which do not so plainly show the recurrence of cycles, because 
5 is not a measure of 12. It is easy however to trace 5 maxima 
and 5 minima. 
The values of ¢, are 
—13 4°13 —-13 4-13 —-13 4°13 —-13 4-13 —-13 4°13 —13 4-18 
which go through their cycle 6 times in the year. Also the sum 
of any consecutive two is 
fe addition, we find the ‘values of t,+¢, +t, +1,+¢, +t,+2, 
to be 
36°62 3861 41-41 46°20 52:90 59:00 61:80 60°99 5649 49°90 4322 39°30 
or, to one place of decimals, 
866 886 414 462 529 590 618 61:0 56:5 499 482 393 
which eres exactly with the monthly means. 
rror committed by stopping at any term, is, of course, 
equal to the sum of the terms omitted. These sums are given 
in the following table; the first line containing the sum of all 
the terms after ¢,, the second line the sum of all after 3 t,, and 
sO on,— 
+08 41-23 a ts rots ht +0 ali +05 —59 ~87 +30 
—63 + 4 84 +01 +29 1 +02 412 -—13 +433 
—56 + 32 fo — 17 +08 +12 a8 +08 +09 —05 —-20 +50 
—32 4+ 26 —'17 + 07 +02 —06 +:06 +00 -09 +19 —26 +32 
—13 4-13 -13 +138 -18 +13 —18 +13 -18 +13 -18 +413 
The terms ¢,,¢,,¢, produce no effect upon the mean tem 
pera- 
ture of a half ~year, for the sum of a any 6 consecutive values of 
these terms is 0; hence, i in deriving the mean temperature of a 
f-year from t. ot+t,, the error committed depends only on ¢, 
and?,. ‘The sums of ¢, and ¢,, for each month, 
—'26 +-30 +03 — 23 4-08 —'02 +26 ~-30 —-03 Sas pail 
and the means of every consecutive six of these, commencing 
with October—March, are 
© 04 —-04 —-01 —02 +07 =-08 oe cee aa —"07 +08 
4147 40°98 42:52 45:81 49°92 53°75 56-27 56°81 55-22 51°93 4782 43-99 
while the means of the actual monthly temperatures are 
4150 4088 4250 45°78 4998 5372 5623 5685 55°23 5195 47°75 4402 
showing the same corrections as above, es differences of 
1 in the last figure for neglected places of decim Hence we 
see that the mean temperature of any 6 aston months at 
Seinack can be calculated from ¢, and ¢, (or from their con- 
stants A, A, E,), subject to errors not exceeding -07 of a degree. 
It may be shown in general, by a theorem proved on p. 80 of 
my former article, that, if the expression for monthly means be 
