464 
tance as the second law of motion, and not 
a mere verbal definition. Experience thus 
gives a dynamical measure of work as well 
as of force. 
The law of equivalence of work and en- 
ergy then establishes work as a dynamical 
measure of energy. 
The laws of motion, combined with this 
law of energy, establish the result that 
kinetic energy is proportional to the prod- 
uct of momentum and velocity, and thus 
furnish a dynamical method of measuring 
energy in its kinetic form. This is the sole 
contribution of the laws of motion to the 
science of energy. 
It is only in the case of bodies whose in- 
ternal forces and motions are known, or 
determinable from assumed data, in other 
words, imaginary bodies, that the laws of 
energy, as far as they are considered in dy- 
namics, are included in the laws of motion 
and therefore become unnecessary, except 
for the purpose of convenience in mathe- 
matical analysis, or economy of thought. 
Even in such cases the expressions for work 
and energy retain a flavor of their original 
meaning and do not altogether degenerate 
into mere mathematical symbols. 
The science of dynamics, as it is under- 
stood at the present day, includes among its 
fundamental principles, in addition to laws 
of motion, the principle of the equivalence 
of work and energy, and the principle of the 
conservation of energy ; energy being meas- 
ured, however, only in terms of force and 
displacement, or momentum and velocity. 
The only actions known in dynamics are 
force and its integrals, impulse and work. 
To identify with these all other actions in- 
volving the transfer and transformation of 
energy, such as the conduction of heat, 
chemical reactions, induction of electric 
currents, etc., forms to-day the severest 
task of mathematical physics. 
JoHN GALBRAITH. 
ScHOOL OF PRACTICAL SCIENCE, - TORONTO. 
SCIENCE. 
[N. 8S. Vou. VI. No. 143, 
MATHEMATICS AND PHYSICS AT THE 
BRITISH ASSOCIATION. 
Mrerine this year at Toronto in the week 
immediately succeeding the meeting of the 
American Association at Detroit, the Brit- 
ish Association had the advantage of secur- 
ing the attendance of a number of distin- 
guished American scientists, who added 
greatly to the strength and interest of the 
proceedings. Taking Section A alone, it is 
sufficient to mention the names of Dr. Hill, 
Professors Michelson and Newcomb, as Vice- 
Presidents; and of Professors Barker, Carl 
Barus, Bedell, Carhart, Merritt, Nichols, 
Rosa, and many others who attended the 
meetings and assisted at the discussions in 
the work of the Section. 
It is generally conceded, even by the rival 
sections, that A is not only the first but also 
the most strongly represented section, if not 
always in the number of its rank and file, 
at least in the distinction of its leaders and 
in the vigor and extent of its work. This 
year, in spite of the distance from home, 
formed noexception to therule. Although 
some familiar faces were absent, the section 
formed a very strong and representative 
gathering of mathematicians and physicists. 
There were no less than fifty names on the 
committee, but it would have been easy to 
add to this number without going beyond 
the list of those attending the meeting 
whose work was already known. 
In many ways, the extremely varied in- 
terests which the Section A represents are 
doubtless a great element of strength, but 
there are certain drawbacks in its excessive 
vitality. It brings together men from a 
number of different but closely allied de- 
partments of knowledge, who, if they did 
not possess some such common meeting 
ground, would be less able to keep in touch 
with each other, and to assist in the general 
advancement of science. At the same time 
it cannot be denied that the section is some- 
what overburdened with an excess of com- 
