320 E. L. DeForest on Reducing Meteorological Observations. 
ing to the beginning and end of a month whose mean is m, and 
let us make 
4(2!’ —2')=a, 4(a”’ +2')=8; 
then the ee mean will be expressed thus: 
* sin 2a in3e 
m=ata, ~ — = sin(8-e,)+a, = ry sin2(8-e,)+a, - oe 
sin3(8-e,)+ &e. 
sin @ tala: 
, &c., depend only on the length of the 
month, and diets hier ees are given in the subjoined table, 
for months of all the different lengths. 
The values of —— 
Month of Month of M 
dt -aaee, 30 days, February. Jini 
log me 9994840 | 9995169 | 9-995719 | 9:995027 
sin 2a 
oe 9:979214 9980547 9982777 | 9979971 
sin 3a . 
a 9952651 9955722 9960852 9954395 
sin 4a 
log = 9:914288 9919945 9-929367 9-917502 
sin 5a 
log — 9862723 | 9:872015 | 9:887409 | 9-868005 
sin 6a ; 
log = 9°795732 9-810048 9-833588 9-803880 
The values of the arc 8, wiioh measures the time from the 
beginning of the year to the middle of a month, are for the cal- 
endar months 
15° 1630” 108° 43 54” «199° 55’ 6” «984° 35/58” 
44 28 25 133 47 38 224 28 25 314 39 37 
73 40 10 163 51 22 254 32 9 344 43 21 
and for mean months they are 15°, 45°, 75°, &e. 
hy the clea for the monthly mean m, let the oe 
stan €,, @,, €,, &c., take those values which have 
found ee shiens in the N ew Haven equation, and the ‘ole eit 
monthly means for the calendar months may be obtained. 
26°530 46°870 71°668 51-093 
287111 57-278 70°313 40°324 
36°056 66-949 62°512 30°424 
The errors of these computed Ag: as compared with the 
monthly means actually obuveved 
0 +030 ean. 008 — 007 
+001 —-002 —-007 +004 
—"034 —011 +012 +004 
This example shows the degree of accuracy with which an 
equation obtained by the method of mean months may be eX 
pected to represent any observed series of means for calendar 
