Mat 22, 1908] 



SCIENCE 



815 



sixth order, inclusive, hence detennining 

 forty-eig'ht coefficients. However, in spite 

 of the increase in the number of terms and 

 coefficients, the results as computed from 

 the formula differ from the observed quan- 

 tities to such an extent that no practical 

 use, whatsoever, can be made of them. 

 For example, in the United States the 

 formula would give magnetic declinations 

 differing at least 1° to 3° from observed 

 values. 



Gauss's formula has only a certain theo- 

 retical significance, but, as said, no prac- 

 tical value as an interpolation formula. 

 Why is this? Is it due to imperfection or 

 incompleteness of the underlying data? 

 Yes, to a certain extent. For example, all 

 of the various analyses to date have had 

 to be based on maps depending largely on 

 land data, i. e., on data covering but a 

 fourth of the area of the globe. Nothing 

 was known as to the reliability of the map 

 data over the remaining three fourths— the 

 ocean areas. Thus the Carnegie Institu- 

 tion work has shown that the magnetic 

 map data over the Pacific Ocean are 

 erroneous 1° to 3° in declination and dip, 

 and about one twenty-fifth part in hori- 

 zontal intensity. So we may confidently 

 expect some improvement with the later 

 more accurate data and it is possible that 

 a new formula as based upon these data 

 will give results sufficiently close in agree- 

 ment with observation over the ocean areas 

 for practical purposes if not for scientific 

 purposes. 



When we come to land areas, however, it 

 is questionable whether any general ter- 

 restrial formula can be established which 

 will represent the land observations suf- 

 ficiently closely, even if the expansion be 

 carried farther than it has already been, 

 viz., beyond the sixth degree. The prime 

 reason for this has been made evident from 

 our study of the magnetic field of the 

 United States. We find, namely, that we 



must deal with irregularities in magnetic 

 distribution of various gradations covering 

 areas of varied extent, a locality, county, 

 state or an entire continent. Thus we 

 may have the magnetic forces observed at 

 any given point in the United States as 

 the resultant effects of (1) a general or 

 terrestrial magnetic field due to the general 

 magnetic condition of the earth, (2) a 

 general, terrestrial disturbing cause which 

 distorts the general magnetic condition of 

 the earth at the place of observation, (3) a 

 continental disturbing effect, due largely 

 to that portion of the North American 

 continent above the general ocean bed, 

 (4) a regional disturbance due to low- 

 lying magnetized masses or earth currents 

 covering a certain region, and (5), a local 

 disturbance due to the magnetized masses 

 or currents in the immediate vicinity. 



Now a formula based upon the entire 

 earth can, of course, not include also dis- 

 turbances of such restricted areas as em- 

 braced under the last two heads, viz., 

 regional and local disturbances, but it ap- 

 pears that the present formulse do not even 

 adequately represent the continental ef- 

 fects. In these formulae we have the vari- 

 ous terms advancing and recurring by 

 trigonometric functions of multiples of the 

 longitude and the latitude. Thus a term 

 involving six times the longitude is sup- 

 posed to continue around the earth sis 

 times in unaltered manner. However, 

 such a term arising from the North Ameri- 

 can continental shelf which in the 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 European or the Asiatic continent is 

 reached. In other words, it must be 

 recognized that with the recurrent or con- 

 tinuous terms embraced in the higher 

 harmonics of Gauss's formula, we can at 

 the best but "counterfeit" the facts of 

 nature but never get at the actual truth. 



