Proceedings of the Royal Society of London

micrometer.

The reason for not forming a direct image with a lens was the varying transparency of glass for radiation at different temperatures; the mirrors also enabled us to "dilute" the heat considerably, and so obtain convenient direct deflections on the radiomicrometer scale.

The sketch (fig. 6) shows approximately the shape of the image formed, on a scale about two-thirds full size.

FIG. 6. Image of the carbons from a tracing. A represents the size of the aperture by which radiation reached the receiving-surface.

The mirror, M2, being provided with adjusting screws, it was easy to bring any part of the image, either of the carbons or the pale violet glow of the arc itself, on to the small aperture, the deflection on the scale of the radio-micrometer then giving readings proportional to the radiation from the chosen point.

Magnified to this extent, however, the arc was never steady enough to allow a detailed "mapping-out" of the carbon surfaces with regard to temperature. Even when the light is apparently steady to the eye, the violet arc itself often shifts its position, while the - pole continually alters in shape from the carbon deposited on it, which causes a bulbous excrescence, somewhat as shown in fig. 7, to form gradually.

When this is the case, the arc naturally strikes across from some such position as A to B; B then becomes, as might be expected, much hotter than any other part of the pole.

As an example of the kind of difference existing between the two poles, the following figures may be given; they correspond to the hottest obtainable point in the crater of the + pole, and to the hottest point on the pole, before any excrecence has had time to grow.

The numbers are scale divisions on the scale of the radio-micrometer, and therefore represent the radiation in arbitrary units:

so that the radiation from the hottest part of the + pole was about three times as great as that from the hottest part of the

pole.

Taking the temperature of the former as 3300° C., this would give

a temperature of about 2350° C. for the latter.

In a case where a "blob" had formed on the the following readings were obtained :

pole, as in fig. 7,

+ pole. Radiation 570, 560, 56.6, and 55·5
Mean 56.3

- pole. Radiation of hottest part = 38.3.

Again, taking 3300° C. for the former, this gives about 2700° C. for the latter, or 350° C. higher than that of the

the arc is started.

pole just after

We may say, then, that if the temperature of the crater is about 3300° C., that of the carbon is ordinarily about 2400° C. in its

hotter parts.

As for the temperature of the arc itself, we can say nothing. Allowing the pale violet glow between the poles to fall on the aperture of the radio-micrometer, we obtained deflections of from 1 to per cent. of those obtained when the hottest part of the crater was used, which seems to indicate a comparatively high radiative power for the hot gases which lie between the carbon poles.

Note on the Effective Temperature of the Sun.

In the authors' work on this subject, radiation experiments were made with bare platinum, at temperatures up to 1600° C. approximately, and it was assumed that a formula of the same form as expressed these results would also hold for a blacked surface, while the ratio of the emissive powers at high temperatures was taken on Rossetti's authority as about 2.9.

The new work, given above, appears to show that the curve for' the black surface does not, however, follow a simple fourth-power law so closely as does that for the bare platinum, and that, taking the law as given on p. 31 of the present paper, a correction must be made to the result obtained by the earlier work.

The approximate value of this correction may be obtained by taking the figures given as a typical case on p. 386 of last year's paper, and applying the new law to them.

In this case, the corrected ratio (i.e., the ratio corrected for atmospheric absorption, and for loss by reflection from the glass of the heliostat) of the apparent areas of the bare platinum and the sun was approximately 1295: 1, and balance was obtained with the platinum at a temperature of 1514 Abs.

Now by the formula on p. 31, the radiation of bare platinum at this temperature

= a. 15143+b. 1514 -0.27 = 311.77

a and b having the values given on p. 31.

The radiation from the sun therefore

= 1295 × 311.77 = 403,450.

To find the effective temperature of the sun, we have, therefore, to solve the equation

403,450+46 = aT3+bT1,

where a and b now have the values corresponding to the curve for the black surface. This gives T 7800° Abs., approximately, instead of

7000°, as given by the older method of working.

That is to say, supposing the new formula to be correct, our estimate of the solar temperature would have to be increased by something like 800°.

If, however, the ratio of the emissive powers approaches a constant value, as the figures and curves on p. 32 make possible, the expression for the curve of the black surface would be somewhat altered, in such a direction as to reduce the correction, so that we may say finally that, taking Angström's estimate of the atmospheric absorption, which gave in our former work an effective solar temperature of 7400° C., its more probable value would now be not very far from 8000° C.

"The Stresses and Strains in Isotropic Elastic Solid Ellipsoid in Equilibrium under Bodily Forces derivable from a Potential of the Second Degree." By C. CHREE, M.A., Fellow of King's College, Cambridge, Superintendent of Kew Observatory. Communicated by Professor W. G. ADAMS, F.R.S. Received March 2,-Read May 10, 1894. Abridged February 20, 1895.

General Formulæ.

§ 1. Let the isotropic elastic solid ellipsoid,

a2x2+b2y2+c22 = 1

....

(1),

of uniform density p, be acted on by bodily forces whose components Px, Qy, Rz are derivable from a potential

V =

(Px2+Qy2+ Rz2). . . . . . . . . .

(2).

Let II denote the determinant

3b*+2b2c2+3c1,

c1—n (b2c2 + c2a2+3a2b2), b1-n (b2c2+3c2a2+a2b2)