116 Aftrontnacal Difficulty anfwéred. ei [ Aug. 
puted by the received hypothefis, that the heat is inverfely as the fquares of the 
diftances. He then ftates, that the {quares of the diftances are in proportion as 10 
to 8, or as 5 to 4, xearly. And becaufe it has not been found, that the -heat at the 
one of the above-mentioned places is not $ (or rather 3 it flould be) more than at 
the other, C. infers, that ‘ confequently the hypothefis (of the earth's orbit) is ab- 
furd, becaufe contrary to faéts well known.” 
Now, fir, all this feems to be very juft and fair reafoning, and unobjeétionable, 
fuppofing no error in the numeral calculations. When examined, however, all Mr. 
C.’s embarrafiment feems to arife froma fmall miftlake he has made, in taking the 
fquares of the numbers above-mentioned, viz. 96s and 933 which he ftates to be in 
proportion as 10 to 8, or 5 tog; for thofe numbers, when fquared, give nearly | 
9335 and 8720, which are in proportion as 1867 to 1744, or nearly as16to 15. So 
that the true difference in the heat, arifing from the faid difference in the diftance, 
when even computed according to the law of the fquare of the diftance, is only the 
rsch or 16th part of the whole; a difference in the degree of heat too inconfiderable 
tobe generally remarked, efpecially as a greater difference than that may be caufed 
by the local difference of circumftances, as to land, water, &c. Hence. then, Mr. 
C. himfelf muft allow, that the hypcthefis of the earth’s elliptic orbit continues firm 
and unfhaken, at leaft fo far as to any affection arifing from the-different degrees of 
hest. 
But this ftability will be perhaps ftill farther confirmed, when it is confidered, 
that the law of the variation of heat, according to the fquare of the diftance, is 
much too great an allowance, confidering the great fize and diftance of the fun, with 
regard to the earth, andthe reft of the planets. That law, of the fquares of the 
diftances, is taken from the cafe of a body illuminated by a radiant point, at differ- 
ent diftances ; for, in this cafe, the rays of light and heat proceed in diverging lines, 
as inthe following figure, from the point P : illuminating the body ABC, at dif- 

ferent diftances, by a cone of rays. Now, the diameter ad, or AB, of this cone, 
is directly as the diftance from the radiant point P ; and confequently the feétions 
at the different diftances, or the furfaces of the bodies adc, ABC, are as the {quares 
of thofe diitances.. Therefore, the denfity, or intenfity, of the heat and light, 
being {pread over the whole feétion or furface, is decreafed in the fame proportion, 
that is, in proportion as the {quare of the diftance is increated. ~ 
But the circumftance feems to be greatly different in the real cafe of the earth il- 
Juminated and warmed by the fun. For, on account of the great magnitude of the 
the fun, whofe diameter is more than 1ro times the diameter of the earth, and fill 
more, on account of his diftance, at 95 millions of miles, or more than 100 times his 
diameter ; on thefe accounts, I fay, the rays from the fun to the earth are confidered 
as proceeding in lines of parallel direétions, thus; where the earth E is feen im- 
merfed in the beams of the fun S, at different diftances. In this cafe, it feems there 
will be little or no diminution from the change of diitance, at leaft froma moderate 
change.. And confequently, the thermometer may well be expeéted not to fhow 
any material difterence, as to the latitude north or fouth, under fimilar circumftances. 
What degree of ivuth and credit may be due to this new f{peculation, your inge- 
nious correfpondents are requefted to confider, and communicate their fentiments 
upon it, through the channel of your Magazine. 
March 18, 1797. 3 NorRTHUMBRIENSIS- 
