III. If the formula with the reduced coefficients be em ployed*, namely then U2N=a,+5a6+4a5 +6α +2a3 + 3u2+α1, U; N=1+10+12+24+10+18+7=82. U," N=3.8+2=26. U""N=3.2+6=12. U N=3.1+2=5. Here (n) = 4. 34. In N, as soon as any value of a, is increased, by the successive addition of units, up to or beyond r, it is transferred to the next higher term, or that containing the factor ɑ2+1, by adding a unit to the higher term and placing the remainder to r, or of the division in the term in which the An lower factor a, occurs; that is, r determines the maximum value of a, in each term. In UN, on the other hand, & may be taken of any integer value in respect to r, and the formula will still be true, but r will have no power to determine the highest value of an in any term; & is the only determinator of the maximum value of an in any term. For illustrations of this see Philosophical Magazine, May 1875, p. 347, and the above instances of U,N and U,N. 35. The value of 8, whether integral or fractional, for instance, determines the degree and kind of discontinuity that exists in UN. For example, in U,671, is taken, by inference, as the unit; the same occurs in U967. In U2;25=3=1}, is the unit. 36. In regard to the arrangement of the terms, N gives simply the arrangement of a number in powers of r; whereas UN gives the arrangement of the same number in powers of (-8). In the most useful form of UN, each power of (r−8) is reduced by substituting for it its remainder to 8. XXXI. The Contact Theory of Voltaic Action. By W. E. AYRTON and JOHN PERRY, Professors of the Imperial College of Engineering, Tokio, Japan. WE To the Editors of the Philosophical Magazine and Journal. The Imperial College of Engineering, GENTLEMEN, Tokio, Japan, December 14, 1877. HEN contributing his paper, "On the Difference of Potential produced by the Contact of Different Substances," to the Royal Society on May 22, 1877, Professor Clifton, of Oxford, seemed to be quite unaware of the elaborate series of experiments on exactly the same subject made by us in the winter of 1875, a full account of which was communicated in a paper on "The Contact Theory of Voltaic Action, Paper No. I.," to Professor Sir William Thomson, May 6, 1876, who at the British-Association Meeting at Glasgow of that year gave a public account of the method employed by us and the results we obtained, reserving our complete paper for the pages of the Proceedings of the Royal Society. If the investigation in question had been of merely ordinary importance, we should not have deemed it necessary to point out the priority of our experiments to those of Professor Clifton; but when the fact is remembered (a fact not very evident from Professor Clifton's paper) that a series of experiments such as we performed clears up the long-standing discrepancies between the chemical and contact explanations of voltaic phenomena, and so is of extremely great importance in the science of energy, we trust we may be pardoned for claiming the priority due to us. Much of the ordinary original work performed in physical laboratories must, of course, be undertaken nearly simultaneously in different countries; and our great distance from Europe necessarily places us in tle unfortunate position of being some months in time behird other men who publish papers in the same societies as ourselves; but in this particular case the work was not of an ordinary kind, and we have not to ask for the indulgence of scientific men in making allowance for our residence in Japan, seeing that, first, our paper reached England exactly one year before Professor Clifton's communication was made to the Royal Society, and, secondly, Sir W. Thomson was so kind as to give an account of our method and results to the British Association several months before Professor Clifton appears to have commenced his earliest experiments on the subject. The method of experimenting employed by this gentleman is essentially the same as that used by ourselves, with this im portant difference, that whereas Professor Clifton only removes the plates of a condenser from a distance a apart to a distance b apart, we removed them to an infinite distance apart, and then put them in such a position that the original charge to be measured was doubled; so that in fact our method was by far the most delicate, and was only limited in sensibility by the natural imperfections of mechanism. All this was clearly shown in the carefully executed drawing that accompanied our paper. The advantages we derived from the superior delicacy of our apparatus are seen if we examine, as may easily be done, the two papers paragraph by paragraph; for the metals and liquids employed by Professor Clifton being the same as those used by ourselves, in every case that he in 1877 was only able to detect the difference of potentials, we in 1876 published not only the sign but also the numerical value of the difference in question (compare pages 301 to 305 of his paper in the 'Proceedings of the Royal Society,' No. 182, with our paper). Considering, too, that the quantities of electricity to be measured are so small, and consequently the slightest loss of electricity is so serious, we fail to see what benefit was derived from using six insulating stems instead of only the two carefully protected rods of our apparatus. We observe that Professor Clifton assumes throughout his paper the "summation law of electromotive force," and that he was compelled to make such assumptions in consequence of his inability to measure directly with his apparatus the difference of potentials between two liquids in contact. But if this be assumed, then we might have employed in our research the method of measuring the difference of potential of two liquids in contact that we have often, as early as 1874, employed as a lecture-illustration to indicate this