masses of magnetite ever permanently magnetised? Are large areas of surface masses, say a few hundred square yards in extent, ever permanently and approximately uniformly magnetised in the same sense? Is there any relation between the geological age and the direction of the permanent magnetism of magnetic rocks?

Inquiries such as these can only be taken up by individual workers, but I venture to think that the comparison of the observatory instruments and the fluctuations of secular change outside the observatories could best be investigated under the auspices of a great scientific society. The co-operation of the authorities of the observatories will no doubt be secured, but it is most important that the comparisons should in all cases be made with one set of instruments, and by the same methods. Whether the British Association, which for so long managed a magnetic observatory, may think that it could usefully inaugurate the work, it would be improper for me in a presidential address to forecast. Who does it is of less importance than that it should be done, and I cannot but hope that the arguments and instances which I have to-day adduced may help to bring about not only the doing of the work, but the doing of it quickly.

The following Papers and Reports were read:

1. Preliminary Experiments to find if Subtraction of Water from Air Electrifies it. By Lord KELVIN, P.R.S., MAGNUS MACLEAN, M.A., F.R.S.E., and ALEXANDER GALT, B.Sc., F.R.S.E.

Experiments with this object were commenced by one of us in December 1868, but before any decisive result had been obtained, circumstances rendered a postponement of the investigation necessary.

A glass U-tube with vertical branches, each 18 in. long and about 1 in. bore, with the upper eight inches of one of the branches carefully coated outside and inside with clean shellac varnish, was held fixed by an uninsulated support attached to the upper end of this branch. The other branch was filled with little fragments of pumice soaked in strong pure sulphuric acid or in pure water; and a fine platinum wire, with one end touching the pumice, connected it to the insulated electrode of a quadrant electrometer. A metal cylinder, large enough to surround both branches of the U-tube without touching either, was placed so as to guard the tube from electric influences of surrounding bodies (of which the most disturbing is liable to be the woollen cloth sleeves of the experimenters or observers moving in the neighbourhood). This metal tube was kept in metallic connection with the outside metal case of the quadrant electrometer. The length of the exposed platinum wire between the U-tube and the electrometer was so short that it did not need a metal screen to guard it against irregular influences. An india-rubber tube (metal, metallically connected with the guard cylinder, would have been better) from an ordinary blowpipe bellows was connected to the uninsulated end of the u-tube. Air was blown through it steadily for nearly an hour. With the sulphuric pumice in the other branch the electrometer rose in the course of three-quarters of an hour to about nine volts positive. When the pumice was moistened with water, instead of sulphuric acid, no such effect was observed. The result of the first experiment proves decisively that the passage of the air through the u-tube gave positive electricity to the sulphuric acid, and therefore sent away the dried air with negative electricity. A corresponding experiment with fragments of chloride of calcium instead of sulphuric pumice gave a similar result. In repetition of the experiments, however, it has been noticed that the strong positive electrification of the U-tube seemed to commence somewhat suddenly when a gurgling sound, due to the bubbling of air through free liquid, whether sulphuric acid or chloride of calcium solution, in the bend of the y-tube, began to be heard. We intend to repeat the experiments with arrangements to prevent any bubbling of the air through liquid.

We have repeated our original experiment with pumice moistened with water

in the insulated U-tube, and with an uninsulated u-tube filled with sulphuric pumice between the bellows and the insulated tube, so that the air entering it is artificially dried. With this arrangement the insulated u-tube was negatively electrified by the blowing of the air through it; but this electrification may have been due to the negative electrification of the dry entering air to be expected from the result of our first experiment. We intend to repeat the experiment with artificially dried and dis-electrified air blown through the y-tube containing pumice moistened with water.

2. Preliminary Experiments for comparing the Discharge of a Leyden Jar through different Branches of a Divided Channel. By Lord KELVIN, P.R.S., and ALEX. GALT, B.Sc., F.R.S.E.

In these experiments the metallic part of the discharge channel was divided between two lines of conducting metal, each consisting in part of a test-wire, the other parts of the two lines being wires of different shape, material, and neighbourhood, of which the qualities in respect to facility of discharge through them are to be compared.

