821 
Comparison with the observations. The excesses of the observed 
longitude of the moon over the longitude as computed by pure 
gravitational theory, which have been given by Newcoms, must still 
be corrected by the differences between the new lunar theory of 
Brown and Hansen’s theory which has been used by NewcomB. The 
corrections necessary on this account have been collected by 
BatTeRMANN'). Out of the 43 terms given by him we need only 
consider the terms of long periods (14)—(22) and (43). For the 
discussion of the non-periodic part of the perturbation in longitude 
we must take account of the terms (16) to (19), which have periods 
between 128 and 1921 years’). I have, however, not applied these 
terms, the reality of the non-periodic part being too uncertain to 
warrant much labour to be bestowed on it. For the discussion of 
the periodic part, we have to consider the terms (14), (15), (20), 
(21), (22) and (43), which can be written as follows: 
(14) + 0".48 sin 40°.67 (¢ — 1894.3) period 8.84 years 
) 
(22) + 0 13 sin 30 .35 (¢ - 1894.6 ae el eee 
(20) +0 .24 sin 20 .66 (¢ — 1890.7) oleae (af ee =| ag 
(43) + 0 .56 sin 19 35 (¢ — 1892.2) met b 2 
(15) +0 13 sin 10 34 (¢ -- 1870.4) dot CM 
(21) +0 .28 sin 9.69 (¢ — 1877.6) Lr ent ee 
The therm (43) contains the correction given by BATTERMAN in 
his “Zusatz’. It is very similar to the term which was already 
applied by Ross, viz: — 0".50 sin 2 = + 0.50 sin 19°.35 (¢ — 1894.8). 
. These corrections must be added to the tabular longitudes, or sub- 
tracted from the residuals. 
Considering now first the non-periodic part, it is very remarkable 
that the values of 4, as given in Table I are between the years 
1703 and about 1894 almost identical to NewcomB’s great fluctuation, 
if 160 of our units are taken equal to 1". This is at once apparent 
from the last two columns of table I, of which the last contains 
the great fluctuation according to Newcoms. Therefore, if we assumed 
the absorption of gravitation to be the true explanation of the great 
fluctuation, we should have 
160 X 1262".y=-1" y= 5.1078 =A = 25.10". 
However, after 1894 the similarity ceases. The agreement before 
that date depends on the assumption of the reality of the values 
1) Beobachtungs-Ergebnisse der K. Sternwarte zu Berlin, N°. 13, 1910. 
*) The most important of these is a correction of 0./85 to the coefficient of the 
well known Venus-term of 273 years period. 
o4 
Proceedings Royal Acad. Amsterdam. Vol. XV. 
