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Personally being charged with the duty of preparing an historical summary of the various units proposed, I shall be grateful if you will favour me with any remarks as to your own labours in this field, or if you could oblige me with references to any papers or works in which the subject is treated.
I am, Sir,
Tour obedient Servant,
Appendix H.—Description of the Electrical Apparatus arranged by Mr. Fleeming Jenkin for the production of exact copies of the Standard of Resistance.
This apparatus is a simple modification of that generally known as "Wheatstone's bridge." It contains, however, some special arrangements, in virtue of which various practical difficulties are avoided, so that very great accuracy can be ensured with comparative ease. The usual bridge-arrangement is shown in Plate I. fig. 9, where the irregular scrolls, A, C, R, S, represent the four conductors of which the resistance is to be compared; the thick black lines show those portions of the circuit which join the coils with the four corners, U, V, Z, Y, and are supposed to have no sensible resistance in comparison with the coils; finally, the thin lines show connexions, the resistance of which in no way affects the accuracy of the comparison between the four coils. By this arrangement the four conductors, A, C, R, S, arc so connected with the galvanometer, G, and the battery, B, that no current passes through the galvanometer when the conductors bear such a relation to one another that A 8
the equation Q=holds good; whereas a current in one or other direction
A S passes so soon as is greater or less than g*. Thus the direction and
strength of the current observed serve as guides by which the resistance of any one of the conductors may bo gradually adjusted by shortening or lengthening the wire, until on the completion of the circuit no deflection whatever can be observed on the galvanometer, however delicate it may be, or however powerful the battery used. When this hasieun done, we may be sure that the above relation exists between the four conductors. In practice, it is seldom desirable to use powerful batteries; the test is made delicate by the use of an extremely sensitive astatic galvanometer.
In speaking of the four conductors, A, C, R, S, which are generally all coils of wire of similar construction, although each fulfilling a distinct function, some difficulty often occurs in explaining readily which coil or conductor is referred to. They can of course be distinguished by letters, but this requires reference to a diagram on every occasion, and the writer has therefore been in the habit of distinguishing the four coils by names drawn from a very obvious analogy existing between this electrical arrangement and the common balance in which one weight is compared with another. The equality between the two weights on either side of a balance, when the index is at zero, depends on the equality of the arms of the balance; and if the arms are unequal, the weights required to bring the index to zero are proportional to the arms (inversely). Let A and C be called the arms of the electrical balance, while S and R are looked on as analogous to the standard weight and mass to be weighed respectively, and let the galvanometer needle
* This statement holds good also if the battery and galvanometer vires, as shown hi diagram, are interchanged.
stand for the index of the balance. Then all the above statements, with respect to the weights and arms, hold good for the electrical arrangement (except that the proportion between the electrical arms and weights is direct instead of inverse). The writer therefore calls this arrangement an electric balance—A and C the arms, S the standard, and R the resistance measured*. In the adjustments of resistance-coils or copies of a standard, the object is to produce a second coil, R, exactly equal to the first or standard, 8; and the arms, A, C, must therefore be absolutely equal before, by this arrangement, an exact copy can be made. Hitherto it has often been the practice to use for the arms, A, C, two coils made as equal as possible, and placed so close as to remain at sensibly equal temperatures; so that the equality between R and S is dependent on the equality between A and C, and cannot be determined with greater accuracy than that between these coils. This limit to the accuracy is a defect for our present purpose, and the writer has moreover found it undesirable to depend on the permanent equality of two coils. It is by no means certain that, without very extraordinary precautions, the two arms will remain unaltered in their original equality. A slight molecular change, or a slight chemical action on the surface of the wires, disturbs this equality permanently; and even if the coils are so constructed as to remain really equal at equal temperatures, the accidental passage of a current through one arm, and not through the other, for a very short time, will disturb their accuracy very sensibly for a considerable time. There are various devices by which the equality to be established between R and S may be rendered independent of the absolute equality between A and C, and the writer has adopted a plan, now to be explained with the aid of the diagrams (figs. 7, 8). This plan allows the approximation to equality between R and S to be almost indefinitely increased.
It will be seen that fig. 7 does not differ from fig. 9, except by the addition of a wire, WX, of sensible resistance, between the two coils A and C. The point U is no longer fixed, but can be moved along WX. The arms of the balance are therefore no longer A and C, but A + XU and C + WU. Thus the moveable point U affords the means of slightly altering or adjusting the ratio of the two arms. A and C are made as equal as possible, independently of WX, which is a very short wire.
