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Phil. Mag. S. 4. Vol. 49. Pl. X.

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Four equal Poles: A and A positive; Band B'negati

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Mintern Bros.

rock under the drift is an argillaceous shale; and here and there are ou crops of a siliceous conglomerate. The diamonds have hitherto been worked only at the surface. The author mentions the principal minerals found associated with the diamonds, which are generally small, and their crystalline forms not very well developed. He also remarks on the general accordance in the geological constitution of various diamantiferous districts.

7. “ Remarks on the working of the Molar Teeth of the Diprotodon." By Gerard Krefft, Esq., F.L.S. Communicated by the President.

In this paper the author criticised a figure of the lower molars of Diprotodon, published by Professor Owen, on the ground that the teeth are represented in it in an unabraded state, and stated that when the last tooth breaks through the gum the first of the series is always worn flat. He also remarked on the peculiar modification of the premolar in the genus Diprotodon.

LVI. Intelligence and Miscellaneous Articles.

ON THE SPECTRUM OF THE AURORA.

To the Editors of the Philosophical Magazine and Journal.

GENTLEMEN, I AM obliged to Dr. Marshall Watts for pointing out the errors

in the wave-lengths of the oxygen- and carbon-lines as compared in my paper. I am aware that in spectrum No. II. of the “ Index” j is given as 5602; but I assumed this to be a misprint for 5622, as these last figures appear in spectrum No. I. against the same scalereading, viz. 58. The wave-lengths in the blue and green were accidentally transposed. The true reading will therefore stand thus :

Yellow. Green. Blue. Dr. Vogel's oxygen-lines

5603 5189 4829 Dr. Watts's carbon-lines..

5602 5195 4834

I am aware of the frequent impurity of vacuum-tubes; but it is hardly probable all the oxygen-tubes examined were impure.

Dr. Vogel, too, does not hint at any suspicion of his tube, which, as I have said, agrees with mine very closely.

I am, &c.,

J. Rand CAPRON. Guildford, May 1, 1875. Phil. Mag. S. 4. Vol. 49. No. 327. June 1875. 2 L

ON THE DETERMINATION OF THE QUANTITY OF MAGNETISM OF

A MAGNET. BY R. BLONDLOT. The notion of instituting a method of magnetic exploration based on the production of induced currents has long been entertained. In 1849 Van Rees published * the result of researches on the distribution of magnetism, the principle of his process being as follows :—The wire of a much-flattened induction-coil is connected with a galvanometer; the bar to be examined is introduced into the coil up to a fixed point of the latter, and is then briskly withdrawn to a great distance: this gives rise to an induction-current, which deflects the needle of the galvanometer a certain angle.

Van Rees lays down a simple proportionality between the intensity of the current and the inducing magnetism, from which it follows that the current observed is a measure for the sum of the free magnetism over which the coil glides; and he concludes, from a known relation, that that sum is equal to the actual magnetism at the place from which the withdrawal of the coil started.

Subsequently, in 1861, in a memoir an abstract of which appeared in Poggendorff's Annalent, M. Rothlauf treats the same subject, commencing with a critical examination of Van Rees's memoir. The theory of the latter is faulty in two points; the principal charge against it is that it supposes the experiments to be made with a coil formed of one circumvolution only, and that the points situated beneath it are the only ones which act by induction. We refer for the details of the criticism to M. Rothlauf's memoir I.

Finally, M. Gaugain has recently taken up Van Rees's method, and made it the foundation of researches, which he is pursuing with success, on magnetism.

It appeared to us important to examine Van Rees's method from the theoretical point of view, to seek the exact signification of the numbers given by it, and to treat in particular a case in which, though generally inaccurate, its application does not involve any appreciable error.

The first impulse measured represents, with respect to the induced current, the integral i dt, i denoting the variable intensity

of the current, and t the time, the limits of which are t, and tj.

Let us go back to the theory of induction-currents given by Neumann.

If we have a fixed pole P, and a closed circuit B moving in relation to the pole, there is produced in the circuit an induction-current in the inverse direction of the current which would give to the circuit the motion which it actually has (Lenz's law).

Let ds be an element of the circuit; this element is the seat of an electromotive force eds. If the circuit B were traversed by a

* Pogg. Ann. vol. lxxiv. p. 217.

+ “Bestimmung der magnetischen Vertheilung mittelst Magnet-Induction," Pogg. Ann. vol. cxvi. p. 592.

I See also G. Wiedemann, Die Lehre von Galvanismus, vol. ii. p. 321, note.

current of the intensity m in absolute measure, ds would be acted on by a certain force from the pole P. Let y be the component of that force along the direction of the motion; the elemental law given by Neumann is the following:

eds=-EVY, v designating the velocity of the element ds, and e being a constant.

Let us consider what takes place in the time dt for the entire circuit. Let R be the resistance; the elementary current produced will be, according to Ohm's law,

idt=- Puydt, the symbol extending to the entire circuit B.

dw But we have v=

dt'

dw representing the element of the trajectory of ds; therefore

dw
idt=seyi
R

Eydw,
dt

R which gives the following enunciation :

The differential current is equal, except a factor, to the sum of the elementary work of the forces to which the pole is subjected on the part of the elements of a current 1 supposed to traverse the circuit B. Integrating between the corresponding limits, we get

Eydw.
R

(A) It follows that, for a given circuit, the first impulse of the galvanometer is proportional to the work which would be necessary to produce the relative motion of the pole and the circuit supposed to be traversed by the current 1.

If we wish to pass to the case of the true magnet, it suffices to consider any number of poles ; and it is seen, by a series of summations, that the theorem applies in the case of any distribution in that of a single pole.

We have now to estimate the work as a function of the data of experiment.

Let V be the potential, relative to the circuit, of any pole P, and р the magnetism of the pole; the work in order that the system may pass from one state to the other, taking into account this pole only, is equal to the corresponding variation of the quantity V; let it be i V-V). We shall therefore have, by substitution in equation (A),

Ř (V,

to the summation here extending to all the poles of the arrangement*.

* This equation agrees with the calculation given by G. Wiedemann, l. c. vol. iii. p. 80.

S'id=

idt=

0

as

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