SEPTEMBER 24, 1897. ] 
If no explanation could be given of such 
discrepancies it is evident that the science 
of dynamics would be resolved into a bun- 
dle of empirical rules, describing the vari- 
ous axes of reference that applied in dif- 
ferent cases, and the range of applicability 
in each case. 
In order to make the comparison, it will 
be necessary to obtain the data required 
for transformation from the absolute set of 
axes with origin at the earth’s center, to 
axes fixed in the earth with origin in the 
locality of the experiments. These data 
are furnished by astronomical observations. 
When the transformation is made there 
appear on the left-hand side, let us say, of 
the equations the rate of change of momen- 
tum of the body relative to the axes fixed 
in the earth, and on the right-hand side the 
attractions, tensions and other impressed 
forces, together with certain terms involv- 
ing the relative motion of the two sets of 
axes. 
In the equations of the original experi- 
ments no terms of the latter kind occurred. 
There are three ways of accounting for the 
difference. Hither the forces are different 
in the two sets of equations, or the new 
terms are so small as to be within the limit 
of experimental error, or each experiment 
or class of experiments requires its special 
set of axes. 
Experience shows that the explanation 
lies in the first or second alternative; the 
the third is not true. 
These terms are generally negligible in 
laboratory experiments. It is necessary to 
consider them in the theory of winds and 
ocean currents. Their presence in the 
equations has suggested certain experiments 
with pendulums and gyrostats, which con- 
firm their truth. We are justified by ex- 
perience, for instance, in believing that in 
the northern hemisphere moving bodies 
tend to the right, in the southern hemi- 
sphere to the left ; bodies moving eastward 
SCIENCE. 
461 
tend to rise, westward to fall; and that 
bodies, whether at rest or in motion, tend to 
move outwards from the polar axis. All 
such tendencies are represented by the terms 
under consideration. They may be re- 
garded when written on the force side of 
the equations as representing relative or 
fictitious forces ; fictitious because they cor- 
respond to no actions of matter, but are the 
consequence simply of the motion of the 
axes of reference relative to the absolute 
axes. 
Sometimes it happens, as has been indi- 
cated, that the discrepancy lies in the fact 
that the forces in the two sets of equations 
are different, although referring to the same 
experiment. Consider the case of a body 
suspended froma spring. Referred to axes 
fixed in the earth it is at rest, and the in- 
ference is that the attraction of the earth 
is equal and opposite to the tension of the 
spring. Referring, however, to the same 
axes by transformation from the absolute 
axes, there appears, in addition to the terms 
representing the tension of the spring and 
the attraction of the earth, a new term, a 
relative or fictitious force, known as the 
centrifugal force. The inference now is 
that the attraction of the earth is greater 
than the tension of the spring, instead of 
being equal to it. If this inference be ac- 
cepted as the true one the question arises, 
which of the original forces was wrong, or 
were both astray? Remembering that the 
intrinsic indication of the force exerted by 
the spring is its elongation, and that of at- 
traction the acceleration caused by it, also 
that acceleration depends on the choice 
of axes of reference, while the elongation of 
a spring does not, there can be no hesita- 
tion in deciding that the error lay alto- 
gether in the estimate of the attraction. 
The fictitious force, while itself invisible, 
also rendered invisible a portion of the 
earth’s attraction. By using proper axes of 
reference its true character is revealed and 
