718 PHILOSOPHICAL Tli ANSACTIONS. [aNNO 1/80. 



subtracting the part pc or radius, there remains tiie perpendicular height of the 

 mountain m/j. Mr. H. has followed the same method, as being the least liable 

 to error. 



Galileo takes the distance of the top of a lunar mountain from the line that 

 divides the illuminated part of the disc, from that which is in the shade, to be 

 equal to a '20th part of the moon's diameter ; but Hevelius affirms, that it is 

 only the 26th part of the same. When we hence calculate the height of such a 

 mountain, it will be found, in English measure, according to Galileo, almost 5-|- 

 . miles ; and according to Hevelius something more than 3J- miles ; admitting the 

 moon's diameter to be 2180 miles. Mr. H. then notices some other remarks of 

 Hevelius ; and then adds, the observations of Hevelius have always been held in 

 great esteem ; and this is probably the reason why later astronomers have not 

 repeated them. M. De Lalande, who is one of our most eminent modern 

 astronomers, agrees to the sentiments above cited, in his Abrege d'Astronomie, 

 p. 435, where he concludes the height of the lunar mountains to be about the 

 338th part of the moon's radius, or 1 French league, or rather 2043 toises. 

 He also mentions the opinion of Galileo, and adds ; but we ought to prefer the 

 observations of Hevelius^ as having been oftener repeated, as well as more de- 

 tailed and exact. 



Mr. Ferguson says (Astronomy explained, ^ 252) " some of her mountains, 

 by comparing their height with her diameter, are found to be 3 times higher 

 than the highest hills on our earth." And Keill, in his Astronomical Lectures, 

 has calculated the height of St. Katherine's hill, according to the observations 

 of Ricciolus, and finds it 9 miles. 



After these observations Mr. H. says that, before reporting his own observa- 

 tions, it will be necessary to explain by what method he had found the height of 

 a lunar mountain from observations that were made when the moon was not in 

 her quadrature ; for the method laid down by Hevelius will only do in that one 

 particular case : in all other positions the projection of the hills must appear 

 much shorter than it really is. Let slm, or slm, fig. 7, 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 observer at e or e, the lines lm, //», will not appear of the 

 same length, though the mountains should be of an equal height ; for lm will 

 be projected into on, and lm into on. But these are the quantities that are 

 taken by the micrometer when we observe a mountain to project from the line 

 of illumination. From the observed quantity on, when the moon is not in her 

 quadrature, to find lm, we have the following analogy. The triangles ool, rjviL, 

 are similar ; therefore, lo : lo :: Lr : lm ; but lo is the radius of the moon, 

 and hr, or on, is the observed distance of the mountain's projection ; and l» is 

 the sine of the angle eol = ols, which we may take to be the distance of the 



