relating to the Mountains of the Moon. 525 
By the nature of the ellipfis it will appear, that, when 
we do not come too near the limb or cufps of the Moon, 
a tangent drawn to a point in the curve of illumination 
will feldom make with the fubtangent an angle that ex- 
ceeds (or is fo much as) 26°; and in all fuch cafes the 
error that can arife from taking the line rn inftead of 
on will be lefs than the tenth part of the whole mea- 
fure: but, if the angle the tangent makes with the fub- 
tangent is only about 18 0 , the error will be lefs than a 
20th part; and all the meafures I have taken, I believe, 
will be found to be much within thefe laft-mentioned 
limits. From this conlideration it will appear, that if I 
had not been aware of this circumftance, my obferva- 
tions would ftill be fufficiently accurate to difprove the 
ufually afligned great height of the lunar mountains; 
but as I took all the precaution the lituation of each 
mountain would afford, by ufing any one of the above 
mentioned three methods, which fuited bell, I believe 
there can hardly be a poffibility of any error that fhould 
amount to a 40th part of the whole height of any 
mountain I have meafured. 
The figure abcd (fig. 5.) contained by the diame- 
ter ab, the arch cd, and the two curve ad, bc, fliews in 
what portion of the Moon’s femi-difk we may fafely 
meafure the line rn, inftead of on, without being liable 
Z z z a to 
