478 



Dr. C. V. Drysdale on the 



in any meridian making an angle with the reference 

 meridian. On expanding we have 



9„J, 



F = iXF 1 -i{cos 202F! cos 2^ -sin 26%¥ l sin 2^ 

 and this is a maximum or minimum for 



2F X sin 2«! 



/' 



tan 2(9 = 



£F 1 cos2a 1 ' 



giving the direction of the axes of the combination, while the 

 maximum and minimum values are given by the expression 



iSFi ± J y 7 ^ Fa sin 2a,)' + (SFi cos 2«,) 2 



corresponding to the convergences in the two principal 

 meridians. Fig. 5 shows curves exhibiting the relation 



Fig. 5. 



Zf 



3 



c2 





SosA 



90° \ 















Power of Combination of two equal cylinders crossed at various angles. 



90 \?>S 180 



rUrucL tan- 



between the convergence and angle for two cylinders crossed 

 at various angles. The properties of such combinations have 

 already been brought before this Society by Dr. Thompson *, 

 but the writer had come to the same conclusions earlier. It 

 is interesting to note that while the displacement of a prism 

 corresponds to an ordinary vector, the curvature of a cylinder 

 is what is called by Steinmetz a double frequency vector, and 

 this can be well illustrated experimentally. In general the 

 distinction which Prof. Thompson has drawn between unipolar 



* S. P. Thompson. Proc. Phys. Soc. 



