64, 65 Mr. WATERSTON: on Solar Radiation. The entire bulb of the thermometer thus raised 3°.045 is thus equal to 1 cub. in. of water raised 0169 +0391 = 0°.056. Now, the transverse section of bulb is o138 square inch; and since specific gravity of ice is o'93, and it requires 140° to melt ice, we have 140 x 0738 × 0·93 × x = 3*045; hence x= 0.00312 inch, the thickness of ice melted by the Sun in 100 seconds, when r = 10°. This is equivalent to 0.001872 inch in 1 minute. With 20° the thickness would be double this amount, and so on. Thus the presumed extra atmospheric value of r being 67° gives oo124 inch thickness melted per minute. From June to December the amount may be expected to varyth, corresponding to alteration of Sun's distance. In Herschel's Meteorology the probable thickness is stated to be 0109 inch. If the law indicated by straight lines on the chart is true it would require extremely accurate observations to give the extra atmospheric constant of solar radiation with precision. From a single observation made in Bombay some years ago I am disposed to believe it may exceed 67° considerably. The mode of approaching the law of absorption is as follows:- Project the values of r as ordinates to the secants of zenith distances as abscissæ. The resulting curve is evidently hyperbolic in character. If it is the conic hyperbola, the reciprocals of the ordinates laid off to the same abscissæ should range in a straight line. The obvious plan is, therefore, to lay off the reciprocals of r in this way, and see how far their range agrees with the straight, and, if it differs, the character of the divergence might lead us to the true function that expresses the natural law, if it was not very complicated, and if the condition of the atmosphere did not vary so rapidly as to obscure it. The observations, though taken under unfavourable condi tions, favour the simple hyperbola. It will be remarked, on inspecting the chart, that the value of at the same altitude of the Sun diminishes with the declination as the season advances. If continuous observations were possible for a few hours each day, when the altitude of the sun ranged between 15° and 45°, we might expect to see the projection of the equalised observations range each day in a different line; but these lines ought all to converge on nearly the same point in the ordinate at the zero of the secant scale, if the law holds good. The lines A C, A D, A E, will exemplify this. Let N, fig. 3, be the position of the observer, z his zenith, Ꮓ 65,66 and NS the direction of the sun. Draw parallel lines a b, c d, &c.; now a cbd rad.: sec. sun's zenith distance, so that the thickness of each stratum varies as the secant; and if the physical condition of the stratum did not alter between two observations, we may take the secant as the representative of the collective thickness of the absorbing medium traversed by the Sun's rays, except at such low altitudes when the curvature of the earth as well as refraction may be expected to introduce uncertainty. The mini a Fig. 3. mum value of the secant is radius, but we may imagine the Sun's rays to pass through a similarly constituted atmosphere in which the thickness of the same layers proportionally diminishes from unity or radius to zero. The reciprocal of r diminished for values below radius at the same rate as for values above radius, attains at zero the extra atmospheric limit which, in all climates and seasons, ought to be determined by the inverse square of our planet's distance from the Sun in its orbit, and should not vary beyond th of its mean value. Le m, m,, be the secants at which the radiation is r。, r,, we have, according to the projection =k, a constant mo m I I Thus the Sun's rays, in passing through a constant element of the thickness of the atmospheric medium, loses a proportionate amount of its power that is not constant, but that diminishes in the simple ratio of that power. As an example, suppose with r = 30°, the value diminishes 1° in passing through 1 mile, it would only lose in passing through the same mile if r = 150, andth of a degree if r = 1°. We might thus expect, when the atmosphere is clear, it does not intercept any sensible proportion of the heat radiated from the earth's surface into space. Compare the value of r with one Sun and with two; the supply from each, supposed equal, doubles the value of r, which, measured at the extremities of the mile nearest and furthest from them, shows that for the same element of the thickness of the medium the proportionate decrement of r is constant. Let a represent the angular space occupied by the Sun's disk, and the potential temperature of its radiating surface, then ta represents the supply of heat by radiation from it upon a unit surface, and is measured by r, so that if a t becomes 2 at, r becomes 2 r. Now, the factor 2 may have reference to a, the magnitude of the Sun's disk, or it may have reference to t its temperature. The fluctuating value of r from change of altitude or climate represents a fluctuating potential value of 67,69 Mr. WATERSTON: on Solar