September 1th, 1820. 31 



two lines of intensely brilliant light, separated by a broad dark 

 space. A short time before the appulse of the lower, bright 

 flashes of light were seen to dart from an opening towards the 

 north ; which, by enlightening the adjacent parts, presented an 

 appearance, as if the extremity of the mountainous ridge had 

 been separated from the general mass. In order to convey a 

 more distinct idea of this effect, these luminous streaks are 

 represented in the figure, although they had ceased for some 

 time before the mountain had reached the position, at which 

 it is there supposed to have arrived. 



I. In order to ascertain the respective elevations of these 

 mountains, by the method now proposed, let M (Fig. 2, Plate II.) 

 represent the body of the moon, when the apex of the mountain 

 at Alias just attained the edge of the solar disc (S), and let 

 its base join the circumference at m, hence km is its perpen- 

 dicular altitude ; also let the curve AB equal the moon's ho- 

 rary motion at the time of observation ; then the angle ACB will 

 express the time, that is 60', in which the radius vector de- 

 scribes the whole area BAG. It is evident, that when the base 

 m has moved to A, the summit will be at x, hence during 

 this interval the moon has travelled in her orbit over a space 

 xk, equal to km, and the angle kCx, that is the angle ACm is 

 the expression for this time, which, if known, km is found. 

 Thus from the laws of planetary motion. 



As ZACB : ZACm: : aABC: AAmC; 

 But on account of the extreme shortness of the time, the ec- 

 centricity of the moon's orbit may be disregarded ; and, for the 

 same reason, its curvilinear direction may be projected into a 

 straight line, the areas then become triangles of equal altitudes, 

 hence 



As aABC : aA7?iC; : AB : km 



consequently As ZACB : ZACm : : AB : km 



From this the altitude of the mountain is found in " and '". 



II. To find A m in miles, let AM represent the semidiameter of 

 the moon in miles 1090 ; then the angle ACM expresses the 

 moon's apparent semidiameter, as found for the time of obser- 

 vation and as before, the angle AC m is the angle subtended by 



