458 
meaning. It will be well, therefore, for 
the student of dynamics occasionally to 
make the endeavor to transform his co- 
ordinates and view the subject from different 
standpoints. For this purpose it is un- 
necessary that he should be an expert in 
refined mathematical analysis. It is requi- 
site, on the other hand, that he should pos- 
sess, in some degree, what may be called 
the mechanical instinct. The whole power 
of modern analysis has not proved sufficient 
to solve, in its generality, the problem of 
the three bodies; a problem extremely use- 
ful, nevertheless, as an illustration of dy- 
namical principles. 
The science of statics, or the laws of 
composition of forces and couples, was de- 
veloped from rude experiments made with 
springs and with strings and weights; the 
tensions of the strings being measured by 
the weights. The conditions necessary in 
these experiments were that the body to 
which the springs or strings were fastened 
should be maintained by them at rest, and 
that all changes of shape and size should 
have ceased. Statics was thus established 
without the introduction of the ideas of 
mass and acceleration. In this stage, how- 
ever, its laws were supposed to apply only 
to rigid bodies at rest. The facts to be 
noted are, that force was recognized as a 
fundamental conception, and that methods 
of measuring it and the laws of composition 
of forces were discovered, without reference 
to motion except in the respect that rest 
was supposed to be a necessary condition. 
The connections between force and mo- 
tion, the subject-matter of dynamics, were 
established by observing the motions of 
falling bodies, pendulums, bodies rolling 
and sliding down inclined planes, colliding 
spheres, bodies connected by strings run- 
ning over pulleys, etc. In making these 
experiments it was necessary to know the 
forces acting. As the only scientific knowl- 
edge of force at the time was contained in 
SCIENCE. 
LN. S. Von. VI. No. 143. 
the laws of statics, the assumption was 
made that these laws were true, even 
though the bodies were moving and 
whether the velocities were increasing, 
decreasing, or changing in direction. This 
was a change of the point of view which 
was fruitful in important results. It was 
found, however, that while the above 
assumption was justified in the case of 
the composition of forces, and in the case 
of weights when considered as _ forces 
acting on the heavy bodies themselves, it 
was not true to assume that the tension of 
a string in motion is measured by the at- 
tached weight. The true indication of the 
tension in a string was recognized to be the 
same asin the case of a spring, viz., the 
elongation. Again, while in statics, the 
principal objects were the strings and 
weights, and the bodies to which they were 
attached were of little or no account, in the 
dynamical experiments the bodies assumed 
importance. The conception of mass was 
introduced, and was found to correspond 
with the commercial idea of quantity of 
material, as determined by the balance and 
weights. The results of these experiments 
are contained in the laws of dynamics, or 
the laws of motion, as they are usually 
called, which may be summarized as fol- 
lows: 
I. That no change in a body’s motion of 
translation takes place except by the action 
of external forces. 
II. That external forces impress on a 
body changes of momentum in their own 
directions at rates proportional to their 
magnitudes. 
III. That action and reaction are equal 
and opposite, and in the same line. 
It seems to be a matter of doubt whether 
Newton, in his statement of the laws of mo- 
tion which I have thus paraphrased, in- 
tended to affirm that action and reaction 
are in the same line. Whether there be 
ground for this doubt or not, the idea is 
