Astronomical and Nautical Collections^, 1 13 



Let R = —HI z=z be the ratio of mean time to sidereal, the lo- 



15 



garithm of which is 0-0011 873 ; then by eliminating the value of m 

 from this expression, and substituting it, we obtain 



d = aR — a. 



h 



The multiplier expresses the ratio of one hour to the 



h 



moon's motion in right ascension during that period, which is evi- 

 dently the same as the ratio of any given period of time to the 

 moon's motion in right ascension during the same period. Now if 

 the moon's motion in right ascension during twelve hours in de- 

 grees, minutes, and seconds, be depressed a denomination, and 

 reduced to minutes, seconds, and thirds, this will be the moon's 

 motion in right ascension in time for three hours, the logarithm of 



the ratio of the latter of which to the former, and consequently of 



15° 

 is equal to the proportional logarithm of the motion in time 



h 



15° 

 for three hours. And thus the logarithm of is obtained by in- 

 spection. 



15° 

 The above formula d — aR •— a, is adapted to mean 



h 



time, but it will equally answer for apparent time, provided R be 



held to express the ratio of apparent time to sidereal, and the 



15° 



logarithm of be taken equal to the proportional logarithm of 



h 



,the moon's motion in right ascension in time, during three hours 



apparent time. The value of R will vary with the sun's motion in 



right ascension. A table of the logarithms of jR is subjoined, in 



which the argument is the sun's motion in right ascension in time 



for twenty four hours apparent time. This manner of applying the 



formula is more convenient for the use of the Nautical Almanac, 



The moon's motion in right ascension is always supposed to be 



kthat answering to the middle point of time between her passages 

 over the respective meridians. 

 • Vol. XIX. I 



