1505 
Adding this to d’H as given by (7) we have altogether 
H — H, = — 0.00000299 + 0,012 (H—H,) 
: 
’ H — H,—=— 0.0000081, 
Then we find by (4) 
& — &, = — 0.0000016 
ele 4 0.14. 
From 
H = 0.0032775 
we find thus. 
HH, = 0.0032806. 
Darwin’s equation then gives 
el 295.82, 
and from the equation of VÉRONNET we find 
295.62 < ¢,—1 < 296.46, 
It has already been mentioned that Darwin’s value may be assumed 
to be very near the truth. Adopting this and adding the value of 
é Lel, which has been found above, we have) 
el =,295.96. 
It is very difficult to estimate the uncertainty of the correction 
H—H,, since it depends not only on the correctness of the data 
used, but also, and probably for the greater part, on the exactness 
of the hypothesis that the compensating defect or excess of density 
is distributed equally over the whole depth Z The whole correction 
to el however only amounts to 0.07, and its uncertainty is almost 
certainly overestimated if we take it equal to the whole amount, 
+ 0.07. Combining this with the m.e. + 0.19 due to the uncertainty 
of H, and of Darwtn’s hypothesis, the total uncertainty of se! is 
found to be + 0.20. 
The greater part of this is due to the uncertainty of H, and this 
is wholly due to that of the adopted value of the moon’s mass. 
Consequently, in order to improve our knowledge of « we must 
determine wu, which is found from the lunar inequality of 
the sun’s longitude and the solar parallax. A correction of + 0.05 
to the adopted value of u! would give —0.10 in e!. 
For ‚the ideal surface 6, = A,, or K,=0. Therefore for the 
normal surface 
ra Se a : ne = 0.00000105. 
Mo? C 
The longest radius of the equator, in the longitude 86°.5 is thus 
en 
1) See note on p. 1304. 
