1896.] 



point in theoretical dynamics. 



195 



Reverting to our original screws a and v, /3 and £, we now see 

 that they must fulfil the conditions 



where the quantities in the brackets denote the anharmonic ratios. 

 On working out the relations they assume the simple forms 



Pa 



cos (arj) 



cos (/3v) + 



cos (a£) = 2ot 0/3 . 



Pp 



cos (ay) " ^ cos(/3£) at ' 



where w a/3 denotes as usual the virtual coefficient of the two screws 

 a and /3. 



I had already given the second of these equations in the Tenth 

 Memoir on the Theory of Screws, Trans. Royal Irish Academy, 

 Vol. xxx., p. 571. I did not then know that there must be the 

 further condition represented by the first. Nor was I then aware 

 of the definite homography between the screws on two cylindroids 

 which expressed the geometrical conditions under which alone one 

 of these cylindroids could be the locus of impulsive screws cor- 

 responding to the screws of the other as instantaneous screws. 



(5) On the maximum deviation of a ray of light by a prism. 

 By Prof. A. Anderson, M.A., Sidney Sussex College. 



Let the great circle N^* be the principal plane of the prism, 

 A r j and N 2 the normals to the faces. With N x and N. 2 as centres 



