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82 PROFESSOR FORBES’ INQUIRIES 
(Plate I.) show that the decrease is least rapid near the equator, becomes more 
rapid afterwards, and again diminishes somewhat less rapidly (or, at least, its rate 
does not increase) in the highest latitudes. 
27. Secondly, The temperature of a given parallel may be considered as com- 
pounded of two distinct temperatures ; that which would belong to a sphere all 
of water placed under the same external heating influences as our globe; and that 
which would belong to a sphere of land in the same circumstances. Or it will be 
more convenient to consider the sphere of water as the normal condition of the 
globe, and the influence of the land as a disturbing effect superimposed upon the 
fundamental condition of an aqueous globe. 
28. Thirdly, As regards the law of temperature on a sphere of water, which by 
the second assumption (27) is to be taken as the basis of our calculation, it 
has been shown in the introductory part of this paper (4), that on those me- 
ridians which pass through one of the great oceans—the Atlantic, for example— 
the decrement of temperature from the equator to the pole follows pretty nearly the 
formula of Str D. Brewster or the simple cosine of the latitude; but when the 
continents are included, it is more accurately expressed by the formula of MavrEr 
or the (cosine)’. These empirical relations are graphically expressed in Plate IIL., 
fig. 2, where the relation is shown between the curve of the simple cosine and 
that of (cos)’ lat. The lower the power of the cosine used (including proper frac- 
tional powers), the more convex is the curve to the axis, or the farther does the 
tropical temperature advance towards the higher latitudes: the higher powers of 
the cosine exhibit a more and more rapid decline towards the middle latitudes, 
while there is a point of contrary flexure, indicating the less rapid rate of diminu- 
tion as we approach the pole.* The character of these two mathematical laws is 
well illustrated by the curve of temperature along the meridians of 0° (or that of 
Greenwich) and 120°E., in the curves of Plate II1., fig. 3, the former representing 
a maritime the other a continental meridian.} The former of these (or the Atlantic 
climate) has the character of the curve which depends on the simple cosine of the 
latitude, the latter (the Asiatic meridian) of some higher power of the cosine. It 
is therefore likely that on an aqueous sphere the temperature will be a maximum 
sensibly at the equator, and will decline on either side according to a regular law 
depending on some power of the cosine of the latitude, and it is moreover pro- 
bable that this power will not differ greatly from unity. Let us, however, consider 
* It is to be well observed, however, that in these mathematical curves the commencement and 
ends of the two curves are wade to coincide. They are merely drawn for the purpose of showing the 
gradation, according to one law or the other, from a given temperature to another given tem- 
perature. A curve intermediate between the two showing the variation of the fractional power 
(cos)?, the upper portion of which is nearly straight, is added for a purpose which will be immedi- 
ately explained (38). 
} The curves are drawn so as to show the general curvature, without following the minor and 
sometimes doubtful inflections. In particular, the tropical part of the water meridian may be con- 
sidered to belong toa longitude a little west of Greenwich, so as to avoid the influence of the African 
continent. 
