1049 
here from the equation (1) is probably more exact than any of these. 
This value of «, has been used for the computation of the values 
of the radiusvector given in the second, third and fourth columns of 
the following table. The third and fourth columns were computed 
by the equation (1), using for g the values g, and g, respectively. 
The table gives ed. 
D 
Equipotential surface | Difference 
d | Ellipsord |—.——— en [2 wrd! | api 
Qo | Q, | Qo / 0, | 
0e 0.00000 | + 0.00042 | + 0.00042 bles 30 
5 | — .00055  — .00014 — 0.00056 | 4 40 | — 0.00001 — 28 
10 — .00216 — .00181 — .00222 | + 35 | — 6 | 0 | 
15 | — .00478 | — .00452 — 00490 ze 2% | — sand 
20 | — .00830 | | — .00850 |= 20; — 14 
30 | — .01750 | | — .01786 | ae A ee 
40 | — .02843 | — .02890 | z= 47| — 34 
50 | — .03968 | — .04014 | ee 46.) — 33 | 
60 | — .04990 — .05026 | =, on HER AE 
70 | — .05799 | — .05819 | \— iN ee: 
80 | — .06317 | — .06322_ _ Gaon 
90 | — .06494 | — .06494 | | 0 
The deviation from the ellipsoid thus consists of a protuberance 
along the equator, produced by the increase of the velocity of rotation, 
and a depression in mean latitudes’). The transition probably takes 
place rather suddenly somewhere near the latitude Tes 
We have up to now taken no account of the variability of in 
1) If quantities of the order of e° are neglected, the deviation from the ellipsoid 
is easily shown to be (for constant w) of the form 
— x sin’? 2d , 
where 
hs 1 2 4 2274 — 9.00088 
a eg T 39 pA zy. . 
The actual depression is only about #/; of this. 
For the earth the value of « is of the order of 0.0000005 = 3 meters. 
