Beam of November 17, 1882. 



331 



used 100 miles station-distance on each side of the shadow- 

 track so as to get two heights, h 1 and K 2 (see fig. 2), the mean 

 of the two heights obtained, viz. 96 and 173 miles, will be as 

 accurate a result as the observations can be expected to afford, 

 and will = 133 miles. 



Upon referring this last projection to Prof. Herschel, after 

 alluding to its being after all only a rough procedure to resort 

 to a triangulation on one side or the other of the moon's appa- 

 rent altitude with a converging angle so large as 10° to fix 

 the beam's intersection by, and after noticing that, if a 100-mile 

 base must be used, then it were better used on the north side 

 of the shadow-line away from the moon, he then continues: — 

 Supposing the rate of parallax close to the shadow-line to have 



been 9^° per 100 miles (i. e. 1° per ( -^ \ miles = 1° per 10'5 



miles), then the best way would be to consider only a small 

 base of 10'5 miles, say, and a small converging angle of 

 1° corresponding with it (fig. 3), and to calculate h trigono- 

 metrically thus: — 





miles. ^ 

 ^=10'5x sin 28 



and 



x=d x sin 1 



and 



h=d x sin 28., 



sin 28° 



and 



" x~~ sinl° ~ 10-5 x sin 28° 



(sin28°) 2 



. . it ■— . , o 



sinT 



x 10*5 miles. 



And then testing the above method's correctness by calcula- 

 ting first for 10*5 miles north of the shadow-line, which gives 

 (with fig. 4) 



miles. 

 ^=10*5 x sin 271 



x=-d x sin 1 



h = d x sin 28 



h sin 28° 



h= 



sinl ( 



sin 27°. sin 28° 



10-5 x sin 27°' 



sinl° 



x 10-5. 



And next (by fig. 5) with the 10*5 mile base south instead of 



north of the shadow-line, obtaining: 



miles. 

 #=10'5 x sin 29 



x sin 1 

 x sin 28 



and .*. h 



sin 29° . sin 28 c 

 sinl° 



xlO-5. 



The mean of these two should be close to 



7 sin 28° x sin 28° 1A K .„ , ' (sin 28) 2 1A K 



h = — — : — to — — x 10*5 miles, or to h = ^ — tt^-xIO'o, 



sinl° 



sinl° 



