THOMSON AND TAIT's NATURAL PHILOSOPHY. 777 



This feeling has been growing upon us during the twelve years we have 

 been exploring the visible part of the work, marking its bulwarks and telling 

 the rising generation what manner of a palace that must be, of which these 

 are but the outworks and first line of defences, so that now, when we have 

 before us the second edition of the first part of the first volume, we are 

 impelled to risk the danger of criticising an unfinished work, and to say some- 

 thing about the plan of what is already before us. 



The first thing which we observe in the arrangement of the work is the 

 prominence given to kinematics, or the theory of pure motion, and the large 

 space devoted under this heading to what has been hitherto considered part 

 of pure geometry. The theory of the curvature of lines and surfaces, for 

 example, has long been recognised as an important branch of geometry, but 

 in treatises on motion it was regarded as lying as much outside of the subject 

 as the four rules of arithmetic or the binomial theorem. 



The guiding idea, however, which, though it has long exerted its influence 

 on the best geometers, is now for the first time boldly and explicitly put 

 forward, is that geometry itself is part of the science of motion, and that it 

 treats, not of the relations between figures already existing in space, but of 

 the process by which these figures are generated by the motion of a point 

 or a line. 



We no longer, for example, consider the line AB simply as a white 

 stroke on a black board, and call it indifferently AB or BA, but we conceive 

 it as the trace of the motion of a point from A to B, and we distinguish 

 A as the beginning and B as the end of this trace. 



This method of regarding geometrical figures seems to imply that the 

 idea of motion underlies the idea of form, and is in accordance with the 

 psychological doctrine which asserts that at any given instant the attention is 

 confined to a single and indivisible percept, but that as time flows on the 

 attention passes along a continuous series of such percepts, so that the path 

 of investigation along which the mind proceeds may be described as a con- 

 tinuous line without breadth. Our knowledge, therefore, of whatever kind, may 

 be compared to that which a blind man acquires of the form of solid bodies 

 by stroking them with the point of his stick, and then filling up in his 

 imagination the unexplored parts of the surface according to his own notions 

 about continuity and probability. The rapidity, however, with which we make 

 our exploration is such that we come to think that by a single glance we 



VOL. n. 98 



