shaped hollows of the beam and exactly balanced. The balance was established by pushing the beam a little in the required direction through the paper loop in which it loosely rested; and to accomplish this with greater ease, two square pieces were sawn out of the sides of the box, and two others were exactly fitted into the spaces thus opened; these pieces could be taken out at pleasure, and the hand introduced without raising the lid. The torsion-head was arranged so that when the beam bearing the balls came to rest, a thin glass fibre attached to the beam pointed to zero on the graduated quadrant underneath, while the index of the head pointed also to the zero of the graduated circle above. A current was sent through the helices so as to make the two magnetic poles which operated on the diamagnetic balls of opposite names. The balls were repelled when the current flowed. Preserving the current constant, the index above was turned in a direction opposed to the repulsion until the beam stood again at zero. The torsion necessary to effect this is evidently the expression of the repulsive force exerted at this particular distance.

Fig. 1 represents the appearance of the beam and helices when looked down upon through the glass lid. Fig. 2 represents the beam and balls attached to the suspending wire.

When the glass index pointed to zero, an interval of about th of an inch usually separated the nearest surfaces of the diamagnetic balls from the core ends. The intensity of the current

was measured by a tangent galvanometer, and it was varied by means of a rheostat. Always before commencing a series of experiments, the little beam was proved. With very strong currents it was found to be slightly diamagnetic; but so feeble, that its action, even supposing it not to follow the same law of increase as the ball (which, however, it certainly does), could cause no measurable disturbance.

I neglected no precaution to secure the perfect purity of the substances examined. The entire investigation was conducted in the private cabinet of Professor Magnus in Berlin; and at the same time Dr. Schneider happened to be engaged in the professor's laboratory in determining the chemical equivalent of bismuth. He was kind enough to give me a portion of this substance, prepared in the following way :-The metal of commerce was dissolved in nitric acid and precipitated with distilled water; whatever iron was present remained in the solution. The precipitate was filtered, washed for six days successively, and afterwards reduced by means of black flux. The metal thus obtained was again melted in a Hessian crucible, and saltpetre was gradually added, the mass at the same time being briskly stirred. Every remaining trace of foreign ingredient was thus oxidised and rose to the surface, from which it was carefully skimmed. The metal thus purified was cast into a bullet-mould, the interior surface of which was coated by a thin layer of oil; the outer surface of each bullet was carefully scraped away with glass, the ball was then scoured with sea-sand, and finally boiled in hydrochloric acid. The bismuth balls thus purified were placed upon the hollows of the beam, Fig. 2, and their repulsions by currents of various strengths determined in the manner indicated. The series of repulsions thus obtained are exactly analogous to the series of attractions in the experiments with the balls of iron. Now the square roots of the attractions give a series of numbers exactly proportional to the currents employed; and the question to be decided is,- Will the square roots of the repulsions give a similar series, or will they not?'

Calling the angle which the needle of the tangent compass, under the influence of the current, makes with the magnetic meridian a, then if the repulsion of the bismuth ball follow the same law as the attraction of the iron one, we shall have the equation

√T=n tan a,

where T represents the torsion necessary to bring the beam back to zero, and n is a constant depending on the nature of the experiment. The following tables will show the fulfilment or non-fulfilment of this equation:

Table I.-Bismuth spheres, 8 millims. diameter.

A second series was made with a pair of spheres of the bismuth of commerce with the same result.

Sulphur is also a diamagnetic substance, but a much weaker one than bismuth. The next series of experiments were made with two balls of this substance.

Table II.-Sulphur spheres, 8 millims. diameter.

A pair of sulphur balls were next taken of nearly twice the diameter of the preceding.

Table III.-Sulphur spheres, 13.4 millims. diameter.

The sulphur from which these balls were made was the material of commerce. After the experiments one of the balls was placed in a clean porcelain crucible and brought over the flame of a spirit-lamp; the sulphur melted, ignited, and disappeared in sulphurous acid vapour. A portion of solid substance remained in the crucible unvolatilised. This was dissolved in hydrochloric acid, and ferrocyanide of potassium was added; the solution turned immediately blue; iron was present. The other ball was submitted to a similar examination, and with the same result; both balls contained a slight admixture of iron.

In this case, therefore, the two opposing forces, magnetism and diamagnetism, were actually present, but we find the equation ✔T=n tan a fulfilled notwithstanding. Did one of the forces increase with the ascending magnetic power more quickly than the other, this result would be impossible.

Flowers of sulphur were next tried, but found to contain a considerable quantity of iron. I have to thank Professor Magnus for a portion of a native crystal of the substance obtained in Sicily, which upon trial was found to be perfectly pure. From this two small pellets were formed and laid upon the torsion-balance: they gave the following results:

The next substance chosen was calcareous spar. The corners of the crystalline rhomb were first filed away, and the mass thus rendered tolerably round; it was then placed between two pieces of soft sandstone, in each of which a hollow, like the cavity of a bullet-mould, had been worked out. By turning the stones, one right and the other left, and adding a little water, and a little patience, the crystal was at length reduced to a spherical form. The ball was then washed, and its surface care

fully cleansed in dilute hydrochloric acid. The first pair of balls were from the neighbourhood of Clitheroe in Lancashire.

Table V.-Spheres of Calcareous Spar, 9.2 millims. diameter.

The spar from which these balls were taken was not quite transparent; to ascertain whether its dullness was due to the presence of iron, a crystal which weighed about 3 grammes was dissolved in hydrochloric acid; the solution was exposed in a flat basin to the air, and the iron, if present, suffered to oxidise; ferrocyanide of potassium was added, but not the slightest tinge indicative of iron was perceptible.

Experiments were next made with a pair of spheres of calcareous spar from Andreasberg in the Harz Mountains.

Table VI.-Spheres of Calcareous Spar, 10.8 millims. diameter.

The spar from which these balls were taken was perfectly transparent. After the experiment, they were partially dissolved in hydrochloric acid, and the solution tested as in the former case for iron. No trace of iron was present.

The conclusion to be drawn from all these experiments, and from many others which I forbear citing, is, that the law of increase for a diamagnetic body is exactly the same as for a