Astronomical and Nautical Collections. 411 



tuted instead of that of the star. Hence, on this account, 

 since the difference of apparent altitudes may annount to 14' 

 or 15', the error in the orbital parallax, as also in the per- 

 pendicular parallax, may vary from to 16". And the sum 

 of the perpendicular parallax, and the nearest distance, may 

 tlierefore err from to 16", according to Axiom 4, Book 1, 

 Euclid. 



Consequently, putting D = the moon's semidiameter, »= 

 the sum of the nearest distance and perpendicular parallax, 

 and a? = the side to be found, we shall have, in the operation 

 marked \1/, the hypotenuse (d) and the perpendicular (s) 



given to find the base a7 = ^D*-~s* .*, $a?= x ^ «= — - 



X ^ s ; that is, aj : s :: ^ s : ^ a?. Whence, should, in any 

 case, the base equal 1', and the perp. s ■=. \5\ which may 

 sometimes happen, we shall have T : 15' :: 16" : 240" = 4'. 

 And supposing the moon's hourly motion from the star to 

 be 30', which it is very nearly when at its mean quantity, 

 this will give 8 minutes of time, or 2 degrees of longitude 

 on the equator ! 



Afar. 20, 1828. T. B. 



Answer, 



Mr. B. has objected to the method for computing an 

 occultation, published in the Nautical Almanac under my 

 name, that ** it is only an approximation, which diverges 

 from the truth, as the observer approaches the perpendicular 

 to the moon's apparent path, the moon and star being nearly 

 in the same vertical circle ; that the error is occasioned by 

 the effects of parallax being computed from the star's alti- 

 tude, instead of the apparent altitude of the moon, and that 

 its quantity may vary from to a whole degree of longitude, 

 and perhaps more." 



On the other hand, I maintain that the effect of parallax 

 is computed upon principles which are mathematically cor- 

 rect ; and consequently that the method in question is not 

 an approximation, for the cause assigned by Mr. B. 



