120 



conjugate axes that is, about axes such that the rotation round one of them 

 does not tnd to produce a force about the other. 



Now let 8 be the driving-power of the shaft on the differential system, 

 and * that of the differential system on the governor; then the equation of 

 motion becomes 



-**n-<> ...... (9); 



r, = 

 and if we put U = 



+ NS 1 \ 



(11), 

 + NS 1 



the equations of motion in 9 and <f> will be 



+ 3f-' 



(12). 



If M' = 0, then the motions in 6 and <f> will be independent of each oilier. 

 If If is also 0, then we have the relation 



LPQ + MRS=0 ................................. (13); 



and if this is fulfilled, the disturbances of the motion in 6 will have no effect 

 on the motion in tf>. The teeth of the differential system in gear with the 

 main shaft and the governor respectively will then correspond to the centres of 

 percussion and rotation of a simple body, and this relation will be mutual. 



In such differential systems a constant force, H, sufficient to keep the 

 governor in a proper state of efficiency, is applied to the axis rj, and tin- 

 motion of this axis is made to work a valve or a break on the main shaft 

 of the machine. H in this case is merely the friction about the axis of 

 If the moments of inertia of the different parts of the system are so arranged 

 that J/' = 0, then the disturbance produced by a blow or a jerk on the machine 

 will act instantaneously on the valve, but will not communicate any impulse to 

 the governor. 



