that care was taken to have the alloy drawn by different persons, in order to see if this would influence the results obtained with them, as well as to ascertain whether the wires would show the same faults as silver and copper does when not carefully drawn. It has been argued that the molecular condition of all alloys is liable to undergo a change by age, and that, therefore, alloys are not fit to be used as standards. Thus, it is well known that brass and German silver become brittle and crystalline by age, and that the same may occur with the gold-silver alloy; but on looking at the composition of the alloy, it will be found to have nearly the same as that of the gold chains of commerce. Now, we do not know of a single instance where such a chain, even after years of use, becomes brittle or crystalline; so that we think it more than possible that the alloy will not change its molecular condition by age. It must also be remembered that even when German silver becomes brittle, it does not materially alter in its conducting power. The same has already been proved, and mentioned in this Report, to be the case with iron and cadmium.

3. On the effect of annealing on the conducting power of the alloy.-When the alloy is heated to redness and cooled slowly, its conducting power was found to have increased only 0.3 per cent.-this value being the mean of eight wires annealed in different ways,-proving, therefore, that if the wires may be only partially hard-drawn, it will make but little difference in the conducting power.

4. On the influence of temperature on the conducting power of the alloy.When wires of this alloy are heated from 0° to 100°, a decrement in the conducting power, amounting to 6.5 per cent., will be found. The same arguments may, therefore, be put forward in favour of the use of the alloy as a standard, as were done in the case of mercury when speaking of this property.

To sum up, therefore, the arguments in favour of and against the use of the three propositions made to reproduce standards of electric resistance, we find in favour of a pure metal in a solid state :

1. That it appears that all descriptions of electrotype copper, when carefully drawn, have the same conducting power.

Against it :

1. That their preparation, with the exception of the electrotype copper in a state of purity, is exceedingly difficult; so that independent persons preparing the same metal find, on comparing the conducting powers obtained for them, that they vary several per cent.

2. That the influence of annealing on their conducting powers is so great that differences may occur simply because the wires are partially hard-drawn. 3. That the influence of temperature on their conducting power is very great; so that slight errors in thermometers, or in the reading of them off, would materially affect the result.

In favour of using mercury as a means of reproducing standards the following may be said :—

1. That no molecular change can take place in the metal, nor can any alteration occur in its conducting power, on account of annealing; for its temper is always the same.

2. That the influence of temperature has only a small effect upon its conducting power.

And against it :

:

1. That there is a difficulty in obtaining absolutely pure mercury; so that the results obtained by different observers show great variations.

2. That the standard tube cannot be kept full of mercury for any length of time, owing to the diffusion of impure metal, arising from the amalgamated terminals into the narrow tube; so that each time the standard has to be used, it must practically be remade.

3. If the tube be broken during the process of cleaning or otherwise, it is not yet certain with what exactitude the standard could be reproduced.

4. It is doubtful whether the resistance of a tube filled with mercury today will have the same resistance if filled a year hence; for we have no proof if the dimensions of the tube will not alter by being kept. It is well known that the bulbs of thermometers are liable to change, and are continually changing, in capacity.

In favour of the gold-silver alloy may be said :

1. That this material, when prepared and drawn by different persons, was found not to vary in its conducting power more than 1.6 per cent.; whereas the variations found with the metals in a solid state, prepared and drawn by different persons, amounts to several per cent., and those found for mercury by different observers amount also in all cases to several per cent.

2. That the homogeneity and molecular condition of this alloy are always the same.

3. That the effect of annealing on the conducting power is very small, being only 0.3 per cent. ; so that if a wire be partially hard-drawn, its conducting power will not suffer to any appreciable extent.

4. That the influence of temperature on its conducting power between 0° and 100°, viz. a reduction of 6.5 per cent., is smaller than either that of the metals in a solid state, viz. 29.3 per cent., or that of mercury, viz. 8.3 per cent.

And against it:

That the conducting power may alter by age, as the physical properties of alloys are more likely to change than those of metals.

