288 Trans. Acad. Sc>. of St. Louis. 



versin &> = 2 — versin &>' and versin a = 2 — versin a' 

 equition (29) becomes 



7?i (versin a>' — versin a') = r-^x 2 , 



which is tbe same as equation (26). Also, for versin co 

 = 2 — versin a>' equation (30) becomes 



iro ix' — x} ) = m versin co , 



which is the same as equation ( 27 ). This shows that the lines 

 of force pro _ from a system consisting of an electrified 



plane and an electrified point are curves of the same kind 

 whether the changes are of like or of unlike signs. ( Figs. 1 

 and 2.) In thi> - lines of force are the e 



Hess of the distance of the el from the 



electrified plane. 



:ng equations were from electrical con- 



In what follows it will be shown how they can be 

 m geometrical 

 In Fig. 1. -•S'ht l' ne (JP rotates about O and the 



jht line PD moves in a direction perpendicular to its 



.irallel to AB. OP n tea in 



such a manner that the ver^ine of the \ . which it n 

 with OY (a peq->emiicular to AB, thro... _ - at a 



uniform r;ite. This _ >ut mechani- 



.-: ng OP the center line or axis of a crank to be 

 --/iead, which 3 a slot ular 



to and a uniform linear moti 



the length of stroke of the crosshead and u the portion of that 

 nich the 



f the crosshead. PD moves in such 

 re the m :ne of a circular cylinder 



. - - P, the area - - - 



wou! . are at a uniform rate. L . - = - - be the 



ki this _ - in a unit of I 



Then if PD st - . >m a position of coincidence ^ r 



t the end of a unit of ill be 



x — - ~ and 



( iett han 



