374 E.. L. DeForest on Correcting an error 
But the means for mean months make the equation stand thus: 
y= 4891 
+ 12°60 sin(a—111° 51’) — ‘80 sin 2(a—75° 30’)-"16 sin 3(x— 23° 28’) 
+28 sin 4(z— 40° 33’)-4-25 sin 5(a—35° 37’) —-24 sin 62, 
It will be seen that these two equations differ somewhat in al- 
most every term, but the most important difference is in the are 
e, which is diminished by 47’ when derived from mean months, 
making the “date of phase” occur apparently more than three- 
quarters of a day earlier. The real difference of date is not 
quite so large, and is in the contrary direction ; because the time 
elapsed from the beginning of the year to the date when the 
term A, sin(c—e,) becomes zero is estimated differently in the 
two equations. In tlie first one each of the months is supposed 
to correspond to 30° of arc; the months of January, February, 
and March will occupy 90°, and the remaining are 112° 88’—90 
=22° 38 will represent a period of time to be found by the pro- 
portion 
30° : 22°38’ = 30 days: 22°63 days, 
which gives the date required, reckoning from the beginning of 
April 
il. 
‘a the second equation the are e, will represent a period of 
time to be found by the proportion 
360°: 111° 51/ = 365} days: 113-48 days. 
But the months January, February and March oceupy 81+28% 
+31=90} days; so that the time from the beginning of April 
to the required epoch is 113-48—90-25=23-23 days. Thus the 
use of mean months shows that the “date of phase” is really 
three-fifths of a day later than it is found to be when only calen- 
dar months are employed. : 
The date we have been considering is the one which occurs 1n 
spring; but if we take the autumnal one instead, then according 
to the method of calendar months the arc between the beginning 
of October and the required date will be 22° 38’ just as in April, 
and the time corresponding to it will be found by the propor: 
tion 
make it appear. 
To determine whether such results are owing to any peculiar- 
