642 THE PRINCIPLES OF SCIENCE. [CHAP. 



form of a shape or a colour ; but we can speak of them and 

 reason concerning them; in short, we often know them 

 in everything but a sensuous manner. Accurate investi- 

 gation shows that all material substances retard the 

 motion of bodies through them by subtracting energy 

 by impact. By the law of continuity we can frame the 

 notion of a vacuous space in which there is no resistance 

 whatever, nor need we stop there ; for we have only to 

 proceed by analogy to the case where a medium should 

 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. 1 



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 of 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 

 figure of two dimensions. 2 



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 



1 Principia, bk. ii. Section ii. Prop. x. 



2 De Morgan, Cambridge Philosophical Transactions vol. 

 Part ii, p. 246. 



* Life of Faradw/, vol. i. p. 216. 



