674 



SCIENCE. 



[N. S. Vol. I. No. 25. 



lowing expression for tlie potential function 

 at any external point, viz. : 



a is the mean radiiis of the earth, r the dis- 

 tance of the point from the origin, and fi 

 the intensity of magnetization per unit of 

 volume. 



For points on the earth's surface, this re- 

 duces to : 





: f ff |U. sm ^ = c. sin I 



(1) 



<P is the geographical latitude and c = | ~/^. 



This formula is doubly interesting just 

 now, as it has been recently deduced em- 

 pirically by Professor W. von Bezold.* This 

 eminent investigator, when considering the 

 mean values of the geomagnetic potential 

 along parallels of latitude, found them sub- 

 ject to the simple law ^''^ = c. sin ^ = 0.330 

 sin <p . Since c = ^ rr fx, and the magnetic 

 moment, M, of the earth is equal to 

 I TT /i. a^, we find that von Bezold's empiri- 

 cal coefficient implies a value of the mag- 

 netic moment equal to 8.52 x 10== against 

 8.55 X 10 = = as determined by Gauss. We 

 thus see the theoretical significance of von 

 Bezold's factor. 



Since for the case supposed the horizon- 

 tal component of the intensity, H, is di- 

 rected meridionally, it follows fi-om (1) that : 



H = 



(Si/; 



(2) 



Furthermore, with the aid of simple 

 transformations : 



V=2o. sin^ (3) 



F = 0. v/S sin^ V> + 1 (4) 



tan I = 2 tan iji (5) 



V being the vertical force, F, the total and 

 I, the inclination. Formulae (2), (3), (4) 

 and (5) are familiar to every nautical geo- 

 magnetician. 



* See his admirable paper ' Uber Isanomalen des 

 erdmagnetischen Potentials,' Sitz. berichte d. Kgl. 

 Preuss. Akad. d. Wiss. zu Berlin. Phys.-math. 

 Classe, April 4, 1895. 



Now the writer finds that these formulae 

 give the mean values of the magnetic ele- 

 ments along parallels of latitude with a high 

 degree of precision. As this paper will be 

 printed in full in the American Journal of 

 Science beginning with the August number, 

 I will select but one typical example. 



1885. 



Since, according to equation (2). 

 o^ f TT fj. = — =H. sec <j> 



(6) 



we can get a fair value of the magnetic 

 moment of the earth ■«'ithout the aid of the 

 laborious Gaussian computation bj' simply 

 scaling the value of H for equidistant 

 points along a parallel of latitude from iso- 

 dynamic charts and substituting the mean of 

 the values thus found in (6). 



Thus I get for 1885 as the mean result of 

 the scalings along -40° N, 20° IST, Equator, 

 20° S and 40° S, the value of 0.325 a^ for 

 M, against 0.322 a^ resulting from the 1885 

 Neumayer- Petersen re-computation of the 

 Gaussian co-efl&cients. 



But why should the values obtained on the 

 assumption that the earth is uniformly magnet- 

 ized, and its magnetic axis coincident with the 

 geograjMcal axis, so nearly agree u'ith those 

 based upon observed quantities F It seems to 

 me that this opens the question whether 

 the asymmetrical distribution of land and 

 water is the primarj^ cause of the asymmet- 

 rical distribution of telluric magnetism, as 

 generally supposed. Why do the ' anoma- 

 lies ' in the distribution so nearly cancel 

 each other in going along a parallel of lati- 



* These quantities are the results of the scalings of 

 Neumayer's charts for the points mentioned. 



