By G. Gore, F.R.S* 



"W7*ATER has long been used as a solvent to bring a large 

 * * number of substances into a liquid state suitable for the 

 exercise of chemical affinity ; and a very large class of chemical 

 reactions is due to the liquefying power of water upon one or 

 both of the two substances which are brought into contact for 



* Communicated by the Author. 



