On finding the Longitude ly Lunar Olservations. 35 



-bringing out the same result, it may also be remarked, that many 

 methods apparently different are essentially the same ; the seem- 

 ing difference arising only from the endless variety of forms under 

 which the (juantities may be analytically expressed. Hence many 

 have fancied themselves the inventors of new methods, who are 

 little, if in any degree, entitled to the name. 



The pretensions to accuracy are likewise of very different de- 

 grees: some of these being also of the imaginary kind ; for some 

 of the greatest efforts to attain exactness are ireeiuently produc- 

 tive of greater errors than those they were intended to remove. 

 Thus, where perfection is aimed at, an allowance is made on the 

 sun and moon's altitudes for the effect of refraction in diminishing 

 their vertical semidiameters, without considering that the centre 

 is seldom the apparent place of the angular point of the spherical 

 triangle ; — sometimes also an allowance is made for the contrac- 

 tion of that semidiameter which is to be applied to the distance. 

 This, as we shall afterwards see, is likewise an elaborate way of 

 creating new errors. 



But at any rate, however great may be the distortion of the 

 disk by refraction, this does not in the least affect the true alti- 

 tude of the centre, when the other corrections are properly ap- 

 plied ; for, if to the observed altitude of the limb, we firsJ; apply 

 the refraction, &c. we get the true altitude of the limb ; and if 

 to this, the horizontal semidiameter be afterwards applied, it 

 gives the true altitude of the centre absolutely free from such an 

 error. This, though hinted at by different authors, seems to be 

 little, if at all, adopted in practice ; for in books of navigation 

 it is customary first to apply the semidiameter to the observed 

 altitude of the liml), as if that would accurately give the apparent 

 altitude of the centre, and then with this altitude to take out the 

 corrections. 



Some sort of re.spect, it is true, may in this way be paid to the 

 centre of the luminarv; but it is only a needless source of error, 

 which might be avoided without any additional labour. It would 

 hence appear, that the sun and moon's " true altitudes " when 

 about 7" are, in addition to other inaccuracies, subjected to an un- 

 necessary error of 18" by the usual careless way of working. But, 

 as we shall afterwards see, this is only half the extent to which 

 the error may go with the apparent altitude. It is in vain that 

 we expect accuracy even from the Ijest observers and instruments, 

 if such needless errors are persevered in. 



Although the common way of first applying the semidiameter 

 does not accurately give tlie apparent altitude of the centre ; yet 

 in some cases it gives that of a point which is very near to that 

 point of the vertical diameter through which the continuation of 

 the arc representing the apparent distance would pass, especially 



C 2 when 



