a 
332 H. Hennessy on the Distribution of Isothermal . 
E(t) representing a complete elliptic function of the se 
order,* whose modulus is 7. The value of 7 being 28° 28, E() 
=1:50658: consequently we may ultimately write 
H=f (l-—A) 
2 ) 
—so1s16 m : sin (4, —4,) cos (4, +4.) +4,—4, 
P . 
But as sin(4,—4,)=4%,—4,, very approximately, this may be 
writt 
en. | 
H=f(l—)+ O(1+c0s2 4) | 
where 
1 
Similarly H, the proportion of heat received by the very — 
; and nearly equal area included between the southern extrem! 
of the isothermals, may be written 
A,=f(ly— 4) (1-+-cos24,) 
where 
—i 
0, = oCs—"4), 4, hak 
. 1 2 : s coast 
and 1,= the latitude of the nearest point of the southern en 
of the island. /(J—A) and /(4,—1,) are both positive, and 
are supposed, in virtue of what has been already stated, * af 
sess the property of varying: inversely with 1—A and 4 bara 
i —Adi 
spectively ; in other words, /(J—.4) increases when / 3 
ishes, and. f(4,—1,) increases when 4,—1/, diminishes. If we 
‘4. I), 0d 
But as cos2.4<cos24,, it follows that f(—4)>f(41—"h 
consequently, /—-4<4,—1,. If the influence of solar ma 
will affect the next adjacent isothermal, and so on in sue 
so that ultimately all the isothermal lines will be 
towards the north. 
As 
c(i 4 0082.4) = 20'c08 24, 
Legendre, 
* Poisson gives 0°17798, as its logarithm from 
sorie de 1s Chales 
p. 490, . 
