FEBRUARY 23, 1912] 
unmeasured quantities, and would mean 
nothing unless we could go further. Now 
the advocates of the purely dynamical defi- 
nition of the concept of force say that we 
ean go further, by observing the mutual 
accelerations of two bodies and using these 
to obtain the ratio of their masses. If this 
ean be done the matter is settled. But 
could it be done by the disembodied spirit? 
In our use of the mutual accelerations of 
two bodies to get their masses we must ex- 
plicitly state that the bodies are arranged 
so as to interact (that is, to exert force on 
each other), and unless that condition is 
established the mutual accelerations of two 
bodies, however often repeated, can tell us 
nothing about their masses. A man at a 
station might observe two trains leaving 
the station in opposite directions with the 
same accelerations every day for ten 
years, and yet he could not compare their 
masses by any such observations. Eyes 
and mind only will not do it. To get the 
measure of mass we must start with the 
intuitional knowledge of force, and use it 
in the experiments by which we first de- 
fine and then measure mass. 
I now come to a much more difficult part 
of my subject, the consideration of the 
other primary concepts of space and time. 
Not many years ago we should have been 
willing to pass them over with a mere men- 
tion, admitting the impossibility of giving 
a definition or even an intelligible descrip- 
tion of either of them, admitting the im- 
possibility of determining an absolute or 
fixed point in space, or an absolute instant 
of time, but still asserting that we knew 
something about them both of which we 
were sure. At present we are driven by 
the development of the principle of rela- 
tivity to examine anew the foundations of 
our thought in respect to these two pri- 
mary concepts. 
SCIENCE 
287 
I suppose that the old ideas about space 
and time that have been of service to 
physicists since the beginning of the sci- 
ence are summed up as well as anywhere 
in Newton’s words: 
Absolute and real time, the time of the mathe- 
matician, flows on equably, having no relation in 
itself or its nature to any external object. It is 
also called duration. Relative, apparent time, the 
time of common life, is an external measure of any 
duration cognized by the senses, by means of 
motion. It is commonly used in place of real time. 
Absolute space, having no relation in its nature 
to any external object, always remains alike every- 
where and immovable. Relative space is the meas- 
ure of this space, or any movable dimension, recog- 
nized by our senses as limited by its situation with 
respect to bodies. This is commonly thought of as 
equivalent to absolute space. 
These definitions have been often justly 
eriticized for the emphasis laid on the un- 
fruitful ideas of absolute time and space. 
Perhaps the criticism has fallen rather 
upon Newton’s subsequent expansion of 
his thought on these ideas. But do they 
not contain in the first place the concep- 
tions of time and space which have been 
uniquely useful up to this time in physics, 
and in the second place, do they not con- 
tain what each one of us really thinks 
about time and space when he makes an 
honest examination of his knowledge? The 
essential feature of both these descriptions 
for our present purpose is Newton’s dec- 
laration, both as to time and space, con- 
sidered as species and not as magnitudes, 
that they are in themselves and in their 
nature without relation to any external 
object. It is this statement which is con- 
tradicted by some of the enunciations of 
the principle of relativity. 
It is not necessary for me to give an ac- 
count of the genesis of the principle of 
relativity. It may fairly be said to be 
based on the necessity of explaining the 
negative result of the famous experiment 
of Michelson and Morley, and on the con- 
