The atomic number in the case of compounds has been taken to mean the sum of the atomic numbers of the elements in the compound.

Significance of K employed in equation (5).

K is an arbitrary constant. Its value for every two isomeric molecules is the same, as shown in Table III., where the values of K have been assembled together with the atomic numbers and the number of atoms in the isomers :

A close examination of the above table shows three significant relations between the values of K:

(a) The values of K increase with the number of atoms contained in the molecule. For example, in the case of molecules having three atoms the value of K is 2·5. For molecules having 13 atoms it is 14.7, and for molecules having 20 atoms it is as great as 18-34.

(b) The values of K for every two isomeric molecules are the same.

(c) In the case of groups of isomers having the same number of atoms in the molecule, the values of K increase with the atomic numbers of the groups. For example (CaSO and K,CO3) and (TeH2O, and ZnSO,) are two groups of isomers having the same number of atoms (six) in the molecule but having different atomic numbers, 68 and 78 respectively. And the value of K in the latter group is greater than that in the former. Similar relations also exist between the groups of isomers having 2 and 14 atoms in the molecule.

Most of the experimental data have been taken from the unpublished work of Messrs. C. L. Dhawan and S. L. Luthra, to whom our thanks are due.

The values of K for the isomorphous series given in Table V. in the previous paper (Phil. Mag., March 1928, vol. 5, No. 29) have not been discussed in this paper on account of the doubtful purity of these substances.

University Chemical Laboratories,

University of the Punjab,

Lahore, India.

23rd February, 1928.

A

XVIII. Frequency Variations of the Triode Oscillator. Reply to Lieut.-Col. Edgeworth, D.S.O., M.C., A.M.I.E.E. By DAVID F. MARTYN, B.Sc., A.R.C.Sc.*

N the April number of the Philosophical Magazine there appears a note by Lieut.-Col. K. E. Edgeworth under the above title, referring to a previous paper of mine (Phil. Mag., Nov. 1927), also with the same title. Edgeworth remarks that it is obvious that I must have overlooked his

* Communicated by Prof. E. Taylor Jones, D.Sc.

previous paper on "Frequency Variations in Thermionic Generators," read before the Institute of Electrical Engineers (Wireless Section) on 6th January, 1926. He further claims that "So far as they cover the same ground, the experimental results appear to be in agreement, and the explanations offered are substantially the same. The main cause of frequency variations is associated with damping of one sort or another in the grid circuit, and, other things being equal, the magnitude of the frequency variation is proportional to the amount of damping. This type of frequency variation is referred to in my paper as a frequency variation of the first type."

At the outset I may state that I had read Edgeworth's paper before writing my own, although I did not see occasion to refer to it. Chief among my reasons for not doing so is the fact that the causes of frequency variation considered by Edgeworth in his paper are totally incapable of explaining the large frequency variations which I obtained. Indeed, investigation of Edgeworth's experimental results, and comparison with those of others, has led me to the conviction that his own results, as well as those of others, are explained completely by the grid current theory developed in my paper, and that the four causes of frequency variation considered by Edgeworth are of very minor importance.

It has been realized for a number of years that the frequency of the triode oscillator was not exactly

1

but depended to some extent on the values of the anode and filament voltages of the triode and on the coupling between. the coils. The extent of the frequency variation has been found to be, at most, 3 per cent. Several experimental investigations of these frequency variations were made, notably by Eccles and Vincent: but, in spite of the great importance of the subject, both in wireless technology and in the laboratory, no attempted theoretical explanation was published until Edgeworth's paper appeared in March 1926. In October 1926, while using the simple "tuned-anode" oscillator, but with abnormal values for the coil inductances and the condenser capacity, I obtained extremely large variations of frequency, extending over several octaves, when the filament current or anode voltage of the valve was altered. In order to explain these effects I developed a mathematical theory of the oscillator which took account of the flow of grid current in the valve. By the aid of this

* Proc. Roy. Soc. xcvi. & xevii. (1920).

theory, as described in my previous paper, I succeeded in explaining every type of frequency variation which I observed. It is Colonel Edgeworth's claim that the theory which he had put forward is capable of explaining these large frequency variations. We shall now proceed to analyse the four causes of frequency variation which he considered.

(1) The first cause of frequency variation is said to be due to "grid damping" when there is a condenser across the grid coil. Equations are developed giving the extent of the frequency variation. This is the cause of frequency variation which Edgeworth specifically claims to be capable of explaining the large frequency variations which I observed. In my experiments there was no condenser across the grid coil. On putting C2-0 in Edgeworth's equation (no. 8 in the paper) we find the frequency at once reduces to

1

so that no frequency variations whatever occur! Even if we allow for a considerable self-capacity in the grid coil, the frequency variation predicted by Edgeworth's theory is exceedingly small, and quite inadequate to explain the variations which I obtained experimentally.

(2) The second cause of frequency variation only applies when a tuned-grid" oscillator is used, and hence need not be further considered.

(3) The third cause of frequency variation is due to the presence of resistance in the anode coil. This, however, has been previously worked out by Eccles, and I have shown that it is much too small to account for the frequency variations which I observed.

(4) An effect due to harmonics, as worked out by Appleton and Greaves t. This effect also I have considered in my paper, and have shown to be exceedingly small and unimportant.

Summing up, then, we see that none of the four causes of frequency variation put forward by Edgeworth is capable even of explaining a frequency variation which in any way approaches the order of magnitude observed by Eccles and Vincent. Still less can they explain the very large frequency changes which I obtained. The correct magnitude of frequency variation is at once obtained, however, from the

Proc. Phys. Soc. xxxi. (1919). + Phil. Mag. xlv. (1923).

Phil. Mag. S. 7. Vol. 6. No. 34. July 1928.