One point still remained to be cleared up. According to the calculation I have been speaking of, in order that the surface may be diminished by the kind of transformation here indicated, it is sufficient that the sum of the lengths of an expanded and contracted part of the figure should exceed the circumference of the cylinder; and this allows us to attribute to this sum an infinite number of different values. But nevertheless, as has been shown in the Second Series, in a cylinder that is very long relatively to its diameter, when the transformation takes place quite regularly, the sum in question is always the same for the same cylinder under the same circumstances, whence we must infer that there is some special condition which regulates the choice of the mass. We may add that analogous considerations apply to the other unstable figures. I examine the matter, and arrive at the following as a very probable conclusion :-that, among all possible changes of shape which would diminish the surface, the molecular forces choose that one which allows the smallest possible departure of the mass from another figure of equilibrium. In the cylinder, for example, the mass will assume at the beginning of the transformation the figure which, considering the resistances, makes the nearest possible approach to the unduloid.

The combination of liquid films, which I have studied particularly in my Sixth Series, likewise presents some remarkable phenomena in relation to their stability. I tried to establish experimentally that every equilibrated system of films in which more than three films meet at one liquid edge, or more than four liquid edges at one liquid point, is an unstable system. M. Lamarle has since discussed the question in detail in his memoir "On the Stability of Liquid Systems formed of thin Films." Setting out from the general principle that I had laid down at the end of my Sixth Series-namely, that in every permanent assemblage of films the sum of the areas of the films must be a minimum, he succeeds in giving a strict demonstration of the conditions above mentioned relatively to the number of films and of liquid edges; and he arrives besides at many other interesting results.

Lastly, I recall the fact that M. Duprez, in his memoir "On a particular case of the Equilibrium of Liquids," has investigated a phenomenon in which the stability or instability of a liquid surface depends conjointly on the action of gravity and of molecular forces. The phenomenon referred to is the familiar one of the suspension of a liquid in a vertical tube open at the lower end when the diameter of the opening is below a certain limit; but M. Duprez has shown that this limit is much greater than was generally supposed. He has held up water in this way in a tube the diameter of whose opening was 19.85 millims.; while

the theory founded upon the conditions of stability of a liquid surface gave him 21.13 millims. as the exact value of the limiting diameter.

I conclude by pointing out that all my Series together, counting from the second inclusively, establish the Experimental and Theoretical Statics of Liquids acted on solely by Molecular Forces. The present Series is followed by an analytical index to the contents of the eleven Series.

XLVII. Proceedings of Learned Societies.

ROYAL SOCIETY.

[Continued from p. 308.]

June 16, 1870.-General Sir Edward Sabine, K.C.B., President, in

Although in the measurement of small quantities of radiant heat by means of the thermopile much may be done towards increasing the sensibility of the apparatus by carefully adjusting the galvanometer and rendering the needle as nearly astatic as possible, there must necessarily be some limit to this; and it therefore appears desirable that the principles on which thermopiles of great sensibility can be constructed should also be carefully attended to.

With the view of obtaining a pair of thermopiles of greater sensibility and of more equal power than I had been able to procure ready made, I made a few experiments with various forms of that instrument; and I was led to the conclusion (one which might have been foreseen) that the sensibility of the thermopile is much increased by reduction of its mass, and more especially by a diminution of the cross section of the elements.

To obtain a clear idea of the problem before us, which is how to construct the thermopile so that, with a given amount of radiant heat falling on its face, the greatest current may be sent through the galvanometer, let us consider the thermopile under two different conditions: :

1. With the circuit open.

2. With the circuit complete.

In the first case, when radiant heat falls on the face of the pile, the whole mass of metal rises in temperature, the rise being greatest at the anterior face, and less and less as you approach the other end. This rise of temperature will increase till the heat radiated from the anterior face, together with that which traverses the depth of the pile and is radiated from the posterior face, is just equal to that radiated to the anterior face at that moment, or when

where (t, t') are respectively the temperatures of the anterior and

and in more experienced hands their construction would be still easier.

