£12 Mr. herschel’s AJlronomical Obfervations 
Mr. ferguson fays (Aftronomy explained, § 252.) 
“ Some of her mountains, by comparing their height 
“ with her diameter, are found to be three times higher 
“ than the higheft hills on our earth.” 
keill, in his Aftronomical Lectures, has calculated 
the height of St. Katherine’s hill, according to the obfer- 
vations of ricciolus, and finds it nine miles. 
Before I report my own obfervations, it will be necef- 
fary to explain by what method I have found the height 
of a lunar mountain from obfervations that were made 
when the Moon was not in her quadrature ; for the me- 
thod laid down by hevelius will only do in that one 
particular cafe: in all other pofitions the projection of 
the hills muft appear much fhorter than it really is. Let 
slm, or slm (fig. a.) be a line drawn from the Sun to 
the mountain, touching the Moon at L or /, and the 
mountain at m or m. Then, to an obferver at e or e the 
lines lm, lm, will not appear of the fame length, though 
the mountains fhould be of an equal height ; for lm will 
be projected into on, and lm into on. But thefe are the 
quantities that are taken by the micrometer when we 
obferve a mountain to project from the line of illumi- 
nation. From the obferved quantity on, when the Moon 
is not in her quadrature, to find lm we have the follow- 
ing analogy. The triangles ool, r ml, are fimilar; 
therefore. 
