from the same quantity of electricity transmitted in a single discharge from the battery, as it would have required the substitution of a larger wire in the electrometer. On passing, however, one such discharge through the wire which I employed, it was melted, clearly showing a very great increase of effect with an undivided quantity.

Having thus ascertained the value of a single discharge from the coil, and established a similar unit with the electrical machine, it was easy to ascertain its equivalent in glass surface submitted to friction; and this quantity, multiplied by the number of discharges which the coil would produce in a second, would show their relative capabilities of developing electricity. My next step was to count the discharges of the coil; and here it may be remarked, that when the jar is employed, the value of each discharge is in no way lessened, but rather increased by the rapidity with which they follow each other. For this purpose I adopted Mr. Grove's suggestion of making the discharges perforate a sheet of paper in motion, but the difficulty was to ascertain the rate at which they were produced; this, however, I accomplished in the following manner, by an apparatus to which I have at present given the name of Spark-counter. It is thus constructed: two circular discs of wood, about 5 inches in diameter, are screwed together upon one common axis, so as to embrace a circular disc of paper, about 12 inches in diameter, between them. One of the discs of wood is made moveable, for the purpose of changing the discs of paper when required. This is mounted with a handle so as to rotate vertically like the plate of an electrical machine. Upon the same stand are placed two vertical brass pillars, having steel bearings on the top, which serve to support the knife-edges of the axis of a half-seconds' pendulum, so situated on the stand as to hang about 2 inches from the edge of the paper disc, and make its oscillations in the same plane. Through a wooden headpiece fastened on the axis of the pendulum, pass two copper wires enclosed in gutta-percha. These wires are about 2 inches apart, and they stand out horizontally about 8 inches in length, like two arms stretching towards the paper disc, one on each side of the top of its periphery. Here the points are turned towards each other, and brought within 4th of an inch of the paper on each side, so that the naked ends of the wires are about a quarter of an inch apart, having the paper disc between them, and are so adjusted as to stand about half-way between the edge of the paper and the wooden plates which hold it. The other two ends of the wires pass about 1 inch through the headpiece, and are there bent into two hooks, the gutta-percha coating being removed from them. Upon these hooks hang the ends of two light and flexible wire-cord conductors, connected respectively

with the inner and outer coatings of the jar, which latter is also in connexion with the coil. The apparatus being thus arranged, if the pendulum be made to swing, the two arms will describe an arc over the periphery of the paper; and if the coil be set in action, discharges will pass between the points, marking the arc with perforations. If, now, the disc be turned slowly on its axis, a series of curves will be described by the perforations from the oscillating points. The number of perforations in each curve may be counted; and if reckoned from the top of one curve to the top of another, we get the number per second; or if from the top of one curve to the bottom of the same one, the number in a half-second. The rapidity of the discharges will depend upon the nature of the interrupting spring employed in the coil, and as many as 100 to 200 per second may be obtained. It is necessary that the paper should be rather slight for this purpose, and not turned too slowly, otherwise each discharge will not make a new perforation for itself, but some will occasionally pass back over the paper through the perforation made by the last discharge. A little observation will, however, soon obviate this.

Having now the means of counting the number of discharges of the coil per second, their equivalent in glass surface was easily calculated, and the following is the result.

I took one of my cylinder machines of 11 inches diameter, having a 10-inch rubber, and which in ordinary excitation will give six straight sparks between 3 and 4 inches long, from a conductor 5 inches in diameter and 18 inches in length, for every revolution of the cylinder, and a strong current of zigzag sparks between 9 and 10 inches in length, from a 2-inch brass ball. The quantity of surface rubbed by this machine to produce a discharge equivalent to a single discharge of the coil, was about 16 square feet; therefore when the coil gave 150 discharges per second, it was equal to 2400 square feet of glass surface per second; and as the machine could not be comfortably worked at the rate of more than 3 square feet per second, the coil was equivalent to the action of 800 such machines, and when giving discharges at a more rapid rate, could be made equivalent to 1000 of them. A 24-inch plate machine, having four rubbers of 5 inches in length, is just equivalent in actual power to one of my 11-inch cylinders; therefore the same number of such machines would be required to do the work of the coil. During my late visit to London I was desirous of obtaining the equivalent of the coil in steam electricity, and through the kindness of my friend Mr. Pepper, who generously placed the powerful hydro-electric machine of the Royal Polytechnic Institution at my disposal, I was able to accomplish this. The machine having been powerfully excited, the steam being at 90 lbs., and the full number of jets in

operation, I connected with the conductor a jar containing a square foot of surface, in communication with which were a Lane's discharger, the spark-counter, and a thermo-electrometer. The discharging interval was adjusted so that each discharge produced one degree of effect upon the thermo-electrometer. This interval was rather more than 0.2 of an inch, and the discharges passed at the rate of seven per second. The discharger was fitted with balls of 1 inch diameter, and the bottom of the jar was connected with the gas-fittings. The total rise of the thermo-electrometer was 20 degrees.

