SEPTEMBER 24, 1897.] 
implied in D’Alembert’s principle and is 
accepted as true. 
The third law is a law of force, the value 
of which is seen when the mutual actions of 
bodies are to be considered. Without this 
law the laws of statics and of motion would 
refer to actions on one body only. 
It was evident that the laws of com- 
position of forces could be considered as 
corollaries of the laws of motion, so that 
from the latter a more comprehensive view 
of the measurement of force was gained 
than from the statical experiments. Thus 
the statical method of measuring force 
by balancing the tension of one string or 
spring against that of another was in- 
terpreted dynamically, by assuming that 
the body upon which the springs acted re- 
mained at rest in consequence of receiving 
from the forces opposite changes of mo- 
mentum at thesamerate. It followed that 
if the springs were to act singly they would, 
other things being equal, produce equal 
rates of change of momentum. Thus dy- 
namics furnished a new method of measur- 
ing forces which agreed with that by means 
of springs. 
Further investigation in the light of the 
new principles showed that the method of 
measuring forces by weights agreed with 
the spring measurement and with the dy- 
namical measurement when the condition 
was observed that the weights were kept 
in the same locality, but in general not 
otherwise. Dynamics gave an explana- 
tion of this anomaly by showing that the 
forces of the weights were due to gravity, 
which evidently might change in intensity 
from place to place, although the masses of 
the weights remained unaltered. The 
measurement of force by weights was thus 
shown to be a special case of the general 
dynamical method. Also it resulted that 
the measurement of force by weights was 
in principle the same as the measurement 
by springs, the weight and the earth to- 
SCIENCE. 
459 
gether constituting a spring whose elastic 
force is gravity. 
It is of little use in the early dynamical 
training of a student to dwell on the fact 
that the unit of force in dynamical measure 
is a force which produces unit acceleration 
in unit mass. It may even do harm. It 
may have the effect of leading him to be- 
lieve that the refined methods of measur- 
ing force by means of weights and springs, 
which are the only methods used in the 
laboratory, are wrong and that the testing 
machines and pressure gauges of the en- 
gineer are beneath contempt. It ought to 
be impressed upon him that all the methods 
of measuring force approved by experience 
are equally scientific and equally absolute, 
and will give exactly the same results, aside 
from unavoidable experimental error, pro- 
vided that the proper conditions in each 
case are observed; also that the choice 
of the method depends, just as in the case 
of everything else in life, upon the objects 
in view and the circumstances. 
We now come to the period of the de- 
velopment and extension of the laws of 
motion. While proved in the case of small 
bodies and motions of limited range, it by 
no means followed that they applied to the 
motions of the tides or of the planets. New- 
ton, by the aid of his happy intuition, the 
law of gravitation, put new meaning into 
them and extended their jurisdiction over 
all visible and measurable motions within 
the solar system. 
All motion is, so we are taught, relative ; 
and the motion which is uniform and in a 
straight line with reference to one set of 
axes may be varying and in a very 
crooked line when referred to another set, 
and perfect rest with regard to a third set. 
The question then is, for what axes are 
the laws of motion true? It is very certain 
that the stresses in the springs by which 
forces are measured are in no wise affected 
by the choice of axes of reference. 
