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66. Again, the intensity of one part of the inductive action, for example that represented by A g. may be supposed so great as to produce a secondary current capable of penetrating the body, and of thus producing a shock while the other parts of the action, represented by g B and CD, are so feeble as to affect the galvanometer only. We would then have a result the same as one of those given in the last section (42.), and which was supposed to be produced by two kinds of induction; for if the shock were referred to as the test of the existence of an induced current, one would be found at the beginning only of the battery current, while, if the galvonometer were consulted, we would perceive the effects of a current as powerful at the ending as at the beginning.

67. The results mentioned in the last paragraph cannot be obtained by plunging a battery into the acid; the formation of the current in this way is not sufficiently rapid to produce a shock. The example was given to illustrate the manner in which the same effect is supposed to be produced, in the case of the more sudden formation of a current, by plunging one end of the conductor into a cup of mercury permanently attached to a battery already in the acid, and in full operation. The current, in this case, rapid as may be its development, cannot be supposed to assume per saltum its maximum state of quantity; on the contrary, from the general law of continuity, we would infer that it passes through all the intermediate states of quantity, from that of no current, if the expression may be allowed, to one of full development; there, are, however, considerations of an experimental nature which would lead us to the same conclusion (18,90.), and also to the further inference that the decline of the current is not instantaneous. According to this view, therefore, the inductive actions at the beginning and ending of a primary current, of which the formation and interruption is effected by means of the contact with a cup of mercury, may also be represented by the several parts of the curve, fig. 2.

68. We have now to consider how the rate of increase or diminution of the current, in the case in question, can be altered by a change in the different parts of the apparatus; and, first, let us take the example of a single battery and a short conductor, making only one or two

• The shock depends more on the intensity than on the quantity, Seo paragraph 13.

turns around the helix; with this arrangement a feeble shock, as we have seen (11.), will be felt at the making, and also at the breaking of the circuit. In this case it would seem that almost the only impediment to the most rapid development of the current would be the resistance to conduction of the metal; and this we might suppose would be more rapidly overcome by increasing the tension of the electricity; and, accordingly, we find, that if the number of the elements of the battery be increased, the shock at making the circuit will also be increased, while at breaking the circuit will remain nearly the same. To explain, however, this effect more minutely, we must call to mind the fact before referred to (17), that when the poles of a compound battery are not connected, the apparatus acquires an accumulation of electricity, which is discharged at the first moment of contact, and which in this case would more rapidly develope the full current, and hence produce the more intense action on the helix at making the circuit.

69. The shock, and also the deflection of the needle, at breaking the circuit with a compound battery and a short coil (9), appears nearly the same as with a battery of a single element, because the accumulation just mentioned, in the compound battery, is discharged almost instantly, and, according to the theory (71.) of the galvanic current, leaves the constant current in the conductor nearly in the same state of quantity as that which would be produced by a battery of a single element; and hence the conditions of the ending of the current are the same in both cases. Indeed, in reference to the ending induction, it may be assumed as a fact which is in accordance with all the experiments (9, 13, 73, 74, 75, 76, &c.), as well as with theoretical considerations*, that when the circuit is broken by a cup of mercury, the rate of the diminution of the current, within certain limits, remains the same, however the intensity of the electricity or the length of the con ductor may be varied.

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Fig. 3,

C

D

See the theory of Ohm-Taylor's Scientifio Memoirs, vol. i. p. 312, $11, and vol. ii. p. 01,

70. The several conditions of the foregoing examples are exhibited by the parts of the curves, figs. 3 and 4. The gradual development of the current in the short conductor, with a single battery, and the gradual decline of the same, are represented by the gentle rise of A B and fall of C D, fig. 3; while, in the next fig. (4.), the sudden rise of A B indicates the intensity which produces the increased shock, after the number of elements of the battery has been increased. The accumulation of the electricity, which almost instantly subsides, is represented by the part B c e, fig. 4; and from this we see, at once, that although the shock is increased by using the compound battery, yet the needle of the galvanometer will be deflected only to the same number of degrees, since the parts B c and c e give inductive actions in contrary directions, and both within the time of a single swing of the needle, and, consequently, will neutralize each other. The resulting deflecting force will, therefore, be represented by ef, which is equal to Ck, or to b B, in fig. 3.

