TRANSACTIONS OF SECTION A, 427 
events, a fuller, and I think a clearer, account of the province and the method of 
Abstract Dynamics is given in a review of the second edition of Thomson and 
Tait, which was one of the last things penned by Maxwell, in 1879.1 A 
‘complete’ description of even the simplest natural phenomenon is an obvious 
impossibility ; and, were it possible, it would be uninteresting as well as useless, 
for it would take an incalculable time to peruse. Some process of selection 
and idealisation is inevitable if we are to gain any intelligent comprehension 
of events. Thus, in Astronomy we replace a planet by a so-called material 
particle—i.c.,a mathematical point associated with a suitable numerical coefticient. 
All the properties of the body are here ignored except those of position and mass, 
in which alone we are at the moment interested. The whole course of physical 
science and the language in which its results are expressed have been largely 
determined by the fact that the ideal images of Geometry were already at hand 
at its service. The ideal representations have the advantage that, unlike the real 
objects, definite and accurate statements can be made about them. © Thustwo lines 
in a geometrical figure can be pronounced to be equal or unequal, and the state- 
ment is in either case absolute. It is no doubt hard to divest oneself entirely 
of the notion conveyed in the phrase det 6 Oeds yewperpel, that definite geome- 
trical magnitudes and relations are at the back of phenomena. It is recognised 
indeed that all our measurements are necessarily to some degree uncertain, but 
this is usually attributed to our own limitations and those of our instruments 
rather than to the ultimate vagueness of the entity which it is sought to 
measure, Everyone will grant, however, that the distance between two clouds, 
for instance, is not a definable magnitude; and the distance of the earth from the 
sun, and even the length of a wave of light, are in precisely the same case, 
The notion in question is a convenient fiction, and is a striking testimony to the 
ascendency which Greek Mathematics have gained over our minds, but I do not 
think that more can be said forit. It is, at any rate, not verified by the expe- 
rience of those who actually undertake physical measurements. The more refined 
the means employed, the more vague and elusive does the supposed magnitude 
become; the judgment flickers and wavers, until at last in a sort of despair some 
result is put down, not in the belief that it is exact, but with the feeling that it 
is the best we can make of the matter. A practical measurement is in fact a 
classification; we assign a magnitude tc a certain category, which may be 
narrowly limited, but which has in any case a certain breadth. 
By a frank process of idealisation a logical system of Abstract Dynamics can 
doubtless be built up, on the lines sketched by Maxwell in the passage referred 
to. Such difficulties as remain are handed over to Geometry. But we cannot 
stop in this position ; we are constrained to examine the nature and the origin of 
the conceptions of Geometry itself. By many of us, I imagine, the first sugges- 
tion that these conceptions are to be traced to an empirical source was received 
with something of indignation and scorn; it was an outrage on the science which 
we had been led to look upon as divine. Most of us have, however, been forced at 
length to acquiesce in the view that Geometry, like Mechanics, is an applied science 
that it gives us merely an ingenious and convenient symbolic representation of the 
relations of actual bodies; and that, whatever may be the @ prior? forms of intuition, 
the science as we have it could never have been developed except for the accident 
(if I may so term it) that we live in a world in which rigid or approximately rigid 
bodies are conspicuous objects. On this view the most refined geometrical demon- 
stration can be resolved into a series of imagined experiments performed with such 
bodies, or rather with their conventional representations. 
It is to be lamented that one of the most interesting chapters in the history of 
science is a blank; I mean that which would have unfolded the rise and growth 
of our system of ideal Geometry. The finished edifice is before us, but the record 
of the efforts by which the various stones were fitted into their places is hope- 
lessly lost. The few fragments of professed history which we possess were edited 
long after the achievement. 
' Na‘ure, vol, xx. p. 213; Scientifie Papers, vol. ii. p. 776. 
