be transformed into a function of p by means of the equations (25) this done, and the integration effected, (26) is evidently the equation of the curve (25), when the cone upon which it is conceived to be described is unfolded into a plane. Again, if by means of (26) we eliminate p from the equation 1 1 dp2 u2 + u22 = 2 + p1 do2 the latter will become the differential equation of the plane curves whose elements attract the pole in the same manner as the corresponding elements of (26),—u being the reciprocal of the radius vector r. If we suppose to be the general integral of this equation, where c is the arbitrary constant, then the equations of the system of curves of double curvature, whose elements attract the pole in the same manner as the corresponding elements of the given curve (25), will evidently be the result of the elimination of p and 0 from the four equations (25), (26) and (27). Pau, March 1857. XLV. On a new Instrument for Registering a rapid succession of Electrical Discharges, and a comparison of the Effects of the Induction Coil with those of Frictional and Hydro-electric Machines. By JONATHAN N. HEARDER, Mechanician, Plymouth*. THE THE induction coil appears to be an instrument so susceptible of extension of power, modification to suit requirements, and practical application to the most important purposes, that experiments calculated to throw light upon its action or develope its capabilities are invested with more than ordinary interest. Without in the slightest degree wishing to detract from the merit so justly due to M. Ruhmkorff, for having first elicited the latent powers of this instrument and exhibited its capabilities by an extension of principles already known and practised, I may venture to express a little surprise that the ingenuity which contrived the instrument did not still further display itself in its subsequent improvement. If, as was stated, however, by Mr. Gassiot on the occasion of a lecture which I had lately the honour of delivering before the Society of Arts, M. Ruhmkorff was actuated more by a desire to make a cheap than a perfect machine, the fact is easily accounted for. The mode of insulation which he has adopted, viz. that of covering the wire with cotton and sepa * Communicated by the Author. rating the layers with paper, is so defective that it would preclude the possibility of any great increase of power by extension of size. It is a source of no small satisfaction to me, that I was unable to get any definite information of the construction of Ruhmkorff's coil when I sought it in 1855, since, had I obtained it, it might have prevented me from acting upon my own experience, and adopting a mode of construction which turns out to be totally different from that of M. Ruhmkorff, and which has been attended with such unprecedented results. As I feel that there is some amount of honour connected with the origination of this new form of the coil in England, I may be pardoned for asserting my priority in this matter. I should not have been induced to do so, but from the fact that the mode in which my name has been coupled with that of a gentlemen who has recently constructed an instrument precisely upon the same principle as my own, has produced an impression that we had both constructed our instruments about the same time, which is not the case. My first instrument was made about the middle of the year 1855, and in November of that year I communicated the minute details of the construction of one or two of my instruments to Mr. Grove, describing the use which I had made of gutta-percha and oiled silk as a medium of insulation. The results which I had obtained with these instruments, particularly with one of them, were of a very exalted character, although an insignificant battery was employed. I am quite sure that the contents of that letter had escaped Mr. Grove's recollection during his very gratifying remarks on my lecture at the Society of Arts, since the general impression produced by an observation which accidentally fell from him was, that my labours had been coincident with those of Mr. Bentley, the gentleman to whom I have alluded. As early as December 1855, I had worked out the major part of the results which I have lately had the honour of detailing to the London Institution and Society of Arts, and in March 1856, gave a lecture on the subject before the members of the Plymouth Institution, an account of which appeared in the Journal of the Society of Arts, May 16, 1856, p. 444. In my first paper in the Philosophical Magazine, November 1856, I had occasion to animadvert on the conduct of Dr. Noad, for having anticipated me by introducing at a public lecture, in October last, a machine almost identical with my own, constructed but a few weeks before by his friend Mr. Bentley, whilst at the same time he refused to allude to the previous existence of mine, the particulars of which he had obtained from me for publication in his new work nearly nine months before, and had bound me in the meantime not to publish myself, but which information, although actually printed, had been kept from the scientific world by the delay in the publication of his work. Dr. Noad having considered these remarks to imply an accusation of plagiarism, I take this opportunity of stating that I did not intend them to convey any such imputation, and that I only wished to complain that Dr. Noad had done me an injustice and a serious commercial injury by suppressing my invention, and giving publicity and precedence to another production of more recent date, and almost identical with my own. During the past nine months I have had opportunities of still further extending the principle upon which my machine is constructed, and with a corresponding increase of power; since I have occasionally, from a single machine, produced sparks 4 inches in length in free air, and I have very little doubt that I could construct machines to give sparks of 12 inches or more. The results obtained by this increase of power are very striking, and phænomena previously unknown are continually developing themselves. I have before alluded to two different classes of thermal effects obtained: first, from the simple spark between the terminals; and secondly, from the spark produced through the intervention of the Leyden jar. The simple spark passing between the terminals is comparatively soft and attenuated, though when of considerable length it is accompanied by a tolerably sharp snap. Sparks of 2 to 3 inches in length are extremely crooked, the deflections sometimes increasing the length of the spark to nearly one-half more than the distance between the terminals. Imperfect conductors, such as paper or wood, assist the spark in overleaping the interval; for if the points be placed beyond the striking distance, and a sheet of paper