The whole motion depends on the following constants:(1) The radius of the sphere c.

(2) The uniform velocity Z.

(3) The minimum value of + V, viz.,

Р
P

II

4. On the Magnetic Shielding of Two Concentric Spherical Shells.
By A. W. RÜCKER, F.R.S.

The formule were found which express the shielding of two concentric permeable spherical shells, and several special cases were discussed. The result was reached that if the smallest and largest radii and the volume of the permeable matter are given, the shielding is a maximum for a given portion of the empty shell. If the magnetic field is produced by a small magnet placed at the common centre of the shells, if the empty space is small and the matter highly permeable, the best position is that in which the volume enclosed by the crack' is the harmonic mean of the volumes included by the outermost and innermost surface.

5. On the Equations for Calculating the Shielding of a Long Iron Tube on an Internal Magnetic Pole. By Professor G. F. FITZGERALD, M.A., F.R.S.

Attention was called to the desirability of having the integrals of the form cos u du plotted or tabulated, as it would very much facilitate the calculation of √pε + us this and other cases to which Bessel's functions were applicable but were complicated in application.

6. On the Equations for Calculating the Effect of a Hertzian Oscillator on Points in its Neighbourhood. By Professor G. F. FITZGERALD, M.A., F.R.S.

Attention was recalled to the error made by Maxwell when he assumes that for variable electrification it is legitimate to assume that A=0 at points of space where there was no electrification. The true expression is AKμ.. The [cos u du evaluation of the integrals was also advocated in order to facilitate √ p2 + u2 the calculation of the effects of a linear Hertzian vibrator on points in its neighbourhood. The elliptic motion of the electric force in the neighbourhood of such an oscillator follows at once from the fact that the vector potential is parallel to the oscillator, and may be taken as AiF. From this we get that the magnetic force is H = VAA, and thence the electric force = VAH.

If the vibration on the oscillator be simply periodic it is easy to see that the form of E is

where E, and E, are two vectors, so that E is the vector of an ellipse.

In determining the period of vibration of an oscillator the difficulty arises that the energy is being dissipated by radiation, and that some impressed forces must

be exerted on the oscillator to keep the vibration simply periodic, and if the impressed force be of a proper period any period of vibration is possible. To solve the problem a system of equal incoming waves is superposed on the outgoing ones, and then the simply periodic vibration is possible without any impressed force, and this condition then gives the free period of vibration.

7. Magnetic Action on Light. By J. LARMOR, F.R.S.

This Paper was ordered by the General Committee to be printed in extenso. See Reports, p. 335.

8. On a Special Class of Generating Functions in the Theory of Numbers. By Major P. A. MACMAHON, R.A., F.R.S.

9. On Agreeable Numbers.

By Lieut.-Col. ALLAN CUNNINGHAM, R.E., Fellow of King's College, London. A number, N, of which the m digits on the right hand are the same as the m digits on the right hand of its nth power (N"), when both are expressed in the scale whose radix is r, is styled an AGREEABLE NUMBER of the mth order and nth degree in the r-ary scale. When the agreement of N, a number of m digits, with its nth power, extends throughout its m digits, the number N is styled a Complete Agreeable Number. The analytical condition is

NN must be divisible by rm.

The properties of these numbers are investigated in a quite general manner applicable to any scale of radix r; and simple rules for their computation given. These rules are completely reduced for the denary scale to their simplest form, and the auxiliary quantities are tabulated. Computations of complete agreeable numbers are given in detail for the denary scale. Tables are given of all agreeable numbers to the fifth order, and in some cases to the tenth order.

Example. The numbers, N, of ten digits (shown in table below), and also the numbers of fewer digits obtainable therefrom by erasing one or more of the extreme left-hand digits of N, are complete agreeables in all the degrees n stated in column n; and are, moreover, the only complete agreeables (of ten digits, or less, ending in 1, 2, 4, 5, 6, 8) in all those degrees, except when n has the critical forms named in column n', in which case there are a number of complete agreeables (increasing rapidly with the value of n' and with the number of digits of N).

The following Reports and Papers were read :—

1. Report of the Committee on Earth Tremors.-See Reports, p. 287.

2. Report of the Committee on the Volcanic and Seismological Phenomena of Japan.-See Reports, p. 214.

A discussion on the Teaching of Elementary Physics was introduced by the three following Papers:

3. Apparatus for Class-work in Elementary Practical Physics.
By Professor G. CAREY FOSTER, F.R.S.

The author described and exhibited samples of simple apparatus which he had devised for the purpose of practical instruction in physics. The object aimed at was to devise arrangements by which the chief quantitative laws of physics could be verified with fair accuracy, and which should at the same time be so inexpensive that they could be multiplied at a small cost, so that all the members of a class could make the same experiments at one time. In addition to the mere saving of expense, it was maintained that the simplification of apparatus, so long as it was efficient for its purpose, had the positive advantage of bringing students into more direct contact with the phenomena to be studied than was the case with more elaborate and complicated appliances.

