36 THE THEORY OF SCREWS. [36- 



work done by the unit wrench on a in a twist of amplitude &&amp;gt;/ about the 

 screw &&amp;gt;! is 



2&)j VTal, 



but this must be equal to the work done in the same twist by a wrench of 

 intensity j on the screw &&amp;gt; 1} whence 



or j = - . 



Pi 



Thus, to compute each co-ordinate a n , it is only necessary to ascertain 

 from the tables the virtual coefficient of e*i and w n and to divide this quantity 



37. The Virtual Coefficient of two screws may be expressed with great 

 simplicity by the aid of screw co-ordinates. 



The components of a twist of amplitude are of amplitudes a a lt ... a a B . 



The components of a wrench of intensity ft&quot; are of intensities @&quot; j3 lt ... 

 /3&quot;#, 



Comparing these expressions with 32, we see that 



and we find that the expression for the work done in the twist about a, by 

 the wrench on ft, is 



a. ft&quot; [2 



The quantity inside the bracket is twice the virtual coefficient, whence we 

 deduce the important expression 



l&aft = S/)j !/?]. 



Since a and ft enter symmetrically into this expression, we are again 

 reminded of the reciprocal character of the virtual coefficient. 



38. The Pitch of a screw is at once expressed in terms of its co 

 ordinates, for the virtual coefficient of two coincident screws being equal 

 to the pitch, we have 



p a = 2^ 1 a 1 2 . 



39. Screw Reciprocal to five Screws. 



We can determine the co-ordinates of the single screw p, which is 

 reciprocal to five given screws, a, ft, y, 8, e. ( 25.) 



The quantities p l} ... p ti , must satisfy the condition 



, = 0, 



