206 wiscoNSii^r academy sciences, arts, akd letters. 



raatico-pliysical discoveries of Kirchoff; the Kinetic Theory of 

 Diffasion, Conduction and Radiation by Maxwell; the thermo- 

 electrical researches of 'fait; and many other researches as well, 

 all tending to the snnplification and unity of the Physical Sciences, 

 by showing a probable similarity or identity of cause for the most 

 diverse phenomena. 



In the present paper I shall merely begin with certain remarka- 

 ble relations between the formulas of electro-magnetism and those 

 of fluid motion, first pointed out, so far as I know, by Helmholtz.* 



vortex motiox. 



In magnetism we have the following formula for the value of V 

 the scalar potential of a magnet of finite dimensions 



X, y, and z, being the coordinates of any point of the magnetic 

 mass, 

 6, being what is called the surface density ot the mag- 

 netic matter, and, 

 9, the volume density of the same. 

 The surface density 6, is the resolved part of the intensity of 

 magnetization in the direction of a normal to the surface of the 

 magnet, and the volume-density 9, is what Maxwell has designated 

 as the " convergence " of the magnetization at a given point within 

 the magnet. 



This expression for V is similar to that for the electric potential 

 at any point, due to the electrification of a body on whose surface 

 there is electricity of density 6, and within its substance a bodily 

 electrification whose density is 9, In both cases, V satisfies La- 

 place's equation for points outside of the electrical or magnetic 

 mass, and Poisson's equation for points inside of the same. That 

 is, for the first case, 



— h' ~\ — 7> + — ^ = ■**• 



dx-^ dy dz- 



* In the paper as read before the Academv, a somewhat complete synopsis was 

 given of Thompson's explanation of Faraday's experiment on the Mas;netifi Rotation 

 of Polarized Light; of Clerk Maxwell's Electro-magnetic Theory of Light; and of 

 the Hypothesis of Molecular Vortices. Many points, also, only briefly summar- 

 ized in this printed paper were elaborated by oral explanations and diagrams, and 

 the terms used in the paper were for the most part carefully defined. 