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The intensity of the shock at the breaking is represented as being the same in the two figures, by the similarity of the rate of descent of the part C D of the curve in each.

71. We have said (69.) that the quantity of current electricity in a short conductor and a compound battery, after the first discharge, is nearly the same as with a single battery. The exact quantity, according to the theory of Ohm, in a unit of length of the conductor, is given by the formula

n A rn+ R

In this n represents the number of elements; A, the electromotive force of one element; 7, the resistance to conduction of one element; and R, the length of the conductor, or rather its resistance to conduction in terms of r. Now, when R is very small, in reference to r n, as

is the case with a very short metallic conductor, it may be neglected, and then the expression becomes

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and since this expresses the quantity of current electricity in a unit of the length of the circuit, with either a single or a compound battery, therefore, with a short conductor, the quantity of current electricity in the two cases is nearly the same.

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72. Let us next return to the experiment with a battery of a single element (68.), and instead of increasing the intensity of the apparatus, as in the last example, let the length of the conductor be increased; then the intensity of the shock at the beginning of the current, as we have seen(14.), will be diminished, while that of the one at the ending will be increased. That the shock should be lessened at the beginning, by increasing the length of the conductor, is not surprising, since, as we might suppose, the increased resistance to conduction would diminish the rapidity of the development of the current. But the secondary current, which is produced in the conductor of the primary current itself, as we have seen (19.), is the principal cause which lessens the intensity of the shock, and the effect of this, as will be shewn hereafter, may also be inferred from the principles we have adopted.

73. The explanation of the increased shock at the moment of breaking the circuit with the long conductor, rests on the assumption before-mentioned (69.), that the velocity of the diminution of a current is nearly the same in the case of a long conductor as in that of a short one. But, to understand the application of this principle more minutely, we must refer to the change which takes place in the quantity of the current in the conductor by varying its length; and this will be given by another application of the formula before stated (71). This, in the case of a single battery, in which n equals unity, becomes

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and since this, as will be recollected, represents the quantity of current electricity in a unit of length; of the conductor, we readily infer from it that, by increasing the length of the conductor, or the value of R, the quantity

of current in a unit of the length is lessened. And if the resistance of a unit of the length of the conductor were very great in comparison with that of r (the resistance of one element of the battery), then the formula would become

A

R

or the quantity in a single unit of the conductor would be nversely as its entire length, and hence the amount of current electricity in the whole conductor would be a constant quantity, whatever might be its length. This, however, can never be the case in any of our experiments, since in no instance is the resistance of R very great in reference to r, and therefore, according to the formula (73.), the whole quantity of current electricity in a long conductor is always somewhat greater than in a short one.

74. Let us, however, in order to simplify the conditions of the induction at the ending of a current, suppose that the quantity in a unit of the conductor is inversely as its whole length, or in other words, that the quantity of current electricity is the same in a long conductor as in a short one; and let us also suppose, for an example, that the length of the spiral conductor, fig. 1, was increased from one spire to twenty spires; then, if the velocity of the diminution of the section of the current is the same (69.) in the long conductor as in the short one; the shock which would be received by submitting the helix to the action of one spire of the long coil would be nearly of the same intensity as that from one spire of the short conductor; the quantity of induction, however, as shown by the galvanometer, should be nearly twenty times less; and these inferences I have found in accordance with the results of experiments (75). If, however, instead of placing the helix on one spire of the long conductor, it be submitted at once to the influence of all the twenty spires, then the intensity of the shock should be twenty times greater, since twenty times the quantity of current electricity collapses, if we may be allowed the expression, in the same time, and exerts at once all its influence on the helix. If, in addition to this, we add the consideration, that the whole quantity of current electricity in a long conductor is greater than that in a short one (73.), we shall have a further reason for the increase of the terminal shock, when we increase the length of the battery conductor.

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