On differentiating twice with respect to 01, it is found that

But from

where A and B are undetermined constants.

considerations of symmetry

Since the integral equation holds for all values of 6'; w<0'<2π-w it holds for 0,=, so that

1+ A cos Eπ/2+В sin VEπ/2=€+

π

1-e
2

(1+A cos √e0/2+ B sin √e8/2). cos 0/2.de.

On integrating this equation and putting

it follows that

and

A=

B=

Hence

B=A tan Veπ/2,

-(1-e) sin w/2.cos Veπ/2

Vecos w/2.sine (π-w)/2+ sin w/2.cose(π-w)/2

√ecos w/2.sin√e (π—w)/2+sin w/2.cos√e(0 — w)/2°

Þ(0)=1—

i. e.,

(1-e) sin w/2.cos Veπ-0)/2

√ecos w/2.sine(π-w)/2+ sin w/2.cos √e(π — w)/2

P(0)=1-C cos√ε(π—0)/2,

where

✅e cos w/2.sine(π−w)/2+ sin w/2.cos√e(π — w) / 2° Now,

is the "defect" from black-body radiation as a function of and of w, the semi-angle of the slit. This is shown graphically in fig. 4 for values of the emissivity of 0.10, 0.25, 0.50, and 0·75 for 0=π, i. e., positions directly opposite the centre of the slit.

The solution of the inverse problem of the brightness of a similar cylinder of reflectivity p, illuminated by a uniform sky of brightness B, is easily obtained as

YB(0)=

TBp sin w/2.cos/1—p(π−0)/2

√1-p cos w/2.sin√1−p(π-w)/2+sin w/2.cos\/1—p(π—w)/2

Defect of black-body radiation opposite slit in infinite cylinder.

Summary.

The paper is a continuation of a previous one in which the effect of multiple reflexion from the walls of a uniformlyheated infinite cylinder in building up black-body radiation is considered. The method is now applied to the case of a finite uniformly-heated cylinder, and an approximate solution is obtained. The results are of interest in showing how closely a uniformly-heated cylinder can approach the ideal black-body radiator.

It is also shown how the brightness of the inside of a non-radiating cylinder illuminated by a uniform sky can be deduced from the solution of the problem of the self-radiating cylinder. This is the case of a light well.

The problem of the radiation from the inside of a uniformlyheated infinite cylinder having an infinite longitudinal slit is also solved. In this case the solution of the integral equation is exact. The results are of interest in showing how closely a radiator of the type of Ives's primary standard of light approaches the ideal black-body radiator.

XLVI. A Quartz Fibre Electrometer. By D. R. BARBER, B.Sc., A.Inst.P., Research Student, Department of Physics, University College of the South-West of England, Exeter *.

1. Introduction.

THE quantity of electricity which escapes from a charged body is very small, and it is necessary that the capacity of the instrument used to measure it should be small. This condition makes it advisable to use a small gold-leaf electroscope. It has been found that the gold leaf may be replaced by a single fibre of quartz, rendered conductive by the deposition of a suitable metallic film. In preliminary experiments the fibres employed, approximately 1 mil (2.5 x 10-2 mm.) diameter, were silvered by chemical deposition. This method ultimately proved unsatisfactory, the films becoming discontinuous a short time after their formation. Cathode disintegration of the metal" in vacuo" was finally adopted, and the "sputtered" fibres obtained by this method have proved very satisfactory. At first the electric field was applied between a single insulated plate and the containing case, the vertically suspended fibre being illuminated laterally and viewed through a microscope against a dark background. An "earthed" metal cylinder provided with windows formed the case of the instrument. It was found, however, that this type of electrometer suffered from two serious defects: (a) an erratic displacement of the fibre, which was independent of the electrical condition of the instrument, and was eventually traced to thermal radiations from the lightsource, incident upon the fibre, causing the metal film and the quartz to dilate by unequal amounts. This effect was apparent even when reflected sunlight was used as the illuminant; (b) there was a non-linear relation between the P.D. applied to the fibre, and the resultant deflexion, except for very small field values. Under these conditions it would thus be necessary to calibrate the instrument over the entire working range. The design of the electroscope was therefore modified by using two parallel plates and direct illumination, i. e. the fibre was viewed against a bright background. The latter method, since it requires only a fraction of the illumination necessary in the former, does not give rise to any extraneous thermal effects.

* Communicated by Prof. F. H. Newman, D.Sc., F.Inst.P.

2. Description of the Instrument.

The instrument in its final form is shown diagrammatically in fig. 1. A silvered quartz fibre F is attached to a copper electrode C by a small globule of Wood's metal, and hangs symmetrically between the two electrodes, E, and E,, of sheet brass 2.5 x 20 cm. and separated by an air-gap 7.5 mm. wide. The leads from the plates pass through short lengths of quartz tube Q, cemented into the lower ebonite cap B and the fibre electrode is similarly insulated

1

by the quartz sleeve Q, cemented into the upper ebonite cap A. The case of the instrument is a glass tube D, 100 cm. long by 3.5 cm. diameter, provided with two windows W1 and W, slightly blown out in order to free the glass of air-bubbles, and, with the exception of the windows, it is coated on the inside with a film of silver, S. Contact with this is made by the platinum wire P, sealed through the glass, and terminating on the exterior in a loop electrode by means of which the silver coating is connected to earth. The ebonite cups were grooved concentrically to fit closely on to the cylindrical glass case, this method of assembly enabling the instrument to be easily dismantled, if the necessity arose

for subsequent modification in the relative position of fibre and plates.

Some trouble was experienced, initially, in mounting the fibre preparatory to the sputtering process, but after several ineffective trials, the following technique was adopted. The selected fibre was stretched across a rectangular glass frame, its two ends being cemented by means of shellac, and the frame was then held horizontally in a clamp, care being taken that the fibre was quite clear of the clamp edges. The electrode serving as the fibre support consisted of a straight copper wire, flattened at one extremity, and in this a fine groove was cut to receive the fibre. The wire was first fitted into its insulating sleeve and cap, and the tip was then "tinned" with Wood's metal, care being taken that the groove was completely filled with the metal. This tinned portion was then bent through an angle of about 20°, and the assembly clamped vertically beneath the fibre frame, in such a position that the wire was just in contact with, and parallel to, the fibre. A well-heated soldering-iron was placed against the under side of the wire, and the Wood's metal melted, a slight downward pressure being applied to the stretched fibre meanwhile, so that it sunk into its groove, this pressure being maintained until the molten metal solidified. The wire was finally straightened and the fibre cut to the requisite length, a fragment of glass being attached to its extremity to keep it taut when placed in the discharge-tube.

The discharge apparatus used for the cathode deposition of silver upon the fibre consisted of a vertical tube in which the fibre was suspended. Sealed to this was a horizontal side tube which served to connect the main tube to the exhaust system. The cathode of 60-mesh pure silver gauze formed a vertical cylindrical tube, concentric with, and entirely enclosing, the fibre and the "tinned" end of the copper electrode. A cup-shaped electrode of brass supported the cathode. The fibre having been lowered into position, its ebonite supporting cap was sealed down with wax and the tube evacuated. A 10 inch induction coil with a mechanical interrupter was used to excite the tube, and a continuous discharge was maintained for 30 minutes. Care was taken to protect the under surface of the insulating cap so as to prevent the possible formation of a silver deposit upon the ebonite surface. "Sputtering" of the silver readily occurred at a pressure of 50 × 10-3 mm. of mercury, and this pressure, after a sudden initial rise, remained constant throughout the period of discharge.