Let us now examine the process for obtaining the readings of the rheometer with this unit.

§8. Determination of the force of a current by its chemical effects.To reduce the magnetic action cf the current in the rheometer to the chemical effect, the current has only to be passed simultaneously through a decomposing apparatus and the rheometer; a voltameter which gives the two gases together a detonating mixture, is the best adapted for this purpose.

A current which, for instance, passed through a Mohr's torsion galvanometer, and a decomposing apparatus, produced 40 cubic centimetres of detonating gas per minute, while the corresponding torsion of the galvanometer amounted to 490°.

40 490

Since the torsion is in this instrument proportional to the force of the current, we should have, for forming one cubic centimetre of the gas, a current corresponding to a torsion of 499 120.2. 40 each degree of torsion should be equivalent to 4% 0.0816 cubic centimetres of detonating gas. To reduce the number of degrees read on this galvanometer to Jacobi's unit, the former need only be multiplied by 0.0816. Hence a torsion of v° is equivalent to the force 0.0816 v.

The process is exactly the same for reducing the data of the tangent compass to the chemical effect. In such an instrument, for instance, a deflection of 22° was observed, while 30.8 cubic centimetres of gas were developed. The temperature being 15° Centigrade and the height of the barometer 740 millimetres, the quantity of this gas reduced to 0° Centigrade and a pressure of 760 millimetres is 28.18 cubic centimetres.

Since in this instrument the forces of currents are proportional to the tangent of the angle of deflection, the tangent of 22° or 0.404 corresponds to the quantity of gas, 28.18; and the tangent 1 corresponds to the quantity 369.7; thus the tangent of any angle of deflection read on this instrument has to be multiplied by 69.7 to find out how many cubic centimetres of detonating gas the current would have produced per minute, if it had passed with the same force through a decomposing apparatus; hence the force 69.7 tang. v corresponds to the angle of deflection v, according to our chemical unit. It is easy to reduce the indication of a compass of sines to this unit in a similar manner.

The factor by which the indications of a rheometer are to be multiplied, to obtain the force of current expressed in chemical measure, must of course be determined with great accuracy, for which a single experiment is not sufficient; a series of experiments must be made with currents of different forces, computing the factor from each, and from the values thus obtained the mean is to be taken. The different current forces are most easily obtained by operating, first with a battery producing a strong decomposition of water, and then weakening the current by removing single elements at a time.

Such a series, instituted by Mohr with his torsion galvanometer, gave the following results:

Since the magnetic and chemical effects are always proportional to each other, the quotient of the quantity of gas divided by the number of degrees must always be the same, if there are no errors of observation; but this is only approximately the case. The mean of all the quotients is 0.08386; thus we get the current force expressed in chemical measure, by multiplying the number of degrees v read on the instrument, by 0.08386, or,

S=0.08386 v.

Let us now consider a similar series of experiments, instituted to determine the relation of two tangent compasses to the chemical unit. The current was passed simultaneously through a decomposing apparatus and the two compasses, the larger of which had a ring 38 centi. metres in diameter, the smaller one of 30 centimetres. That the needles of the two compasses might have no influence upon each other, they were placed twenty-five feet apart. The following are the results of the observation :

During the period of the experiment, three minutes, in which the gas was caught, the needle vibrated very little; it receded regularly, but the rate was at most 0°.5 in three minutes. The number of degrees of the table are the means of all the angles read from the beginning to the end of the three minutes.

The quotient obtained by dividing the quantity of gas for one minute by the tangent of the corresponding angle of deflection should be properly a constant quantity, indicating how much gas a current develops per minute, which produces in the tangent compass a deflection of 45°, (because tang. 45°1). The following values of these quotients were obtained from the different experiments:

During the experiments the temperature of the room was 15° Cent., and the height of the barometer 744 millimetres. The gas was caught in a graduated tube, and the surface of the water in the tube stood about ten centimetres higher than that without, which is equivalent to a pressure of seven millimetres of mercury. Hence the gas sustained a pressure of 733 millimetres. Reduced to 0° Cent. and a barometric height of 760 millimetres, the quantities of gas, 76.5 cub. centimetres and 70 cubic c., obtained from the observation at 15° Cent., and 733 millimetres, are respectively 69.94 and 64.01 cubic centimetres, or, in round numbers, 70 and 64.

Thus a current which produces in the large compass a deflection of 45° will yield 70 cubic centimetres per minute; one producing in the small compass the same deflection will yield 64 cubic centimetres per minute of detonating gas, at 0° Centigrade, and under a pressure of 760 millimetres.

Hence, in chemical measure the force of a current which produces a deflection of v° in the large tangent-compass is,

S70 tangent v.