The two test-wires were, as nearly as we have been hitherto able to get them, equal and similar, and similarly mounted. Each test-wire was 51 cm. of platinum wire of 006 cm. diameter and 12 ohms resistance, stretched straight between two metal terminals at the ends of a glass tube. One end of the platinum wire was soldered to a stiff solid brass mounting; the other was fixed to a fine spring carrying a light arm for multiplying the motion. The testing effect was the heat developed in the test-wire by the discharge, as shown by its elongation, the amount of which was judged from a curve traced, by the end of the multiplying arm, on sooted paper carried by a moving cylinder. Two of Lord Kelvin's vertical electrostatic voltmeters, suitable respectively for voltages of about 10,000 and 1,500, were kept constantly with their cases connected with the outer coatings of the leyden, and their insulated plates with the inside coatings of the leyden.

I. In the experiments hitherto made the two wires to be tested have generally been of the same length. When they were of the same material, but of different diameters, the testing elongation showed, as was to be expected, that the test-wire in the branch containing the thicker wire was more heated than the test-wire in the other branch. In a continuation of the experiments we hope to compare hollow and tubular wires of the same external diameter, and same length and same material.

II. With wires of different non-magnetic material-for example, copper and platinoid-of the same length, but of very different diameters, so as to have the same resistances, the testing elongations were very nearly equal.

III. In one series of experiments the tested conductors were two bare copper wires, each 16 cm. diameter, 9 metres long, and resistance 085 ohm, which, it will be observed, is very small in comparison with the 12 ohms in each of the platinum test-wires. One of the copper wires was coiled in a uniform helix of forty turns on a glass tube of 7 cm. diameter. The length of the helix was 35 cm., and the distance from centre to centre of neighbouring turns therefore rm. The middle of the other copper wire was hung by silk thread from the ceiling, and the two halves passed down through the air to the points of junction in the circuit. The elongation of the test-wire in this channel was more than twice as much as that of the test-wire in the channel, of which the helix was part.

IV. One hundred and seventy-one varnished pieces of straight soft iron wire were placed within the glass tube, which was as many as it could take. This made the testing elongation ten times as great in the other channel.

V. The last comparison which we have made has been between iron wire and platinoid wire conductors. The length of each was 502.5 cm. The diameter of the iron wire was '034 cm., and its resistance 6.83 ohms. The diameter of the platinoid wire was '058 cm., and its resistance 6.82 ohms. Each of these wires was supported by a silk thread from the ceiling, attached to its middle (as in III. and IV.

for one of the tested conductors). Fourteen experiments were made, seven with the test-wires interchanged relatively to the branches in which they were placed for the first seven. The following table shows the means of the results thus obtained, with details regarding the electrostatic capacities of the leyden-jare and the voltages concerned in the results.

In each case four leyden-jars, connected to make virtually one of capacity 02742 microfarad, were charged up to 9,000 volts, and discharged through divided channel. The energy, therefore, in the leyden before discharge was 11.105 x 10" ergs. In each of the first three cases 1,450 volts were found remaining in the jars after discharge; in each of the last four 1,400.

The mode of measuring the elongation of the test-wires was, as may be understood from the preceding description, somewhat crude, but it is reassuring to see that the mean results in the cases of 10.82 and 10 84 megalergs of energy used are so nearly equal. The ratios for the two circuits are, in the two cases, respectively 1.48 and 1:46. The conclusion that the heating effect in the test-wire in series with the platinoid wire is nearly one-and-a-half time as great as that of the test-wire in series with the iron is certainly interesting, not only in itself, but in relation to Professor Oliver Lodge's exceedingly interesting and instructive experiments on alternative paths for the discharge of leyden-jars, described in his book on 'Lightning Conductors and Lightning Guards,' which were not decisive in showing any general superiority of copper over iron of the same steady ohmic resistance, but even showed in some cases a seeming superiority of the iron for efficiency in the discharge of a leyden-jar. Our result is quite such as might have been expected from experiments made eight years ago by Lord Rayleigh and described in his paper 'On the Self-induction and Resistance of Compound Conductors.'1

3. On Photo-electric Leakage. By Professor OLIVER J. LODGE, F.R.S.

4. Report on the Present State of our Knowledge of Thermodynamics, Part II., On the Laws of Distribution of Energy and their Limitations.' By G. H. BRYAN, M.A.-See Reports, p. 64.

5. On the Possible Laws of Partition of Rotatory Energy in Non-colliding Rigid Bodies. By G. H. BRYAN, M.A.-See Reports, p. 98.

