E. L, DeForest on Reducing Meteorological Observations, 319 
y h 
day is 31+28+4 of 0°2422=59-1211 days, and the correspond- 
ing abscissa is found to be 58° 16’. 
The monthly means of temperature at New Haven, as given 
in the Transactions of the Connecticut Academy of Arts and 
Sciences, from 86 years’ observations, are 
26°53 46°84 71°66 51°10 
28°11 57:28 70°32 40°32 
36:09 66°96 62°50 30°42 
When reduced to mean months they become 
265811 47°3076 71°7307 ‘50°9438 
28°2410 57-7081 70°2452 40°1992 
36°5263 67:2372 62°3404 30°3442 
From these data I have obtained the equation of mean daily 
temperatures throughout the year, in the way already stated in 
this Journal, xli, 878, except that instead of finally reducing it 
from the usual form, - 
y=a--a, sin(z-E,)+<a, sin(2e+E,)-++a, sin(3z--E,)+ &c., 
into a form where the signs before the terms are sometimes plus 
and sometimes minus, I have reduced it to 
y=a-a, sin(x—e,)-+-a, sin2(x—e,)+a, sin8(4—e,)-+ &e., 
in accordance with the formula 
1 
sin(na--E, )=sin n { 2——(360°—E,) ie 
This prevents confusion of signs, and at the same time preserves 
the significance of the are e,, making it measure the time elapsed 
from the beginning of the year to the first ascending node of the 
term in which it occurs. 
he New Haven equation of temperatures then is 
y=49-112-+-22-902 sin(x—110° 39’ 22”)-+"289 sin 2(x— 20° 56’) 
+443 sin 3(2—57° 42/)-+-022 sin 4(7—75° 22’) 
+402 sin 5(a—8° 53’)+-098 sin 6a. 
An equation of this kind, to be perfect, ought to express ac- 
curately all the facts implied in the observed series of monthly. 
means, so that the mean for any one of the calendar months 
may be derived from it with precision, by integrating ydx be- 
tween the proper limits for the beginning and end of the month, ~ 
and dividing by the are which measures its length. Let t 
general form, 
| y=a-+a, sin(z—e,)-+<, sin 2(e—e,)+a, sin 3(r—e,)+ &e., 
be treated in this way between the limits 2’ and a” correspond- 