be held parallel to them and nearly an inch distant from each, sparks will frequently pass from one point to the paper and across its surface to the other point. In this way I have often obtained sparks nearly 6 inches in length. The chief characteristic of this spark is its power of igniting or burning substances which are either non-conductors or bad conductors; and some of these effects are very remarkable. On one occasion, when experimenting with one of my large coils, two wires from the terminals were accidentally lying with their ends at a distance of several inches from each other upon the table. I happened to set the machine in action, and instantly the table burst into flame in the two spots on which the ends of the wires rested, and the combustion went on rapidly increasing until I stopped the machine. Noticing this, I took a piece of deal and slightly moistened its surface with nitric acid and placed it on the table of the universal discharger, with the points about 4 inches apart. On connecting it with the machine, the combustion commenced at the points as before, and the flames ad vanced along the surface of the wood towards each other, and in the course of a minute or two united near the middle, forming a long crooked line of fire between the points. This effect took place most rapidly when the points were placed on the longitudinal section of the wood of the same year's growth; for if placed indiscriminately on different portions of the wood, the sparks would advance from each point a certain distance, following the course of the grain, and then suddenly jump over into the next layer, and so on at irregular intervals until they both reached the same longitudinal layer, when they would rapidly advance towards each other, and the combustion would instantly increase throughout the whole of the crooked circuit thus produced. On connecting with the wires of the universal discharger the ends of a slip of deal about as thick as a goose-quill, and 5 or 6 inches long, slightly moistened with nitric acid, it instantly takes fire at the points of contact, and the sparks pass along its surface, rapidly kindling it throughout its whole length, when it assumes the appearance of a bar of fire in vivid combustion and is speedily consumed. Sometimes the spark, instead of passing over its surface and kindling it, will rise from one portion and leap to the middle or some other spot, where it instantly burns through the wood and generally breaks it. This remarkable action is not confined to inflammable imperfect conductors, and would appear to arise either from the heat elicited from the air in the passage of the spark, or from an immediate heating power of the spark itself; for even thin glass will fuse and become vividly ignited when sparks are made to pass over its surface. The interposition of the Leyden jar, as is well known, produces a marked change in the character of the spark it increases its volume, light and sound, but diminishes its length; and the larger the jar or battery, the more is the length of the spark diminished, the excitation of the coil being the same. The thermal effects also undergo a curious change, and the induced current appears to be endowed with a new character which it did not before possess, viz. that of heating an intermediate portion of the metallic circuit when of small dimensions (Phil. Mag. vol. xii. p. 380. par. 7). Since I first noticed these results, I have repeated them with more powerful machines, and the following experiment exhibits the effect in a striking manner. I connect with the terminals of the induction coil, by means of two long and flexible conductors, a discharging electrometer, set so as to give sparks of 0.3 or 0.4 of an inch in length. In immediate connexion with the discharger, and forming an intermediate portion of the circuit, I place a piece of fine platina wire about 4 or 5 inches in length. I then connect one of the con ducting wires in any portion of its length, between the terminal and the discharger, with the outside coating of a Leyden jar containing two or three square feet of surface, and by means of an insulating handle, hold the wire proceeding from the other terminal by the middle, or any convenient part of its length, so as to be able to bring it in contact with the knob of the Leyden jar, and thereby make it a part of the arrangement, and charge it. If a current of sparks from the coil be made to pass through the fine platina wire whilst the inner coating of the jar is unconnected with the transmitting wire, no heating effect is produced, as may be observed by including the wire in the bulb of the thermo-electrometer; but if, whilst the sparks are passing, the transmitting terminal wire be brought in contact with the knob of the jar, the loud discharges are produced, and the platina wire instantly becomes white-hot, elongates, and vibrates with great rapidity. If the wire be too short, or the charge of the jar too strong, it is melted; or if too long and the charge too weak, it merely becomes red-hot. This effect appears and disappears on alternately making and breaking connexion with the jar. Whilst the jar is disconnected, the sparks in the discharging interval instantly burn paper, wood, &c.; but when connected, the noisy sparks have scarcely any such power, though if the discharging interval be made much shorter, this effect is considerably increased. The coil which I have used for these and the subsequent experiments, contains rather less than four miles of fine wire, and the primary coil is usually excited with twelve nitric acid cells having platina plates immersed, 2 inches by 4, and used collaterally as a double set of six. The rationale of these changes is not very obvious, nor have I much desire to speculate upon the matter, as I hold the registration of facts under present circumstances to be of much greater importance. It has, however, suggested itself to my mind, that in each impulsive wave of the induced current, a certain quantity of electricity, or rather amount of electrical force, is accumulated at the terminals, and the attraction resulting from their opposite electrical states causes them to induce upon each other, and determine the discharge through the interval between them. Now in every case of electrical discharge, its character and appearance will be materially influenced by the conditions of the conductors between which it passes, viz. their extent of surface considered as separate and independent conductors; and secondly, the extent of the respective areas approximated to, and inducing upon each other, and between which the discharge takes place. Every freely-insulated conductor undergoes induction from the influence of surrounding bodies whenever an electrical charge is thrown upon it, and I know of no condition in which a body |