194. ZL. A. Bauer— Variation of Terrestrial Magnetism. 
xz 
(1) Y= $mHa. 
a, is the mean radius of the earth, 7 the distance of P from 
the origin, and yp the intensity of magnetization per unit of 
volume. For points on the earth’s surface (1) reduces to 
(2) VW =47ya.cosu=¢.asin p 
u being the geographical polar distance, g = 90°—w, or the 
geographical latitude and ¢= 4zy, a constant for any particu- 
lar time and perhaps for all historic times.* Since for the case 
supposed the horizontal component, H, of magnetic intensity 
is directed tangentially along the meridian, we obtain by par- 
tially differentiating Y according to the variable w’=a.u=a 
(90° —@): 
b tee anes 
(3) i= Se ieee eee 
And for the vertical component, V, directed radially : 
POA MORE Mes Dy 4 é mr )= Pye 1 
Vv Rh; = 2 (gape, a =26.@ sIn @. 
Putting 7 = a, we get: 
(4) V =e. sin @ 
(5) Total force, F = o/ FH? + V2 =e. Ay eas sin? p 
If I be the inclination, then is 
(6) tanI=7=2tan 
Furthermore for all points on the earth the declination D: 
(7) Dis 0 
Formule (3), (5) and (6) will be recognized by every nautical 
geomagnetician. They were deduced empirically, theoretically 
(in a different way than above) and practically applied to the 
determination of the compass deviation due to iron on board 
* Prof. W. von Bezold in an admirable paper entitled ‘‘ Uber Isanomalen des 
erdmagnetischen Potentials,” Sitzungsberichte d. Kgl. Preuss. Akad. d. Wiss. zu 
Berlin, Phys. Math. Classe, April 4, 1895, has deduced the expression 
ne e 
— =c.sin 
es p 
empirically with the aid of the mean values of the potential along geograph- 
ical parallels of latitude. The value of his empirical coefticient was found 
to be 0°330 for the date 1880. He regarded this empirical formula as one of the 
most important contributions of his paper. 
