172 NEWTON S PKINCJPIA. 



and comparative. Absolute gravity is the whole force 

 with which the body tends downwards. Relative gravity 

 is the excess of gravity with which the body tends down 

 wards more than the ambient fluid. The bodies, therefore, 

 which we call light, and which appear to fall so slowly, or 

 even seem to rise in the air, are light only in comparison 

 with the air. If there were no air, their apparent gravity 

 would be their real gravity, and all bodies are found to 

 fall when placed in a vacuum. 



II. 1. Having discussed some of the fundamental proper 

 ties of fluids, and obtained the equations of equilibrium, we 

 can proceed to apply them to some of the great problems 

 that Nature presents us with. The first case which Newton 

 considers is the law of density in a compressible fluid 

 which is attracted according to any law by a force tending 

 towards a given centre. He does not consider this pro 

 blem in its most general form, nor would there be any 

 advantage in doing so. The only forces which present any 

 interest are those which vary according to some power of 

 the distance. 



Let us assume that the attraction upon any particle 

 whose mass is a unit, and distance from the centre x, is, 



_ 



x n 



where \L is some constant quantity, of n + 1 dimensions. 

 The fluid will manifestly arrange itself symmetrically round 

 the centre of force. We may therefore consider only those 

 particles that lie in the axis of x. Take therefore a small 

 rectangular element at a distance x from the centre of the 

 earth, and whose sides are dx dy dz. This element must 

 be at rest under the action of the fluid pressures on its 

 sides and its own gravity. If p be the pressure referred 

 to a unit of area at this point, these two pressures will be 

 clearly 



