WILLIAM SIEMENS, F.R.S. 1 07 



ON UNIFORM ROTATION. 

 BY C. W. SIEMENS, F.R.S.,* Mem. Inst. C.E. 



AMONGST the means at our disposal for obtaining uniform rota- 

 tion, 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 regularity 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 pen- 

 dulum, it will 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 = cj> *Jl cos a, the coefficient < being a function due to 

 gravitation. The value of t being dependent upon a, it follows 

 that " uniform rotation of a conical pendulum cannot be 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 pendulum varies with every change in 

 the relative condition of power and load on the 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 must be consequent on a 

 reduction of the speed of the engine. 



Considering this dependence of the action of the instrument 



* Excerpt Philosophical Transactions of the Royal Society, 1866, pp. 657-670. 



