method of the variation of parameters, proper for determining directly the motion of the apses of an orbit. III. “On some of the Products of the Distillation of Boghead Coal at low temperatures.” By C. Greville Williams, In presenting a brief preliminary notice of an investigation of the substances obtained by distilling boghead coal at low temperatures, I may observe that I was induced to undertake it from remarking the low density of the naphtha produced in the process; it being only 750 at 60° F., although its boiling-point, previous to the rectifications, was as high as 290° F. After fifteen complete fractionations of the portion distilling below 310° F., boiling-points were obtained as low as 170°, and it was found that the fluid could be separated, by careful treatment with fuming nitric, or a mixture of nitric and sulphuric acids, into two bodies, one forming a nitro-compound, the other being unacted on. The latter was washed several times with a strong alkaline solution, and, after being digested for a few days with sticks of potash to remove adherent moisture, rectified over sodium. In this manner I obtained a colourless and very mobile fluid with a pleasant odour, distantly resembling that of hawthorn blossoms. Its density at 60° was 725. I selected the fraction boiling in the fifteenth rectification at 240° F. to make a preliminary experiment upon, and, after purification in the manner described, it gave in three perfectly concordant analyses, exactly the per-centage of carbon and hydrogen required for butyl (valyl of Kolbe), the radical of the butylic alcohol. Two determinations of the vapour density, taken respectively at 80° and 107° above its boiling-point, gave numbers closely coinciding with theory. When it is considered that 68° or more of difference of boilingpoint only cause a variation of 0:3 in the per-centage of carbon and hydrogen of bodies of this class, it becomes evident that if I had taken the fraction boiling at 223° (Wurtz) or 226° (Kolbe), it would have yielded the same results. This point is now under examination. The formula C16 H18=4 vols., corresponds not only to butyl, but also to the hydruret of caprylyl, and, of course, both these bodies have the same vapour density ; but several circumstances lead me to believe the hydrocarbon I have obtained to be the radical of the butylic alcohol. The density of the fluid, and the temperature at which it distils, are also rather in favour of this view. It will be seen that 247° E. should be the boiling-point of butyl if Frankland's determination of that of amyl be correct, and Kopp's law hold with these bodies. A careful study of the papers already published on the radicals of this series, shows that more than one anomaly appears to exist in their physical properties, the gradations usually observed in homologous groups not being so distinctly marked as with most others, and this fact somewhat impedes their identification. The large quantity of substance which becomes at our disposal from the source mentioned, will, by facilitating the study, throw light on these points. I believe I shall be able to isolate at least four of the radicals, viz. propyl, butyl, amyl, and caprotyl, from the coal distillate. The per-centage composition varying so little with the different homologues, I rely chiefly on vapour density and products of decomposition as the means of proving their presence. The hydrocarbons accompanying the radicals are also quite distinct from the benzole series, as shown by the low density of the nitrocompound. The latter is extremely difficult of reduction by sulphide of ammonium or protacetate of iron, but it furnishes a volatile oily alkaloid by distillation with an alcoholic solution of potash. The tedious purifications and the numerous operations required before the substances can be obtained in a state of sufficient purity for analysis from the coal distillate, will probably cause a considerable period to elapse before a detailed account of all the bodies can be published. a IV. “On Peristaltic Induction of Electric Currents." By Pro fessor WILLIAM THomson, F.R.S. Received May 10, 1856. Recent observations on the propagation of electricity through wires in subaqueous and subterranean telegraphic cables have brought to light phenomena of induced electric currents, which, while they are essentially different from the phenomena of what has hitherto been called electro-dynamic induction, are exactly such as might have been anticipated from the well-established theory of electrical equilibrium, had experiment afforded the data of relation between electrostatical and electro-dynamic units wanted for determining what dimensions of wire would be required to render these phenomena sensible to ordinary observation. They present a very perfect analogy with the mutual influences of a number of elastic tubes bound together laterally throughout their lengths, and surrounded and filled with a liquid which is forced through one or more of them, while the others are left with their ends open (uninsulated), or stopped (insulated), or subjected to any other particular conditions. The hydrostatic pressure applied to force the liquid through any of the tubes will cause