490 THE THEORY OF SCREWS. 



But as the wrench is very great the initial acceleration is great and conse 

 quently the second term on the left-hand side is negligible compared with the first. 



dT C 



Whence -^ = 2^ a \ifdt = 2isr 1?a i 7 &quot; ; , 



CX/CL J 



but T=Mu a *a*(89), 



whence 2Mit a 2 a=2 ar ria r) &quot;, 



or &quot; = 77 &quot;2 V- 



The kinetic energy 



T=Mu^ = ^^ &quot;\ (91). 



NOTE IV. 



Professor C. J. Jolys theory of the triple contact of conic and cubic. 



Professor C. J. Joly has pointed out to me that the conies of 162 and 165 

 which have triple contact with the nodal cubic are but particular instances of the 

 more general theory which he investigates as follows. 



Let t be the parameter necessary to define a particular generator on a given 

 cylindroid ; we first show that the condition that a line, i.e. a screw of zero pitch 

 should intersect this generator may be expressed in the form 



at 3 + W + ct + d = 0, 



where a, b, c, d are linear functions of the co-ordinates of and, of course, functions 

 also of the constants defining the cylindroid. 



For if a and ft be the two principal screws on the cylindroid then the co 

 ordinates of the screw e on the cylindroid making an angle X with a are 



cos Xc^ + sin X/3j , ... cos Xa^ + sin X/? 6 , 

 whence OTf0 = cos Xw ea + sin X-57 e/3 , 



cos (fO) = cos X cos (ca) + sin X cos (e/3), 



p f = cos 2 \p a + 2 cos X sin Xt3- aj3 + sin 2 \pp. 

 If c and 6 intersect then 



2-5T te = cos 

 or putting t = tan X) 



+ (COS (eo) p ft + 2 COS (/?) -57 a - 2OT ea ) t 2 



+ (cos ( /3) p a + 2 cos ( 6a ) -G7 a/3 - 2r e 0) t 



which has the form just given. 



