Casselmann used a wire-holder similar to that represented in fig. 49. By observing attentively a wire held by it while it is red hot, we perceive that in the immediate vicinity of the clamps its glow is considerably less than in the middle. If now the wire be so far shortened that the cooling influence of the clamps extends to its middle it seems easy to explain how, by shortening the length of the wire, the phenomena of ignition finally disappear. This is also seen from the following observation :

A platinum wire 0.21 metre in diameter was inserted in the circuit of a single carbon-zinc cup. With a length of 3 centimetres it became feebly red hot, while the tangent compass indicated 26°; but when the same wire was shortened to 1 centimetre no ignition was produced, even with a current of 34°.

When, instead of the single element, two Bunsen's cups were used, the appearances of ignition were entirely identical with the lengths of both 3 and 1 centimetre, though the corresponding deflection in the former case was 34°, and in the latter (the shorter wire) 44°.

§ 57. Relation between the diameter and force of current in metallic wires ignited by the galvanic current.-The above experiments do not illustrate the relation between the force of current and the diameter of the wires, as corresponding to a certain degree of ignition, because only the length, but not the diameter of the wire, was varied.

The following table gives the results of a set of experiments made with platinum wires of 1 decimetre in length and variable diameters:

The experiments marked * are taken from the former series, (on page 420.)

From this series of experiments we may assume that, in order to produce the same degree of ignition, the force of current must increase proportionally to the diameter of the wires. According to this law, for

the same degree of ignition the quotient of the diameter of the wire into the corresponding force of current should be a constant quantity. The last column of the previous table contains this quotient. It is: For feeble ignition—

The deviations from the mean are so irregularly distributed, in respect to their quantity as well as to their sign, that without hesitation we may attribute them to errors of observation. That these deviations are so considerable, varying up to 7 per cent. of the corresponding quotients, will not surprise us if we consider that the degrees of ignition are not measured, but only estimated.

A set of experiments similar to the above, with iron wire, gave the following results:

H

This series therefore confirms the results we obtained from the experiments with the platinum wire.

With copper wire the following results were obtained:

§ 58. Comparison of the laws of galvanic ignition with those of Lenz for the development of heat.-According to the laws of Lenz, the quantity of heat liberated in a metallic wire increases proportionally to the square of the force of the current, and to the resistance to conduction of the wire. But with equal length the resistance to conduction is inversely proportional to the square of the diameter. If, therefore all the other conditions remaining unchanged the force of current increases as the diameter of the wire, the quantity of heat developed must remain the same.

But if in a thicker wire just as much heat is evolved as in a thinner one, we should certainly expect that the former would not attain the same degree of ignition as the latter, because the thicker wire imparts more heat to the surrounding air; therefore, in order to obtain an equal degree of ignition in a wire of n times the diameter, we should have to employ a current more than n times stronger, while according to the above experiments a current with n times increased force is sufficient.

Let us more accurately determine this relation. According to the researches of Lenz, above discussed, the heat produced in metallic

Melted after a while.

wires by a galvanic current is proportional to the square of the force of current and to the resistance to conduction of the wire. We can, therefore, put

W = s2 l . . . . 1.)

where W denotes the quantity of heat produced (within a given time) in a wire, the resistance of which is for the strength of current 8. We may now consider W the quantity of heat which must be produced in a given time in the wire in order to make it red hot. If this wire be replaced by one of the same metal and of equal length, but n times the diameter, its surface will also be n times as great, and this surface gives to the surrounding air-cæteris paribus-n times as much heat, and therefore n times as much heat, viz: n W, must be evolved in the thicker wire in order to produce the same appearance of red heat. But the resistance to conductions of the wire of n times greater diameter is

n2

Denoting by the strength of current

which makes it red hot, we obtain the equation:

Thus, according to this reasoning, a current of 2.83 and 5.19 times the strength should be necessary in order to make red hot, wires, the diameter of which is twice or three times as great, while, according to my observations, a two and three times stronger current proves sufficient; in short, instead of equation 3), according to my observations, that of sns holds good. The deviations are far too considerable to allow of the supposition that they proceed from errors of observation.

How this difference is to be accounted for I am at present unable to decide. It is, indeed, conceivable that with thicker wires and an equal strength of current the outermost stratum reaches so low a temperature that the loss of heat is not greater than from thin wires, but that towards the interior the temperature increases so rapidly that the outer colder strata have no perceptible influence upon the appearance of the wire. Small differences, too, are lost by the defective estimation of ignition, and it is therefore to be expected that deviations from the above law relating to the thickness will be found, when the diameter is more varied than in these experiments. I intend to continue the investigation of this subject.

The laws of ignition by the galvanic battery and by the discharge of the Leyden jar differ entirely. While the strength of current must be increased in equal, or at least nearly equal proportions to the diameter, the charge in the Leyden jar has to be augmented in proportion to the fourth power of it, if the degree of ignition is to be

kept unchanged. This difference already shows that the galvanic ignition is essentially of another nature from that produced by the discharge of the jar.

§ 59. Determination of the voltaic combination required to produce ignition in given metallic wires.-The mean values above obtained for the quotient indicate the force of current necessary to bring a wire

D

of 1 millimetre in diameter into the corresponding degree of ignition. Therefore, for a platinum wire 1 millimetre in diameter, to make it feebly red the force of current required is 165; to make it red hot the force of current required is 172; to make it nearly white hot the force of current required is 220.

For an iron wire 1 millimetre in diameter to make it feebly red the necessary force of current is 121; to make it red hot the necessary force of current is 135. To make a copper wire 1 millimetre in diameter red hot a force of current of 433 is required; for silver this value is 432. I consider these numerical values only as first approximations. Denoting by 8 the force of current which is required to bring a wire 1 millimetre in diameter to a certain state of ignition, thens.d indicates the force required to produce an equal amount of heat in a wire of the same metal whose diameter is d.

If once we know the force of current a required to produce a certain degree of ignition in a piece of wire of given diameter, and also the resistance to conduction r, which this wire in connexion with the other part of the closing circuit offers, then it is easily computed what combination of voltaic elements, of a known nature, has to be employed for the purpose.

Let e denote the electro motive force, w the specific resistance of one of the cups employed. These have to be so combined that they form a battery of n elements, each consisting of m cups placed together. Now, the values of n and m are to be determined.

The cups must be so combined that the resistance of the battery is equal to that of the closing wire; the total resistance, therefore, must be equal to 2r. We have, therefore,