480 
PROFESSOR A. SCHUSTER OH THE DIURHAL 
sin ii(, sin 6 m in terms of sin u / eZ/x^. This gives, by substitution and integration 
with respect to 
- Y^^'/a = (- 0-0401 TgS + 0-1426 T,3 + 0-2523 cos 3X 
+ (0-0319 Tg^ - 0-0936 TgS - 0-5577 sin 3\ 
+ (0-00033 T/ + 0-00279Td' - 0-00411 T/) cos 4\ 
_p (_ 0-00075 T/ -+ 0-00078 T/ — 0-01978 Tg^) sin 4X. 
We liave obtained thus finally, 38 coefficients in the expansion of V/a, which, for the 
sake of reference, I collect into Table VII. 
In this Table 0,^”* is the coefficient of T,/" cos m\. 
S/' ,, ,, T/'sin wX. 
Table VII. 
The unit of force is C.G.S. 10~®. 
48-00 
Co 2 
2-948 
cp 
0-252 
Cd 
— 
81-52 
C 32 
— 
7-936 
Ce* 
— 
0-143 
Cg' 
5-66 
cp 
— 
0-630 
+ 
0-040 
+ 
7-62 
C 52 
— 
0-341 
+ 
1-09 
Ce' 
+ 
0-200 
cp 
+ 
0-00411 
Cd 
5-78 
cp 
+ 
0-407 
cp 
— 
0-00279 
cp 
+ 
1-57 
*-9 
— 
0-00033 
sp 
+ 
24 09 
Sp 
+ 
10-764 
sp 
+ 
0-578 
sp 
+ 
35-59 
S 33 
+ 
4-715 
Ss^ 
+ 
0-094 
S;P 
— 
8-45 
sp 
— 
0-214 
sp 
— 
0-032 
sp 
+ 
2-39 
R 2 
— 
0-731 
Sp 
— 
2-41 
R 2 
Og 
+ 
0-293 
Ss^ 
+ 
0-01978 
S 1 
Og 
— 
1-64 
0 2 
+ 
0-264 
sp 
— 
0-00078 
sp 
— 
0-34 
^'9 
+ 
0-00075 
In order to show how far these numbers correctly represent the forces \Yhich have 
been made use of in their computation I have calculated backwards from the potential 
the force to geographical West. Table VIII. exhibits the results, showing by comparison 
the coefficients calcidated from the formulae for the potential with those obtained 
directly by observation. It will be seen that the agreement is satisfactory, except 
for the coefficients and h^. 
In figs. 1. 2, 3, and 4 the curves for the mean of the yeair are plotted. In these 
curves only the first four terms cos t sin t cos 2t + Z>o sin 2t have been 
used. The numbers from which the curves are plotted are given in Table IX. 
The curves are seen to be almost identical, and having, therefore, obtained an 
expression for the potential which correctly represents the observed West force, we 
may turn to tlie main object of this inquiry and calculate the vertical forces. 
The calculation of the various components from the potential involves the knowledge 
of the differential coefficients of zonal harmonics and of the tesseral harmonics for the 
