ABOUT TERRESTRIAL TEMPERATURE. 87 
accuracy with which it applies to more than one-half of the surface of the southern 
hemisphere. Indeed, the distinction between an Empirical and a Rational for- 
mula,—one founded on the mere law of continuity, and one on a rational basis,— 
is well illustrated by applying to this case the purely mathematical law (18), 
which for the northern hemisphere alone represents the observations there even 
better than our physical theory as yet does, but which yet egregiously fails when 
extended to southern latitudes, as the following table shows :— 
Tasie LV. 













iat Soci. Temperature by Difference from Difference according to 
Empirical Law of par. 18. Dove’s Table. Rational formula. 
74°°3 — 8°7 +0°1 
64°7 — 9-4 —0°8 
52 +2 —14°7 —2°:0 
38 *3 —16°3 +0°9 

37. With this strong testimony to the reasonableness of our fundamental as- 
sumptions as to the influence of land, we may, by using the observed temperatures 
of corresponding parallels in the two hemispheres, obtain an expression for the in- 
fluence of land in each of those parallels, disengaged from any assumptions as to 
the effect of latitude in modifying the gradation of temperature on a globe whether 
composed of land or of water, such as we made in paragraphs (26) and (28) of 
§ 3. This is to be accomplished in the following way :— 
38. By our fundamental assumptions of § 3. we attribute to the land and the 
water of any parallel an influence on the temperature in proportion to their respec- 
tive extent on that parallel. Thus, for the parallel whose latitude is A, let L, denote 
the fraction of the circumference composed of land, W, the remainder which is 
covered by ocean; by J, and w, the temperatures to be found for that parallel on 
a globe all land and a globe all water respectively ; and by T, the observed tem- 
perature on the given parallel, we have, by hypothesis, 
T,=W, .w,+L,.1 
ar? 
and as the temperatures will be the same in the same north and south latitudes on 
a homogeneous sphere of either kind, we may eliminate the unknown quantities 7, 
and /, between two equations of the above form, furnished by the observed values 
of T, on the corresponding parallels of the two hemispheres. Using the tempera- 
tures of the parallels slightly modified from those of M. Dove in Table L, by draw- 
VOL. XXII. PART I. Z 
