the Longitude hj Lunar Olservations. 22 1 



limbs " is nothing ; and it is this difference which, as he says, 

 *' constitutes the augmentation." He is, perhaps, uotnow In- 

 clined to deduce from this fact so ahsurd a consequence. 



Mackav's mistake respecting the correction of the azimuth arose' 

 from his writing the numernior in place of the denominator, in 

 the analytical expression which furnishes the rule. The whole 

 of the investigation is so simple and so short, that if Mr. M. had 

 it not to seek, I cannot conceive why he should have thought it 

 worth while to announce that it might form the subject of a fu- 

 ture communication. Put A = the azimuth, a — the declina- 

 tion, c = the latitude, B = the hour angle, and r = rad. 



Then Keith's Trig. chap. ix. prop. vii. edit. 2d, A: a : :r^: 

 cos c. sin B ; whence A = : = a. sectc. cosectB, radius 



cos (. sill li ' 



unity. 



So much for the first part of his reply. We come now to the 

 second ; and here, in strict accordance with his determination to 

 be ori0nal, he has adopted a line of defence perfectly new, I be- 

 lieve, in the annals of printed controversy. I had proved that 

 all his objections to the common method of finding the distance 

 in lunars were uithout foundation. He read my observations, 

 and in reply declared, that he had not yet found that in his ob- 

 jections there was " anything amiss ;" and that those objections 

 were ^' truths which rested securely on their own basis." He 

 now comes forward in a letter bearing date December 3, 1819, 

 and says in effect : " Sir, all that you say on the subject of cor- 

 racting the altitudes and clearing the distance is quite true, hut 

 I never made amj such objections as those vldch you Impute to 

 me.'" In answer to this sweeping asseveration, I shall merely 

 contrast Mr. Meikle with himself, and in his own words. 



In his letter of December 3d, 1819, page 401 of wur Maga- 

 zine for that month, he says " it is not the method with i\\Q re- 

 duced semidiameter on which I animadverted with so much se- 

 verity." And again in the same page, " in the common method 

 the reduction of the semidiameter by refraction is neglected al- 

 together, and it icas for this veri/ reason that lanimadverled on ' 

 it." And again," Mr. R. has beertat great pains to prove trifles, 

 the truth of which nol)ody doubts, and which I never denied." 



The animadversions to which he refers were printed in your 

 Magazine for last July. Let him state for hin)sclf on u-drit he 

 did there animadvert. In page 35 of the Number referred to he 

 says, " Some of the greatest efforts to attain exactness arc fre- 

 quently productive of greater errors than those they are intcndcil 

 to remove. Thus where perfection is aimed at an allowance is 

 made for the effect of refraction in diminishing the vertical se- 

 midiametcrs. Sometimes also an allowance is made for the •'oii- 



tractiou 



