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XXIII. On Uniform JRotation. By C. W. Siemens, F.B.S., Mem. Inst. C.E. 



Eeceired March 10,— Head April 12, 1866. 



Amongst the means at our disposal for obtaining uniform rotation, there is none for 

 which the same degree of accuracy can be claimed as that which distinguishes the 

 vibrating pendulum, or the oscillating spring-wheel of the common watch ; yet there 

 are many purposes, both in physical science and in the mechanical arts, for which 

 smaller subdivisions of time than the period of one oscillation are matter of considerable 

 importance, and which can only be measured by uniform rotation. 



Conical Pendulum. — The apparatus by which continuous rotation of the greatest regu- 

 larity has hitherto been obtained, is the conical pendulum, which was first applied by 

 James Watt to regulate the speed of his engines, and which has since received further 

 development in the instrument known as the Chronometric Governor. 



On examining into the principle involved in the conical pendulum, it \vill be found 

 that the time t of its rotation is dependent upon its length I, and on the angle a which 

 it makes with its vertical axis of rotation, which dependence is expressed by the formula 



t-=.<P\/l cos a, 



the coefficient ^ being a function due to gravitation. The value of t being dependent 

 upon 06, it follows that " uniform rotation of a conical pendulum cannot he obtained 

 except on condition that the angle of its rotation remains constant." 



Watt's Governor. — In the case of Watt's centrifugal governor, the angle of rotation of 

 the p(>ndulum varies with every change in the relative condition of power and load on 

 tlie engine, and the change of angle is, indeed, taken advantage of to close or open the 

 steam-supply valve. In order to close the steam- (or throttle-) valve the angle of rotation 

 has to be increased, which necessitates a corresponding increase of the engine's velocity ; 

 on the other hand, an increase of the valve-orifice cannot be efi'ected without a reduction 

 of the speed of the engine taking place. 



Considering this dependence of the action of the instrument upon permanent change 

 of speed of the engine, the name of " governor" seems inappropriate, the instrument 

 being, in fact, only a " moderator " of the amount of fluctuation to which the engine 

 would be subjected without its agency. The amount of these fluctuations depends, in a 

 great measure, upon the mechanical construction of the instrument, which is, generally 

 speaking, very objectionable, inasmuch as the pendulous arms arc mostly suspended at 

 points beside the common axis of rotation, giving rise to an increased variation of time 

 for a given change of angle ; the reason being that the true pendulous length has to 

 be measured from the point of intersection of the pendulums or rods with the axis of 



4x2 



