7aa» PHILOSOPHICAL TRANSACTIONS. [aNNO 1780. 



as the illuminating ray sl is also in this plane, it follows, that the line l?- ( = on) 

 will always be perpendicular to the right line which joins the cusps of the moon;* 

 and the truth of the theorem delivered in the observations, depends on this 

 circumstance. For this reason he look care in all the observations to measure 

 the line, which in fig. 8 is marked on, parallel to the line cd, or perpendicular 

 to AB, and not the line rn, perpendicular to the elliptical curve AroB. The 

 manner of taking it is easy enough: however, he occasionally used 3 ditFerent 

 methods. The first method was to set the immoveable hair hh (fig. g) of the 

 micrometer parallel to a line ab, joining the cusps of the moon; then, by open- 

 ing the moveable parallel hair till it included the projection on, intended to be 

 taken, he marked that down as the measure of on. As this method required 

 some attention (that part of the ellipsis of illumination avb which is the vertex 

 V of the lesser axis may serve as a direction) and took up some time, on account 

 of the small field of view of the telescope, he used occasionally these 2 following 

 ways. 



When there was any remarkable figure on the disc of the moon near the line 

 of illumination, he put on a compound eye-piece, whose magnified field of view 

 is full 40°, and power about go times, so that it takes in the greatest part of 

 the whole moon; by this means he was enabled to view the projection intended 

 for measuring at the same time with the rest of the moon, and to fix on some 

 mark in the disc very near to its edge towards which he judged the line on should 

 be directed; then, putting on the eye-piece which carries the micrometer, he 

 took the distance according to this judgment as well as he could. 



The 3d method he took, was the following, which he considers as the best 

 of all, and which he therefore most frequently put in practice. He took a view 

 of some neighbouring shades of rocks or mountains, if there happened to be 

 any near, and directed the measure of the micrometer by them, as they plainly 

 pointed out the direction of the illuminating ray; or, which is the same thing, 

 indicated the line perpendicular to a line joining the cusps. Mons Leucopetra 

 was measured by this last method, which circumstance he mentioned in the 

 observations of the 12th of March, where he saw the whole rock and its highest 

 point, as well as the whole shade, and its last termination, on very even ground, 

 at the same time that he directed the micrometer in that line, to take the pro- 

 jection on, of the abovementioned mountain. Sometimes he compared together 

 a measure taken in the direction on, and one taken in the direction rn; but as 

 most of his observations were made on mountains not situated near the cusps or 



• It is here supposed, that rays from tlie sun s, and the eye of the observer e, to any part of the 

 moon L, may be taken for parallel ; and therefore, that different planes, made by several sections 

 of the moon, according as the point L is taken nortli or soutli of the diameter of the moon, which 

 is at right angles to the line joining tlie cusps, may also be taken to be parallel to that diameter. — Orig. 