On comparing these effects with those of the coil, it would appear that since the latter is capable of producing from 100 to 150 discharges per second, or even more, each raising the fluid 1 degree of the thermo-electrometer, it would be equivalent to fifteen or twenty such hydro-electric machines. I next disconnected the jar and caused a current of dense sparks of 2 inches in length to pass from the conductor through the spark-counter and thermo-electrometer, the latter being in connexion with the gas-fittings, and with this arrangement I obtained sparks at the rate of thirteen per second, producing a rise in the thermometer of only 5 degrees. I had the curiosity to receive a few of these sparks on my hand; they were extremely violent, and were felt very powerfully in the legs and heels, although the floor was wood. They were not, however, so painful as static sparks from the outer terminal of the coil.

The quantity of electricity developed by this hydro-electric machine must have been very great, since on attempting to reduce the rapidity of the discharges of the jar by placing an imperfect conductor in contact with the machine, I found that my oak walking-stick produced scarcely any effect when laid upon the conductor, until the portion between the conductor and my hand was reduced to 3 or 4 inches.

The quantity of static electricity developed by the coil appears by these comparisons to be very great, but its effects are of a very peculiar kind. One cannot help being struck with the difference between the character of the current which excites the machine and that developed by it. The former possesses no tension, but great thermal and magnetic power; the latter great tension, and, if unassisted by the jar, no thermal power in a metallic circuit, except at the discharging ends; and here, as I have before stated, it is doubtful whether the heat is elicited from the intervening medium or the metal itself. The thermal effect, however, produced by the jar opens a curious inquiry as to the extent to which it might be increased by increasing the size of the coil. I have hitherto only produced, by the induced current and the jar, the ignition of 4 or 5 inches of fine platina wire; whereas

the battery used to excite the machine would ignite nearly three times the length of the same wire. Now I venture to throw out for the consideration of those engaged in the interesting and important investigation of the correlation and conservation of physical forces, and who have more time to prosecute their inquiries than I can possibly command in the occasional intervals snatched from active business occupations, that it would be very curious to ascertain the relation between the thermal characters of the current employed and the current produced; and if, by any augmentation in the size of the apparatus, the secondary thermal effects should be ever made to equal those of the primary current, what would be the intermediate relationship of the magnetism which would then almost appear to be an extraneous development. I do not throw out this hint by way of expressing any want of confidence in a theory, the truth of which, if not already established, is pretty nearly so, but merely to suggest what appear to me new conditions and relationships which require to be harmonized with each other, and included in the general consideration of the phænomena.

XLVI. On the Problem of the In-and-circumscribed Polygon. By the Rev. GEORGE SALMON, Trinity College, Dublin*.

THE

HE following is the conclusion of my investigations on this subject published in the last Number. It is found by the method there described, that if two sides of a triangle touch a Iconic U, and the third side a conic aU+6V, if the two base angles move on the conic V, then the locus of the vertex will be one or other of two conics touching the four common tangents of U, V, and whose equations are of the form

▲▲λ2V+λμF+Uμ2=0,

where X is given by the quadratic equation

a(ab-ẞa)λ2+a(4▲a+2®b)λμ—b2μ2=0,

where a=4AA', B=02-4AO'.

Now if it be required to find the locus of the free vertex of a polygon, all whose sides touch U, and all whose vertices but one move on V, this is immediately reduced to the last question, since the line joining the two vertices of the polygon adjacent to that whose locus is sought, touches a conic whose equation is of the form aU+bV=0.

The locus will therefore always be of the form

▲▲λ2V+λμF +μ2U=0.

* Communicated by the Author.

Phil. Mag. S. 4. Vol. 13. No. 87. May 1857.

2 A

It may be seen without difficulty, that if X', u' be the values for a polygon of n-1 sides, and X", " those for a polygon of n sides, then the values for a polygon of n+1 sides are

\""=μ'μll2, μ!" =▲'2'2" (aμ" — A'BX").

And since in the case of the triangle we have λ=a, μ'=D'ß, and in the case of the quadrilateral we have "B2, μl=ay, where y=4Aa+280, we can form, step by step, the equation for any polygon.

From these we can deduce the condition that it should be possible to describe a polygon inscribed in V, and circumscribed about U. These conditions are,—

and so on. I suppose these values will be found to coincide with those found by a different method by Mr. Cayley in a former Number of this Journal, but I have not verified this.

Trinity College, Dublin,

April 13, 1857.

XLVII. On the Constitution of Allophane. By AUGUSTUS BEAUCHAMP NORTHCOTE, F.C.S., Senior Assistant in the Royal College of Chemistry*.

THE

HE occurrence of the mineral allophane at New Charlton, near Woolwich, appears to be quite of recent discovery. In the summer of last year, my friend Mr. Bullen, of the School of Mines, observed this substance occupying the position of a vein in a chalk-pit at that place, which from its existing at both sides of the quarry, had in all probability stretched across before the clearing away of the chalk had been effected. This vein had, it appears, about the same time attracted the attention of other observers, for on the 19th of November last Mr. Morris read a paper before the Geological Society upon its existence and composition +.

My own analyses of the specimens which Mr. Bullen was kind enough to procure for me were unavoidably delayed; but not

* Communicated by the Author.

+ Quart. Journ. Geol. Soc. vol. xiii. p. 13.