These four very simple examples of the use of Weber's and Thomson's system might be multiplied without end, but it is hoped that they will suffice to give some idea of the range and importance of the relations on which it depends to those who may hitherto not have had their attention directed to the dynamical theory. No doubt, if every unit were arbitrarily chosen, the relations would still exist in nature, and, by a liberal use of coefficients experimentally determined, the answer to all the problems depending on these relations might still be calculated; but the number of these coefficients and the complication resulting from their use would render such an arbitrary choice inexcusable. A large number of units of resistance have from time to time been proposed, founded simply on some arbitrary length and section or weight of some given material more or less suited for the purpose; but none of these units in any way possessed what we have called the second and third requisite qualities, and could only have been accepted if the unit of resistance had been entirely isolated from all other measurements. We have already shown how far this is from being the case; and the Committee consider that, however suitable mercury or any other material may be for the construction or reproduction of a standard, this furnishes no reason for adopting a foot or a metre length of some arbitrary section or weight of that material. Nevertheless it was apparent that, although a foot of copper or a metre of mercury might not be very scientific standards, they produced a perfectly definite idea in the minds of even ignorant men, and might possibly, with certain precautions, be both permanent and reproducible, whereas Weber's unit has no material existence, but is rather an abstraction than an entity. In other words, a metre of mercury or some other arbitrary material might possess what we have called the first, fourth, and fifth requisite qualities, to a high degree, although entirely wanting in the second and third. Weber's system, on the contrary, is found to fulfil the second and third conditions, but is defective in the fourth and fifth; for if the absolute or Weber's unit were adopted without qualification, the material standard by which a decimal multiple of convenient magnitude might be practically represented would require continual correction as successive determinations made with more and more skill determined the real value of the absolute unit with greater and greater accuracy. Few defects could be more prejudicial than this continual shifting of the standard. This objection would not be avoided even by a determination made with greater accuracy than is expected at present, and was considered fatal to the unqualified adoption of the absolute unit as the standard of resistance. It then became matter for consideration whether the advantages of the arbitrary material standard and those of the absolute system could not be combined, and the following proposal was made and adopted as the most likely to meet every requirement. It was proposed that a material standard should be prepared in such form and materials as should ensure the most absolute permanency; that this standard should approximate as nearly as possible in the present state of science to ten millions of metre seconds' but that, instead of being called by that name, it should be known simply as the unit of 1862, or should receive some other simpler name, such as that proposed by Sir Charles Bright and Mr. Latimer Clark in the paper above referred to; that from time to time, as the advance of science renders this possible, the difference between this unit of 1862 and the true ten millions of 1862. K metre should be ascertained with increased accuracy, in order that the seconds error resulting from the use of the 1862 unit in dynamical calculations instead of the true absolute unit may be corrected by those who require these corrections, but that the material standard itself shall under no circumstances be altered in substance or definition. By this plan the first condition is fulfilled; for the absolute magnitude of this standard will differ by only 2 or 3 per cent. from Dr. Siemens's mercury standard. The second and third conditions will be fulfilled with such accuracy as science at any time will allow. The fourth condition, of permanency, will be ensured so far as our knowledge of the electrical qualities of matter will permit; and even the fifth condition, referring to the reproduction, is rendered comparatively easy of accomplishment. There are two reasons for desiring that a standard should be reproducible: first, in order that if the original be lost or destroyed it may be replaced; secondly, in order that men unable to obtain copies of the true standard may approximately produce standards of their own. It is indeed hoped that accurate copies of the proposed material standard will soon be everywhere obtainable, and that a man will no more think of producing his own standard than of deducing his foot rule from a pendulum, or his metre from an arc of the meridian; and it will be one of the duties of the Committee to facilitate the obtaining of such copies, which can be made with a thousandfold greater accuracy than could be ensured by any of the methods of reproduction hitherto proposed. It is also hoped that no reproduction of the original standard may ever be necessary. Nevertheless great stress has been lately laid upon this quality, and two methods of reproduction have been described by Dr. Werner Siemens and Dr. Matthiessen respectively; the former uses mercury, and the latter an alloy of gold and silver, for the purpose. Both methods seem susceptible of considerable accuracy. The Committee have not yet decided which of the two is preferable; but their merits