APPLICATION OF MATHEMATICS IN METEOR¬ 
OLOGY. 
BY 
Professor Frank H. Bigelow, 
U. S. Weather Bureau. 
[Read before the Society January 17,1903.] 
There are three processes which are generally essential 
for the complete development of any branch of science, and 
they must be accurately applied before the subject can be 
considered to be satisfactorily explained. The first is the 
discovery of a mathematical analysis, the second is the dis¬ 
cussion of numerous observations, and the third is a correct 
application of the mathematics to the observations, including 
a demonstration that these are in agreement. As a matter 
of fact, however, the history of science shows that there has 
been great difficulty in the course of the working out of new 
problems to bring this about satisfactorily. Sometimes the 
theory is in advance of the observations, as in Maxwell’s 
theory of electricity and magnetism. Again, the observa¬ 
tions are in advance of the theory, as in solar physics and 
terrestrial magnetism. Often a good theory is misapplied 
to good observations, or good observations are explained by a 
poor theory. Whenever any of these unfortunate procedures 
take place, the progress of science is retarded. When a good 
theory is misapplied, there must follow it a searching criti¬ 
cism and all things must be rebuilt from the foundations. 
Thus the Ptolemaic cycles and epicycles were good as theor}^ 
for a geocentric solar system, but the Copernican and the 
Newtonian theories could be applied to Kepler’s observations 
only by a complete destruction of the ancient astronomy. 
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