Farther Reply to Mr. Riddle on the Lunar Observations. 243 



I formerly adduced Professor Playfair's definition of parallax, 

 as of the first authority, and of a more general nature than the 

 limited one given in several books. That Mr. Playfair's not 

 adopting the latter definition was from a conviction of its imperr 

 fection,is evident from his rejection of some definitions in Euclid 

 for a like reason. He therefore gave his more general definition. 

 In short, nothing can be more plain than that the limb of the 

 moon is either affected by parallax or it is not. If it is, astro- 

 nomers are right in applying a correction for parallax to the ob- 

 served altitude of the limb ; but if; as Mr. Riddle would have 

 us believe, it has no parallax, then we obtain the true altitude 

 by using the refraction only. Such is the result of his counter- 

 feit definition. 



In the common method of correcting the moon's altitude, the 

 corrections are taken out for the centre in place of the observed 

 limb ; the error is therefore the difference of the corrections for 

 parallax and refraction at two altitudes differing by a semidra- 

 meter of the moon, or 16', and this, as I have repeatedly stated, 

 amounts to IS" at the altitude of 7°. How Mr. R, can take 

 upon him to reduce the semidiameter itself to 18" is best known 

 to himself. I may likewise observe that the augmentation of 

 the diameter parallel to the horizon is more accurately the dif- 

 ference of the parallaxes of its opposite limbs, than in tlie case of 

 any other diameter whatever. Of this Mr. Riddle is no doubt 

 sufficiently aware, but he must needs bring himself off in some 

 $jhape or other. 



Mr. R. must also be aware that he has entirely misapplied his 

 inaccurate quotations from my papers ; since in mo'-.t of the^e 

 passages ii is not the altitude of the centre 1 am complaining of. 

 So that, after all, he is still proving his own favourite trifles; and 

 i would further remark, that the method with the excentric 

 point will accurately give the true distance of the centres, whether 

 that is the thing required or not. 



It is very extraordinary indeed, that he should still obstinately 

 persist in asserting that there is nothing vague or unsatisfactory 

 in the popular explanation of the quadrant. I would beg to ask 

 him, how much worse ao explanation can really be than one that 

 is not true. 



The rest of his remarks being much of the same sort as the 

 above, it is useless to multiply words on such an unprofitable sub- 

 ject ; since it is plain that " though vanquish'd, he can argue 

 •>till." 



I am, sir, your most obedient servant, 

 ricriicff sii'-Ft, Apiil n, 1820. Henry Meikle. 



Q2 XXXVIII. Ca- 



