118 
BAUER. 
Let us suppose, for illustration, we are dealing with a 
phenomenon which almost entirely unfolds itself during 
the time between sunrise and sunset — the well-known diurnal 
variation of the earth’s magnetism is a striking case of the 
kind. Following the usual method, the phenomenon is 
resolved into component parts with the aid of a Fourier 
series. The formula as generally adopted includes the four 
terms having, respectively, periodicities of 24, 12, 8, and 6 
hours. For ordinary magnetic latitudes the striking result 
is obtained that the second term — the 12-hour one — is as 
important as the first, or 24-hour, one; so we might equally 
as well say u tlie semidiurnal” as “the diurnal variation of 
the earth’s magnetism.” In fact, as the semidiurnal term 
unfolds itself twice in 24 hours, it is in reality more impor- 
tant than the purely diurnal one. 
Does the resolution into Fourier terms of a phenomenon 
of the kind given really prove their existence in Nature? 
Can we conclude, without question, e. g., that in addition 
to the diurnal term we also have a semidiurnal one? Even 
with four terms, the series does not represent each hourly 
observation of the 24 with the same degree of precision. In 
fact, the residuals for the night hours are nearly of the same 
order of magnitude as the observed quantities. If the physi- 
cal existence of the 12-hour term is not proved, then there 
is no need of racking our brains as to its physical origin. 
The difficulty disclosed by this example is of the same 
kind as the one treated in spherical harmonics, viz., that 
we are attempting to represent a discontinuous function hav- 
ing a duration commensurate with that of the daylight hours 
by functions running smoothly through their individual 1 
courses for 24 hours. 
Babbage, the inventor of the calculating machine named 
after him, said he once had the following question put to 
him: “Pray, Mr. Babbage, if you put into the machine 
wrong figures, will the right answer come out?” Do we not 
at times attempt to put wrong premises into Nature’s ma- 
chinery and then expect correct answers? 
We cannot close this section better than by quoting the 
