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In this we have assumed that V, the intensity of the heat before absorption, is the same at all points of the disc. Laplace, on the other hand, considers that if the sun's atmosphere were removed it would be found to radiate more heat from the regions near the limb than from the centre. He says: "Une portion du disque du soleil transportée, par la rotation de cet astre, du centre vers les bords du disque, doit y paraître avec une lumiere d'autant plus vive qu'elle est aperçue sous un plus petit angle; car il est naturel de penser que chaque point de la surface du soleil renvoie une lumiere égale dans tous les sens." He accordingly assumes that the intensity varies as sec 0. It is, however, more natural to suppose that the sun's surface would behave similarly to other radiating surfaces, in which the inclination of the surface will not increase the intensity, and this is borne out to some extent by the following Table in which we give the values of

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calculated from the

on both hypothesis for every tenth degree of 0:

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This Table shows that down to D 94, or for the most reliable

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part of the curve, the different values obtained on the hypothesis of a uniform radiation agree fairly well together, while even beyond this they compare favourably with those in the second column of the Table. The gradual rise and fall in these values as increases seem to

R.I.A. PROC., SER. III., VOL. II.

2 E

show that the law we have assumed does not exactly represent the radiation, and these results might be brought better together by assuming that, if Vo is the intensity at the centre before absorption, V = V。 (1 − b sin 20) sece-1, in which 6 = 0·322, or better still, if we take V = Vo[1 b sin (20 + a)] seco -1 where b = 0·235, and a = = 20°. Such a law as this would seem to indicate a radiating stratum of limited extent whose temperature increases towards the centre, so that the colder layers on the outside would absorb some of the intenser radiation coming from the interior. It would, however, be unsafe on such slender foundation to adopt such an artificial law of radiation as that represented by the equation just given, and we have preferred, for the present at least, to assume that V = V。 all over the disc.

If we take the mean of the results in the third column of the Table, omitting the last, which rests on observations at the limb, we find

V

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= 1.275. We thus see that a vertical passage through the sun's atmosphere diminishes the intensity of the heat by about 4th of its amount, while at the limb nearly 3rds of it is lost.

In order to calculate how much the total heat is reduced we observe that on the assumption of uniform radiation

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Also the total radiation is, if we put the radius of the sun equal to unity,

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We may also assume 80 = a tan 0, which will represent the refraction very nearly except for values of corresponding to points very close to the limb from which but a very small proportion of the heat If now we put v。 = 1, x = cos 0, and = V, this expression

comes. becomes

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But since the total heat which we should receive if there were no

absorption is me, we find as the proportion (R) of the heat penetrating the atmosphere

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The expression found by Laplace on the same assumption as before

with regard to the local intensity before absorption is feda, which

he shows can be reduced to the continued fraction,

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We have already found = 1.275, whence we obtain ƒ = 0·2429, q = 4.1169, and e-' = 0·7843, and substituting these values in the expression for R we find that it lies between 0.668 and 0-623, or that more than one-third of the sun's heat is intercepted by his atmosphere.

In conclusion, we may observe that if photographs are from time to time taken in the manner here described, and are all reduced in an

exactly similar manner, even though the assumptions made with regard to the laws governing the radiation at the sun's surface do not exactly represent the real state of affairs [and that they are not in error to any great extent seems clear from the agreement found in the values of or, still any variation in the resulting values of R would represent a real change in the absorbing power of the sun's atmosphere, and would thus enable us to detect an alteration in the state of the solar surface which would be wholly masked in direct observations by the varying conditions of the earth's atmosphere under which the observations would necessarily be conducted.

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XXI.

REPORT ON THE BOTANY OF THE MOURNE MOUNTAINS, COUNTY DOWN. BY SAMUEL ALEXANDER STEWART, F.B.S. Edinburgh; and R. LLOYD PRAEGER, B.E., M.R.I.A.

[Read FEBRUARY 22, 1892.]

THE district to which the present Report refers forms the southern corner of the county of Down, and comprises the barony of Mourne, and a strip of the barony of Upper Iveagh. Its north-eastern and northern boundary line may be drawn from Narrow-water, at the upper extremity of the Lough of Carlingford (which separates Down from the adjoining counties of Louth and Armagh), in a north-easterly direction, along the base of the mountains, passing through the village of Hilltown, and by Lough Island Reavy to Castlewellan; thence it runs south-east to Newcastle, where it meets the waters of Dundrum Bay. In other directions a natural boundary is supplied by the Irish Sea, which stretches on the east and south-east, and by Carlingford Lough, which lies to the south-west. The greatest length north and south of the district thus enclosed is 13 miles, and its extreme breadth east and west 16 miles; its area is 180 square miles, or somewhat less than one-fifth of county Down, and about one-seventeenth of District 12 of the "Cybele Hibernica."

The Mourne Mountains, which form the highest and finest mountain-range in Ulster, and (excepting some of the lower hills of Antrim) the most easterly highlands of Ireland, occupy almost the whole of this area, stretching in a broad ellipse east-north-east and west-south-west, and at each extremity descending steeply into the sea. Southward, a tract of flattish cultivated land slopes gently from the mountains to the water, terminating in the low sand-dunes of Cranfield Point. On the northward, our boundary line keeps close to the base of the hills, rising from sea-level at each end to some 600 or 700 feet on the watershed east of Hilltown.

The highest peaks of the range, and all the more interesting mountains, lie towards the eastern extremity, the culminating points being Slieve Donard (2796 feet), Slieve Commedagh (2512), Slieve Bingian

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