456 



Capt. J. Hollingworth 



p is proportional to the wire diameter, and so the thicker 

 the wire and the slower the speed the larger the value o£ p. 



It will be seen later that in the most unfavourable case, 

 i. e., with the largest wire in ordinary use travelling at the 

 slowest practicable speed, the value of p is slightly over 0*25 

 and is more generally of the order of 0*1 ; hence only small 

 errors will be caused by neglecting squares and higher 

 powers of p. 



This causes considerable simplification in the evaluation of 

 equation VIII. 



For from VI., 



vy + 4)- ^ 



2 ~ ± 2" 



(3 



x/(/ + 4)+y> p 



9 — ■»- I" 9 



y 



IX. 



-j 



and from VII., 



P + " _ P/ 2 + 1 





13 



p — $ _l>i 



P 



2 



(/3 + sin<9) 2B _ Qg + sinfl)* 2 - 1 

 (a— sin 0) 2A ~ (a -sin 6>)^ 2+1 



(a-sin0)(/3 + sin<9 



/ /3 + tin 0\p<' 2 

 ) \cc— sin 6/ 



{l + (pl2 + sm6) f . 



\ p/2 



cos- -p sin 6 ' { 1 - (p/2 + sin 0) }p' 2 

 1 l+p/"2sin# 



since powers 

 throughout. 



cos 2 0—p sin ' 1 — p/2 sin 



— 1 + psinfl 

 cos 2 — psin 0' 



of p above the first have been neglected 

 ds _ 1 + p sin 6 -^ 



T6~~c^s Y e-psmd ; 



C 2 



and this is the first integral of equation III. To determine C 

 consider the lowest point on the wire. If the weight is heavy 



