50. —-L. W. Meech on the Sun’s Daily Intensity: 
Since heat varies “inversely as the square of the I ire 
this equation evidently measures it intensity. ‘T’o ain the.» ° 
sum of the intensities in a year, the equation must be rind 
through by the unifagn dy, and integrated between the limits 0° 
and 27: then rejecting thé constant factor Pie there remains the 
falative 
Annual amount of heat = 
“7s 1) 
Again, let the slight decrement of ¢ in one or more centuries 
be denoted by h; writing e-h in place of e and developing for 
the first power of h by. Taylor’s Theorem; there results the 
proportional 
aed o-oo 
On January 1, 1801, the value of e was 0-01678357, with a 
centurial decrement of —0-00004163, the centurial value of h. 
And at this rate the orbit would become a circle in 40,300 years, 
though it is improbable that it will reach this limit. The dim- 
inution in a century is readily ascertained by substituting the 
values of ¢, h, in the last formula, which gives — 0:000 000 69; 
and it will be shown hereafter in the computation for Mendon, 
that such numbers are nearly or quite proportional to the corres- 
ponding degrees of Fahrenheit’s scale. Hence the secular de- 
crease of the annual quantity of heat, arising from secular change 
of the sun’s distance alone, is too small to be sensible to the ther- 
mometer ina hundred years, in a thousand, or in ten thousand 
years, and scarcely so, at the utmost yao when the orbit be- 
comes a circle. For even then, the mean temperature on the 
equator, which is now 82°, would not fall. more than 0-025 of a 
degree of Fahrenheit. 
~ Jt is thus demonstrated that the mean annual heat received by 
the earth as a whole, is virtually constant during a sidereal year, 
so far as secular change of the sun’s distance alone is concerned ; 
and by reason of the nearly constant excess, the same may 
concluded of the tropical or civil year. 
II. Again, let it be proposed to ascertain the sun’s relative 
estan at any given instant during the day. For this 
purpose 
Foe L= the ‘ apparent? Latitude of the ‘ais 
D= the sun’s meridian Declinat 
j= the sun’s semi-diameter, 
= the sun’s Altitude, and 
H= the Hour-angle from noon. 
Secular diminution = 
The horizontal projection of the sun’s disc on a plane at the 
exterior surface of the earth is well known to be an ellipse ; 
ee 
