*s “L. “W. Meech on the Sun’s Daily Intensity. 51 
tir 1 denote“ the sun’s radius, 1 will likewise denote the semi- 
_ conjugate axis of this projected ellipse ; while the horizontal pro- 
"jection of 1, which is Sn A’ will be the semi-transverse axis. 
ans at pe 1 
Thesarea of the elliptic projection is therefore 1 Xana X™ But 
the intensity of the same quantity of heat being inversely as the 
Space it covers; the ene of this area ——, or rejecting the 
constant divisor 2, sin A will measure the esi s sntenaty at the 
altitude A, supposing the distance to be constan 
But the sun’s intensity further Varies pases as the square of 
the distance, that is, directly as the et of the apparent diam- 
eter or semi-diameter of the disc. en 
4° sin A measures the sun’s intensity at any given instant dur- 
ing the da ri 
To assign the value of sin A, by spherical trizonometry, the 
sun’s tenes from the pole or co-deelination, and from the pole 
to the zenith or co-latitude, and the in neluded hout-a ngle from 
oon H, are given to find the third side, or co-altitude. The 
well-known formula for this case becomes, by writing sines in- 
stead of the cosines of their complements, 
sin A= sin D sin L+cos D cos L cos H, and 
4? sinA= 4?sinD sinL+44? cosDcosLeosH. (3.) 
At the time of the equinoxes, D becomes °, Pee the expression 
of the sun’s intensity reduces to 4? cosL cosH. That is, the 
degree of heat at different places, then, peepinay from the equator 
toward each pole, proportional to the cosines of the respective lati- 
tudes. At other times of the year, however, a different law of 
distribution 5 ey as indicated above. 
e sun’s intensity at a fixed distance being as the sine of the 
altitude, it follows that the sun shining for sixteen hours at an 
"altitude of 30°, would raise the temperature of a plain as high, 
as if it shone for eight hours from an altitude of 90°, or from the 
zenith, since sin 30° is -5, and sin 90° is 1. 
III. ‘Proceeding now to the general problem, it is required to 
determine the quantity of heat radiated upon a given place at the 
exterior of the earth on any given day. The quantity radiated at 
any instant, has already been made known, as 4? sin A: hence 
multiplying the last equation above by the uniform dH, and 
J#? sinA dH =4? sinD sinL.H+4? cosDcosL sinH. (4.) 
Regarding H as a semi-diurnal arc, the second member will 
express the daily quantity of heat for a half day, and so for the 
whole day. Also by integrating between the limits of any two 
hour-angles H’, H”, the quantity of heat will be found for any 
