the coefficients and their physical significance. Thus in (3) for the electrical case it will be seen that the same coefficient occurs on the right side of each equation. This is M the coefficient of mutual induction. Also the first coefficients at the left of each equation respectively are L and N the separate self-inductions. Now this correspondence of coefficients does not hold between (3) and (2) but does hold between (3) and (1). And for this reason the form (1) is probably preferable to the experimental physicist, though the other form (2) is distinctly illuminating and may be preferred by the mathematician. 4. That the pendulums represented by equations (1) and (2) are not in the complete sense an exact analogy to the electrical case of (3) may also be seen from the relations of the frequencies of the coupled vibrations in the two cases. Suppose the two separate vibrations for pendulums or those for the electrical circuits to be equal and denote them by cos mt. Let the superposed coupled vibrations for each system be denoted by cos pt and cos qt. Then, for the electrical case, we have p>m > q. Whereas, for the mechanical analogy, we have p = m, and m > q. 5. What would seem to the writers to be an exact mechanical analogy to the electrical case would be one capable of representation as follows: In these P and Q denote the masses which vibrate in the two systems. Their separate vibrations are to be obtained by writing J=0. Thus giving as their separate vibrations cos mt and cos nt respectively. Further, it should be noted that in the above we are supposing that the introduction of the cross-connexion terms on the right has not modified the coefficients on the left. A model fulfilling these conditions seems to be still a desideratum. In these equations it may be seen by the theory of dimensions that J must be a mass like P and Q. Phil. Mag. S. 6. Vol. 35. No. 206. Feb. 1918. Q 6. Prof. Plummer appears to consider it a mistake to regard as a mass the mutual induction M of the electrical case. But does not the current view regard the mutual induction as an inertia factor of some sort? Thus in Sir J. J. Thomson's model referred to in the October paper (p. 251) both self and mutual inductions are represented by masses. In Prof. J. A. Fleming's Alternate Current Transformer' (vol. i. pp. 97-98, 1889), the electrical energy Li2 is likened to the mechanical energy of rotation Iw. Again, in Sir Oliver Lodge's 'Modern Views of Electricity' (p. 496, 1907), coefficient of induction (self or mutual) is given as inertia per unit area. It is true that the coupling in the electrical case is made by a change of configuration which fixes the value of M. But this does not prevent M from being a mass (i. e., an inertia) like the inductances L and N which are also dependent solely on configurations, provided no iron or other magnetizable substances are present. As to whether the coefficient M in the electrical equations is to be represented by a mass in any one mechanical model incompletely analogous to it, is another matter. Nottingham, Dec. 17, 1917. XXIII. The Radioactivity of Archæan Rocks from the Mysore State, South India. By W. F. SMEETH, D.Sc., A.R.Š.M., and H. E. WATSON, D.Sc., A.I.C.* THIS Preliminary Investigation. HIS investigation was started some years ago on a number of samples of the hornblendic schists of the Kolar Gold Field, selected by Mr. H. M. A. Cooke, Superintendent of the Ooregum Gold Mining Company. The samples were taken from the Kolar mines at different depths, with a view to ascertaining whether the radium content varied with the depth from the surface in rock of fairly uniform character and composition. These hornblendic schists and epidiorites are all ancient lava flows, or sills, of fairly uniform composition, notwithstanding petrological distinctions in texture and structure. Communicated by the Authors. An account of the method used and results obtained was published in the Philosophical Magazine (6) xxviii. p. 44, 1914, and the results are repeated in Table I., Nos. 1 to 15. It will be seen that the radium content is very low, remarkably constant, and that there is no variation in depth down to a vertical depth of some 3500 feet from the surface. Two of the samples-Nos. 12 and 15-gave results considerably higher than the others, but microscopic examination showed that these samples did not represent normal types of the hornblendic schists or "country" of the mines, but had undergone considerable mineral alteration, such as is common in the immediate vicinity of the quartz veins or other acid intrusives, and there is no doubt that the higher values are due to the intrusion of acid material of higher radium content. Further Investigation. It was then decided to obtain a number of representative samples from the various components of the Archæan complex of Mysore, in order to ascertain how far the various formations or groups might be distinguishable from one another by their radioactivity, and what variations existed amongst the members of each group as a result of magmatic segregation. The experimental procedure was the same as before, viz., 10 gms. of the finely powdered rock were fused with potassium hydroxide, under reduced pressure, and the resulting gases led to an electroscope after removal of the hydrogen and drying. Towards the middle of the experiments the leaf system in the electroscope broke down, and was replaced by a smaller and more sensitive one, which was subsequently carefully standardized. With this a leak of 1 scale division an hour corresponded to 167 × 10-13 gm. of radium. Control experiments showed no discontinuity between the two series of values obtained. All experimental details have already been given (loc. cit.), and will not be repeated. Altogether, fifty samples have been selected from specimens in the Department of Mines and Geology of Mysore and the radium determined, but each group is itself so complex and variable that a much larger number would be required before fair averages or estimates could be obtained. In spite of this, certain interesting variations appear to be indicated, and the results obtained have been grouped, in Table I., under the various formations taken in order of from the oldest to the youngest. age The following classification is inserted for convenience of reference, and shows the order of succession and relationship of the various formations in Mysore as at present adopted by the Mysore Geological Survey *. Archæan. Classification of Mysore Rocks. 1. Recent soils and gravels. Possibly Tertiary. 2. Laterite. Horizontal sheet capping Archæans. Pre-Cambrian (Animikean) } 3. 3. Basic dykes. Chiefly various dolerites. Great Eparchean Interval. 4. Felsite and porphyry dykes. 5. Closepet granite and other massifs of corresponding age. 6. Charnockite, norite, and pyroxenite dykes. 7. Charnockite massifs. (Complex.) 8. Various hornblendic and pyroxene-granulite dykes. We may now very briefly consider the groups of figures presented in Table I., and the following summary of the results will help to bring out such points of similarity or distinction as exist amongst them, although the cbservations are too few in number to permit of final conclusions being drawn. * 'Outline of the Geological History of Mysore,' by W. F. Smeeth, Bulletin No. 6-Department of Mines and Geology, Mysore State. (Numbers in brackets refer to the classification given above.) The hornblendic rocks of the Dharwar System (Nos. 1-18) are low in radium and exhibit no great variation from the mean, though many petrological types are included, such as hornblende schists, hornblende diabases, amphibolite, and hornblende granulite. When, however, these rocks are altered in contact with intrusions of the Champion gneiss and of the related quartz veins of the Kolar Field (Nos. 2630), all of which contain much more radium than the normal schists, the radioactivity of the altered types is considerably increased (Nos. 12, 15, and 16) to a point intermediate between the radioactivities of the two reacting masses. The rocks of the Chloritic series (Nos. 19-21) do not appear to differ much in radium from those of the hornblendic series. The higher value in No. 21 may possibly be the result of alteration due to a neighbouring granitic intrusion. The basic intrusives of Dharwar age-that is to say, intrusives into the general body of the Dharwar schists prior to the period of the Peninsular gneiss-contain much less radium than even the schists themselves. This is particularly noticeable in the Bellara trap (No. 23) and the Grey trap of Chitaldrug (No. 24), and these rocks afford an interesting example of the possible use of such determinations in the correlation of these very old and much altered Archæan types. Some years ago the Grey trap was considered to be a modification of the less altered Bellara trap, but subsequent |