An experiment was made with one of the piles to ascertain whether, when the heat was not directed centrally on the pile, much diminution of power would take place. There was less deviation, in consequence of the increase of the mean distance which the heat had to travel before it reached the soldering; but I believe that this defect might be remedied, probably without diminution of the power of the pile, by increasing the thickness of the face and leaving the dimensions of the bars the same.

"On the Radiation of Heat from the Moon.' -No. II. By the Earl of Rosse, F.R.S.

In a former communication to the Royal Society I gave a short account of some experiments on the radiation of heat from the moon, made with the three-foot reflector at Parsonstown, during the season of 1868-1869. I then showed ::

1st. That the moon's heat can be detected with certainty at any time between the first and last quarter, and that, as far as could be ascertained from so imperfect a series of observations, the increase and decrease of her heat with her phases seems to be proportional to the increase and decrease of her light as deduced by calculation*.

2ndly. That a much smaller percentage of lunar than of solar rays is transmitted by a plate of glass; and we therefore infer that a large portion of the rays of high refrangibility which reach the moon from the sun do not at once leave the moon's surface, but are first absorbed, raise the temperature of the surface, and afterwards leave it as heat-rays of low refrangibility.

3rdly. That, neglecting the effect of want of transparency in our atmosphere, and assuming, in the absence of any definite information on the subject, that the radiating-power of the moon's surface is equal to that of a blackened tin vessel filled with water, the lunar surface passes through a range of 500° F. of temperature; consequently the actual range is probably considerably more.

4thly. The proportion between the intensity of sunlight and moonlight, and between the heat which comes from the sun and from the moon, as deduced from those observations, agreed as nearly as could be expected with the values found by independent methods, and for this reason might be considered the more reliable.

During the past season these observations have been continued: but much time has been spent in trying various modifications of the apparatus; and a satisfactory comparison of observations made on different nights, under different circumstances, has been impossible. However, by more numerous and more complete experiments, made alternately with and without an interposed plate of glass, the second conclusion arrived at during the previous season has been to a great extent confirmed.

The following Table gives the values found for the percentage of the moon's heat which passes through glass :

:

* See Phil. Mag. vol. xxxviii. p. 317.

The same plate of glass which was used in I. and II. on April 15th, and in the experiments on the two following nights, was tested for the solar rays, and the following values of the percentage of heat transmitted were obtained :

The piece of glass used on the other occasions, instead of being placed at six or eight inches from the pile, was laid against the end of the protecting cone, or about half an inch from the face of the pile. When it was placed in this position and tested for solar rays, an increase of deviation in the proportion of 1.1 to 1 was obtained, owing to the "bottling up" of the sun's rays as in an ordinary greenhouse, and the keeping off of currents of air.

It seems therefore to be clearly proved that there is a remarkable difference between the sun's and the moon's heat in regard to their power of passing through glass. The amount transmitted varies from night to night; and in the later observations the value was generally larger than in the earlier ones. Possibly this may have arisen from the formation of a slight and imperceptible film of moisture on the surface of the glass, which was much more unlikely to form during the much shorter period* of exposure to the night air in the later observations.

* About 12 minutes in place of 30 to 60 minutes.

The experiment made during the previous season to determine the ratio between the heating-power of the moon and of the sun was repeated with more care; and the value found, taking what appeared to be the most probable mean heating-power of full moon, as determined on various nights, was

Taking the percentage of light transmitted by glass* =92

and luminous rays present in the moon's radiant heat, and

the corresponding quantities for the sun's radiant heat,

In all the foregoing experiments on lunar radiation the quantity measured by the thermopile was the difference between the radiation from the circle of sky containing the moon's disk and that from a circle of sky of equal diameter not containing the moon's disk; we have obtained no information in reference to the absolute temperature of either the moon or the sky.

The following experiment was therefore made with the view of trying to connect the radiation of the sky with that of a body of known temperature. The deviation due to each degree (Fahrenheit) difference of temperature between a blackened tin vessel containing hot water and subtending a given angle at the pile and a similar vessel containing colder water was first ascertained; then a similar determination of that due to the difference of radiation from one of these vessels, and from a portion of sky of equal diameter, was made. The following was the result::

* All these values, except the first, were determined by experiment for the specimen of glass employed.