1884.] 
G. Tliibaut —Vardlia Mihira^s PancliasiddlicintiTid, 
271 
being contained in 65,746,575 days tlie mean place of tbe moon for any 
given abargana miglit of course be deduced directly; smaller numbers 
were, liowever, desirable as facilitating the calculations, and Yaraha 
Miliira therefore substituted the relation of 900,000 revolutions to 
24,589,506 days which o:ffers the advantage of a smaller divisor, and a 
not only smaller but also much simpler multiplicator. The substitution 
involves indeed a slight inaccuracy since 900,000 revolutions of the moon 
746166 
take place in 24,589,506 + 2 ^Q ' 0 ggp fractional part of which 
quantity is neglected in the general rule. The error which results 
therefrom is, although insignificant, not to remain uncorrected and 
Yaraha Mihira adds therefore (after one intervening verse about the 
mean place of the moon’s uchcha) the following rule : 
“ Multiply the (elapsed) revolutions of the moon by 51 and divide 
by 3,120 ; the (resulting) seconds are to be deducted (from the mean 
place of the moon as found by the general rule).” (The second part of 
the rule refers to the moon’s uchcha). The correction stated here is 
easily accounted for. By a proportional calculation we find that the 
moon performs in 
746166 
2406389 
of a day about 14,708 seconds of a circle. 
To 
so much consequently the error resulting from the neglect of the frac¬ 
tion amounts for 900,000 revolutions. The error for one revolution is 
14708 
therefore equal to 
900000 
seconds or, as Yaraha Mihira prefers to ex¬ 
press it, reducing both numbers by 288, to (about) seconds. The 
explanation of the kshepa, 670,217 is not quite so simple as that of the 
solar kshepa. We of course again employ the kalpMy-ahargana which 
had led to a satisfactory result in the case of the sun’s mean j)lace. If 
we, however, proceed according to the general rule given by Yaraha 
Mihira, multiplying that ahargana by 900,000 and dividing by 24,589,506 
and finally applying the prescribed correction, we find that the remainder 
combined with the moon’s mean motion for half a day does not equal the 
stated kshepa. The fact is that approximately correct rules and approxi¬ 
mately accurate corrections are applicable to comparatively short periods, 
but become altogether misleading if periods of very considerable length 
as for instance the kalpady-ahargana are concerned. In such cases we 
must discontinue the use of reduced factors and employ absolutely connect 
numbers. In the present instance we consequently have to employ the 
L L 
