104 A perpetual Moon Table. [No. 134. 



In constructing this Table, I have used methods of approximation 

 more or less exact, according to the exigency of the case, so as to retain 

 as much correctness as is consistent with convenience, and also to 

 allow of the admitted errors being corrected in the least troublesome 

 way I could devise. 



A mean lunation consists of 29d. 12h. 44m. 03s.* If this be sup- 

 posed to occupy the circumference of a circle, it will, when divided 

 into days, have 29 parts each equal to a day, and a space corresponding 

 to 44m. 03s. more than half a day. It will, however, be vastly more 

 convenient to divide the circumference into 29^ equal parts, each of 

 which will correspond to 89.593s. or about lm. 30s. more than a day, 

 but in ordinary cases of finding the Moon's age, or time of New Moon, 

 &c. the small quantity by which the subdivisions exceed the exact 

 value of a day, may be disregarded without inconvenience. 



The days of the month are written in order from right to left on 

 the inner card, which of course contains 29J divisions, corresponding to 

 those of the lunation ; the days beyond 29 being written intermediate- 

 ly to those at the beginning of the month. 



As January contains 31 days, or nearly 1 J day more than a lunation, 

 the next month February is written to the left of January by a cor- 

 responding quantity. February having only 28 days, falls short of a 

 lunation by nearly 1| day, and hence March is written to the right of 

 February, and would fall exactly under January if the lunation con- 

 tained exactly 29^ days. In like manner April falls nearly under 

 February ; and May near half a day to the left of April ; and so on, 

 each month falling to the left by a quantity corresponding to the 

 Epact of the preceding month. If the lunation contained exactly 29^ 

 days, December would fall 9^ days to the left of January, but this 

 must be diminished by 1 1 times, 44m. 03s. = 8h. 04m. 33s., leaving 9d. 

 3h. 55m. 27s., and if this be estimated by the scale of the Table, it 



* In most modem works the lunation is stated at 29d. 12h. 44m. 02.8s. This num- 

 ber is given under Moon in Barlow's Dictionary, while on the opposite page a lunar 

 month or lunation is stated at 29d. 12h. 44m. 03s. lit. This latter quantity agrees best 

 with the ancient observations, and the former quantity with the modern. The quantity 

 here used is pretty nearly the mean of the two, and is that usually given in common 

 works. The difference of 2-10th of a second on each lunation amounts in 4000 years to 

 about 2h. 44m. 54s., and therefore in a Table like the present, scarcely requires farther 

 notice. 