difference. This method consisted in attaching to the terminals of a quadrant-electrometer two platinum wires, of which the ends were respectively dipping into two liquids separated by a porous diaphragm; but to make any use of the observations obtained from such an experiment, it must be assumed that the observed deflection of the electrometer represents the algebraic sum of the three contact differences of potentials such as might be measured separately. At first sight, not to assume this might appear to be a refinement of caution on our part; but in reality it was imperative to prove experimentally that this assumption was true when it was taken in connexion with the statements generally made by the supporters of Thomson's theory of contact. For example, Professor Fleeming Jenkin says, on p. 44 of his 'Electricity and Magnetism':-"When a single metal is placed in contact with an electrolyte, a definite difference of potentials is produced between the liquid and the metal. If zinc is plunged in water the zinc becomes negative, the water positive. Copper plunged in water also becomes negative, but much less so than zinc. If two metals be plunged in water (as copper and zinc), the copper, the zinc, and the water forming a galvanic cell, all remain at one potential, and no charge is observed in any part of the system." Consequently in 1875 we discarded our original proposed method of experimenting, which was to use an apparatus somewhat similar to that employed by Professor Clifton, as far as we can understand it without a drawing; and we constructed the apparatus described in our paper, which enabled us to measure any single contact difference of potential, whether of a metal with a metal, or a metal with a liquid, or a liquid with a liquid, or a combination of any two or more contacts. The very important fact that the rise of the difference of potentials between the plates of a voltaic cell on first immersion, when the circuit remains open, is due to the same cause as polarization of the plates when the circuit is closed but operating in the opposite direction, as explained by Professor Clifton, was clearly stated by us in our paper in question under "the three states of a cell;" and our subsequent papers showed that we considered this effect to be analogous with the so-called soaking in and soaking out in any dielectric, or what is called the residual charge in a Leyden jar—a subject to which we have been since devoting much attention. But we even went further; for we found that even when the circuit was closed directly after immersion, there was first a rise of difference of potentials, followed afterwards by a fall; and this is an explanation of a want of constancy observed in many cells, and notably in the two-fluid cell described by Professor Clifton, page 309. We take the liberty of observing that although a table of the difference of potentials of the terminals of different cells is of great value to practical men, still we should hardly have expected to find such a table at the end of Professor Clifton's paper with one number only (almost without exception) given for each cell, since he was quite aware that the difference of potentials between the electrodes alters from the first instant of immersion of the plates. Again, we do not understand how he can say that no current has passed; for it is evident that a current may pass without the electrodes being externally connected. A table such as is given by Professor Clifton would be very valuable if it gave the difference of potentials between the electrodes when the plates had been kept immersed for a sufficient length of time for the difference of po tentials to reach its maximum value; but it would be more valuable if it gave in addition the time-rise of the difference. We confess, however, that it is only with exceptional cells that we have succeeded in getting on different occasions exactly the same results with the same combination. Such a table as we suggest, which would be a great improvement on that given by Professor Clifton, could of course be constructed by any one possessing an electrometer without employing any special apparatus. In conclusion we notice, page 299, that Professor Clifton sees the necessity of changing his apparatus, which could not measure directly the difference of potential between two liquids in contact, before he can obtain satisfactory measures of the difference of potential in certain important cases. We may mention that although the apparatus employed by us in our investigation described in our paper of 1876 enabled us to do this with considerable accuracy, still we thought it advisable, in the summer of that year, to construct a new apparatus, the accurate results obtainable with which will form the subject of our next paper on this subject. We beg to remain, Gentlemen, W. E. AYRTON. XXXII. On the Colour Relations of Copper and its Salts. By THOMAS BAYLEY, Assoc. R.C.Sc.I.* COPPI YOPPER in solution, as is well known, imparts to the liquid a blue colour. In the case of the chloride the colour inclines to green, but becomes blue on dilution. Wishing to see what relation the light transmitted by such solutions bears to that reflected from the surface of the metal, I made the following experiments. An extremely dilute solution of cupric sulphate having been prepared, it was placed in a glass tube closed at the end by a thin plate of glass similar to those used for covering objects under the microscope. The tube had a narrow side-tube near the bottom; this was fitted with a piece of caoutchouc tubing and pinchtap, so that any liquid contained in the tube could be drawn off. A flat plate of copper carefully polished, first with trent sand and oil and then with rotten-stone, was placed beneath the tube in such a manner that the diffused *Communicated by the Author. |