APPENDIX E. 



MECHANICAL AND ELECTRICAL ANALOGIES. 



The mechanical analogies which are pointed out in Art. 62 of 

 Chapter V, in Chapter VI, in Arts. 89 and 93 of Chapter VII, 

 and in Arts. 106, 107 and 108 of Chapter VIII are here collected 

 together for convenience of reference, and the mechanical anal- 

 ogies of electrical oscillations are added : 



x vt (i) 



in which x is the distance 

 traveled in t seconds by a 

 body moving at velocity z>. 



W=Fx (4) 

 in which W is the work 

 done by a force F in pull- 

 ing a body through the dis- 

 tance x. 



P=Fv (7) 



in which P is the power 

 developed by a force F act- 

 ing upon a body moving at 

 velocity v. 



W=\mvt (10) 



in which W is the kinetic 

 energy of a mass m mov- 

 ing at velocity v. 



F = m 7[ (I3 > 



in which F is the force re- 

 quired to cause the velocity 

 of a body of mass m to in- 



dv 



crease at the rate -^. 

 dt 



x=-.aF 



(16) 



= ut (2) 



in which is the angle 

 turned in t seconds by a 

 body turning at angular 

 velocity a. 



in which W is the work 

 done by a torque T in turn- 

 ing a body through the 

 angle <f>. 



p 77 /O\ 



r Ju () 



in which P is the power 

 developed by a torque T 

 acting on a body turning at 

 angular velocity u. 



W=\Ktf (n) 



in which W is the kinetic 

 energy of a wheel of mo- 

 ment of inertia K turning 

 at angular velocity u. 



T=K W (I4) 



in which T is the torque 

 required to cause the angu- 

 lar velocity of a wheel of 

 moment of inertia K to 



increase at the rate . 

 . dt 



$=bT (17) 



f = * (3) 



in which q is the electric 

 charge which in / seconds 

 flows through a circuit, car- 

 rying a current i. 



W=Eq (6) 



in which W is the work 

 done by an electromotive 

 force E in pushing a charge 

 q through a circuit. 



P = Ei (9) 



in which P is the power 

 developed by an electro- 

 motive force E in pushing a 

 current i through a circuit. 



W=\LP (12) 

 in which W is the kinetic 

 energy of a coil of induc^ 

 tance L carrying a current i. 



E = L -d7 (IS) 



in which E is the electro- 

 motive force required to 

 cause a current in a coil of 

 inductance L to increase at 



di 



the rate -7-. 



at 



q=CE (18) 



342 



