NA TURE 



213 



THURSDAY, JULY 3, 1879 



THOMSON AND T AIT'S NATURAL 

 PHILOSOPHY 

 Treatise on Natural Philosophy. By Sir William Thom- 

 son, LL.D., D.C.L., F.R.S., Professor of Natural 

 Philosophy in the University of Glasgow, Fellow of 

 St. Peter's College, Cambridge, and Peter Guthrie 

 Tail, M.A., Professor of Natural Philosophy in the 

 University of Edinburgh, formerly Fellow of St, Peter's 

 College, Cambridge. Vol. I. Part i. New Edition. 

 (Cambridge, at the University Press, 1879.)] 



THE year 1867 will long be remembered by natural 

 philosophers as that of the publication of the first 

 volume of "Thomson and Tail." They had long been 

 waiting for the book, and in the preface the delay was 

 accounted for by the necessity of anticipating the wants 

 of the other three volumes, in which the remaining 

 divisions of Natural Philosophy were to be treated. The 

 reader was also reminded, that if in any passage he 

 failed to appreciate the aim of the authors, the reason 

 might be that what he was studying was in reality a pro- 

 spective contrivance, the true aim of which would not 

 become manifest until after the perusal of that part of 

 the work for which it was designed to prepare the way. 



What we have had before us now for twelve years was, 

 the authors reminded us, strictly preliminary matter. 

 The plan of the whole treatise could only be guessed at 

 from the scale on which its foundations were constructed. 



In these days, when so much of the science of our best 

 men is dribbled out of them in the fragmentary and im- 

 perfectly elaborated form of the memoirs which they 

 contribute to learned societies, and when the work of 

 making books is relegated to professional bookmsikers, 

 who understand about as much of one subject as of 

 another, it was something to find that even one man of 

 known power had not shrunk from so great a work ; it 

 was more when it appeared that two men of mark were 

 joined together in the undertaking ; and when at last 

 the plan of the work was described in the preface, and 

 the scale on which its foundations were being laid was 

 exhibited in the vast substructure of Preliminary Matter, 

 the feeling with which we began to contemplate the 

 mighty whole was one in which delight was almost over- 

 powered by awe. 



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 de- 

 fences, so that now, when we have before us the second 

 edition of the first part of the first volume, we are im- 

 pelled to risk the danger of criticising an unfinished work, 

 and to say something 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 

 Vol. XX.— No. s^S 



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 geo- 

 metry itself is part of the science of motion, and that it 

 treats, not of the relations between figures already exist- 

 ing 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 A B 

 simply as a white stroke on a black board, and call it 

 indifferently A B or B A, 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 indiyisible 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 

 continuous line without breadth. Our knowledge, there- 

 fore, 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 accord- 

 ing to his own notions about continuity and probability. 

 The rapidity, however, with which we make our ex- 

 ploration is such that we come to think that by a single 

 glance we can thoroughly see the whole of that surface of 

 a body which is turned towards us, if, indeed, we are not 

 prepared to assert that we have seen the other side too, 

 when after all, if our attention were to leave a trace 

 behind it, as the point of the blind man's stick might do, 

 this trace would appear as a mere line meandering over 

 the surface in various directions, but leaving between its 

 convolutions unexplored areas, the sum of which is still 

 equal to- the whole surface. We are at liberty no doubt 

 to course over the surface and to subdivide the meshes 

 of the network of lines in which we envelope it, and 

 to conclude that there cannot be a hole in it of more 

 than a certain diameter, but no amount of investiga- 

 tion will warrant the conclusion, which, nevertheless 

 we draw at once and without a scruple, that the sur- 

 face is absolutely continuous and has no hole in it at all. 

 Even when, in a dark night, a flash of lightning dis- 

 closes instantaneously a whole landscape with trees and 

 buildings, we discorer these things not at at once, but by 

 perusing at our leisure the picture which the sudden flash 

 has photographed on our retina. 



The reason why the phenomena of motion have been 

 so long refused a place among the most universal and 

 elementary subjects of instruction seems to be, that we 

 have been relying too much on symbols and diagrams, to 

 the neglect of the vital processes of sensation and 

 thought. 



It is no doubt much easier to represent in a diagram or 

 a picture the instantaneous relations of things coexisting 

 in space than to illustrate in a full and complete manner 

 the simplest case of motion. When we have drawn our 



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