A current producing a deflection of w degrees in the small compass has, in chemical measure, a force

S'64 tangent w.

The constant factor for the reduction of the reading of a torsion galvanometer, a Weber's tangent-compass, or a compass of sines, may be

obtained by a series of very simple experiments. It is perfectly evident that this factor holds good for only a special rheometer, and for that special instrument only as long as the experiment is made in the same place. For instance, if the compass were removed from Freiburg to Marburg, the reducing factor would receive another value, because the horizontal intensity of the earth's magnetism is less in Marburg, and thus a current producing less detonating gas, would still produce a deflection of 45°.

The above series of observations also present us with a proof that Weber's tangent-compass can be used for determining the current force in absolute measure only when its diameter is not much less than 40 centimetres, (the length of the needle being three centimeters.) According to formula 4, the force of a current is proportional to the radius of the ring, the angles of deflection of the tangent compass being equal. The currents which produce a deflection of 45° in the two compasses above mentioned, are to each other in the proportion of 38 to 30. The quotient of these diameters is 1.2666, while the quotient of the corresponding forces of the current is 1.0937. 70 =

Having determined the reducing factor of a large tangent-compass by accurate experiments, we can compute from it the horizontal intensity of the earth's magnetism at the place of observation. The current which produces a deflection of 45° in our large compass, (380 millimetres in diameter,) has, in chemical measure, the force of 70; in absolute measure the force is,

g=

T: 190
2: 3.14

But chemical measure is to the absolute measure as 1.0477: 1; therefore in absolute measure this current has the value 70 = 66.813; and we have,

1.0477

According to the chart the value of T at Freiburg is 2.21, which accords very well with that computed above.

To determine the quantity of chemical effect which a current produces, we might, instead of measuring the quantity by the volume of explosive gas evolved, determine the quantity by weight of water decomposed, as Kesselman has done, (Über die galvanische Kohlenzink Kette,) and from that compute the volume of gas evolved. This method of observing is susceptible of great accuracy, and it is to be recommended on that account to those having an accurate balance at command. The experiments given above prove that the direct measurement of the volume of gas also yields very accurate results.

§ 9. Resistance of the element.-The force of current of a galvanic combination can be measured directly by means of a rheometer, and reduced in accordance with the principles stated above, to a determinate unit, for which the chemical unit is preferable on account

of its simplicity. But the knowledge of the force which the apparatus yields in a special case, with a definite quantity of contingent resistance, is not sufficient for determining the effect of the apparatus in all cases; for this purpose the actual resistance of the battery and its electro-motive power must be known. We now pass to the determination of the actual resistance.

The resistance, as well as the force of the current, must be reduced to a definitive unit, to admit of the comparison of different experimenters. For this, also, different units have been proposed and used. Many physicists assume as a unit of resistance, the resistance of a copper wire one metre long and one millimetre in diameter. This unit I shall adopt.

To determine the resistance of a battery, the force of its current, of course, must be measured, if different resistances are inserted successively in the circuit.

The resistance of the inserted piece of wire must be first brought to the adopted unit. The simplest way of doing this would be to use only copper wire of one millimetre in diameter and of different lengths; for a piece 10, 15, 20, &c., metres long, of this normal wire, the resistance would be 10, 15, 20, &c. But, since it is difficult to obtain wires having exactly this diameter, it must be measured accurately, and the computation made how long a copper wire one millimetre in diameter should be, which makes the same resistance. In computing the actual resistance of the battery, this reduced length of wire is used.

This section of our normal wire has a surface of 0.785 square millimetre. Since, with equal resistance the length of the wire increases in proportion to its section, it is evident that a copper wire 7 metres long, with a radius r, and section 2, excites the same resistance as a normal wire of the length,

in which L is the reduced length of the wire. A wire, for instance, having a diameter of 0.74 millimetre, a section of 0.43 square millimetre, and a length of 6 metres, will exert the same resistance as a 6 x 0.785 copper wire 10.95 metres long and 1 millimetre in 0.43 diameter; thus 10.95 is the reduced length of the wire used in the experiment.

From this inserted copper wire many pieces of different lengths may be obtained, 5, 10, 20, &c., metres long, for similar experiments, and ready at all times. Instead of longer copper wires, short pieces of wire of badly conducting metals, as platinum, iron, or German silver, are best; their resistance reduced to the normal wire must be determined by experiment. Wires to about 10 metres long can be wound suitably into coils and fixed in wooden cylinders from 2 to 3 inches in diameter, and corresponding lengths. Longer wires are covered with silk and wound on wooden rollers and used thus. these cylinders or rollers, the length of the wire reduced to the normal wire can be written so that there will be no further necessity for a reduction of the inserted wire.