118 PHILOSOPHICAL SOCIETY OF WASHINGTON. 
be distinguished by his facility in getting a patent on his discovery, 
in forming joint stock companies and watering stock, and in sud- 
denly becoming rich at the expense of his fellow-men. Such a 
career may be a natural result of our present system of sociology, 
but it does not seem to be in harmony with scientific thought and 
research, and our social need is for men of a different character. 
Far nobler is the life of one who devotes himself to the study of 
the most abstract forms of science; winning for us, if haply he 
may, another forward step up the hill of knowledge. 
But when we come to the field of applied mathematics we soon 
learn how necessary are the studies of the pure mathematician. 
Nearly all the researches in natural philosophy, where the action of 
forces is concerned, require the formation and solution of differen- 
tial equations, and hence the theory of such equations becomes 
important, and in some cases almost essential, for the advancement 
of physical investigations. It is not, of course, to be supposed that 
experiment and observation are to be done away with or neglected, 
or that mere skill in differentiating, integrating, and solving equa- 
tions can supply the place of correct thinking. In fact, we may be 
sure that Leibnitz was mistaken when he declared that the inven- 
tion of the differential calculus had made known that royal road to 
knowledge for which the king had inquired in vain of Euclid. But 
still it remains true that this calculus forms the most powerful 
engine we have for the solution of questions in natural philosophy. 
It enables us to adopt the old maxim, “ divide et impera.” If we 
can reduce the problem to its elements, and can form its true differ- 
ential equation, the rest of the work is purely mathematical. Un- 
fortunately, the differential equations that occur in the problems of 
nature are very different from those given in our text-books, and 
their exact solution is in most cases impossible. Here we must rely 
chiefly on that happy device of the variation of constants, by means 
of which the solution of simpler forms is extended to the more 
complex. 
One of the great advantages of putting a question in a mathemati- 
cal form is the precision with which it can bestated. If we are right, 
the truth of our assertion will be the sooner acknowledged, and if 
we are wrong, our error can be the more easily detected. Fre- 
quently it has seemed to me that disputes would be avoided in the 
meetings of our scientific societies if men would take the trouble to 
put their assertion into a formula and write it on the blackboard ; 
