VOL. LXX.] PHILOSOPHICAL TRANSACTIONS. 7'23 



limb of the moon, he never found so much difference between these 2 measure? 

 as could have occasioned any very material error, if he had entirely neglected it. 



By the nature of the ellipsis it will appear that when we do not come too 

 near the limb or cusps of the moon, a tangent drawn to a point in the curve of 

 illumination will seldom make, with the subtangent, an angle that exceeds, or 

 is so much as, 26°; and in all such cases the error that can arise from taking 

 the line rn instead of on, will be less than the lOth part of the whole measure: 

 but if the angle the tangent makes with the subtangent be only about 18", the 

 error will be less than a 20th part; and all the measures taken, he believes, will 

 be found to be much within these last- mentioned limits. From this considera- 

 tion it will appear, that if he had not been aware of this circumstance, his 

 observations would still be sufficiently accurate to disprove the usually assigned 

 great height of the lunar mountains; but as he took all the precaution the 

 situation of each mountain would afford, by using any one of the above- 

 mentioned 3 methods, which suited best, he believes there can hardly be a 

 possibility of any error that should amount to a 40th part of the whole height 

 of any mountain he measured. 



The figure abcd (fig. 10) contained by the diameter ab, the arch cd, and the 

 two curves ad, bc, shows in what portion of the moon's semi-disc we may 

 .safely measure the line rn, instead of on, without being liable to so great an 

 error as -^ part of the whole; and the figure ABcrf contains that part wherein 

 the measure rn being taken instead of on, the error will be less than the 20th 

 part of the whole measure. In a portion something more confined the error 

 will soon vanish, so that the difference may be safely neglected entirely. Thus 

 in the space abx?/ the error cannot amount to lOOth part. These figures may 

 be constructed by taking the several points d, d, y, and c, c, x, 26°, 18°, 8° 

 respectively, from the vertex, the curves ad, xd, at/, bc, bc, bx, being the loci 

 of those points of the tangents which touch the several ellipses of illumination 

 that may be contained in the semi-disc of the moon, when these tangents make 

 those several angles of 26", 18°, 8°, with their sublangents. 



XXX. Of an Extraordinary Pheasant. By Mr. John Hunter, F. R. S. p. 527. 

 Reprinted in Mr. J. H.'s Observations on the Animal Economy, 4to. 1786. 



XXXI. On the Distemper among the Horned Cattle. By Daniel Peter Layard, 



M.D., F.R.S. p. 536. 



In consequence of the essay which Dr. L. published in 1756, he was called on 

 in 1769, by Government, to assist with his advice towards stopping the progress 

 of the contagious distemper among the cattle, which had broken out in Hamp- 

 shire : and by mere accident he discovered how the infection was brought from 



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