836 
Finally we give in Table VII the new reduction of the meridian 
observations by Prof. BAKHUYZEN, which was referred to above. The 
column M—N, contains the excess of the observed correction to the 
tabular longitude of the moon over Newcome’s “great fluctuation”. 
The systematic corrections mentioned in Part I have already been 
applied. For the years 1905 to 1912 two results are given: the upper 
one is derived from the observations of the limb, the lower from 
the crater Mösting A. The third column contains the means of the 
numbers of the second column and the results from the occultations, 
i.e. Newcome’s minor fluctuations. The latter were however corrected 
by -+ 0".18 for reasons stated in Prof. BAKHUYZEN's paper (these 
Proceedings, Jan. 1912). For the years 1905.5 to 1908.5 the mean 
given depends on the observations of the limb. and the crater alone. 
From these means I have subtracted the sum of the corrections for 
the difference between the theories of Hansen and Brown, which 
were given in Part I of this paper. This sum was computed by a 
graphical process, of which I estimate the maximum error at about 
+ 0.05. The thus corrected mean is given in the fourth column. 
The second decimal, which has no real value, has been dropped. 
The last column gives the residuals remaining after subtracting Ross’s 
empirical formula, without its constant term — 0".18, viz.: 
+ 2".9 sir 6°.316 (t— 1844.5) + 0".8 sin 15°.65 (t— 1880). 
It will be seen that these residuals, although small, are as 
a rule somewhat larger than those found previously by Ross 
himself and by BAKHUYZEN. The explanation of this is as follows. 
The residuals A-Ross given by BAKHUYZEN in 1911 (these Proceedings 
Jan. 1912, p. 691) showed a marked period of nine years, which 
entirely disappears by the application of the perturbational corrections 
(14) and (22). The term (43) is nearly identical to the term which 
was already applied by Ross, and consequently does not affect the 
residuals to any appreciable extent. The terms (20), (15), and (21) 
however, especially (21), produce a considerable increase of the 
residuals. No doubt it would be possible by a small adjustment of 
Ross’s formula considerably to improve the representation, but it is 
evident that a perfect agreement with the observations can never be 
reached by a formula containing only two terms. If a new empirical 
formula were to be derived it would, of course, be necessary first 
to correct the term of long period, and to apply the corresponding 
corrections to the theory. It seems opportune to defer such an inves- 
tigation until the moon’s longitude for the next few years will be 