have been discussed from a chemical point of view in the appended Report C, by Prof. Williamson and Dr. Matthiessen. An interesting letter from Dr. Siemens on the same point will also be found in the Appendix E. This gentleman there advocates the use of a metre of mercury of one square millimetre section at 0° C. as the resistance unit; but his arguments seem really to bear only on the use of mercury in constructing and reproducing the standard, and would apply as well to any length and section as to those which he has chosen. When the material 1862 standard has once been made, whether of platinum, gold and alloy, or mercury, or otherwise, the exact dimensions of a column of mercury, or of a wire of gold-silver alloy, corresponding to that standard can be ascertained, published, and used where absolutely necessary for the purpose of reproduction. It should at the same time be well understood that, whether this reproduction does or does not agree with the original standard, the unit is to be that one original material permanent standard, and no other whatever, and also that a certified copy will always be infinitely preferable to any reproduction. The reproduction by means of a fresh determination of the absolute unit would never be attempted, inasmuch as it would be costly, difficult, and uncertain; but, as already mentioned, the difference between new absolute determinations and the material standard should from time to time be observed and published. The question, whether the material standard should aim at an approxima tion to the the metre foot was much debated. In favour of the latter it was argued that, so long as in England feet and grains were in general use, metre second dynamical calculations. In favour of the would be anomalous, and would entail complicated reductions in metre second it was argued that, when new standards were to be established, those should be chosen which might be generally adopted, and that the metre is gaining universal acceptance. Moreover the close accordance between Dr. Siemens's unit and the decimal metre multiple of the second weighed in favour of this unit; so that the question was decided in favour of the metrical system. In order to carry out the above views, two points of essential importance had to be determined. First, the degree of accuracy with which the material standard could at present be made to correspond with the metre ; and second secondly, the degree of permanency which could be ensured in the material standard when made. The Committee are, unfortunately, not able yet to form any definite opinion upon either of these points. Resistance-coils, prepared by Professor W. Thomson, have been sent to Professor Weber; and he has, with great kindness, determined their resistance in electro-magnetic units as accurately as he could. It is probable that his determinations are very accurate; nevertheless the Committee did not feel that they would be justified in issuing standards based on these determinations alone. In a matter of this importance, the results of no one man could be accepted without a check. Professor Weber had made some similar determinations with less care some years since, but, unfortunately, he has not published the difference, if any, between the results of the two determinations. Indirect comparisons between the two determinations show a great discrepancy, amounting perhaps to 7 per cent.; but it is only fair to say that this error may have been due to some error in other steps of the comparison, and not to Professor Weber's determination. Meanwhile, it was hoped that a check on Weber's last result would by this time have been obtained by an independent method due to Professor Thomson. Unfortunately, that gentleman and Mr. Fleeming Jenkin, who was requested to assist him, have hitherto been unable to complete their experiments, owing chiefly to their occupation as jurors at the International Exhibition. The apparatus is, however, now nearly complete, and it is hoped will before Christmas give the required determinations. If Professor Weber's results accord within one per cent. with these new determinations, it is proposed that provisional standards shall be made of German-silver wire in the usual way, and that they should be at once issued to all interested in the subject, without waiting for the construction of the final material standard. The construction of this standard may possibly be delayed for some considerable time by the laborious experiments which remain to be made on the absolute permanency of various forms and materials. An opinion is very prevalent that the electrical resistances of wires of some, if not all, metals are far from permanent; and since these resistances are well known to vary as the wires are more or less annealed, it is quite conceivable that even the ordinary changes of temperature, or the passage of the electric current, may cause such alterations in the molecular condition of the wire as would alter its resistance. This point is treated at some length in the two Reports, B and C, appended, by Professor Williamson and Dr. Matthiessen. The experiments hitherto made have not extended over a sufficient time to establish any very positive results; but, so far as can be judged at present, some, though not all, wires do appear to vary in conducting power. Mercury would be free from the objection that its molecular condition might change; but, on the other hand, it appears from Report C that the mercury itself would require to be continually changed, and that consequently, even if the tube containing it remained unaltered (a condition which could not be absolutely ensured), the standards measured at various times would not really be the same standard. A possibility at least of error would thus occur at each determination, and