ON MAPPING THE SURFACE OF THE MOON. 295 



of the moon and the object. This method, proposed by Encke, has been 

 employed by Lohrmann and Beer and Madler. Third, by measuring the 

 lengths and position-angles of two lines on the moon's surface ; one joining 

 two objects, the coordinates of which have been already determined by one 

 of the'methods above mentioned; the other joining one of the same two ob- 

 jects, and a third, the position of which is to be determined. The difference 

 of the position-angles will give the angle between the two lines from which, 

 with the lengths of the two lines, the position of the third object may be 

 known. Beer and Madler employed this method for the determination of 

 positions of the second order. 



The latitudes and longitudes of lunar objects require to be expressed by 

 the rectangular coordinates X and Y in parts of the moon's semidiameter, 

 which is regarded as unity. This is for the purpose of properly inserting 

 them in a map on the orthographical projection. The latitude of an object, 

 which we may call /3, being its distance from the moon's equator, X is 

 equal to the sine of the latitude or ft, and the expression for X becomes 

 X=sin /3. The longitude of an object, which is designated \, is its distance 

 east or west from the moon's central meridian on the same projection, which 

 is proportional to multiplying the sine of the longitude into the co- 

 sine of the latitude ; for on the equator the longitudes are simply pro- 

 portional to the sines, the distance of an object 30° E. longitude, for 

 example, from the centre of the moon's disk on the equator is equal to the 

 natural sine of 30° or 0-5 ; but at 10° of latitude and 30° of longitude, an 

 object is nearer the moon's central meridian in the above-named proportion, 

 and the expression for Y becomes Y=sin \ cos (3, which, when computed, 

 gives 0-49240, and we have X=0-17365, Y=0-49240. In Form No. 3 pro- 

 vided by the Committee the column (2) for the reception of the symbols is 

 followed by four (3/4, 5, and 6), for inserting the values of the coordinates 

 X and Y, and the latitudes and longitudes. 



Next to position comes size or extent of lunar objects, which may be 

 expressed in two ways, and for which the Committee has provided two 

 columns, one (7) headed " Mag.," a contraction for magnitude, the other (8) 

 " Miles," in which it is intended to enter the values of the diameters of 

 lunar craters in English miles, and also, as suggested by W. De la Rue, Esq., 

 in French kilometres. As both these elements, magnitude and diameters in 

 miles, must be ascertained by measurement — estimation being altogether too 

 rough — a word or two on the method of effecting it may be acceptable. It 

 is intended to express the magnitude by a number showing the ratio as to 

 size which the crater, mountain, or spot, dark or light as it may be, bears to 

 one chosen as a standard (Dionysius for example) ; any given measure of the 

 standard, which may be called " s" — however the* measures may vary from 

 time to time, arising from differences of distance, effect of libration, dif- 

 ferences in the Hues measured, and other circumstances — is considered equal 

 to unity, and if the measures of any other spots, made on the same evening, 

 be designated a, b, c, d, &c, the magnitude m of each will be determined by 



the simple formula ?n="> m'=_' m" =.1, and so on. 



s s s 



For the cohimn (8) headed "Miles," it is necessary to measure across the 



crater, but as it has been assumed that most of the lunar craters are strictly 



circular, and the experience which has been gained relative to the standard 



Dionysius, appears to point, in this instance at least, to some irregularity of 



form, the determinations of the extent in miles can only be considered as 



approximate. Beer and Madler give a list of 149 objects, the diameters of 



