460 
Imagine a cube of rubber, with several 
points marked on its faces, and consider 
the lines joining one of these points with 
the others. Theangles between these lines 
measure the relative directions of the ter- 
minal points from the initial point. Now 
set the cubein motion ; stresses and strains 
are generated, in consequence of which the 
relative directions of the lines undergo 
small alterations. Why do these changes 
of direction remain within small limits? 
Evidently on account of the nature of the 
material connecting the points. 
Consider now another system of points 
whose relative directions as time goes on 
remain almost unchanged, viz., the fixed 
stars. Is it possible that they may be 
moving like the points on the rubber cube? 
Observational astronomy indicates that they 
are at immense distances from the earth and 
from each other. If the law of gravitation 
holds for them their mutual attractions 
must be so feeble that they form a practi- 
cally unconnected system. The constancy 
of their relative directions cannot there- 
fore be accounted for as in the former 
cease by the action of the matter between 
them, but must be attributable to some other 
cause. The distinction between the two 
cases, which is very real, is recognized by 
assuming that a line may have absolute 
direction; and the stars are said to pre- 
serve their absolute directions from the 
earth. Again, the assumption that both 
the law of gravitation and the laws of 
motion are true for the solar system leads 
to the result (in consequence of its vast 
distance from the stars) that its center of 
mass has little or no acceleration; in other 
words, is either at rest or in uniform mo- 
tion in a straight line. 
Now, although the ideas of absolute di- 
rection and absolute rest or uniform motion 
in a straight line may from the kinematical 
point of view be incomprehensible, yet in 
dynamics these terms indicate very defi- 
SCIENCE. 
(N.S. Von. VI. No. 143. 
nite facts. It is only by the choice of the 
center of mass of the solar system as origin 
and by using the stars to fix the directions 
of the axes that it is possible to make the 
observed motions of the planets fit, at the 
same time, the law of gravitation and the 
laws of motion. It is unnecessary to enter 
into the details of the work; suffice it to 
say, it is a process of trial and error, of 
assumption, computation and check by 
observation. 
The following dynamical consideration 
enables, in certain cases, a more convenient 
origin to be used than the center of mass of 
the solar system. 
If equal accelerations are impressed on 
the bodies whose motions and mutual 
forces are under consideration, by the at- 
traction of the remainder of the solar sys- 
tem, it is evident that their motions re- ~ 
ferred to an origin at their common center 
of mass, with axes fixed in direction by the 
stars, will be affected only by their mutual 
actions. Also assuming the laws of motion 
to apply, these motions so measured will 
show the whole effect of their mutual ac- 
tions, since the latter have no effect on the 
motion of their center of mass. It is thus, 
possible, in discussing the lunar tides, to use 
as origin the center of mass of the earth and 
moon, and in the ease of terrestrial bodies 
the center of mass of the earth. It may 
be noted that whether the primary origin 
or such subsidiary origins be used, the 
equations for the mutual forces under con- 
sideration are the same; the effect of the 
change of origin appearing only in the con- 
stants of integration. It will be conven- 
ient to term all such sets of axes, including 
the primary set, absolute axes. 
It now remains to determine whether the 
absolute axes will give results agreeing 
with those already obtained in the small 
scale experiments, with axes fixed in the 
earth ; and if they do not, whether the dis- 
erepancies can be explained. 
