by Lunar Olservations. 245 



and determines the altitude of a point which, as we have already- 

 seen, has nothing to do with the computation. The difference 

 between the true and apparent altitudes, technically called the 

 correction of the altitudes, which is a most important circum- 

 stance to be attended to, will in this way be erroneous by the 

 whole eifect of refraction in contracting the vertical semidia- 

 meters. 



I have now shown the reason which has hitherto induced as- 

 tronomers to follow *' the old established method" of estimating 

 the apparent distance from the apparent place of the centre ; 

 and that there is nothing erroneous in the principle of making a 

 deduction from the horizontal semidiameters before they are ap- 

 plied to the observed distance.— I have also shown that the cen- 

 tre is the point from which the distance must be estimated ; and 

 that if the reduced semidiameters be applied to the observed di- 

 stance of the limbs, no appreciable error can arise from consi- 

 dering the result as the apparent distance of the centres. And 

 I have lastly shown, that as the semidiameters and other correc- 

 *k)ns are usually applied by careful computers, in correcting the 

 altitudes, the true and apparent altitudes of the centres are cor- 

 rectly determined. The distance computed from these data may 

 therefore be depended on as correct in theory. 



It is obvious also that Mr. M.'s proposal of applying an atig- 

 mentation to the semidiameter applied to the distance, instead 

 of making a deduction from it — and of taking an excentric point 

 in the disk for the angular point of the triangle — is founded on 

 misconception, and must produce error. Such is the consequence 

 that would result from the adoption of Mr.M.'s theoretical views. 



I shall now inquire whether any error would arise worth notice 

 in the practice of lunars at sea, from neglecting some of the cor- 

 rections of which I have shown the existence in theory. It is 

 obvious that if any small correction be omitted which ought 

 to be directly applied to the apparent distance, the true distance 

 will be erroneous by nearly the same quantity. The deduction 

 from the semidiameter applied to the distance is therefore a cor- 

 rection which cannot be dispensed with where great accuracy is 

 required ; though when the altitudes are above 15° the correc- 

 tion becomes so minute, that in observations taken at sea it will 

 generally bear but a small proportion to the unavoidable errors 

 of observation. 



With respect to altitudes for correcting lunar distances, it may- 

 be observed generally, that if the apparent central distance be 

 correctly obtained, no conceivable mistake in the application of 

 the semidiameters in correcting the altitudes, can entail a mis- 

 take worth regarding on the result of the computation. — If the 

 apparent altitudes be determined to a minute or two, the dif- 



Q 3 tcrence 



