Thus the resistance of the wire of the multiplier is less than onetenth that of the pile.

Denoting the electro-motive force of the thermo-pile by E, the strength of the current is

this is conveyed around the needle in n coils; hence the magnetic effect is

If the same mass had been drawn out into three times the length, its resistance would have been 9 times as great, or 9 × 1.75 = 15.75, thus nearly equal to that of the thermo-pile. The strength of the current now would be

because the current is now conveyed in 3 n coils around the needle. The value M' is thus nearly double that of M.

With the same quantity of copper wire, the multiplier for the said thermo-pile could have been made twice as sensitive by drawing the wire to thrice the length, so as to give it three times as many coils with a section of only one-third.

Hence there is no doubt that the reason for making the wire of this multiplier too short and too thick, arose from the assumption that the resistance of the thermo-pile composed of a number of metals could not be great, and thus only a wire tolerably thick and not too long should be selected. It is thus shown that mere conjecture will not suffice in such matters.

§ 25. Comparison of the effects of different batteries in given cases.— The strength of the current for any given case can be computed from the constants of different batteries. If the resistance of the closing arc is l, for a zinc and carbon battery with a mean surface of one square decimetre, and using Stöhrer cells with dilute sulphuric acid, the strength of current is

For a Daniells element, of the same size, with sulphuric acid of the same degree of dilution, the force of the current would be

If is very small compared with the resistance of the elements, the

strength of their currents will be to each other as

824

470

to

12

21.6'

or

as 68.6 to 21.8; hence the current of the zinc and carbon battery is

more than three times as strong as the other. When the current is well closed, a zinc and carbon element will effect as much as a Daniells element of three times as great a mean surface.

When the resistance is very great, the ratio is different; then the strength of the current is proportional to the electro-motive force, or as 470 to 824. In this case, by increasing the surface of the zinc and copper element, but little would be gained. Two Daniell's elements would have to be united to obtain the same effect as with one zinc and carbon element.

The effect of a zinc and carbon battery can be attained in all cases with a Daniells battery by giving to single elements of the latter a three-fold surface, and using twice as many of them as would be required of zinc and carbon elements.

What has been said of the zinc and carbon battery holds good for Grove's battery, since the constants are nearly the same in both.

As a conclusion of this section we present the description of a few instruments which have been used for measuring, in the course of the previous experiments.

§ 26. Rheostats.-To accomplish a gradual change of the resistance in the closing circuit of an electro-motor within the desired limit, without being obliged to open the circuit, several instruments have been proposed, chiefly by Jacobi and Wheatstone. Jacobi called his instrument agometer. The descriptions are to be found in Poggendorff's Annalen, LIV 340, and LIX 145. An instrument of this kind is very costly, and therefore will not be generally employed, especially since Wheatstone's instruments, constructed for the same object, besides answering the purpose equally well, are far simpler and more convenient in manipulation. In my treatise on physics (Lehrbuch der Physik 3 te., aufl. 2 ter. Bd., S. 193) I have described Wheatstone's rheostat with thick wire, which is to be used when the resistance of the closing conductor is not very great. But when the entire resistance in the battery is very considerable, a great length of this thick wire would have to be wound or unwound to produce a sensible change in the strength of the current; consequently, in such cases a rheostat with a thin wire must be used, and which, of course, must have a different construction.

Wheatstone's rheostat with thin wire is represented in Fig. 18. g is a cylinder of dry wood about 6 inches long and 1 in diameter; h

Fig. 18.

is a cylinder of brass having the same dimensions. The axes of the two cylinders are parallel. A screw-thread is cut in the wooden cylinder, and at its end (the one seen in the figure) there is a brass ring to which the end of a long and very fine wire is fastened. This is so wound upon the wooden cylinder as to fill all the screw-threads, and its other extremity is the then fastened to the opposite end of the brass cylinder. The small brass columns fan nie J and k, designed for clamping the wires,

rest upon metal springs, one of which presses against the front end of the brass cylinder h, the other against the brass ring of the wooden cylinder, (the springs are not shown in the figure.) The winch m, which can be removed, serves for turning the cylinder about its axis. Placing it on the cylinder h, and turning to the right, the wire is unwound from the wooden cylinder and wound upon the brass one; on the other hand, placing it upon g, and turning to the left, the reverse takes place. Since the coils are insulated on the wooden cylinder, and kept apart by the screw-thread, the current traverses the wire throughout its whole length on this cylinder; but on the brass cylinder, where the coils are not insulated, the current passes at once from the point where the wire touches the cylinder to the spring at k. The resisting part of the length of the wire is therefore the variable portion which may happen to be on the wooden cylinder.

There are forty screw-threads of the wooden cylinder to an inch. The wire is of brass, and 0.01 of an inch in diameter.

For counting the number of coils unwound, a scale is placed between the two cylinders, and the fraction of a turn is estimated by an index fastened on the axis of one of the cylinders, and which points. to the divisions of a graduated circle.