Radiation. The heat-pulse travels, carrying with it an intensity that it borrows from the temperature of its source, and encounters a deflecting or absorbing power in passing through a constant element of the atmospheric medium that is exactly proportional to that intensity. It would be simpler if the resistance was uniform,- if the proportion of force absorbed was constant; but the observations do not admit of the possibility of this. The curve traced out by the co-ordinates, r and secant zenith distance, would in that case be no longer the conic hyperbola, but the logarithmic curve. At 6 o'clock in the evening of the 31st July, while making an observation, an extensive shower of thin rain took place overhead and westward towards the Sun, without sensibly obscuring its light or affecting its image when examined through a telescope. The value of r descended immediately from 15° to 13°. The single observation I took in India, compared with those taken at the same altitude in this country, indicates that the value of r is there fully double what it is here, while the quantity of vapour held in suspension estimated from the dew-point is certainly greater. It would seem probable, therefore, that the absorbing power of the atmosphere depends on the watery particles contained in it, not upon the aqueous vapour dissolved in it. [The Appendix, received simultaneously with the foregoing, is printed infra.-ED.] 26 Royal Crescent, Edinburgh, Nov. 25, 1861. Explanation of the figures. 69, 70 Fig. 1. T, U, B, E, is a square tube of brass, mounted with motion in altitude upon an upright, R, fixed into a round slab of lead. The inner surface of this tube is blackened, and at each end, at l and c, a film of transparent talc was stuck on to prevent the wind from moving the air within the tube. H, D, D, H, a double screen made of cardboard and cork, coated on both sides with tin-foil, and fitted to slip on the extremity of the tube presented towards the sun. m, the hole in centre of screen, about th inch greater diameter than the bulb of the solar thermometer, X. The tale film, l, was also coated with tin-foil except the central circle. X, the thermometer in sun with spherical bulb fixed in a cork that fitted the hole, L, L, in top of brass tube. Y, the thermometer in the shade fixed in the hole, N, N, with cork and soft wax as shown. z, a thermometer applied to outer surface of tube. Fig. 2 is a transverse section of vacuum bath, employed to ascertain the rate of cooling of the solar thermometer, x, in air and in vacuo. It consists of a cylindrical vessel of brass, coated internally with lamp-black; the lid, L, is ground to the upper edge of the cylinder, and in its centre is a stuffing box, s, with Indianrubber collar, through which the stem of the thermometer is passed, as shown in the figure; c, is a stop-cock, upon which, N, the nozzle of a flexible tube communicating with an air-pump, is ground air-tight. H is a wooden handle for removing the apparatus to and from the bath without touching the metal. VOL. XXII. January 10, 1862. No. 3. Dr. LEE, President, in the Chair. The Rev. Thomas Pyne, Hook, near Kingston-on-Thames; John Kidd, Esq., Sherborne, Dorset; and were balloted for and duly elected Fellows of the Society. An Account of Experiments on Solar Radiation.-Appendix describing the Method employed to discover the Influence of the Air in the Cooling of the Sun Thermometer X., and of Ascertaining the Correction required to be Applied to Observations of r, so as to reduce them to a Vacuum. By John James Waterston, Esq. Fig. 2 is an upright section of the little apparatus or vacuum-bath. It consists of a cylindrical vessel of brass * See Plate; the scale of fig. 2 is 1 in. = 4 in.—ED. coated internally with lamp-black. The lid was ground airtight to the upper edge, and had a stuffing-box in the centre, through which the stem of the thermometer was passed. A stop-cock enabled a communication to be made with an airpump. With a plentiful supply of lard to the stuffing-box and ground surfaces, a good vacuum could be maintained for a day unimpaired. The time was measured by the beats of a clock: to register the number of these at each degree as the mercury of the thermometer descended, a scale of equal parts was prepared extending to 1000, and with distinguishing marks at each 5, 10, 50, and 100. Then with a pencil in the right hand over the scale and a magnifying glass in the left over the scale of the thermometer, I counted the beats, and when the mercury came to the line of a degree, made a mark on the scale of equal parts opposite the number of beats, and at the same time continued to count on; e. g. if 57 was the number when the mercury came to a line, a pencil-mark was made at 57 on the scale of equal parts, and the counting went on,-58, 59, &c. until the mercury came to the next line. Thus, not a beat was lost from beginning to end, and the accuracy was only limited by the accuracy of the divisions on the scale of the thermometer. Indeed, this method is a severe 70, 71 Mr. WATERSTON: on Solar Radiation. test to the equality of