The dependence of the principal current on the shape of the wire through which it passes, or in other words, the action of the current upon itself, has been already demonstrated. This action is exhibited in a more striking degree by the secondary current. A small induction-disc was introduced into the primary circuit, and a corresponding one into the secondary circuit; the remaining portion of the secondary circuit consisted of 44.7 feet of copper wire ths of a line in thickness, and the wire of the thermometer. The 447 feet of copper wire were first so stretched out, that when a secondary current passed through it the action of one portion of it upon another was null, and the strength of the secondary current under these circumstances was measured. The same wire was then wound into a spiral shape, the form alone of the circuit being thus altered, its length remaining as before, and the strength of the secondary current in this case was also measured. The following are the results obtained :

Thus we see that by a mere alteration of the form of the circuit, without any diminution whatever of its length, the secondary current is weakened in the proportion of 100:11. In this case the direction of the secondary current was the same in both the spirals through which it passed, the shape of the circuit being therefore that which has already been illustrated by the letter N; we observe that the effect of this shape is exactly similar to that which occurs in the primary circuit under the same circumstances. The large proportion of the entire circuit which, in the above experiment, received the spiral form, accounts for the magnitude of the diminution; in the following experiments another arrangement was adopted. From a copper wire gths of a line in thickness, three portions, each 53 feet long, were cut; the first was stretched out so that no action could occur between its parts; the second was wound into a plane spiral, similar to the induction-discs so often alluded to; and the third was carried back and forward, in a zigzag manner, from side to side of an oblong frame about a foot in width; twenty-five Us were thus formed, the legs of which were 1-2 line apart. In order to limit the

action to that of the one leg of the same U upon the other, and prevent its extension from U to U, each alternate U was bent upward, so as to form an angle of 50 or 60 degrees with the horizon. A large induction-disc was placed in the primary cir cuit, and a corresponding one in the secondary circuit, which, together with this, contained the thermometer and one of the lengths of copper wire just described. The current through the stretched-out wire was first proved, then through the spiral, and finally through the system of Us. The following are the results obtained :

The strength of the secondary current, when no action takes place between its various parts, is thus shown to be intermediate between those of the N-form and U-form. In passing through the former, the current is weakened in the ratio of 100: 60, while in passing through the latter it is strengthened in the ratio of 100: 114. The law of the primary current is therefore applicable to the secondary :-Two portions of a secondary current which run closely parallel, act upon each other: when the directions of the current through both portions are identical, a weakening is the consequence; and when the directions in both portions are opposed to each other, a strengthening of the current is the result.

What is the cause of this? During his investigation of the primary current, M. Riess conjectured that the action of the primary upon itself was due to the formation of a secondary current in the primary wire. Consistent with this view, we should infer that the action of the secondary upon itself is due to the formation of a tertiary current in the mass of the secondary wire, an inference which the author has established experimentally in the following manner:-It has already been shown that a secondary current is greatly weakened if the portion of the primary wire

which excites it excite at the same time a second secondary in a well-closed circuit, a case to which the reader's attention has been directed in a note; hence the possibility of lessening the supposed tertiary current by the intentional formation of a second tertiary. This was effected as follows:-The primary circuit contained a large induction-disc; the secondary circuit a similar one, the wire of the thermometer and 53 feet of copper wire, which was first stretched out, and afterwards exchanged for a plane or a cylindrical spiral formed from the same length of wire. Parallel to this plane or cylindrical spiral, and at about a line distant from it, ran another spiral, which we shall call the tertiary spiral; the secondary current was first measured while the tertiary spiral remained open, and afterwards when it was closed by 23 feet of copper wire. The following are the results :

The secondary current, which, with a stretched-out wire, had the value of 100, was weakened to 74 when the same length of wire was wound to the shape of a cylindrical spiral, and to 65 when its shape was that of a plane spiral. But on permitting of the formation of a tertiary current by closing the ends of the tertiary spiral, the current rose to 98 and 95 in these respective cases. Thus the production of a second tertiary checked, as conjectured, the formation of the one to which the weakening of the secondary was due, a striking increase of the latter being the consequence. It was proved by other experiments that the strengthening of the secondary current by the U-form of its wire is also due to the formation of a tertiary current in the mass of the latter.

