819 
body of the earth. If a distrubution differing from Wircuert’s is 
adopted, the function ./, is considerably altered. What is the effect 
of this on the final result can only be decided by actually carrying 
out the computation with a different hypothesis. This has been done, 
as will be related in the second part of this paper. Here it must 
suffice to state that, although there are some differences, the general 
character of the results is remarkably similar to those of the first 
computation. It may be mentioned that also my preliminary inves- 
tigation of 1909, though ‘based on a totally different and only 
roughly approximate formula, gave results of the same character. - 
The hypothesis that the sun and moon can be treated as points, is 
also, of course, only approximate, and it is very difficult to say in how 
far it affects the reliability of the results. It seemed however better, at 
the present state of the question, to rest content with this approximation. 
The function J, however gives rise to errors in still another way. 
It is tabulated with the half-duration 7’, as argument. This is taken 
from the Canon, where it is given in minutes of time, and can thus 
be a half, or in some cases perhaps.even a whole minute in error. 
The resulting error in dr may occasionally amount to 4 units. Thus, 
neglecting the uncertainty introduced by the hypothesis regarding 
the distribution of density, the purely numerical error in dn may 
reach an amount which can be taken to correspond to a mean error 
of say + 3 units. The mean error of the perturbation in after p 
eclipses is then + 3//p. For a Saros (30 eclipses) this gives + 16. 
Also the m. e. of the second sum (i.e. the perturbation in longitude, 
if we neglect the fact that sometimes the interval between succes- 
sive eclipses differs from the normal value) is found to be 
=e 1 V6 p (p+1) (2 p+I). For the Saros this becomes + 292. 
It thus appears that all the values which have been found for 
An might very well be due to accidental accumulation of the inaccu- 
racies of the computations. On the other hand the circumstance that 
they have the same sign throughout might lead us to consider them 
as at least partly real; by which I- mean as necessary consequences 
of the adopted hypotheses. The values of 4,2 also are not so large 
that their reality can be considered as certain, but here also the 
systematic change with the time may be an indication of their being 
not entirely due to accidental errors of computation. The only thing 
that can be asserted with confidence is that the values of A,» and 
4), are small, and consequently that the non-periodic part of the 
perturbations in longitude has a smooth-running course: no other 
irregularities with short periods can exist in the longitude than those 
which are contained in the periodic part. 
