158 Wisconsin Academy of Sciences, Arts, and Letters. 



of these quotients for tlie whole body." [This is expressed 

 by the above integral] 



It will thus be seen that Green's definition is purely 

 mathematical ; and, moreover, that he supposes the nature 

 of the function already well known. The object of his 

 essay was " to deduce certain relations between the values 

 of this function for different points, and the densities of 

 Electricity or Magnetism that give rise to these ' values.' " 



The object of the present paper is to attempt to give a 

 Physical interpretation to this Function and to illustrate 

 it and its use by some simple example. Suppose, then, a 

 body, say a material particle, be lifted to any point p 

 above the surface of the earth ; the co-ordinates of this 

 point p, referred to the earth's center, being x, y, z. It 

 is e\-ident that, to do so, work must be done by some 

 agent against the earth's gravity; tlie amount of this 

 work depending solely on the distance of p and the total 

 attraction of the earth, the mass of the particle raised 

 being supposed constant. This particle contains this 

 work, as it were, stored in it, and will give it oif in over- 

 coming resistances on its way back to the earth. The 

 Sun expends work — its heat — in raising the waters of the 

 earth into clouds. These clouds overcome resistances, or, 

 in other words, do work on their way as cataracts back to 

 the sea. For all different values of the co-ordinates x, y, z, 

 of the point p, we shall have different values for the work 

 done against gravity in raising the particle to this point. 

 Were the particle to remain stationary a,t p, having con- 

 stant co-ordinates a, b, c, this work would chano-e in 

 amount also, by supposing the mass or attracting power 

 of the central body to change. There is thus seen to be a 

 certain definite quantity of worh-power between bodies 

 endowed with mutually attractive or repulsive forces, 

 which work-power depends in amount on the strength of 

 the mutual forces and the space separating the bodies of 



