304 THE PRINCIPLES OF SCIENCE. 



accelerate the motion of bodies passing through it, some- 

 what in the mode which Aristotelians attributed falsely 

 to the air. Thus we can frame the notion of negative 

 density, and Newton could reason exactly concerning it, 

 although no such thing exists 3. 



In every direction of thought we may meet ultimately 

 with similar failures of analogy. A moving point gene- 

 rates a line, a moving line generates a surface, a moving 

 surface generates a solid, but what does a moving solid 

 generate ? When we compare a polyhedron, or many- 

 sided solid, with a polygon, or plane figure of many sides, 

 the volume of the first is analogous to the area oi the 

 second ; the face of the solid answers to the side of the 

 polygon ; the edge of the solid to the point of the figure ; 

 but the corner, or junction of edges in the polyhedron, 

 is left wholly unrepresented in the plane of the polygon. 

 Even if we attempted to draw the analogies in some 

 other manner, we should still find a geometrical notion 

 embodied in the solid which has no representative in the 

 plain figure r . 



Faraday was able to frame some notion of matter in a 

 fourth condition, which should be to gas what gas is to 

 liquid 8 . Such substance, he thought, would not fall far 

 short of radiant matter, by which apparently he meant 

 the supposed caloric or matter assumed to constitute heat, 

 according to the Corpuscular Theory. Even if we could 

 frame the notion, matter in such a state cannot be known 

 to exist, and recent discoveries concerning the continuity 

 of the solid, liquid, and gaseous states remove the basis 

 of the speculation. 



From these and many other instances which might be 



Q ' Principia/ bk. II. Section II. Prop. X. 



r De Morgan, ' Cambridge Philosophical Transactions,' vol. xi. 

 Part ii. p. 246. 



8 'Life of Faraday,' vol. i. p. 216. 



