and R is found without focussing on the meniscus. The position of the meniscus centre may easily be got from the reading of the reflected image by subtracting R/2. The above method was tested by readings with olive oil, the surface of which can generally be focussed on, by calculating the position of the surface of the meniscus, and also getting it by direct focussing: the results agreed to a high degree of accuracy. It is obvious that for opaque liquids (e. g. mercury) this reflexion method can be used to find the radius of curvature of the centre of the meniscus provided the surface can be accurately focussed on.

The following tables give a series of readings with tubes of different diameters for olive oil and mercury. As the surface-tension of mercury varies considerably, freshly distilled mercury was not used, but clean mercury which was filtered through a pin-hole in a paper funnel before each reading. This was done as we wished to keep the mercury in as far as possible the same condition in order to test the method of finding angles of contact, mercury being the only liquid whose angle of contact is known to any degree of accuracy. The readings with the narrower tubes in the case of mercury could not be taken exactly as described owing to the meniscus being so far below the surface in the vessel, so with these a piece of the tube was sealed to a wide-mouthed funnel and then bent in U-shape until the end of the tube was slightly below the top of the funnel: the readings were then easily taken. r, R, and h are given in cm., T in dynes per cm.

The values found for the surface-tensions of glycerine and turpentine were:

All the above readings were taken at a temperature of approximately 16°. The glass vessel and tubes were cleaned with concentrated sulphuric acid, caustic potash, and alcohol, being washed between each two in running water, and finally dried and immersed in the liquid to be used.

To apply the method to finding angles of contact it is only necessary to remark that, either from an approximate solution of the equation to the capillary surface (see Ferguson, Phil. Mag. July 1914) or by assuming the meniscus to be spherical in the limit, it follows that lim r/R= cos 0, where

is the

angle of contact. Thus if we plot values of r as abscissæ and values of R as ordinates, we get a curve the inclination of the tangent to which at the origin is tan-1 (cos e). If the tangent makes an angle of 45° with the axis of x, the value of is 0° and the liquid may be truly said to wet the tube. The following tables give readings of r and R for glycerine and turpentine respectively :

The curves (fig. 2) were obtained by plotting r against R for water, glycerine, olive oil, turpentine, and mercury. It will

be noticed that all appear to approach the origin at an angle of 45° with the exception of mercury. This points to a zero angle of contact with all except mercury. Mercury gives an angle of nearly 41°, or rather, a little greater than 180°-41° 139°.

=

University College, Galway

XXI. The Complete Photoelectric Emission*. By Professor O. W. RICHARDSON, F.R.S., Wheatstone Professor of Physics, University of London, King's College †.

IT

T is well known that when light of sufficiently short wave-length is allowed to fall on metals, an emission of electrons takes place under its influence. Since all substances emit light when they are raised to a high temperature, an emission of electrons from hot bodies owing to the action of light will occur even when they are not illuminated from an external source. The emission of electrons which arises in this way may conveniently be termed the "complete photoelectric emission," to indicate that it is excited by the complete (black body) radiation with which the material is in equilibrium at the temperature under consideration. It is of interest to enquire whether this emission will resemble in its behaviour the thermioniceffects which have been investigated experimentally, and to seek to determine how its magnitude compares with that of the observed thermionic emission.

The most striking property of the thermionic emission of electrons is that expressed by the current temperature relation i= AT e-b/T

(1) (i=maximum current from unit area, T=absolute temperature, A, λ, and b constants). The writer has shown that it follows from simple thermodynamic considerations that the complete photoelectric emission is also governed by an equation of type (1)§. The thermodynamical argument does not determine the numerical value of the constants A and b ( is unimportant) which enter into the formula for the complete photoelectric emission. It does, however, determine the meaning of b, which is closely related to the work done by an electron in escaping from the metal. The values of the minimum frequency of the light which is able to excite any photoelectric emission from metals show that b is not very different in the case of photoelectric and thermionic emissions from a given material. It is not

*Part of an address delivered by the Author in opening the discussion on Thermionic Emission at the Manchester Meeting of the British Association, 10th September, 1915.

+ Communicated by the Author.

Phil. Mag. vol. xxiii. p. 619 (1912).

The same conclusion has been reached by W. Wilson by a direct application of the quantum hypothesis (Ann. der Physik, vol. xlii. p. 1154 (1913)).

certain that the values of b for the two effects are not identical for the same substance. The value of A, on the other hand, is left entirely arbitrary by the thermodynamic considerations, which do not therefore enable us to determine the scale of magnitude of the complete photoelectric emission. Thus the theoretical argument leads us to the conclusion that the complete photoelectric emission varies in the same general manner with temperature as the observed thermionic effects: it is possible, although not certain, that the indices λ and b are identical in the two cases contrasted, in which case the two emissions would be in the same relative proportion at all temperatures; on the other hand, the absolute value of the complete photoelectric emission is left entirely undetermined, so that we are unable to determine by such calculations what proportion it bears to the observed thermionic emission.

This information can, however, be obtained from known photoelectric data in the case of the metal platinum. The calculations are not exact, but it is improbable that the sources of uncertainty in the calculations will lead to errors in the final results which are as great as those pertaining to the experimental measurements of the absolute values of photoelectric and thermionic emissions from a given material. Data now available give the number of electrons emitted from certain metals, including platinum, when unit light energy of the different effective frequencies falls on them at normal incidence (or at some other angle which is definitely specified). The magnitude of the complete photoelectric emission will not, however, be obtained if we simply multiply this number by the corresponding intensity of the light in the black-body spectrum and integrate the product over the whole range of frequency, on account of the different optical conditions in the two cases. In the photoelectric experiments in which a beam of light is incident normally, the intensity of the exciting illumination is greatest at the surface and falls off exponentially as the depth of penetration increases. In the natural emission, on the other hand, the electromagnetic radiation is isotropic, and its intensity is the same at all depths. This particular difference between the two cases can be allowed for if we have a knowledge of the coefficients of absorption of the electromagnetic radiations of different wave-lengths and of the electrons which they cause to be emitted.

It is usual to assume that both the light and the electrons

* Richardson and Rogers, Phil. Mag. vol. xxix. p. 618 (1915).