4. On Physics Teaching in Schools. By W. B. CROFT, M.A.

It must be remembered that there are several classes of students:

1. Those who aim at scientific or technical careers, but are compelled to make their education as brief as possible.

2. Those to whom science is the best education.

3. Those who may aspire to be mathematical physicists, and can afford to enjoy the benefit of wide and varied education.

4. The great majority receiving at our schools the usual general training in preparation for various professions. None of these should be without the benefits of science.

Of the first two classes I have not the experience to speak. The latter two appear to me to be well provided for under one scheme. Soon after the Duke of Devonshire's commission twenty years ago action was taken by the new governing bodies of public schools to make effective the recommendations of the British Association in 1867. At Winchester teachers and suitable apparatus were provided for the following scheme:

If a boy were to pass up the school between the ages of twelve and nineteen, he would learn

First year: Geometrical drawing, botany, physical geography.

Second year: Simple mechanics and graphics, hydrostatics, heat.

Third year: Chemistry.

Fourth year: Chemistry.
Fifth year: Geology.

Sixth year: Electricity.

Seventh year: Acoustics, geometrical and physical optics.

Two hours per week, with one or two hours out of school work.

This is

Biology purposely has no place. It is better to be able to engage the interests of boys in it without reference to their age or position in the school. excellently done by a Natural History Society.

The general nature of teaching in the sixth and seventh years consists of experimental demonstrations of phenomena over as wide a range as possible. Boys who survive in a school to this stage are usually capable of appreciating scientific ideas through lectures, but in a public school they are seldom able to give time for practical work done by themselves. Those who may afterwards be thorough physicists had better be much occupied at this age with mathematics. So far as

'The full paper is published in the Educational Times.

possible they should avail themselves of the opportunities which most schools give for learning drawing, carpentering, and photography.

There is a significance in the order of subjects as arranged above. Experience shows that the subjects are suited to the various ages.

5. Notes on Science Teaching in Public Schools. By A. E. HAWKINS, B.Sc.

The following 'items' represent convictions formed after twenty-two years' experience, the greater part of which (fifteen years) have been spent in the Bedford Modern School of about 600 boys.

I. The subject must be taught experimentally. The author has known splendid examinational results obtained without a single experiment having been performed by either teacher or taught.

In the hands of an experienced and vivacious teacher it is astonishing what mere drawings on the blackboard can accomplish for examinational purposes, disastrous, however, to real science.

Experiments involve the expenditure of much time; very frequently one is enough for a lesson-e.g., determination of a specific heat or the resistance of a wire. If it is asked how an examination can be passed when time is so short, the answer is 'Teach, and let the examination take care of itself.' Where real teaching exists a pupil, worthy of the name, will soon find ways and means of getting up collateral matter.

But an experiment is not everything. It must be led up to. It must be preceded by discussion, and questions and answers should follow.

The conversational method is very difficult, especially with classes of thirty or more. Only one or two points can be made in a three-quarters of an hour lesson, and the matter must be clearly summed up at the end. The other quarter of an hour should be spent in writing an answer to a good comprehensive question. The answers should be marked and returned at the beginning of the next lesson.

II. But this is only half the work; experiments must now be done by the boys themselves. But practical work means plenty of apparatus, which in the majority of cases is not expensive. For a class of thirty boys ten sets at least will be required, which will allow three boys to work together. It is, however, much better if they can be arranged in pairs.

The boys, having done their experiments, should take their rough results home, and bring to the next lesson a clean copy and a detailed account of the method, with a drawing where desirable.

III. The work required of a pupil must frequently be, as far as he is concerned, original. A class, long accustomed to mere reproduction of the teacher's words and ideas, will feel unwonted life and delight if requested to devise some improvement upon a method just used, or to say what they would expect to happen if some modification were made. This is one of the surest ways of engendering an intelligent interest in the subject taught.

IV. What science should be taught? Heat and magnetism are the two best where expense is a primary consideration, and it is desired to get to work at once. Electricity should come afterwards, as so much of the subject, even in the simplest experiments, requires explanations which must be based on theory.

V. The teacher must have time allowed him to prepare the apparatus. Like other masters he has to prepare his lectures and also to correct exercises, but besides the preparation he has frequently to manufacture apparatus. This requires an expenditure of time which is, unfortunately, sometimes unrecognised.

6. Report of the Committee on the Application of Photography to Meteorological Phenomena.-See Reports, p. 140.

7. Report of the Ben Nevis Committee.-See Reports, p. 214.