arsenic spectrum, as we first observed it, we did not think it advisable to use the full power of the instrument. We therefore used five prisms, as stated, and read to one minute of arc. We always began each series of observations by setting the cross-wire of the micrometer on the sodium line, after the telescope had been adjusted to the angle of minimum deviation of this line as first observed. There was seldom any observed difference in this angle. But when by change of temperature, or otherwise, an alteration of two or three minutes had taken place, we found, on readjusting the cross-wire, that the relative position of the spectrum lines was, to the limit of accuracy of our measurement, wholly unchanged.

We give below the table of wave-lengths of the principal lines of the arsenic spectrum.

The wave-lengths printed in heavy type denote the bands which are most brilliant and give character to the spectrum. The other lines are less constant and less distinct, and in some instances may be due to accidental causes.

We were surprised to find among the bright lines, that the one which in the table is enclosed in brackets corresponds to the green thalium band, and upon examining the spectrum it appeared evident that thalium must be present in the arsenic in large quantities, as the thalium band was fully as bright as any of the arsenic bands.

The accompanying diagram (Fig. 3 of plate) will give some idea of the general appearance of the arsenic spectrum.

INVESTIGATIONS ON LIGHT AND HEAT, PUBLISHED WITH AN APPROPRIATION FROM THE
RUMFORD FUND.

THERE are two theories regarding the cause of the thermo-electric current. That held by Le Roux, Clausius, and most French physicists is that the heat effects which cause the current take place only at the junctions. The theory held by Sir William Thomson, Tait, and Maxwell is that the heat effects which cause the current take place, not only at the junctions, but along the metals themselves.

Let and 1 denote the heat-measured in dynamical equivalents absorbed and evolved at the hot and cold junctions respectively in unit time by unit current. Let E be the electromotive force of a battery, maintaining a current I in such a direction as to cause absorption of heat at the hot junction. Then if R be the whole resistance of the circuit, we have by Joule's law and the first law of thermodynamics:

Supposing the whole energy of the current wasted in heat. Also:

:

(2)

It appears, then, that, owing to the excess of the absorption of heat at the hot junction over the evolution at the cold junction, there arises an electromotive force π-, helping to drive the current in the direction giving heat absorption at the hot junction. We may suppose, and shall henceforth suppose, that EO, and then the current will be maintained entirely by the electromotive force π—1•

Now, apply the second law of thermodynamics. "The application of the second law is of a more hypothetical character. Still it seems a reasonable hypothesis to assume that the Peltier effects, and other heat

effects, if any, which vary as the first power of the current strength, taken by themselves, are subject to the second law of thermodynamics."

6 and 61 being the absolute temperatures of the hot and cold junctions.

C being a constant, depending only on the nature of the metals.

(3)

In accordance with this, the electromotive force in the circuit = C(0—01).. it would be proportional to the difference between the temperatures of the junctions.

"Now, this conclusion is wholly inconsistent with the existence of thermo-electric inversion. We must, therefore, either deny the applicability of the second law, or else seek for reversible heat effects other than those of Peltier." This was essentially the reasoning that led Thomson to the discovery of the Thomson effect. Before questioning Thomson's conclusion, it is best to consider the formula which are deduced from his hypothesis.

Suppose we have a circuit of two metals. Let the heat absorbed by the Thomson effect in passing from a point at temperature to a point at temperature +de in one metal be odo per unit current per unit time. Let σd be the corresponding expression for the other metal. and 02 are functions of the temperature. They depend on the nature of the metals, but are independent of the form or magnitude of the section of the conductors. These effects are proportional to the first power of the current strength.

σι

If EO we have as the electromotive force of the thermo-electric current, by the same reasoning as before:

If, as Tait supposes, σ is proportional to the first power of the absolute temperature, oko equation (w) becomes :

e=- - [k92 + k'0 + k"]

..the thermo-electric curve is a parabola.

The basis of all the preceding is taken from the British Encyclopædia. Maxwell's demonstration is essentially the same. (§§ 249-251, Vol. I., Maxwell's Electricity and Magnetism.)

When no current was passing from an external battery eq. (2) became

In other words, it was said that the heat absorbed in unit time by unit current in exceeding that evolved at the cold junction

a current of strength I.

-

the amount of heat crossing the hot junction was sufficient to produce

Now, when a current from an outside source is passed through the circuit in the same direction as I, an amount of heat

disap

pears, C being the strength of the external current: what becomes A certain amount of energy disappears: what is its

of this heat?

equivalent ?
If the heat

is sufficient to produce a current of strength I, the C is great enough to produce a current C times as strong as I.. a current of strength CI.

heat

When the current Cis passing through the circuit we should then expect to find it increased (or decreased) by a current CI-the equivalent of the amount of heat absorbed by C. Thus, when an external current passes through a thermo-electric element, we should expect to have as the total current in the circuit, C++ CI; that is, the resultant current should be much greater (or much less) than C+I.

But, in several experiments that were made, it was observed that the resultant current always equalled exactly C+I.

Now, if the Peltier effect is the cause of the thermo-electric current, enough heat has disappeared to create a current C times as strong as the proper thermo-electric current; but experiment shows that the thermo-electric current is perceptible, while this other current is imperceptible. We must, therefore, conclude that this current, which is equivalent to an amount of heat 9 C, is not C times as great as the proper thermo-electric current; and hence the proper thermo-electric current cannot be the equivalent of the amount of heat 9. In other words, the Peltier effect cannot be the cause of the thermo-electric current.

An unsuccessful experiment was made to prove that the Peltier effect was not great enough to be the cause of the thermo-electric current. The failure was due to the fact that the heat absorbed was too small to be measured. The principle of the experiment was as follows:

Place the thermo-electric junction in a vessel of mercury, after heating the mercury to a certain temperature let it cool, the circuit being broken so that no current passes. From a thermometer placed in the mercury read the temperatures at definite times, and construct a curve, having the temperatures as ordinates, and the corresponding