] I g GOVERNORS. 



In Mr Siemens's governor there is an arrangement by which a fixed rela- 

 tion is established between L and z, 



L=-Sz .................................... (12), 







. --**+ ........................ < 13 >- 



If the conditions of overflow can be so arranged that the mean square of 

 velocity, represented by w , is proportional to 

 the spring which determines S is also arranged so that 



the velocity, represented by w , is proportional to Q, and if the strength of 



the equation will become, if 2gh = a>V, 



. ,-( '-')+% -(3 -) ................... <>*> 



which shews that the velocity of rotation and of overflow cannot be constant 

 unless the velocity of rotation is w. 



The condition about the overflow is probably difficult to obtain accurately 

 in practice ; but very good results have been obtained within a considerable range 

 of driving-power by a proper adjustment of the spring. If the rim is uniform, 

 there will be a maximum velocity for a certain driving-power. This seems to 

 be verified by the results given at p. 667 of Mr Siemens's paper. 



If the flow of the fluid were limited by a hole, there would be a minimum 

 velocity instead of a maximum. 



The differential equation which determines the nature of small disturbances 

 is in general of the fourth order, but may be reduced to the third by a 

 proper choice of the value of the mean overflow. 



Theory of Differential Gearing. 



In some contrivances the main shaft is connected with the governor by a 

 wheel or system of wheels which are capable of rotation round an axis, which 

 is itself also capable of rotation about the axis of the main shaft. These two 

 axes may be at right angles, as in the ordinary system of differential bevel 

 wheels; or they may be parallel, as in several contrivances adapted to clockwork. 



