330 HH. Hennessy on the Distribution of Isothermal Lines. 
tendency will be to transport the centres of the isothermals to- 
wards the pole, in whatever hemisphere the island may be situ: 
ated, and that the isothermals at the centre sball be more affected 
rom this cause than those at the coast. Let us suppose, for 
precision, the island in the northern hemisphere. 
Let us at first abstract the effect of all other sources of terres 
trial temperature but solar radiation, and consider the propor 
tions of heat that may be received by two elements of t @ sur- 
face of the island included between two adjacent isothermal lines. 
It will suffice to determine the quantities for the spaces included 
between each of their northern and each of their southern ex 
tremities respectively. From the great distance of the sun, its 
rays may be supposed nearly parallel, and from the limited area 
_ We are considering, the earth’s figure may be supposed perfectly 
spherical. By the laws of radiant heat, the amount of heat re 
ceived by an element s of the surface of the earth, will be rep 
resented by* 
s Geos 
RP ss 
G being a coefficient, independent of the state of the earth's sur 
face, and expressing the amount of heat that passes from i. es 
to a unit of surface placed perpendicularly to the direction 
sun’s rays at a certain unit of distance, the inclination oad 
sun’s rays to a perpendicular to the plane of the element $0 
earth’s surface, and F the radius of the earth’s orbit. But 
sa? cosididu, ; 
where.@ is the earth’s radius, 4 the latitude of the point ne 
the element s is situated, and u its longitude. But in the sp 
cal angle whose sides : —#,=—4i, include the angle y, which 
subtends 9, we have 
cos p = sin Asin d+ cos4cosd cos ¥, 
where 9 is the sun’s declination, and w an angle depending Y 
: ‘a the 
is proportional to 
IL (1d) costdadudt. 
* Poisson Théorie Mathématique de la Chaleur, No. 210 
area of the sphere the quantity of heat received in th 
x 
: 
