12 REPORT—1868. 
Nat sin of alt = nat sin of mer alt minus ver sin hour-angle x cos 
lat x cos dec and checked by 
Ver sin zen dist = yer sin (lat + dec) plus ver sin hour-angle x cos 
lat x cos dec. 
One or two trials for obtaining the longitude of the terminator will be 
quite sufficient for finding the altitude for any given interval. In the case 
of the morning terminator, if its longitude is east of and differs from the 
longitude of the spot a few degrees only, the altitude will be found between 
interval 0 and 12 hours. It will, however, be best to compute a longitude 
of the terminator as near as may be to that of the spot, from the epoch of 
which intervals of 12 hours to meridian passage may very readily be found. 
In addition to the period of similar phase, 594 1" 28", we have a still closer 
one of 442¢ 235 0™, or 15 lunations. The numbers in the column on page 
xx of each month of the Nautical Almanac, headed “ Days elapsed of the 
Julian Period,” will greatly facilitate the application of this longer period. 
Changes arising from season and libration may, in consequence of comparing 
observations at epochs so distant, become more strikingly manifest. 
Area IV AB, 
Introduction. 
A few remarks upon the classes of objects found on this area and one or two 
other points may not be inappropriate; they are given under the following 
heads :—Points of the first order. Extent of surface. General features. 
Mountain-chains. Faults. Levels. Craters. Sequence of objects. 
Points oF THE FIRST OrpER.—The determination of one or two points of the 
first order in this area would be very advantageous for correcting the positions 
of objects in this and the neighbouring areas. For the mode of observing and 
computing, with an example, see Report Brit. Assoc. 1866, pp. 233 to 238. 
There are no isolated objects near the centre that would be suitable for this 
purpose; but IV Af 19 is well situated for areas IV A*, IV AS, and LV A”, and 
the crater [TV Af * for the N.W. part of area IV AF. 
Extent or Surrace.—This is the same as area lV A*, viz. 8877-925 square 
miles English, but, in consequence of foreshortening (see ante, p. 8), it does not 
appear to be so. The difference, however, is slight ; for 1V A* occupies on the 
moon’s equator 0872 parts of the moon’s radius considered as unity, and LV Af 
‘0865 such parts. 
Greyerat Freatures.—This area consists principally of an elevated district 
bordering upon the lower surface of the W. part of Hipparchus. It is not 
marked by any very bold features, except the W.N.W. border of Hipparchus, 
which presents apparently a steep slope towards the lower land. This slope 
may be well studied under the evening illumination, at about 19 or 20 days 
of the moon’s age. With this exception, the surface is slightly irregular, 
dotted here and there with low mountains. The N.W. angle contains the 
central portion of what appears to be the remains of a large walled plain, but 
so altered by subsequent changes of the surface as to be scarcely recognizable. 
(See IV Af 2, p. 16.) Acomparatively undisturbed tract extends across the 
area from N.E. to S.W. ewternal to the 8.E. portion of the ancient ring sur- 
rounding the plain IV Af?, IV A’®, This tract is situated entirely on the 
high land N.W. of Hipparchus, and separates two regions of considerable 
disturbance, viz. that marked by the cliffs which extend from the plain 
IV A®?, TV A’3, to the ancient ring, and that characterized by the three 
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