From the foregoing statements, based on facts at present known, it would appear that the best method of reproducing standards, for those who are unable to procure copies of the British Association unit of electrical resistance, is that they should make, or have made, a certain amount of the gold-silver alloy (as described in the Phil. Mag., Feb. 1861), by two or three different persons, in order to ensure a correct result, and take a given length and section or weight of it, at a given temperature, which has been found equal in resistance to the British Association unit. We would recommend, in order further to test what we have stated in the foregoing Report, that three or more scientific men and electricians be requested to compare the resistances of pure mercury, obtained by them from the best sources they are able, and of the gold-silver alloy (made in the manner described in the Phil. Mag.) with a German-silver standard supplied to them by your Committee. If this be done, results would be obtained which would put an end to many disputes on the subject, as well as decide which of the above means is practically the best for reproducing standards of electrical resistance where no copies of the British Association unit can be obtained.

APPENDIX D.-Professor KIRCHHOFF's Letter.

To Fleeming Jenkin, Esq.

Heidelberg, June 8, 1862.

DEAR SIR,-I have the honour to acknowledge the receipt of your letter of the 31st of May, in which you inform me of the labours of the Committee appointed by the British Association, to try and bring about the general

introduction of one unit of electrical resistance. I gladly respond to the invitation to express my view on the manner in which the desired object might be best attained.

To define the unit of resistance by the resistance of a wire of given dimensions of a pure metal appears to me impossible, for the reasons which have been urged by the Committee; hence, of the three proposals discussed by the Committee, there only remain two for our consideration.

1. To adopt the unit proposed by Weber; or, 2. To establish, as unit of resistance, the resistance of a column of pure mercury of given dimensions and at a given temperature.

I do not think that to these a third of equal value can be added; for to define the unit of resistance by the thermal action of an electrical current would certainly never answer the purpose, because this thermal action cannot be measured with the necessary accuracy, and the resistance of any wire which is to be permanently kept cannot be fixed as unit; for the resistance of any wire for a given temperature certainly undergoes changes if electrical currents are transmitted through it, and it is exposed to fluctuations of temperature.

Of the above two units, the first recommends itself by coming up more satisfactorily to the demands of science; the second, as I think, by being capable for the present of being practically carried out with greater accuracy. But is it really necessary to decide for one and against the other of these two units? I think not. If the ratio between them is established with the accuracy which is now attainable, there can, I think, arise no more confusion from their simultaneous use, than from the practice of expressing lengths sometimes in metres and sometimes in millimetres. You say, "It is proposed that the unit adopted shall be represented by one particular standard, constructed of very permanent materials, laid up in a national repository;" and further, "The Committee will probably endeavour to devise some plan by which copies of the actual material standard adopted may be easily procured at a reasonable cost." This plan, the execution of which I consider highly desirable, might evidently be realized in all its essential points without its being necessary to give the preference to one of these units over the other: it would only be necessary to measure the resistance of the normal standard in both units, and to add to each copy its resistance expressed in both units. In choosing the metal or the alloy of which the normal standard and the copies are to be made, care must undoubtedly first be taken that the resistance is as unalterable as possible for one temperature. It is undoubtedly desirable that the resistance shall not vary rapidly with the temperature. This is, however, not very important, provided that the temperature of the wire can be accurately observed at any moment. To satisfy this condition, the wires must not be coiled upon cylinders, but fastened so that, for the greater part of their extent, they lie clear, and hence rapidly assume the temperature of the surrounding air or of the non-conducting liquid in which they may have been immersed.

You request me to point out to you any researches of mine which refer to a unit of electrical resistance. I have to mention a short treatise only, which appeared in vol. lxxvi. of Poggendorff's Annalen,' under the title "Determination of the Constants on which the Intensity of Induced Electrical Currents depends," and which formed the answer to an academical prize-question which Professor Neumann, in Königsberg, had proposed in the year 1846. In this treatise a unit of electrical resistance has not been suggested; but in it the resistance of a wire has been measured by the unit (or rather by double the

unit), which was afterwards proposed by Weber in his "Electrodynamic Measurements." Professor Weber has subsequently had the kindness to compare the copper wire whose resistance I measured, with those whose resistances he himself had determined (Pogg. Ann. vol. lxxxii. p. 360); he thereby found the resistance of my wire about one-seventh greater than I had found it. The reason of this want of agreement consists partly in the imperfection of the instruments which I had used, and partly in the fact that in my experiments the temperature was little above 0° R., while in Weber's experiments it was about 20° R.

Allow me, my dear Sir, to record the very great respect with which I have the honour to be,

APPENDIX E.-Dr. SIEMENS's Letter.-Suggestions for the adoption of a Common Unit in measurement of Electrical Resistance.

