32 On the Solar Eclipse, 



Am] but since the moon's semidiameter, and the height of the 

 mountain, are viewed under the same angular distance, a si- 

 milar relation subsists between the real and apparent lengths 

 of both ; hence 



Z ACM : Z AC m : : AM : A TO 



Let H = the moon's horary motion, as found for the time of 

 observation, T = 60' and t = the time observed during the 

 passage of the mountain ; also D = the moon's apparent semi- 

 diameter for the given day, and d = her semidiameter in miles, 

 and, lastly, y — the elevation required. By substituting the 

 value of .V, as found in the former case, there results this ge- 



Uy.dt . , , • w r. .1 



neral formula 2/ = ^^ expressmg the height of the moun- 

 tain in feet. 



The moon's horary motion on 7th of September, as calcu- 

 lated in the usual way, is found to have been 27' 1" 4", and 

 her semidiameter 14' 41" 2"'; hence, by substituting their values, 

 the elevation of the higher and isolated mountain is shewn to 

 have been 7353 feet nearly. In like manner, the height of the 

 other appears to have been 5783 feet. 



The elementary reasoning employed in the preceding in- 

 vestio-ation, has been preferred, from the extreme simplicity of 

 the result thus obtained. This motive may seem to have in- 

 duced the adopting of principles apparently liable to objection, 

 in as far as no portion of the moon's orbit can, strictly speaking, 

 be considered as rectilinear, nor the motion in that orbit 

 uniform. The effects arising from these causes are, however, 

 so inconsiderable as to be safely omitted ; and are accordingly 

 neglected in several cases, embracing both a greater extent of 

 orbicular space, and longer duration of time, than are com- 

 prehended in the present observations. To produce a similar 

 instance: Dr. Halley, in describing a method of determining 

 the limits of the penumbra in a solar eclipse, by means of cer- 

 tain properties of the sphere and cone, proposes to consider as 

 straight lines, not only the cuces of the eclipse formed by the 

 common intersection of the conical shade with the earth's cir- 

 cumference, and extending several hundred geographical miles 



