218 Selenography : tts Past, Present, and Future. [April, 
trustworthy map on an adequate scale of the surface of our 
satellite, they should consist of standard points, and points 
of the first, second, and third orders. The accuracy of the 
first should be sufficiently great to enable all the others to 
be measured direct from them: the points of the first order 
would be employed for the same purposes as the present 
members of this class, whilst the points of the third order 
would comprise all those auxiliary objeéts whose, at least, 
approximate position must be known for the proper con- 
struction of the outlines of the larger formations, and to serve 
as nuclei round which group the smaller not measurable 
details. 
In measuring points upon the moon, the limb is consider- 
ably inferior as the origin of measures to any small con- 
spicuous object on the surface, such asa small bright crater- 
let, not only from its irregularity and the irradiation accom- 
panying it, but also from the considerable personal equation 
known to exist in observing it. To eliminate as far as 
possible the effects of these, if measured from the limb it 
should be from all four, which would considerably weaken 
the above disadvantages. When practicable, however, far 
more accurate results might be expected by measuring from 
some of the smaller lunar formations, preferably one of the 
bright lunar craterlets, such as are equally distinct in high 
and low illumination. These objects would constitute the 
first class, or standard point, and should rest on the results 
of from 40 to 50 measures, so as to reduce the probable 
error of the position to a minute amount, and so render 
them available as points from which to measure the rest. 
The members of the second class, which were termed by 
Madler points of the first order, should be founded on 
from I0 to I5, or, in the more important, 20 measures, so 
as to Increase their accuracy, and would be generally mea- 
sured from the last, unless, as might be in some special 
cases, the limb offered superior advantages. The third class, 
or points of the second order, as here termed, would consist 
of objects whose place had been determined from 5 to 8 
measures from points of the first class, and therefore pro- 
bably be as accurately known as most of Madler’s points of 
the first order, and could be employed alone or in conjunc- 
tion with one of the last class, to determine points of the 
third order within a convenient distance from them. ‘The 
formations included in the third class would consist of the 
points of the second order of Madler, and comprise all the 
principal smaller lunar formations, whose position was 
necessary for the proper mapping of the surface, or else 
