^{page 76 note *} The Distribution of Heat over the surface of the Globe, &c. Plates IV. and V. 4to. London, 1853.

^{page 77 note *} The Distribution of the Heat of the Globe, &c, p. 13, &c. London, 1853. [The same work was published in German at Berlin. In point of fact, the annual mean temperatures of the parallels are derived by M. Dove from the average of the twelve months separately considered, and projected in monthly isothermal lines. It would probably be preferable to deduce them from the annual curves alone, which rest on a surer basis.]

^{page 77 note †} See his “Five Memoirs” in the Berlin Transactions, “Ueber die nicht periodischen Aenderungen der Temperatur vertheilung aufder Oberfläche der Erde,” and his “Temperature Tables,” in Report Brit. Assoc., 1847.

^{page 79 note *} It is by no means an easy matter to deduce the mean temperature of a given parallel correctly from an isothermal chart. What precise method M. Dove adopted I am not aware. After various attempts, I found the following procedure to be the only satisfactory one. Taking eighteen equidistant meridians (20° apart), I projected the temperatures indicated by the isothermal lines as perpendiculars erected on a straight line at intervals corresponding to the latitudes at which they intersect the given meridian. An interpolating curve being drawn easily among the extremities of these perpendiculars, the abscissæ corresponding to every 5° of latitude are ascertained and tabulated. The mean of these numbers, taken round the whole circumference, gives the required number for each parallel. I think it worth while to preserve the numbers I have obtained, which are given in the following table, as they may be of service in future inquiries. I may here add, that the character of the climatic gradation in different latitudes is highly instructive. The curves of temperature corresponding to oceanic meridians, such as that of Greenwich, are everywhere decidedly concave to the axis (representing a variation depending nearly on the simple cosine), while those of the continents, such as longitude 120° E., tend to become convex towards the axis in the higher latitudes (inclining to the law of the (cosine)²), or else they form almost a straight line sloping towards the pole. This is in conformity with what has already been said in par. 4. See also par. 28 below.

^{page 80 note *} The great simplicity of the formula (par. 18) turns upon the accidental circumstance of the zero of Fahrenheit's scale so nearly coinciding with the temperature of the pole, as Sir D. Brewster long ago remarked. The formula would represent the numbers of M. Dove slightly better if a small constant term were introduced; thus, T = 1° + 80° cos² (λ−6° 30ʹ), and in using any other thermoinetric scale this might be preferred. This formula becomes

T = −17°·2 + 44°·4 cos² (λ − 6° 30ʹ) on the Centigrade scale.

T = −13°·8 + 35°·5 cos² (λ − 6° 30ʹ) on Reaumur's scale.

^{page 82 note *} It is to be well observed, however, that in these mathematical curves the commencement and ends of the two curves are made 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 temperature. A curve intermediate between the two showing the variation of the fractional power , the upper portion of which is nearly straight, is added for a purpose which will be immediately explained (33).

^{page 82 note †} 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 considered to belong to a longitude a little west of Greenwich, so as to avoid the influence of the African continent.

If it were practicable to go into such details, it is probable that the influence of continents might be more accurately expressed by a different law from one depending on their simple breadth. A narrow land with ocean on both sides will have a slighter peculiarity of climate than if it were attached to a wide continent, and partook of a thoroughly continental character. In like manner, if ninety-nine hundredths of the circumference of the globe in any parallel were land, the small residue of ocean would affect the continental character of the climate even less than in proportion to its small extent. Let the circumference of the globe in any parallel be denoted by the line AB ( = 1); the fraction representing the land on the parallel by the abscissa AM ( = L); let. also, BC express the extreme value of the term which expresses the effect of land on the temperature of the parallel; then, for any value of L less than unity, the magnitude of the temperature-correction due to land would not be MN but Mn, which increases slowly when L is very small or very great, and most rapidly when L = ½. Such a co-efficient might be adequately represented by such a function of L as

But such a mode of calculation would be perhaps a needless refinement, as we should have to take into account not only the sum of the land in the parallel, but also its continuity, or the contrary.

^{page 84 note *} It may he satisfactory to add, that the results obtained by using M. Dove's numbers without any modification lead to an almost identical result when the same latitudes are employed.

^{page 85 note *} Thus treated, the numbers of Table II., par. 22, give the following results:—

^{page 88 note *} I employ the “equalized” mean values of Land and Water on three adjacent parallels as in the footnote to par. 32, where the footnote these numbers (for the proportion of Land) are designated as Lʹ. But it is worthy of notice that the simple numbers given in Tables I. and II., both for temperature and amount of land, would lead to nearly the same results.

^{page 89 note *} It will be recollected that the change of sign was made to coincide with 45°, merely for the purpose of simplifying the formula. (See par. 31.)

^{page 90 note *} “Up to 40° south latitude the temperature of the southern hemisphere is lower than that of the northern; this may not be the case in higher latitudes.” Dove,—The Distribution of Heat, &c., p. 15.

^{page 91 note *} Among other tests to which I have put my hypothesis, I have calculated what ought to be the magnitude of the coefficient Lʹ in the third term of the formula, so that it might in each parallel represent the numbers of Dove (Table I.), supposing the other constants of the formula to be exact.

^{page 93 note *} I have been unable to verify the reference to “London's Magazine of Natural History” for this entry.