ON MAPPING THE SURFACE OF THE MOON. 215 



Of existing photographs, I am a^yal•e of only ouo that can be emploj'ed 

 in connexion with positions of the first order for obtaining an approximation 

 to the true places of unmeasured points ; but this, which was taken by "Warren 

 De La Eue, Esq., on October 4, 1865, at 9'' 0"^ 4% G. M. T., represents 

 the disk at an epoch so near that of mean libration, which occurs only once 

 in three years, that the abscissas X may be measured on it without appre- 

 ciable error, and the ordinates Y require but a small correction. I now 

 proceed to notice the work done under these heads. 



My first step was to project orthographically on one sheet of paper a 

 .quadrant of the moon's disk of 50 inches radius. The quadrant chosen as 

 the most convenient was the fourth. After laying down the meridians 

 and parallels, I inserted in this quadrant all the points of the first order, 

 amounting only to twenty-three (see Appendix I.). It is greatly to be regretted 

 that these points are so few, and that the triangles of which they form 

 the points are so large, as in employing photographs taken at any other 

 epoch than that of mean libration, or, indeed, by using any method, so far 

 as I am aware, except determinations of the first srder, libration enters so 

 extensively, that even at short distances from these points the results of 

 measures become very uncertain ; and as the formula; for computing the 

 existing libration at any given epoch are only available for determining the 

 selenographical longitude and latitude of the centre of the apparent disk at 

 that epoch, and do not assist in the determination of the position of any other 

 point except by the aid of direct measures and the computation of certain 

 angles, it is the more important to augment the number of positions of the 

 first order. With this view, I have prepared from Lohrmann's work, ' Topo- 

 graphic der Sichtbaren Mondoberflache,' compared with Beer and Madler's 

 ' Der Mond,' a modification of the forms adopted by those selenographers for 

 this purpose according to the method of Encke, which necessarily includes 

 the computation of the libration. (See Appendix II.) 



The twenty-three points of the first order in Quadrant IV. were carefully 

 laid down by du-ect measurement from the equator and first meridian, and 

 checked in every case by measuring from point to point the sides of the 

 triangles formed by them, and given by Beer and Miidler in ' Der Mond,' pp. 

 80-82. Taking the moon's semidiameter equal unity, the greatest error (a 

 solitary instance) amounted to -0008, which is much less than errors arising 

 from contraction &c. of the paper employed. In addition to points of the 

 first order, several of the second order have been inserted. 



The coincidence of the equator of the photograph of October 4, 18(35, 

 enlarged to 10 inches in diameter, with that of the moon was next ascertained. 

 At mean libration the moon's equator is projected on the disk as a straight 

 line, and if the i^hotograph be taken at the exact instant of mean libration, 

 the moon's equator will coincide with a straight line across the disk equally 

 distant from each pole. The appearance of the moon Avhen full difi'crs, as 

 is well known, fi-om that which is presented at the various phases ; many 

 prominent objects quite disaj^pcar, and it is not so easy to pick out those 

 that can be seen as when they are near the terminator. I was able, how- 

 ever, to ascertain, with some degree of precision, the following points : — South 

 of the Equator— Messier, Theophilus, Dollond, Albategnius, Herschel, and 

 Gassendi ; North of the Equator — Picard, Dionysius,- Linne Aristillus, Pico, 

 and Kepler. Appendix IV. contains the measures of these points from the 

 apparent equator on the photograph, and the comparison of them with the 

 abscissse of the same points given by Beer and Miidler. The mean diff'erence 

 for those south of the equator is -0019, and for those north of the equator 