the divisions, because the reciprocal of the differences in the number of the beats for each degree, if laid off as ordinates to the total number of beats, ought to range in a straight line, and any saw-like irregularities indicate inaccuracy in the divisions of the scale of the thermometer. To heat the bulb of the thermometer a funnel was placed over the small flame of a Bunsen; then holding the plate (having the thermometer fixed in its place) by means of the stop-cock, the bulb was brought over the top of the funnel until the mercury had risen to near the top of the scale. The plate was then quickly placed on the cylinder, communication made with the air-pump, and the air exhausted from the cylinder by 20 strokes, the capacity of the pump being about one-third that of the cylindrical vessel or vacuum-bath. vessel thus exhausted was placed in a water-bath, the temperature of which was ascertained at the beginning and end; the difference seldom amounting to th of a degree. The The following table exhibits two series of observations on the cooling of the sun thermometer, x, in the vacuum, and in air taken while the water-bath remained steady at 48°. This basal temperature being at an exact degree enables the rate of cooling to be studied easily without fractional parts or interpolation: 71, 72 we have 594 beats 298" Difference 296 Mean Difference 291 286 12 "" r = 28 99 119 19 r = 9° we have 484 beats r = 18 1st Difference 240 217 2d Difference 23 1st Difference 230 T. 254 44 2d Difference 20 210 36 3 24 Thus, it appears that in air the cooling takes place in a ratio greater than r, the 1st difference of the times diminishing and the 2d difference slightly increasing between 247 and 210. The limiting value of the 1st difference must be 294 when r = 0, and 294 minus the 1st difference increases nearly as √r. An empirical formula constructed in conformity with this ratio cannot differ much from the observations. Let A represent 1st difference and g a constant, Mr. WATERSTON: on Solar Radiation. - log (r, — 0°•1)} Nra = 1 17 131 Hence r, may be ascertained by inspecting the differences of a table of logarithms; and it was from these that a scale was constructed for reducing the values of r taken in air to what they would be if taken in a vacuum, where the emission of heat was by radiation alone. The cooling of the sun thermometer in air when fixed in its place in the tube, as in fig. 1, was found to be exactly the same as when fixed in the cylinder, fig. 2, unexhausted. A chemical thermometer with cylindrical reservoir was 73, 74 tried in the vacuum-bath, and the cooling was found to take place exactly in the logarithmic curve. It is difficult to adjust the vacuum-bath in time to observe a high value of r, but good observations were obtained from r = 190° downwards; so there is little doubt that the law of cooling by radiation is general and independent of the shape of the cooling body. I purpose extending these observations with different surfaces. One result is interesting, as showing the perfect reciprocity of the radiation, viz. a gilt bulb radiating against a blackened metallic surface loses heat at the same rate as a blackened bulb against a bright metallic surface; the rate being slower than when both are blackened. Another fact that it is well to keep in view is that, although the uncoated glass bulb radiates as quickly as the same coated with black, it does not absorb the incident rays of heat to the same degree; nearly one half being reflected without entering the glass. Aug. 6 8 7 A.M. 16.2 19'1 6.6 9 8 18.0 21.2 7'7 25°7 28.9 cosec. have found on trial. Now the potential temperature being equal to the product of r by the reciprocal of the angular space occupied by the flame, it is in the one case about five times greater than in the other. In the same way we might compute the potential temperature of an angular space occu1484 pied by many thousand flames placed one behind the other, extending in a line from the observer, and probably we should find it cumulative in the ratio of the number of flames. 1'926 *0389 31 17 *0346 42 21 9 32 18.3 21.6 8.0 29.6 *0338 45 12 I'409 Note. Referring to the method of computing the Sun's potential temperature, described in the proceedings of the Society for March 1860, and employing the same rule with R, the extra atmospheric value of r equal to 70° at Earth's mean distance, we arrive at 12,880,000° as the potential temperature of its radiating surface. If we expose the flame of a bat's-wing-jet to one ball of a differential thermometer, the effect is the same, whether the broad side or the narrow side of the flame is presented, as I From observations I have made on gas flames with the radiation meter, fig. 1, it would seem to require about 4000 bat's-wing-flames ranged behind each other to give a potential equal to that of the Sun. If the upper radiating matter of the Sun is in any degree transparent or permeable to radiation from lower strata, it is obvious that the actual temperature may thus be much below the potential. 26 Royal Crescent, Edinburgh, November 25, 1861. |