ANNALS

OF

PHILOSOPHY.

AUGUST, 1824.

ARTICLE I.

Remarks on Solar Light and Heat. By Baden Powell, MA. of Oriel College, Oxford, and FRS.

(Continued from vol. vii. p. 406.)

(27.) In the conclusion of a former paper I alluded to some further experiments which were to follow, relative to the question of the proportion obtaining between the heating and illuminating effects of the solar rays. The method of experimenting alluded to is one which I have not been able to apply to any extensive series of different intensities. It consists in compar ing the effect produced on a blackened thermometer by the focal light of different lenses, with the relative calculated intensities of the rays in those foci. Thus we may ascertain whether at these high intensities the same proportion is maintained. Without proof we cannot assume that it is; and a very few comparisons may be sufficient to show, whether the proportion is nearly preserved, or whether there be any considerable deviation from it.

(28.) When thermometers are exposed to the action of radiant matter there are several considerations to be attended to in comparing their observed risings; and it will be convenient in the first instance to bring these considerations into one point of view.

A thermometer exposed to radiant matter absorbs heat only on one-half of its surface, while the other half is radiating again its acquired heat, and the observed effect depends upon the equilibrium which obtains between them. In particular cases only part of one surface may be exposed to heat: the difference. between such part and the whole surface, together with the absorbing and radiating powers of the surface, must, therefore, be taken into consideration, as also the rate of communication of heat dependent on the mass.

New Series, VOL. VIII.

G

Let the portion of the surface of the bulb exposed to

The observed rise in a given time

The power of the coating for absorbing heat (of what

ever kind).....

And for radiating it..

The intensity of heating power

And if the coating be the same, it = 1⁄2, and if h =

and if h=h, it = 1.

When the whole bulb is exposed, we have

k

If in this last case the thermometers be exposed to simple radiant heat, assuming the universality of the law, that the absorptive is proportional to the radiating power of a surface, we shall have

Or hence we might derive a neat and simple method of verifying that law.

The relative values of p and k as compared with a surface of glass in particular cases, may be obtained by coating only half

the surface of the bulb, and exposing either the plain or coated side to the same intensity of heat. The ratio may be obtained

by heating two bulbs completely coated to the same point, and observing their rates of cooling.

The case (C) is the same as that investigated in the Phil. Trans. 1800, No. 19, note, p. 447.

(29.) Comparison of the Focal Effect of Two Lenses on a Thermometer coated with Indian Ink.

In order to proceed to this comparison, we must first observe, that when in the formula we take a . d, it is on the supposition that parallel rays impinge on a spherical surface. With the focus this is not the case, and from the convergence of the rays, as well as from their greater intensity at the outer edge, we may in this case assume, without fear of error, that a = the area of the section of the rays impinging, and thus apply the formula. Thus we have the following data:

10, r 31: it is also By measurement, the diame

From the above experiments, r1 = evident, that p = p1 and k = k1. ters of the focal disks were:

and we have to apply the case of the formula (B)

(30.) In order to calculate the respective intensities of light, or number of rays collected in the focus of each lens, we may easily proceed by the well-known theorem,

I, and I,

Let d

diameter of aperture,

f focal length of lens, No. 1. And d', f', those of lens, No. 2.

the respective intensities of the rays collected in

the sun's image, or focal luminous disk.

By measurement I found

In Lens, No. 1, d = 3·25 in. ..d2 = 10·56,

f = 7:5

..f=56.25,

In Lens, No. 2, d'1.75 in...d2 = 3.06,

I
Hence =
I'

f = 3

=

1

172-12 1.81 nearly.

If we admit the validity of certain experiments which seem to prove the existence of an exterior heat surrounding the luminous cone of rays, this would affect the bulb in each case by a small quantity in addition to the direct effect of the light. But since the total effect has been shown to be very closely in proportion to the intensity of focal light, it would follow that this exterior heat must be in extent, or in energy, exactly in the same proportion, supposing its absolute value sufficiently great to produce a perceptible effect.

These experiments prove for the two particular intensities under examination, that the proportion of heating to illuminating. intensity is closely maintained. It might be satisfactory to extend the comparison with lenses of other powers, qualities, &c. but as the above result is not of a nature which requires the admission of any new principles, and agrees with what we should be prepared to expect, I conceive it unnecessary at present to carry the examination any further.

(31.) With a similar object in view in some subsequent experiments, I employed such a difference of intensity as is afforded by two sections of the luminous cone formed by a lens, one being made near the lens, and the other near the focus.

In two such positions, one, at inch from the lens, the other near the focal point, or at about seven inches distance, the thermometer, blackened as before, was placed successively. The rise in 30 seconds was (mean of three trials),

At inch from lens.
Near focus...

2o = r

40

To obtain the proportions of light in the two cases, I measured the diameter of the luminous circle formed by the larger section when the rays were intercepted by a plane at the distance of one-quarter of an inch below the lens. The diameter was very nearly 2.8 inches d, whose square = 7·84; the diameter of

the bulb (as before) 0:45 inch; the diameter of the section near the focus d1 = 0·3 inch; its square

⚫09.

In order to obtain the true ratio of the heating effects, we have to apply the case of the formula (B). By experiment, we have by measurement a, = 0706.

T

= 20

Here also the case of the formula (C) applies, and we have

s-a

a

= 2; thus on the whole since p = P1, and k = k1

Hence also we have for the intensities of light in the two

In obtaining this ratio, however, there are evidently several sources of error; the loss of many rays before they arrive at the focus; the less intensity towards the central part of the cone (where the thermometer was placed), on these, and, perhaps, other grounds, it would be necessary to reduce the ratio obtained.

The former ratio (as also in other instances) is subject to some uncertainty, owing to the difficulty of observing accurately the rise of the thermometer under the strong impression of focal light; but upon the whole it is evident that here also an equality of ratio may be inferred as nearly as the nature of the operations will allow.

If there be an exterior heat about the focus, this should affect the above ratio; but since the proportion obtaining is very close, we may infer that the ratio of the intensities of light is really greater than that of the heating effects, but that the proportion is preserved by the sum of the heating effect of the focal light, together with the exterior heat. The above experiment cannot be considered sufficient to enable us to determine such a point, but I hope shortly to be able to give it a more complete examination,

(32.) In like manner we might proceed to compare the effects of the rays in their natural diffuse state, and when brought to a focus, if we had any tolerably accurate method of allowing for the quantity of light lost in passing through the lens, and in not converging accurately to the focus. The former datum might, perhaps, be supplied from Sir W. Herschel's determination (Phil. Trans. 1800), and the latter we might probably estimate by successively diminishing the aperture till the focal effect on the thermometer becomes diminished. The least aperture with which it continues undiminished, compared with the whole, would give nearly the proportion of rays brought to the focus. (33.) In the preceding instances we have compared the pro