(52] THE REPRESENTATION OF THE CYLINDROID BY A CIRCLE. 55 



but, as in 58, we have 



(p a -TT + pp- TT ) cos - d aft sin = ; 



Fig. 12. 



whence the virtual coefficient is simply, 



AS 



OS 



and we have the following theorem : 



The virtual coefficient of any pair of screws varies as the perpendicular 

 distance of their chord from the pole of the axis of pitch. 



We also notice that the line TF expresses the actual value of the virtual 

 coefficient. 



The theorem of course includes, as a particular case, that property of 

 reciprocal screws, which states that their chord passes through the pole of the 

 axis of pitch ( 58). 



62. Another Investigation of the Virtual Coefficient. 



It will be instructive to investigate the theorem of the last article by a 

 different part of the theory. We shall commence with a proposition in ele 

 mentary geometry. 



Let ABC (Fig. 13) be a triangle circumscribed by a circle, the lengths of 

 the sides being, as usual, a, b, c. Draw tangents at A, B, C, and thus form 

 the triangle XYZ. It can be readily shown that if masses a 2 , b&quot;, c&quot; be placed 



