1921.] 
Farr.—Relativity. 
237 
same circumstances as the other, as the one was with and against, whilst 
the other was across and back. He suggested, therefore, that in measuring 
with and against the stream the measuring-rod (yard measure, two-foot 
rule, or whatever you like to think of) contracted, and was not really the 
same length as it was in measuring across and back. For a given speed 
of the ether past the earth it was quite easy to ascertain what the contraction 
would have to be to bring about the compensation-, but if the compen¬ 
sation comes about automatically it explains the failure of the experiments 
devised to measure the drift of the ether past the earth. 
I trust no one will worry unduly, and imagine I am going to get beyond 
their depths, if I put up on the board the mathematical expression for the 
necessary contraction. It is this— 
1 
B = 
where B is the ratio of the length measured across and back to that 
measured up and against. Such a contraction as this (if it occurs) will 
render nugatory the experiment I have described, and would be the 
explanation of the failure of many other ingenious experiments which have 
been devised to test this question of the earth’s drift through the ether. 
Before going any further, let us for a moment or two see the extent 
of the necessary contraction in certain cases. Let us take, that is to say, 
a few hypothetical cases. Suppose, for instance, that the earth moved 
through the ether at a speed of 121,000 miles per second—and there is no 
reason that I know of why it should not be moving at this velocity—then 
the factor B would amount to 2, and the cross and back lengths would 
really—that is to say, if the word “ really ” means anything—would really 
be twice as long as that up and down, although to measurement and to 
our eyes they would be the same. Thus the up-and-down-stream swimmer, 
if he swam at the speed of 121,000 miles a second against a stream of 
186,000 miles a second, would have the distance he had to swim cut down 
to half as compared with his equally stupendous companion who swam 
across and back. Of course, the first time one comes across a suggestion 
like this it sounds impossible, but one gets used to it after a while, and there 
is nothing impossible about it—indeed, it is quite probably true. I do not 
mean to say it is true that the earth is moving through the ether at 121,000 
miles a second, but that, if it were, this contraction would take place, and 
so cover up our means of finding it out. We know the earth’s velocity 
in its orbit, which is about nineteen miles a second. If, then, the ether 
is fixed in space, the earth must be all the time moving through it with 
this velocity. Why can’t we find it out ? Fitzgerald says, because the 
earth contracts in the direction of its motion through the ether by just 
enough to smother up our means of finding it out, and that in this case 
would be about 2J in. in that diameter that was in the direction of its 
motion through the ether. 
Of course, do not for one moment let yourselves imagine that scientific 
men would accept such an hypothesis as this without confirming it, if it 
were possible to confirm it — indeed, without pulling it inside out and 
haggling over it in every possible way. I cannot hope to indicate even 
the work which has been done either to substantiate or to contradict (as 
the facts of the case so determined) Fitzgerald’s suggestion. Though he 
first made it, the hypothesis is known as the Fitzgerald-Lorentz contraction 
hypothesis, as Lorentz made the same suggestion almost simultaneously, 
