210 Selenography : its Past, Present, and Future. (April, 
personality acts as a constant error always in one dire¢tion, 
and cannot be eliminated, whilst escaping consideration in 
the resulting ‘‘ probable error.” It is true, on some occa- 
sions, Madler measured from opposite limbs, but then always 
through the aid of an intermediate point, consequently 
introducing double errors, from having to make two separate 
measures, whilst these measures were too few to exert much 
influence. By comparing Lohrmann’s measures with Mad- 
ler’s, the influence of this personal equation, combined with 
some differences due to the effect of aperture on the irradia- 
tion at the limb, is at once revealed, for there exist a mean 
difference of 23’in longitude and over 17’ in latitude be- 
tween the places of the points they have both measured ; 
and this would appear to be too great a difference to be 
ascribed merely to errors introduced by the few observations 
made by each of these spots, even were it not noticeable 
that all Madler longitudes are nearer the centre of the 
moon than Lohrmann’s, and, with one exception, all his 
latitudes further north. This would indicate, probably, a 
personal difference in the method of observing similar to 
that known to exist in ordinary lunar observations, and it 1s 
unfortunate that the few spots observed by both astronomers 
renders its direct determination impracticable. 
Besides measures of points of the first order, Madler made 
numerous determinations of the position of points of the 
second order, as he termed those points of minor import- 
ance, whose place he ascertained by measuring their dis- 
tance and position angle from a line joining two of his points 
of the first order. This method gives, however, very in- 
ferior results to the results of measures of the first order, as, 
in addition to errors incidental to measurement, the position 
carry all the errors in the determination of the points of the 
first order, and when the distance amounts to more than 
some five or six degrees, is liable to considerable errors of 
its own. The great majority of these points rest on a single 
measure, and as their distance from a point of the first order 
is usually considerable, much uncertainty must attach to 
their position, which cannot be considered as having a pro- 
bable error of under three or four times that of the neigh- 
bouring point of the first order. 
Madler likewise determined the diameter of 148 of the 
principal formations, and made 1095 measures of the height 
of 830 lunar peaks, whilst he also considerably increased 
and improved the lunar nomenclature, adhering, of course, 
to Riccioli’s system, with Schréter’s modifications, distin- 
guishing the smaller objects by Greek and Roman letters 