certainly no two successive determinations would absolutely agree. If, therefore, wires can be found which are permanent, they would be preferred to mercury, although, as already said, no conclusion has been come to on this point. Some further explanation will now be given of the resolutions passed from time to time by the Committee, and appended to this Report. Dr. Matthiessen was requested to make experiments with the view of determining an alloy with a minimum variation of resistance due to change of temperature. The object of this research was to find an alloy of which resistance-coils could be made requiring little or no correction for temperature during a series of observations. A preliminary Report on this subject is appended (A), in which the curious results of Dr. Matthiessen's experiments on alloys are alluded to, and, in particular, the following fact connected with the resistance of alloys of two metals is pointed out. Let us conceive two wires of the two pure metals of equal length, and containing respectively the relative weights of those two metals to be used in the alloy. Let us further conceive these two wires connected side by side, or, as we might say, in multiple arc. Then let the difference be observed in the resistance of this multiple arc when at zero and 100° Cent. This difference will be found almost exactly equal in all cases to the difference which will be observed in the resistance of a wire drawn from the alloy formed of those two metal wires at zero and 100°, although the actual resistance at both temperatures will in most cases be very much greater than that of the hypothetical multiple arc. In order to obtain a minimum percentage of variation with a change of temperature, it was consequently only necessary to make experiments on those alloys which offer a very high resistance as compared with the mean resistance of their components. The results of a few experiments are given in the Report, but these are only the first of a long series to be undertaken. Hitherto an alloy of platinum and silver is the only one of which the conducting power and variation with temperature are less than that of German silver. Professor W. Thomson and Dr. Matthiessen were requested to examine the electrical permanency of metals and alloys. A preliminary Report on the subject by Dr. Matthiessen is appended (B), in which he shows that, after four months, one copper and two silver hard-drawn wires have altered, becoming more like annealed wires, but that no decided change has yet been detected in the great majority of the wires. Several eminent practical electricians were requested to advise the Committee as to the form of coil they considered most suitable for a material standard, and also to furnish a sample coil such as they could recommend. Sir Charles Bright informed the Committee that he was ready to comply with the request. The point is one of considerable importance, respecting which it was thought that practical men might give much valuable information. Coils of wire may be injured by damp, acids, oxidation, stretching and other mechanical alterations. They may be defective from imperfect or uncertain insulation; and they may be inconveniently arranged, so that they do not readily take the temperature of the surrounding medium, or cannot be safely immersed in water- or oil-baths, as is frequently desirable. No definite conclusion as to the form of coil to be recommended, even for copies, has been arrived at. It was resolved "That the following gentlemen should be informed of the appointment of the present Committee, and should be requested to furnish suggestions in furtherance of its object: Professor Edlund (Upsala). Professor Neumann (Königsberg). Werner Siemens, Ph.D. (Berlin). A letter, appended to this Report, was consequently addressed to each of these gentlemen. Answers have been received from Professor Kirchhoff and Dr. Siemens, which will be found in the Appendix. The resolution arrived at by the Committee to construct a material standard will entirely meet Professor Kirchhoff's views. The Committee have been unable entirely to adopt Dr. Siemens's suggestions; but his statements as to the accuracy with which a standard can be reproduced and preserved by mercury will form the subject of further special investigation, and the Committee will be most happy to take advantage of his kind offers of assistance. A letter was also received from Sir Charles Bright, containing an ingenious method of maintaining a constant tension or difference of potentials. This point will probably come before the Committee at a later period, when Sir Charles Bright's suggestion will not be lost sight of. The Committee also received on the 29th of Sept., after the present Report had been drawn up, a letter from Dr. Esselbach, a well-known electrician, who had charge of the electrical tests of the Malta and Alexandria Cable during its submergence. In this letter Dr. Esselbach arrives at substantially the same conclusions as those recommended by the Committee. Thus, his first conclusion is " to adopt Weber's absolute unit substantially, and to derive from it, by the multiple 1010, the practical unit." This practical unit is precisely that recommended by your Committee. Dr. Esselbach uses the millimetre multiple 1010, starting from the where your Committee recommend second, metre second the multiple 107, starting from the : the result is the same. Dr. Esselbach's next conclusion is also of great practical value. He points out that the electro-magnetic unit of electromotive force, also multiplied by 101o, differs extremely little from the common Daniell's cell, and that, without doubt, by proper care such a cell could be constructed as would form a practical unit of electromotive force. This suggestion has the approval of |