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THURSDAY, MARCH 4, 1915. 


TIME AND SPACE. 
A Theory of Time and Space. By A. A. Robb. 
Pp. vi+373. (Cambridge University 
1914.) Price tos. 6d. net. 
HE appearance of Dr. Robb’s treatise, if 
such a word can be applied to a volume 
which opens out a new field of philosophical 
inquiry on the basis of modern physical science, 
is a very welcome event, and more especially to 
students of the fundamental nature of the con- 
ceptions which we employ in our attempts to 
describe physical experiences. There is a general 
feeling, at least in this country, that in spite of 
. the remarkable success of the principle of rela- 
_ tivity in simplifying our descriptions of physical 
science, the more logical aspect of the principle is 
seriously at fault, and herein lies the reason for the 
' noticeable decline in favour which the principle 
| F 






Press, 
has experienced recently. The present work, as 
its title implies, is a definite theory of space and 
time, and although its aim is strictly logical 
throughout, it deals with its subject in a simple 
| geometrical manner, readily followed by anyone 
' who has made a study of Euclid. The author’s 
selection of a model is very judicious, and makes 
‘the argument flow so smoothly that the reader 
will probably realise with a shock, at some point, 
the far-reaching nature of the conclusions to which 
e has been led. 
The author had already published the introduc- 
tion to the work as a tract, but it is reproduced 
in the present volume. It gives a brief statement 
of the history and essential meaning of the prin- 
ciple of relativity, pointing out the more important 
difficulties which are felt, and which the more 
formal treatises on the principle, by tending to 
_ emphasise unduly the purely mathematical aspect, 
‘NO. 2366, VOL. 95 | 

ILLUSTRATED JOURNAL OF SCIENCE. 
“To the 
Of Nature trusts the mind which builds for aye.”’ 
solid ground 
—WoRbDSWORTH. 
As is well known, rela- 
tivity demands that events which are simultaneous 
events for one observer not necessarily so 
This is at variance with the funda- 
mental principles of logic, which demand that “a 
thing cannot both be and not be at the same time.” 
do not attempt to meet. 
are 
for another. 
| But the simplicity brought about by the intro- 
| duction of such postulates is such that physicists 
have allowed them to pass for a time, always, 
however, realising that our ideas of space, and 
more especially of time, must be so modified as to 
make them intelligible and part of a logical 
system. This simple example will illustrate the 
scope of Dr. Robb’s work, and the exact manner 
in which it differs fundamentally from the more 
usual treatises. He has shown that, as a corollary 
from his treatment of space and time relations, 
such a logical scheme of geometry and of time 
can be built up, in which our ordinary geometries 
find a place. 
The foundation of the work involves a new idea 
—that of conical order. The spacial relations are 
to be regarded as. the manifestation of the fact 
that elements of time, or instants, form a system 
in conical order. This conception may be analysed 
in terms of the relations of after and before. From 
some twenty-one postulates involving these rela- 
tions it is possible to set up a system of geometry 
in which any element can be represented by four 
co-ordinates, x, y, z, t. The first three correspond 
to space co-ordinates, and the fourth to time as 
generally understood. But since an element in this 
geometry corresponds to an instant, and bears the 
relations of after and before to other instants, the 
theory of space appears as a part of the theory 
of time. Simple geometrical interpretations of the 
initial postulates in three dimensions are given in 
the volume. One remarkable feature is that it 
seems necessary for a really consistent theory to 
limit the number of dimensions to four. The geo- 
B 
