C 48 ] 



VI. On the Manner of estimating the Difference of Longitude 

 in Time. By A Correspondent. 



"VTO part of astronomy is more abstract, or more liable to 

 -^ error, than what regards computations in time. In the 

 Conn, dcs Terns 1825, M. Bouvard has calculated the dift'e- 

 rence of longitude between Paris andGreenwich, by means of the 

 moon's observed motion in right-ascension in the time elapsed 

 in passing between the two meridians. This calculation is ani- 

 madverted on in the Quarterly Journal of Science published in 

 March last; and as I observe that, in the discussion, what is 

 true is mixed with notions not quite correct, it may be per- 

 mitted to bestow a few lines on the subject. 



M. Bouvard's method of calculation may be thus explained. 

 Conceive a fictitious sun moving equably in the equator at the 

 rate of 360° 59' 8"^ in 24 hours, and consequently marking 

 mean solar time by the arcs which it describes. Let the fic- 

 titious sun and the moon be upon a meridian at the same in- 

 stant of time; and, after a given interval elapsed, the moon 

 having come to a second meridian, the fictitious sun will be 

 past that meridian. It is manifest that the time of describing 

 the arc of the equator between the fictitious sun and the se- 

 cond meridian is equal to the moon's variation in right-ascen- 

 sion estimated m mean solar time. If the moon's change of 

 right-ascension in sidereal time be equal to a, and the ratio 

 of sidereal to mean time be equal to r, then the mean time of 

 describing the arc of the equator between the fictitious sun 

 and the second meridian will be equal to a r. Again, let 



m = — -—- : then 15"^ + m will be the rate at which the fic- 



24 



titioiis sun separates from the first meridian in an hour of 

 mean time : and if h be the moon's motion in right-ascension 



in an hour of mean time, then ar x — ^ will be the arc 



of the equator between the fictitious sun and the first meri- 

 dian expressed in mean time. Hence the mean time of de- 

 scribing the arc between the two meridians is equal to 



ffr X 



15°+ OT / 15°-fTO - h 



/ 15^-fTO -h\ 



h 



This is M. Bouvard's formula ; but it certainly is not the 

 difference of longitude sought. For, according to the defini- 

 tion of the term, the difference of longitude is found in time 

 by converting the arc between the two meridians at the rate 

 of 15° to I'' ; and this is true whether we use mean time, or 

 sidereal time, or any other time, provided the interval between 



one 