The test is made as follows:—When the standard and coil to be measured have been put in their places as in fig. 7, the point U is moved along the wire WX until the galvanometer-index is not deflected when the circuit is closed. The position of the point U is noted by a scale. R and S are then reversed, so as to occupy the position relatively to A, C shown in fig. 8. The point U is again moved until the galvanometer-needle remains undeflected on the circuit's being closed. The new position of U is again observed by a scale. If the point U does not require to be moved at all, we may be quite sure that R is exactly equal to S, and that A+XU = C+WU, since it would
A I YTT T> Q
be quite impossible that the ratio ..,,T should be equal to both - and =,
L+WU S K
unless this ratio were equal to 1. Moreover, if WX be made of the 6ame
• The name of parallelogram, sometimes given to the arrangement, is objectionable, inasmuch as the relation obtaining between the four conductors is not that which exists between the four sides of any parallelogram, except in the one case of equality between all four conductors. The connexions are, however, most easily followed in a drawing when arranged as the four sides of a quadrilateral figure. Professor Wheatstone's original name of Differential Resistance Measurer does not, as it seems to the writer, sufficiently distinguish this arrangement from other differential methods.
■<vire as the coils A and C, and if those coils are formed of about 100 inches of wire, and if the observed positions of U differ by a given distance, x, this length, x, measured in inches, will express very nearly the difference between It and 8 in a percentage of the whole length of R. Thus, if a; be one inch, the standards 8 and R differ by about one per cent. If the point U, when adjusted in each case, be found nearer R than 8, then R is the smaller of the two, and vice versd. The percentage of error in R, thus measured, is not of course strictly accurate, inasmuch as the ratio between the two arms is not exactly
; but if WX be not more than three or four inches long, the percentage
of error measured in this way is quite sufficiently accurate to allow the new coil to be so exactly adjusted after very few trials, that no greater movement of U than (say) jjjth of an inch is required to prevent any deflection on the galvanometer when R and 8 are reversed. We may then be sure that no greater error than (say) about 0-1 per cent, exists in the equality between the new coil and the standard. Two fresh coils, A,, C„ are then taken, containing each about 1000 inches of wire similar to WX, or an equivalent resistance. It will thon be found that, to maintain the index at zero when R and S are reversed, U must be moved about ten times as much as before, or (say) one inch. R can then be still further adjusted till U is not moved more than -j-^th of an inch, when a new degree of approximation to equality, with an error of not more than 0-01 per cent., will have been reached. Then the coils A,, Ct are changed for a fresh pair, A2, Ca, with a resistance equal to about 10,000 inches of the wire WX: one-tenth of an inch on WX will then represent an error of only 0*001 per cent. By a repetition of this process, quite independently of any absolute equality between the pairs A, C, A,, C,, A2, Ca, &c, a gradual approximation to any required extent may be ensured. The delicacy of the galvanometer used, and the nicety of the means available for increasing or diminishing the resistance of R, form the only limits to the approximation. A slight want of equality between any pair of arms will simply bring the point U a little to one side or the other of the centre of WX, as the final adjustment with that pair is made, but will not affect the truth of the comparison between R and 8. Each pair must, however, be so nearly equal that the addition of part of the short wire, WX, to one side will be sufficient to correct the other; otherwise the adjustible point TJ would not bring the index to zero, even when at one end of the wire.
This arrangement, besides rendering us independent of the accuracy of any two arms, has some incidental advantages of considerable practical importance. At each test it gives a measure of the amount by which tho new coil to be adjusted must be lengthened or shortened. The test is at first comparatively rough, or adapted to errors of one or two per cent., and only gradually increases in delicacy as the desired equality is more and more nearly approached. It is not necessary that the resistance of WX should remain absolutely constant, since it is only used (numerically) to give a rough approximation to the percentage of error. It is desirable that the battery should remain in circuit as short a time as possible; the circuit is therefore broken between 1 and 2, figs. 7 and 8, by a key, K, with which contact should be only momentarily made, when all the other connexions are complete. The direction of the jerk of the galvanometer-needle to one side or the other need alone be observed; no permanent deflection is required with this arrangement as a guide to the amount of error. This is a considerable advantage, inasmuch as it avoids heating tho wires, and saves time. The induction of the coils on themselves might lead to some false indications,
unless special precaution were taken against it, as pointed out by Professor W. Thomson*. To aroid this source of error, the galvanometer circuit is broken between 3 and 4, figs. 7 and 8, at K,, and should only be closed after the battery circuit has been completed at K and equilibrium established throughout all the conductors.
Before passing to a detailed description of the apparatus as actually constructed, some remarks are required as to the means of making temporary connexions. All connexions which require to be altered may be the means of introducing errors, inasmuch as the points of contact are very apt to offer a sensible but uncertain resistance. In measuring small resistances, the resistance at the common binding-screws is found to create very considerable errors. Binding-screws have therefore to be avoided at all points where an uncertain resistance could cause error. Mercury-cups, made as follows, have been found in practice very suitable for temporary connexions, and have been adopted in the apparatus. The bottom of each cup is a stout copper plate, with its surface well amalgamated, forming one of the two terminals to be joined. A stout copper wire, -J- inch in diameter, with a flat end well amalgamated, forms the other terminal. When the amalgamation is good, and care is taken that the wire shall rest on the plate, this form of connexion offers no sensible resistance. The amalgamated wire is easily kept bright and clean by being dipped from time to time in a solution of chloride of mercury and wiped. The copper plate should also be removed from the cup, cleaned, and re-amalgamated occasionally. All permanent connexions should be soldered.