6. On the Law of Molecular Distribution in the Atmosphere of a Rotating Planet. By G. H. BRYAN, M.A.-See Reports, p. 100.

Phil. Mag., vol. xxii. 1886, p. 469.

7. On the Application of the Determinantal Relation to the Kinetic Theory of Polyatomic Gases. By Professor LUDWIG BOLTZMANN.-See Reports, p. 102.

FRIDAY, AUGUST 10.

(Joint Meeting with Section G.)

The following Papers were read :

:

1. On Planimeters. By Professor O. HENRICI, F.R.S. This Paper was ordered by the General Committee to be printed in extenso. See Reports, p. 496.

2. Note on the Behaviour of a Rotating Cylinder in a Steady Current. By ARNULPH MALLOCK.

3. On the Resistance experienced by Solids moving through Fluids. By Lord KELVIN, P.R.S.

4. A Discussion on Flight was opened by Mr. HIRAM S. MAXIM.

SATURDAY, AUGUST 11.

The Section was divided into three Departments.

The following Papers and Reports were read:

DEPARTMENT I.

:

A Method of Determining all the Rational and Integral Algebraic Integrals of the Abelian System of Differential Equations. By W. R. WESTROPP ROBERTS, M.A.

The method of treatment adopted in this paper, though pregnant with facts calculated to throw light on the general theory of Abelian functions and integrals, has been strictly confined to the determination of the forms of the algebraic integrals which are rational and integral functions of the variables and arbitrary constants which enter into them. Jacobi's method of treatment enables us to determine many of the algebraic forms of the integrals of the differential system, but none of them are rational or integral, and even in the case of elliptic integrals the one rational algebraic integral which the differential equation possesses, involving an arbitrary constant, is arrived at with some difficulty from the known forms of the integral which are not integral functions of the variables. In the case of hyper-elliptic integrals I am not aware that rational and integral forms have yet been given. The result of the present paper enables us to write down for any case the forms of the algebraic integrals which are all rational and integral.

Again, being given one of these forms, all the remaining ones can be determined by the application of an operator 8.

With regard to the method adopted in the paper, I first show how to find all

the conditions which must be satisfied in order that a binary quantic of this degree 2n may be a perfect square, and show that they may be all found from a matrix which I call the square matrix for the functions of the degree 2n. I have not entered on any discussion of these curious conditions and their intimate relationship, which are well worthy of examination, insomuch as their number is the number of ways in which 4n-3 quantities may be taken 2n-2 together, and are still equivalent to but n conditions.

The Abelian system of differential equations may be written

where there are m quantities 1, 2, ≈m, and m-1 equations, as is clear from the above method of writing them if we suppose that can have any integer value from i=0 to im−2; also f(z) = x2m + P ̧z2m−1 + P2m-2+ . . . P,

.

2m'

I now form a function which I call F (≈), and which is of the degree 2m-2 in the following manner.

which is easily seen to be of the degree 2m -- 2 in ; also its source is

Ao {Pm2 −2^mPm + P2n}.

Now I say this function F (z) must be a perfect square. Forming, then, the various conditions from the square matrix of F (2), we have all the forms of the algebraic integrals of the Abelian system

which are rational and integral, involving m−1 arbitrary constants A2, À ̧

2. On a Graphical Transformer. By A. P. TROTTER.

. . λπ.

This instrument is intended for the expeditious replotting of a curve with transformed ordinates without calculation or scaling. It consists of a rectangular frame and a curved template or cam, and is used in conjunction with a straight ruler.

Let the scale of one system of ordinates be set off upwards along the edge of one of the perpendiculars, and the scale of the other along the edge of the other perpendicular, but downwards. Join the corresponding points on the scale by straight lines. The envelope of this system of lines may be thus drawn, and to this curve a cam is cut in thin wood or ebonite.

To transform any ordinate, set the frame against a T square, adjusting the edge to the ordinate, and the zero to the zero of the scale. Set a needle at the extremity of the ordinate; bring a straight edge to touch the needle and the cam; prick off a point at the intersection of the straight edge with the other edge of the frame. This point determines the length of the new ordinate.

An instrument provided with a logarithmic cam was exhibited. With this instrument the product or quotient of two curves can be found by adding or subtracting the logarithms of the ordinates; or the logarithms of a series of observations can be plotted. Cams for other functions can be easily made; but it must be

Printed in extenso in the Electrician, August 17, 1894, vol. xxxiii. p. 465.