them to swell and to press against the others, which will thus, by peristaltic action, compel the liquid contained in them to move, in different parts of them, in one direction or the other. A long solid cylinder of an incompressible elastic solid *, bored out symmetrically in four, six, or more circular passages parallel to its length, will correspond to an ordinary telegraph cable containing the same number of copper wires separated from one another only by gutta-percha : and the hydraulic motion will follow rigorously the same laws as the electrical conduction, and will be expressed by identical language in mathematics, provided the lateral dimensions of the bores are so small in comparison with their lengths, or the viscosity of the liquid so great, that the motions are not sensibly affected by inertia, and are consequently dependent altogether on hydrostatic pressure and fluid friction. The electrical induction now alluded to depends on the electrostatic forces determined by Coulomb; but it would be in * Such as india-rubber very approximately is in reality. one respect a real, and in all respects an apparent, contradiction of terms, to speak of electrostatic induction of electric currents, and I therefore venture to introduce the term peristaltic to characterize that kind of induction by which currents are excited in elongated conductors through the variation of electrostatic potential in the surrounding matter. On the other hand, as any inductive excitation of electric motion might be called electro-dynamic induction, it will be convenient to distinguish the kind of electro-dynamic induction first discovered by Faraday, by a distinctive name; and as the term electro-magnetic, which has been so applied, appears correctly characteristic, I shall call electro-magnetic induction that kind of action by which electric currents are excited, or inequalities of electric potential sustained, in a conductor of electricity, by variations of magnetic or electro-magnetic potential, or by absolute or relative motion of the conductor itself across lines of magnetic or electro-magnetic force. The most general problem of peristaltic induction is to determine the notion of electricity in any number of long conducting wires, insulated from one another within an uninsulated tube of conducting material, when subjected each to any prescribed electrical action at its extremities; without supposing any other condition regarding the sections and relative dispositions of the conductors than-(1), that their lateral dimensions and mutual distances are so small in proportion to their lengths, that the effects of peristaltic induction are paramount over those of electro-magnetic induction ; and (2), that the section of the entire system of conductors, if not uniform in all parts, varies so gradually as to be sensibly uniform through every part of the length not a very large multiple of the largest lateral dimension. In the present communication I shall only give the general equations of motion by which the physical conditions to be satisfied are expressed for every case; and I shall confine the investigation of solutions to certain cases of uniform and symmetrical arrangement, such as are commonly used in the submarine telegraph cable. At any time t, let 91, 92, 93, &c. be the quantities of electricity with which the different wires are charged, per unit of length of each, at a distance x from one extremity, 0, of the conducting system; and let 1';, V.V.3, &c. be the electrostatical potentials in the same parts of those conductors. Let w,9), zu,9), w,8), &c., w."), w., 20. ,, &c., w,""), w,a,,, &c. be coefficients, such that the electro () 1) statical potentials (, V.&c.), due to stated charges (91, 92, &c.) of the different wires, are expressed by the equations V=@,"91+a," 92 +0,23+ &c. (1). &c. If the sections of all the conductors are circular, these coefficients (@,1), a 1(2), &c.) may be easily determined numerically to any required degree of accuracy, in each particular case, by the method of electrostatical images. The electromotive force per unit of length at the position « will be, in the different wires, dv. dv.dug d.x' da dx respectively, and therefore if y1, 72, 73, &c. denote the strength of current at the same position, and kj, k,, kz, &c. the resistances to conduction per unit of length in the different wires respectively, we have by the law of Ohm, applied to the action of peristaltic electromotive force, dvi dv, (2). dr Now unless the strength of current be uniform along any one of the wires, the charge of electricity will experience accumulation or diminution in any part of it by either more or less electricity flowing in on one side than out on the other; and the mathematical expression of these circumstances is clearly dai dy (3). dt dt dx Using in these equations the values of 70 72 73, &c. given by (2), and then substituting for vi, V.,, , &c. their expressions (1), we obtain d [ 1 da,"2.), 1 d(0, (2) (3) 93) + + dt da lk, dir k, dx kg dx d92 di dw.9.) 1dw,99) d + + + &c. dt dix k. (), dx kz dx 1dw,"9) 1 dlw31893) dx dx kz dx dqu 293) } } de lk d | 1 dx Ak d93 dt xka 1.d(,12) '92) + + &c. which are the general equations of motion required, |