The apparatus itself, as actually constructed, will now be described (figs. 1 to 6). It consists of a wooden board, about 12 in. x 7 in., containing the mercury-cups, the adjusting wire, WX, the key, X, and the terminals to which the battery and galvanometer are connected. The letters in the figures 1 to 6 correspond exactly to those used in the diagrams 7 and 8; and the apparent complexity of the connexions can thus be easily disentangled, cc,, aal are two pairs of mercury-cups, into which the terminal wires on the bobbin, C, A, dip. This bobbin contains the two coils, C and A, forming the arms of the balance. rrl and sst are mercury-cups, into which the terminals of the standard and coil to be adjusted are placed. These mercury oups are so connected with the four cups, d,d,,f,fv that when d is connected with dt, and/with/,, by a couple of wires in a small square of wood, D, then A, C, S, and E are connected as in fig. 7; but when D is turned round, so as to connect d with / and dl with /„ A, C, R, and S are connected as in fig. 8. D is called the commutator. The same end might be effected without a commutator by simply interchanging R and S; but it is frequently inconvenient to do this. All these connexions are made by short stout copper bars, dotted in fig. 2. The wire WX, the sliding brass piece H, carrying a spring for the contact at U (fig. 4), and the scale E, by which the position of H is observed, will be readily understood from the drawing. The sliding piece, H, is connected with the proper points by the helix of copper wire, h, and the screw, I. G G, and B B, are common binding-screws, to which the wires from the galvanometer and battery are attached. K is the key, by depressing which, first, the battery is thrown into circuit, and then the galvanometer. It consists of three brass springs, 1,2,3 (fig. 5), each insulated one from the other, and connected by three screws, 1, 2, 3 (fig. 2), with the necessary points of the arrangement. A fourth terminal, 4 (figs. 2 and 6),
* rule Phil. Msg. August 1802.
is immediately under the free end of the springs, and is armed with a small platinum knob or contact-piece. The three springs are also all armed with platinum contact-pieces, all in a line one above the other (fig. 6). When the finger-piece, T, is pressed down, 1 and 2 are first joined, and then 3 and 4; 3 is insulated from 2 by the vulcanite, Q. All the connexions permanently made, under the board, are shown in fig. 2. Those which have no sensible resistance are stout copper bars, and form the bottoms of the mercury-cups: those of which the resistance is immaterial are made of wire, insulated by gutta percha, and are simply shown as dotted irregular lines in fig. 2; they will be found, on comparison, to correspond with the thin lines on fig. 7. It will also be found that all those parts shown by thick lines in the diagram are made by thick bars or rods and mercury-cups.
Three sets of arms, CA, C, A,, C2Aa, are provided; the shortest pair is first used, and U adjusted by the slide, H, till the galvanometer does not deflect when T is pressed down. The commutator, D, is then turned round, and TJ adjusted afresh. The coil, R, is then altered according to the two positions of U, and this process repeated, using the second and third pair of arms as required, until the desired approximation between R and 8 has been obtained. An astatic galvanometer, with a very long coil, will, for most purposes, give the best results; and one or two elements will be found a suflicient battery. The construction of R and S recommended, and the precautions to ensure perfect equality of temperature, will form part of next year's Report.
The apparatus, although specially designed for the production of equal coils, is applicable to ordinary measurements of resistances by comparison with a set of resistance-coils; for this purpose the terminals of the resistance-coils should be put in the place of the standard 8, and any conductor of which the resistance is to be measured in the place of R. If a comparison by equality is to be made, the wire WX can be used as already described; it is, however, frequently desirable to make a comparison with one arm tenfold or a hundredfold greater than the other, by which means measurements of resistances can be made ten or a hundred times greater or smaller than could be done if equality alone between R and S were measured; for this purpose the three pairs, A C, A, C,, A2 C2, are made exactly decimal multiples one of the other, and then, by taking A and C,, or A and C2, &c, in the cups aal and cCj, the required decimal ratio is obtained. The resistance of the wire WX would, however, falsify this ratio, and it is eliminated by a simple copper rod, which is placed for the purpose between the two cups e eit and maintains the whole wire WX at sensibly one potential. The commutator also is useless in measurements of this kind, and should be left untouched in the position shown in fig. 1.
The apparatus exhibited was manufactured for the Committee by Messrs. Elliott Brothers, of London, and gives excellent results.
Preliminary Report of the Committee for Investigating the Chemical and Mineralogical Composition of the Granites of Donegal, and the Minerals associated with them.
In accordance with the resolution of the General Committee at the Manchester Meeting, the Committee, consisting of Sir R. Griffith, the Rev. Prof. Haughton, and Mr. Scott, proceeded to investigate " the chemical and mine