APPLICATION OF MATHEMATICS IN METEOROLOGY. 221 
that the events shall be independent of each other , and if this 
criterion fails, then the entire process is invalid. Thus, the 
independent observations on a star’s place, the separate 
measures of a physical quantity in the laboratory, and such 
like matters, may be tested for probable accuracy by this 
method. The distribution of all the waves emitted by a 
black body at a given temperature T being according to the 
law of errors, this may be computed as a probability curve, 
since the normal energy gives a spectrum curve with lines 
of variable intensity for the several independent wave lengths. 
In the kinetic theory of gases, the several independent veloc¬ 
ities which inhere in the moving molecules may be tested 
for their respective intensities wdien the total kinetic energy 
of the mass is known. Suppose, now, one proposes to apply 
that theorem to the events recurring in the circulation of the 
earth’s atmosphere, such as the temperature changes, the 
variations of the pressure in cyclones, or the observed condi¬ 
tions of the aqueous vapor as vapor tension or precipitation 
at a given station. What reason is there to assume that 
these elements as they occur from day to day are independent 
of each other? The pressure, temperature, and vapor tension 
at a station are in fact the results of a very complex circula¬ 
tion which passes over a station as the effect of conflicting 
currents flowing from the polar and the tropical zones, due 
to the incessant struggle of the elements toward equilibrium 
in this thermodynamic medium. We have to deal with no 
single system of independent events, as the waves in a nor¬ 
mal energy spectrum, or the molecular velocities in a gas of 
given energy, but there are many series of interdependent 
events inextricably interwoven. It is seldom that the me¬ 
teorologist has a pure series of events to work with, as the 
astronomer or the physicist has in many of his observations, 
and that is why the meteorologist has a peculiarly difficult 
task, and why it is late on the field as a perfect science. 
Nevertheless, these problems are most fascinating, and they 
will probably in the future engage more of the attention of 
astrophysicists and of mathematical physicists, because they 
32—Bull. Phil. Soc., Wash., Vol. 14. 