§ 27. Differential measurer of resistance. For determining the resistance of metallic wires, Wheatstone has given a very simple pro-cess. The rheostat is inserted in the conducting arc of a constant element with the galvanometer and the wire whose resistance is to be determined, and the whole resistance is so regulated that the needle. can come to rest at any desired point a of the graduated circle. Now,. removing the wire from the circuit, the needle will indicate a greater deflection, and to bring it back to the point a, a definite number of turns of the rheostat must be added to the existing resistance. We find in this manner how great the resistance of the wire in question is, expressed in turns of the rheostat.

By this method nearly equally accurate results are obtained, whether a multiplier, the much less sensitive tangent compass, or any other galvanometer, be used. The reason is as follows: To produce in a tangent compass a deflection of, say 45°, the entire resistance of the closing conductor must not be very great. Suppose R is the entire resistance of the whole battery, and an increase or decrease r of this resistance produces such a change in the strength of the current that the deflection of the needle is varied by 1°.

Now, by using a multiplier, which is about 150 times more sensi-tive than the tangent compass, the entire resistance of the battery must be about 150 R to cause a deflection of the needle of 45°.

To produce a like change in the strength of the current as that above mentioned, the resistance must now be increased or decreased by 150 r. But, since the multiplier is 150 times more sensitive than the tangent compass, the 150th part of this change of resistance, or r, will suffice to advance or bring back the position of the needle by 10; thus the same change of resistance r produces in both instruments nearly equal. changes of deflection.

If the multiplier is required to indicate very minute changes in the closing conductor, care must be taken that the corresponding difference of current shall act in the multiplier, without a very considerable resistance being inserted in the conductor. Wheatstone has accomplished this by means of the contrivance represented in Fig. 19, which he calls a differential measurer of resistance.

On a board about 14 inches by 4 wide, the small brass knobs a, b, c, and d are fastened, forming a paralellogram, and between a and d are placed e and f, and g, h between d and b. These knobs, which are furnished with binding-screws, are connected by wires, as seen in the figure.

One of the wires of the pole of the electro-motor is screwed in a, the other in b; the ends of the wires of the multiplier are fastened in c and d, so that the knobs c and d are in conducting connexion through the multiplier m; between e and ƒ a piece of wire is inserted, and another between g and h. The currents here diverge in various branches; but we have to consider only those which pass through the multiplier.

A current passes from a to c, from c through m to d, from d past g and h to b, as indicated by the unbroken line in Fig. 20; another

current, which traverses the multiplier in the opposite direction, goes from a, through e and f, to d; from d, through m, to c, and finally from c to b, as shown by the dotted line in Fig. 106. If the resistances in the two conducting wires a, c, d, b, and a, d, c, b, are perfectly equal, so are also the two currents passing through the multiplier equal; consequently the needle will remain at rest at the zero point. Now, by making the wire, inserted between e and f, only a little longer or shorter, the two currents going in opposite directions through the multiplier will be no longer equal, and the difference of

strength of the currents will deflect the needle. But since the sum of all the resistances is not great here, a very minute change in the resistance inserted between e and ƒ will cause a sensible change in the strength of the current, and therefore a sensible deflection of the needle.

Now, to obtain by this contrivance the resistance of a wire expressed in turns of the rheostat, the following method can be adopted: Insert between e and ƒ a few of the turns of the rheostat, and between g and h a wire, whose resistance is nearly equal to that of the inserted part of the rheostat on the other side, and adjust everything so that the needle may come to rest at O*. Now, inserting between g and h, besides the wire already there, the wire whose resistance is to be determined, there must be inserted on the other side a series of n turns of the rheostat to bring the needle back again to O. This number n of revolutions of the rheostat wire is the measure of the resistance of the wire in question.

Wheatstone has constructed other instruments besides this for the same object; but the description of this, the simplest one, will suffice.

SECTION THIRD.

RESISTANCE OF METALS AND LIQUIDS, GALVANIC POLARIZATION AND PASSIVITY.

§ 28. In order to compute by Ohm's formula the strength of current in a given case, it is not sufficient to know merely the constants of the electro-motor-we must also know the resistance of the solid conductors which are inserted in the closing circuit; and in case the current has to traverse a decomposing cell, besides the resistance of the liquids, we must also know the electro-motive opposing force appearing at the electrodes, or what is called the galvanic polarization. The conduction of the current, it is well known, depends upon the dimensions of the body, and also on its specific conductive capacity, which we shall now consider.

§ 29. Resistance of metals.-Buff has determined the resistance of a few of the metals by Wheatstone's method, as follows (Jahresbericht von Liebig und Kopp für 1847 and 1848, s. 286:)

He has taken the resistance of silver as unity; but since all resistances have been compared here with copper, I have reduced the data of Buff to this metal.

To distinguish the absolute value of resistance of a wire from these proportional numbers, I propose to call them the specific resistance to conduction. The specific resistance to conduction of a metal is the

To facilitate such an arrangement Wheatstone has introduced a special contrivance into his instrument. The knob d rests firmly upon a piece of brass. At the other end of this strip of brass another piece n turns about a pin, its free end resting on the wire. When n lies on d it has no effect, but the further it is turned from d towards g the more will the resistance on the course dg be reduced. If necessary the movable piece of brass n can also be brought to the other side of d.