370] ON THE SIGNIFICATION OF AN ELEMENTARY FORMULA &C. 499 
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 to about the given line, then P' lies on the line PK at a distance PP', —wPK, 
from the point P, and the displacements of P in the directions of the axes are con 
sequently equal to 
« (cy — bz —/), ft) (az — cx — g), eo (bx — ay — h) 
respectively, which is a fundamental formula in the theory of the infinitesimal rotations 
of a solid body. 
Cambridge, October 26, 1865.