Following up the system of procedure indicated in the foregoing pages, M. Riess has subjected currents of the third, fourth, and fifth orders to experimental examination. The laws of action in each respective case are precisely the same as those which apply to the secondary current, and which we have just described. The tertiary reacts upon the secondary in a manner similar to the reaction of the secondary upon the primary; in fact, the relation of any given current to that of the next higher order is in all respects that of primary to secondary; the tertiary current is modified by changing the shape of its wire, being

weakened by the N-form and strengthened by the U-form thereof; and the same is true of currents of all other orders.

With regard to the directions of these currents much uncertainty exists; Henry, Matteucci, Verdet and Knochenhauer have given utterance to various and contradictory opinions on this subject. With admirable ingenuity M. Riess has brought the foregoing experiments to bear upon this point. Let us suppose an induction-disc to be placed in the primary circuit, and parallel to it another with its ends united, thus forming an isolated circuit in itself. The passage of a current through the former will arouse an induced current possessing a certain direction, either opposed to the primary or coincident with it, in the latter. Without altering the relative position of the discs, let the second one be conceived to be brought into the primary circuit; the current, in passing through the first, will, as in the former case, induce a current in the second; but now primary and secondary are in the same wire, and it evidently depends upon the manner in which the two discs are connected with each other whether both currents meet in opposition* or flow on in the same direction. If by the N-combination secondary and primary flow on together, then by the U-combination they will oppose each other, and vice versa. Now the constant weakening effect of the N-form, and strengthening effect of the U-form in currents of all orders, demonstrate a constant relation between the directions of the induced and inducing currents. If the relation of any one secondary to its primaryt, with respect to direction, be determined, the same relation holds good in all other cases; if the currents have the same direction in one case, they will have it in all cases; if opposed once, they are opposed throughout the entire series. Commencing at the current which passes direct from the battery, it is easy to see that whatever be the direction of the secondary which it arouses, the tertiary evoked by the secondary must necessarily have the same direction as the current passing from the battery; for if the secondary be opposed to the primary, the tertiary will be opposed to the secondary, and hence have the same direction as the primary; and if the secondary have the same direction as the primary, the whole series will have this direction. Thus we arrive at the following necessary conclusion:-Currents of the third, fifth, and other odd orders, have the same direction as the original

* We must guard ourselves here against the notion that the opposition of primary and secondary is in any degree similar to the mechanical opposition of two forces, or even to the opposition of two currents of the same order.

†The terms secondary and primary are used here in a relative, not in an absolute sense.

current; and those of the second, fourth, and other even orders, have among themselves one and the same direction.

With regard to the direction of the currents of even orders as compared with that of the primary current, the author arrives at the probable conclusion, that they also have the same direction as the primary; but as this portion of the subject remains hypothetical, we will content ourselves with the mere indication of the author's opinion.

I

Queenwood College,

November 1851.

XXVIII. On some Thermo-electrical Experiments.
By RICHARD ADIE, Esq.

To the Editors of the Philosophical Magazine and Journal. GENTLEMEN, Liverpool, Feb. 10, 1852. SHOULD be glad to be allowed to avail myself of the medium of your Journal to give a brief notice of some thermoelectrical experiments which I made in the years 1812 and 1843*, and which I believe may be of service in elucidating some of the results noted in your February Number in Dr. Tyndall's interesting review of Professor Magnus's researches on this subject.

Where thermo-electrical couples are formed of feebly thermoelectric agents, such as bars of the same metal in different states of density, particularly of the softer malleable metals, the electrical force developed is so weak, that slight changes in the mode of manipulation, or small differences in the elements employed, which are either unknown to the operator or are generated during his experiment, will produce contradictory results. On which account it appears to me to be better to leave that class of agents and first study the production of thermo-electricity by metals, where the force is so decided, that, in the hands of different experimenters, uniform actions can be obtained.

Steel is a substance possessed of the advantage of being readily changed in density in opposite directions by two modes of hardening; and as these different methods are accompanied by a thermo-electrical current governed in its direction by the kind of hardening employed, the experiments with steel appear to me to show that the molecular arrangement of the particles of a body exercises a constant influence over the thermo-electrical currents generated by the unequal heating of it. When a couple is made by joining to a bar of soft steel a similar bar hardened by hammering, on heating the junction of the steel in the two different states an electrical current passes from the soft to the hard.

* See Edinburgh Philosophical Journal, Nos. 70 and 71.