574 
GEOPHYSICS: L. A. BAUER 
Proc. N. a. S. 
United States has a width in longitude of about 60°, would not continue 
around the earth but would in all probability die out before the Euro- 
pean or the Asiatic continent is reached. In brief, the higher harmonic 
terms of the mathematical formula introduced by Gauss and based on 
the potential theory, could at the best but simulate or "counterfeit" 
the facts of nature and not represent the actual truth. 
Thus the question arises how far it is really worth while to proceed in 
the establishment of such a theoretical formula. Although the mathe- 
matical expressions may be extended so as to include forty-eight or more 
unknowns, it has been found that the computed results, magnetic declina- 
tions, for example, depart so much from the actual observed results^ — 
several degrees — that they could not be used even for purely practical 
purposes such as those of the surveyor and the navigator. The conclu- 
sion therefore reached was that it may be found sufficient for many pur- 
poses to restrict the theoretical formulae to a certain finite number of 
terms involving a limited number of unknowns which represent, from a 
physical standpoint, the chief and principal facts of the magnetic condi- 
tion of the earth, as resulting, for example, from system (1) mentioned 
above, or perhaps better, systems (1) and (2). The magnetic field repre- 
sented by this limited expression might be called the normal, or reference 
field, just as the geodesist, who restricts the constants to be determined 
for the figure of the earth to two or three, calls his adopted figure, the 
"spheroid of reference." Residuals from the magnetic field of reference 
would then receive separate or special treatment in accordance with their 
extent and their character. 
Respecting the existence of possible vertical currents, the preliminary 
analysis of the data of the magnetic survey of the United States indicated 
a definite system, related in some manner to the general atmospheric 
circulation and with an average current strength of about ^/so ampere 
per square kilometer, just as the writer had found in his previous inves- 
tigations pertaining to the entire earth. ^ The additional data acquired 
in the United States since the preliminary analysis, will make possible a 
more complete investigation of this important matter. Of special in- 
terest in this connection will be found the quotations regarding Dr. Wil- 
son's investigations (see paragraph 4). 
We see then that the data obtained by the United States Coast and 
Geodetic Survey in the prosecution of the magnetic survey of the United 
States afford opportunities for interesting and fruitful research of various 
kinds. There may be mentioned, for example, the correlation between 
magnetically disturbed areas and geological formations or local devia- 
tions of the plumb-line, in which Section a (Geodesy) is also interested. 
Possibly also the data obtained in the United States may throw some 
light ultimately upon the problem as to the variation of the magnetic 
elements with altitude, and upon the question as to the effect of local or 
regional disturbances upon the secular changes of the earth's magnetism. 
