On the Determination of Resistance in Terms of Mutual InductanceAuthor(s): Albert CampbellSource: Proceedings of the Royal Society of London. Series A, Containing Papers of aMathematical and Physical Character, Vol. 107, No. 742 (Feb. 2, 1925), pp. 310-312Published by: The Royal SocietyStable URL: http://www.jstor.org/stable/94251 .

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310

On the Determination of Resistance in Terms o0 Mutual Inductance.

By ALBERT CAMPBELL, B. A.

(Communicated by F. E. Smith, F.R.S.-Novemnber 22, 1924.)

Some years ago* the author made a determination of the ohm in absolute umnits by two alternating-current methods, both of which depended on a calculated standard of mutual inductance and a measured frequency. Each of those methods had certain disadvantages: the first required a very steady running two-phase alternator, and the limits of accuLracy depended on the readings of an electrostatic voltmeter; the second method employed a condenser as intermediary and required an assuimption regarding the behaviour of the condenser which was probably not quite justifiable.

The following method requires simpler apparatus than the two former, and is free from the difficulties inherent in them. The connections are shown in the figure.

-A G

M1 and M2 are two mutual inductances, MS being variable. Their secondaries are connected, along with added resistance, to form a loop having total resistance R and self-inductance L; r is a non-inductive resistance, A a source of alternating current, and G a vibration galvanometer or telephone. A portion, s, of the added resistance in the loop is tapped off into the galvanometer circuit, and can be adjusted by a slide-wire contact without altering the total R. Let o _ 2-n, where n is the frequency of the. source. Then, when G shows no current,

2M1M2 =Rr (1)

and Mls Lr. (2)

If we fix M1, R, r and L, s can be adjusted once for all so as to satisfy condition (2). Then, for any given value of c, condition (1) can be also

* ' Roy. Soc. Proc.,' A, vol. 87, p. 391 (1912).

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Determinartion of Reststance in Terms of Mutual Inductance. 311

satisfied by adjusting M2. If the frequency is not quite constant, and has to be averaged, M2 can be adjusted at regular intervals. In the above simple case we have taken r as non-inductive, and the direct mutual inductance (m) between P and Q as zero. If these conditions do not quite hold, let 1 be the self-inductance of r. Then we have

o2 [M1M2-L ( - m)] =Rr (3)

and Mls- Lr + (-m) R. ()

It is quite easy by experiment to set m to be zero, in which case a small correction due to I alone remains. But if m be set equal to 1, the equations reduce to the original simple conditions (1) and (2). If the self-inductance of s is not quite negligible a small correction for it can be applied to M2.

It will be noticed that the comparison thus obtained involves two mutuaI inductances and two resistances. The two mutual inductances can each be accurately determined against a standard calculated from its dimensions. The resistance r is an ordinary non-inductive standard, but R includes inductive copper coils. Even when moderate frequencies are used (e.g., 100 to 200 cycles per sec.), the resistances of the copper portion of the loop can be made so small as to render the variation of R with temperature and frequency comparatively slight.

The method has been used to determine the ohm in absolute units. The mutual inductances Ml and M2 were about 14 and 10 rnH respectively, and were checked against a standard kindly tested by Mr. Dye at the National Physical Laboratory, being thus derived from the calculated standard of mutual inductance set up by the author in 1907.* The resistances R and r were about 30 and 2 ohmsX respectively, and were checked against coils also tested at the National Physical Laboratory. L was about 3.5 mH and s about 0 5 ohm. The frequency used was about 100 cycles per sec., and was determined by a standard tuning fork which was checked by the help of a phonic wheel. The alternating current (30 to 40 milliamperes) was obtained from a single-valve generator, and the detecting instrument was a vibration galvanometer. The experiments were made in the author's small laboratory with home-made instruments.

The final results gave

International ohm/true ohm 1 a 00054 ? 0 0001.

The limits of accuracy are perhaps worse than ? 0 0001, but the agreement

* 'Roy. Soc. Proc.,' A, vol. 79, p. 428 (1907).

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312 E. C. Stoner and L. H. Martin.

of the result with the figures given by Smith and Giebe (1. 00052 and 1 00051 respectively) shows that with a little more elaboration very high accuracy should be attainable. The use of the method for accurate measurement of frequency will be described elsewhere.

The Absorption of X-Rays.

By E. C. STONER, B.A., Lecturer in Physics at Leeds University, and L. H. MARTIN, M.Sc., 1851 Exhibition Scholar (Melb.), Trinity College, Cambridge.

(Communicated by Prof. Sir E. Rutherford, F.R.S.-Received Dec. 5, 1924.)

Introduction. An account is given here of the measurement, by a balance method, of the

mass-absorption coefficients of a number of elements, primarily relative to aluminium, over a range of wave-lengths from 0 3 to 0 7 A.U., and of the absolute coefficient of aluminium itself for three wave-lengths.

The main objection to the direct method of measuring absorption coefficients is the difficulty, with ordinary facilities, of obtaining an even approximately constant source of X-rays. This necessitates the use of some form of com- pensation or comparison method.

Siegbahn* has described such a method. Two similar monochromatic beams from the same X-ray tube are obtained with the aid of two " half spectrometers." The currents through the two ionisation chambers are opposed, and a null method is used, with an electrometer as detector. With the absorbing screen in the path of one beam, the intensity of the second is equally reduced by mearns of a rotating disc, the transmitting sector of which can be varied.

The present method embodies essentially the same idea, but its much greater simplicity gives it an added advantage. A single spectrometer is used, the two beams, one above the other, being reflected by a single crystal into the two ionisation chambers, which are fixed together and replace the usual single chamber of the Bragg spectrometer. After the beams are equalised in intensity

* Siegbahn and Wingardh, ' Phys. Zeit.,' vol. 21, p. 83 (1920); Winggrdh, ' Zeit. f. Phys.,' vol. 8, p. 363 (1922).

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