830 
less. This one experiment is the aberra- 
tion of light, but even here Stokes has 
shown that it may be explained in either of 
two ways: first, that the earth moves 
through the ether of space without disturb- 
ing it, and second, if it carries the ether 
with it by a kind of motion called irrota- 
tional. Even here, however, the amount 
of action probably depends upon relative 
motion of the luminous source to the re- 
cipient telescope. 
So the principle of Doppler depends also 
on this relative motion and is independent 
of the ether. 
The result of the experiments of Foucault 
on the passage of light through moving 
water can no longer be interpreted as due 
to the partial movement of the ether with 
the moving water, an inference due to im- 
perfect theory alone. The experiment of 
Lodge, who attempted to set the ether in 
motion by a rapidly rotating disc, showed 
no such result. 
The experiment of Michelson to detect 
the etherial wind, although carried to the 
extreme of accuracy, also failed to detect 
any relative motion of the matter and the 
ether. 
But matter with an electrical charge 
holds fast to the ether and moves it in the 
manner required for magnetic action. 
When electrified bodies move together 
through space or with reference to each 
other we can only follow their mutual 
actions through very slow and uniform 
velocities. When they move with velocities 
comparable with that of light, equal to it 
or even beyond it, we calculate their mutual 
actions or action on the ether only by the 
light of our imagination unguided by ex- 
periment. The conclusions of J. J. Thom- 
son, Heaviside and Hertz are all results of 
the imagination and they all rest upon as- 
sumptions more or less reasonable but al- 
Ways assumptions. A mathematical in- 
vestigation always obeys the law of the 
SCIENCE, 
[N.S. Von. X. No. 258. 
conservation of knowledge: we never get 
out more from it than we put in. The 
knowledge may be changed in form, it may 
be clearer and more exactly stated, but the 
total amount of the knowledge of nature 
given out by the investigation is the same 
as we started with. Hence we can never 
predict the result in the case of velocities 
beyond our reach, and such calculations as 
the velocity of the cathode rays from their 
electromagnetic action has a great element 
of uncertainty which we should do well to 
remember. 
Indeed, when it comes to exact knowl- 
edge, the limits are far more circumscribed. 
How is it, then, that we hear physicists 
and others constantly stating what will 
happen beyond these limits? Take veloci- 
ties, for instance, such as that of a material 
body moving with the velocity of light. 
There is no known process by which such 
a velocity can be obtained even though the 
body fell from an infinite distance upon the ~ 
largest aggregation of matter in the Uni- 
verse. If we electrify it, as in the cathode, 
rays, its properties are so changed that the 
matter properties are completely masked by 
the electromagnetic. 
It is a common error which young physi- 
cists are apt to fall into to obtain a law, a 
curve or a mathematical expression for 
given experimental limits and then to apply 
it to points outside those limits. This is 
sometimes called extrapolation. Such a 
process, unless carefully guarded, ceases to 
be a reasoning process and becomes one of 
pure imagination specially liable to error 
when the distance is too great. 
But it is not my purpose to enter into 
detail. What I have given suffices to show 
how little we know of the profounder ques- 
tions involved in our subject. 
It is a curious fact that, having minds 
tending to the infinite, with imaginations 
unlimited by time and space, the limits of 
our exact knowledge are very small indeed. 
