NovemsBer 8, 1918] 
in fact is international and universal. There 
is not an English entomology, nor a French 
paleontology, any more than there exists a 
Roman Catholic algebra or a Presbyterian 
geometry. We certainly have provocation, 
but the test of our scientific fitness is found 
in our ability to avoid the mistake of attempt- 
ing to beat the Prussian by Prussianizing our- 
selves. 
W. J. Hotianp 
CARNEGIE INSTITUTE, 
October 18, 1918 
THE FOUNDATIONS OF MECHANICS 
Mr. Paut J. Fox, in his comments! on our 
article of August 2d seems to us to be mis- 
taken in two particulars. Surely to identify 
a force, so that the same force can be repro- 
duced at will and caused to act at one time 
on one body and at another time on another 
body, is not the same thing as to measure the 
force. If we are to compare the accelerations 
of different bodies due to a given force, some 
basis of identification of the force is necessary ; 
for example, it may be the force which will 
produce a certain stretch of a given spring. 
To identify a force, or a temperature, is not 
the same thing, by any means, as to measure 
the force or temperature. 
If Mr. Fox will read our article carefully he 
will see that we do not even imply that the 
quantitative idea of mass is necessary for 
either the identification of measurement of 
force. Every physicist knows, and knew long 
before Perrin’s time, that a rigorous quantita- 
tive definition of force is possible in terms of 
stretched springs without assuming Hooke’s 
law. But no one, perhaps, has ever measured 
a force in this way, and by measuring we do 
not refer to any kind of thinking nor to any 
mathematical operation, much as we love both 
of these categories; we mean a laboratory 
operation (troublesome though such things 
be), and especially we mean a_ laboratory 
operation which gives an invariant result irre- 
spective of special properties of particular sub- 
stances and independently of time and place. 
Perhaps our deeper source of confusion may 
1 Scrence, October 4, 1918. 
SCIENCE 
471 
be, as Mr. Fox says, “in not making a dis- 
tinction between mechanics as a ‘ doctrinal 
function’ and as an experimental science.” 
But we do not believe it; and for Mr. Fox to 
borrow the term in mild ostentation from Bert- 
rand Russell leaves us unimpressed. Surely it 
is no mark of fixity of ideas on our part not to 
take Bertrand Russell over-seriously even in 
doctrinal mechanics and to always attend care- 
fully to what has been said by Newton and 
Thomson and Tait, and Larmor. 
Our mathematicians are rightly interested 
in the invariance of all kinds of functions with 
respect to a wide variety of transformations, 
and the physicist has seen many remarkable 
applications of this sort of invariance, the 
most remarkable of all being the recent gen- 
eralized form of the principle of relativity; 
‘but the mathematician does not seem to under- 
stand that there is a kind of mathematics in- 
volved in the always more or less idealized 
operations and transformations of the labora- 
tory with their amazing groups of invariances. 
Indeed, when we read such passages as the 
following from Mr. Fox’s communication, fear 
that our mathematicians may never be able to 
fathom the deeper phases even of doctrinal 
physies—for the whole of the logical structure 
of the physical science is, let us borrow the 
phrase from Bertrand Russell, doctrinal. 
“Thus it is clear that the units we have in 
the Bureau of Standards need not be the same 
as the undefined elements in the doctrinal 
function. We do not need even to imagine 
that Bureau keeping standard springs, rubber 
bands, strong armed men, etc., any more than 
it would keep a standard point (!) instead of 
a standard meter, for Veblen’s system of 
geometry. Any equation may be made use of 
to measure any quantity which it contains.” 
Mr. Fox, further on, quotes Frederic Soddy’s 
statement that “the conception of force and 
its psendo physical reality undoubtedly delayed 
for centuries the recognition of the law of the 
conservation of energy, ete.,” and states that 
there seems to a certain mysticism in Soddy’s 
contention. Not at all. Let Mr. Fox read and 
digest the remarkable appendix on The Scope 
of Mechanical Explanations in Larmor’s 
