49 
leading to transverse strength of beams, their deflections, slopes and elas- 
tic curyes; it establishes the strength of thick hollow cylinders and 
spheres upon which is based the design of fire-arms and ordnance; com- 
putes suspension bridges; determines stresses in arched ribs of iron, steel, 
or timber, or in stone arches. 
It gives the mathematical theory of .maps, derives formulae for com- 
puting geographical co-ordinates and for map projection; adjusts observa- 
tions in triangulation and determines the probable error. 
It analyzes and improves the steam engine; it studies the effects of 
reciprocating parts, studies the balance wheel, the shaft, rods, and cranks; 
it enters the steam box and discusses steam pressure, horse power, and 
efficiency. It measures the contents of irregularly shaped vessels. 
It may sometimes seem that the problems along these lines have been 
worked out and embodied in the shape of formulae and that there is no 
more use to study the method further for these purposes. That, however, 
is not true. A man should always be master of the tools he is using if 
he wishes the best results. The man who can derive a formula under- 
stands best its applications and limitations. Moreover, occasionally new 
and important questions arise which can not be answered at all unless one 
is versed in the use of the calculus. ° 
It has largely developed the dynamo and has given us Fourier’s series 
upon which the theory of this machine rests. 
IXlein once said to a former pupil of his: 
“You know that I have been too busy with theoretical matters to keep 
up with the practical things; what is the greatest recent discovery in the 
application of electricity to the arts?’ The pupil replied: ‘“‘The greatest 
recent discovery in electrical engineering is a method by which a current 
may leave a long circuit at a higher potential than it entered it.” This 
is the well-known principle by which Niagara Falls, for example, becomes 
available many miles away from the fall itself, as a source of power. 
Klein said: ““Wait. That,” he presently exclaimed, ‘‘depends on the second 
differential coefficient.” 
Problems such as I have thus far alluded to are the problems of civili- 
zation. Light, heat, power, architecture, water supply and distribution, 
dissemination of news, transportation—did you ever think how closely 
these things affect us? Chemistry and mathematics have done their best 
in providing for our locomotive a rail that would resist the strain of a 
4—ScIENCE. 
