Yat Meech on the Sun’ s Daily intensity. AS * 
V. Are the winters now, as cold as at the first settlement of: 
New England : ? The impression generally prevails that the win- » 
ters are growing milder, and the spring is later than formerly... 
norma the snows have not been so deep as in the days of Cot- 
ather; neither has Boston bay nor the Chesapeake of late 
hime been frozen over, as far as the eye could reach. So far as 
this ehange is astronomic, and not the result of local cha it 
may be determined by means of the formula 
Dai ily intensity = 4? sin D (H—tan nae i 
In the first place, let it be proposed to ascertain the change of 
each factor, for the last two centuries, which will refer the form- 
ula to the epoch of A. D. 1650, the period of our colonial history. 
The first factor 4°, depends for its value on the anom maly 6, whic 
has an annual change of 11.8, and on the eccentricity e, which 
has a secular variation of 0.000041. Accordingly, introducing 
these increments into the analytic expression for the inverse 
square of the radius-vector, which is the value of 4?, and devel- 
oping by Taylor’s Theorem, it is found that both sources of vari- 
ation cannot affect the present values of 4 within the fourth sig- 
nificant figure, in two centuries: hence these sources of change 
may be safely neglected in the present calculation. 
The second factor, sinD=sinw sin’; where » denotes the 
obliquity of the ecliptic, and 'T' the sun’s Tongitdds: Since the 
tropical or civil year is the interval between two successive re- 
turns to the same longitude, sin T ought in the present case to be 
regarded as constant. But in referring back, » has a secular in- 
crease of 45.7, or 91.4 in two centuries. Let this increment 
be denoted by w’’, and the contemporary increment of D by D” 
Then developing for the first power of each in the above equa- 
tion, by Taylor’s Theorem, cosD.D”=cosm sinT.”. Here 
substituting the value of sin T from the preceding equation, and 
dividing by cos D, 
“=coto» tan D. w” 
For the third factor involving the Gest icrial arc H, astrono- 
my gives —cos H=tan L tan a en developing as before, by 
Taylor’s Theorem, sin H.H”=tan L. D’~cos?D. Substituting 
for D” its value found above, sek dividing by the preceding equa- 
tion, ~ cos H=tan 
Coto. oo! 
tan H.H”= atD 
Recurring now to the formula of daily intensity, let it be de- 
noted by S, at the same time developing for the first power 0 
2 increments of the two variables, D, H; the resulting incre- 
ent is 
tt or 
gars) 
sin D °° D- ee 
