476 
PROFESSOR A. SCHUSTER ON THE DIURNAL 
make our expression agree with observation. We have then eight values for the 
different terms of Y through which we might at once proceed to draw a curve ; but, 
making use of the observed variations of Northern force, we can also calculate the 
direction of the tangent of the required curve for the same eight points. This has 
been done as follows. Let Y be expressed as 
and X as 
!£(«„ cos n\ + l>,i sin n\), 
cos nX + sin n'k). 
Tlie existence of a potential implies the relation 
clY sin 00 dX. 
du 
d\ 
or 
dY dX , 
~ — cosec u — 1 cot u, 
du d\ 
from which, by substitution. 
. / d(tfi dh,i , 
A — COS nk 4- — sm nk 
\ du du 
and, therefore, 
= cosec u — cot u) cos nk — cosec u + cot u) sin J?X] ; 
— = na,, cosec u — a,, cot u, 
dio 
dh,t . j , 
— = — na,i cosec u + b„ cot u. 
du 
These equations give the rate of change per radian ; to get the rate of change per 
degree of colatitude we have to multiply the differential coefficients with the circular 
measure of one degree. The following Table gives the rate of change of the West 
force per degree of colatitude, calculated as explained from the Noith force. 
Table V. 
Tlie unit of force in this Table is lO"*" C.G.S., and the unit of latitude is 1 degree. 
Bombay. 
I Lisbon. 
Greenwich. 
St. Petersburg. 
Summer, 
1 
IViuter. 
Summer. 
Winter. 
Summer. 
1 AViuter. 
Summer. 
i Winter. 
da-^jdu . 
- 0-201 
+ 0-714 
- 1-210 
- 2-561 
+ 0-356 
- 2-793 
+ 1-951 
— 3-086 : 
dhjdu 
- 7-853 
- 6-326 
+ 0-432 
+ 0-931 
+ 2-118 
+ 2-053 
+ 2-342 
+ 1-107 i 
da r, Idol . 
- 1-184 
+ 0-258 
- 2-087 
- 2-207 
+ 0-150 
- 0-330 
- 0-079 
- 0-605 
dhifjdii 
- 6-079 
- 4-754 
+ 0-948 
+ 1-684 
+ 5-445 
+ 3-318 
+ 7-185 
+ 2-689 
da.^ld,u . 
- 2-9-21 
- 1-968 
- 1-218 
— 0-658 
- 0-416 
+ 0-600 
+ 2-805 
+ 1-650 : 
dJ\Jdu . 
- 2-420 
- 2-277 
- 0-527 
+ 0-580 
+ 0-988 
+ 1-564 
- 0-030 
4- 1-112 
dajdii . 
- 1-125 
- 1-768 
- 1-084 
+ 0-503 
+ 0-501 
+ 0-622 
+ 0-329 
+ 0 640 - 
dbjdti 
+ O-407 
- 1-117 
- 0-471 
+ 0-018 
- 1-036 
+ 0-109 
F 0-936 
1 
+ 0-137 : 
1 
1 
