On Potentials and their A'pplication. 155 



ON POTENTIALS AND THEIR APPLICATION TO 

 PHYSICAL SCIENCE. 



BY PKO-- ESSOK JOHN E. DA VIES, M. T>. 

 Of the Wisconsin State University. 



In most of the recent Mathematical discussions of Phy- 

 sical Theories and Problems, or where laws of nature, first 

 established by observation or experiment, are afterwards 

 followed to their legitimate consequences by the applica- 

 tion of analysis, we find a certain Function used, which, 

 on account of the admirable simplicity it introduces, gives 

 great elegance and brevity to the demonstrations, and the 

 nature of which should, therefore, be thoroughly known. 



For attracting bodies, we read of the Potential of the 

 attracting mass, at some given point external or internal 

 to the mass itself ; of Heat Potentials ; of Potentials of 

 Stress, Elasticity, &c., &c. In short, the Function is evi- 

 dently one of such great generality and power, as to be 

 adapted to most cases where the effects of any forms of 

 Force (attractive or repulsive) are to be considered. It is 

 thus of indispensable service in the Dynamical Theories 

 of Heat, Light, Electricity, &c., now so universally ac- 

 cepted as the true ones. 



Any attempt, then, to present the exact meaning and 

 nature of this Function in a clear light, ought to be of 

 service to those who wish for that thorough comprehension 

 of Physical laws, which mathematical analysis so much 

 aids in giving. 



The Potential Fanction for Gravitation was first intro- 

 duced by Laplace in discussing the attractions of Spheres 

 and Spheroids. (Mecanique Celeste, Book II, Chap. II, 