To the Committee appointed by the British Association to report on Standards of Electrical Resistance.

GENTLEMEN,-I beg to acknowledge, with thanks, the honour you have done me, in requesting me to furnish you with suggestions in furtherance of your endeavours to procure the adoption of a common unit of electrical resistance.

I proposed in Poggendorff's Annalen (vol. cx. p. 1) to supply this want by the adoption of the conducting power of mercury as unit, and of the resistance which a prism of that metal a metre long, and a square millimetre section, at 0° C., opposes to the passage of a current, as unit of resistance.

The method by which I constructed standards in this unit was as follows: From the ordinary glass tubes of commerce, pieces were selected whose calibre was found to vary most regularly. After the selected tubes had been ground to the length of a metre, they were carefully cleaned and filled with pure mercury-the temperature being measured. The contents were then weighed, and the values reduced to 0° C. for expansion of glass and metal. The resistances of the tubes were calculated by the formula

which represents the resistance to a current in the longer axis of a prismatic conductor either in the above unit or in 0.001 unit, according as l is expressed in metres and g in grammes, or lin millimetres and g in milligrammes respectively. =13.557, the specific gravity of mercury, at 0° C.

1

1+Na+ √a
3

is the coefficient for conicalness, which in good tubes equals 1, very nearly. a is the ratio of the greatest to the least transverse section of the tube.

All the data therefore necessary for the value of W are exact measures of length and weight. Measurements of the same tube, at different times, gave results corresponding within 0.01 per cent. with each other.

The first objection which is raised against the adoption of mercury as unit, "that the tubes cannot be made of uniform or similar wires, and that the

standard once broken is lost for ever," is clearly untenable, since the tubes are not required to be uniform, and the breakage of the standard involves only the necessity of a new tube, and the determinations of length and weight anew, to put the operator in possession of a new standard, whose agreement with the broken one will depend solely on his own handiness in manipulating. Every standard, of whatever material, is liable to injury; but the breakage of a glass is infinitely to be preferred to the treacherous results of a bruised wire.

Mercury is, of all metals, that which is best suited to supply a reproducible standard.

In the first place, it is procurable pure in sufficient quantities. I heated for some hours samples of commercial mercury under sulphuric acid containing a few drops of nitric acid, and found their conducting powers afterwards to be precisely the same as that of a quantity of chemically pure mercury reduced from the oxide.

Secondly, mercury has always the same molecular structure, and has therefore, at the same temperature, always the same resistance.

From these two grounds it is possible to couple with this unit a geometrical conception which is indispensable in practice.

Thirdly, of all metals capable of being used for resistances, mercury has the lowest conducting power; and of all pure metals capable of the same application, its resistance varies least with variations of temperature.

Having formed such original standards, it only remained to copy them in a convenient form for employment in practice. This I have done,— 1. In mercury contained in glass spirals, and

2. In German-silver wire.

The resistance-bridge which I made use of in these measurements, with a reflecting galvanometer in its circuit, enabled me to attain a precision of within 0.01 per cent.

The mercury spirals, as may be seen by the accompanying drawing*, are provided with cups at their ends. for convenience of filling and for receiving the contacts of the measuring apparatus. They are either of known resistances, approximating only to a multiple of the unit, or may be adjusted to an exact multiple by boring out one of the ends of the tube, which, in this case, must stand up half an inch inside the cup. The resistances of the bridge must then be arranged so that no current passes through the instrument only when the desired resistance in the fourth side is reached. When the spiral is filled, a vulcanized india-rubber ring is put round the cups, and the spiral is suspended in a vessel of ice-water or water kept in circulation by passing a current of air through it, and the temperature measured by a delicate thermometer.

The electrical value of each spiral which I have made has been determined by comparing it with at least two of the straight normal tubes, both being kept during the measurement in ice-water. The greatest differences which I have found between such determinations do not exceed 0.05 per cent., to which limit the copies may be trusted.

In answer to the objection that an admixture takes place between the mercury and the solid metal used for the terminals, I must remark that I have found this occasion really less inconvenience than is generally believed. I kept the copper connexions immersed in the mercury a whole week, but could not perceive the slightest decrease in its resistance. Platinum elec

* The drawings have been omitted, the descriptions being intelligible without them.