reduced in the course of the circulation, oxidizing a portion of the substances derived from the food or of the tissues. The purplish colour now assumed by the solution illustrates the tinge of venous blood, and a fresh shake represents a fresh passage through the lungs. XIX. "Further Inquiries concerning the Laws and Operation of Electrical Force." By Sir W. SNOW HARRIS, F.R.S., &c. June 8, 1864. (Abstract.) Received 1. The author first endeavours to definitely express what is meant by quantity of electricity, electrical charge, and intensity. By quantity of electricity he understands the actual amount of the unknown agency constituting electrical force, as represented by some arbitrary quantitative 'electrical' measure. By electrical charge he understands the quantity which can be sustained upon a given surface under a given electrometer indication. Electrical intensity, on the contrary, is the electrometer indication' answering to a given quantity upon a given surface. the 2. The experiments of Le Monnier in 1746, of Cavendish in 1770, and papers of Volta in 1779, are quoted as showing that bodies do not take up electricity in proportion to their surfaces. According to Volta, any plane surface extended in length sustains a greater charge,- -a result which this distinguished philosopher attributes to the circumstance that the electrical particles are further apart upon the elongated surface, and consequently further without each other's influence. 3. The author here endeavours to show that, in extending a surface in length, we expose it to a larger amount of inductive action from surrounding matter, by which, on the principles of the condenser, the intensity of the accumulation is diminished, and the charge consequently increased; so that not only are we to take into account the influence of the particles on each other, but likewise their operation upon surrounding matter. 4. No very satisfactory experiments seem to have been instituted showing the relation of quantity to surface. The quantity upon a given surface has been often vaguely estimated without any regard to a constant electrometer indication or intensity. The author thinks we can scarcely infer from the beautiful experiment of Coulomb, in consequence of this omission, that the capacity of a circular plate of twice the diameter of a given sphere is twice the capacity of the sphere, and endeavours to show, in a future part of the paper (Experiment 16), that the charge of the sphere and plate are to each other not really as 1.2, but as 1:2, that is, as the square roots of the exposed surfaces; so that we cannot accumulate twice the quantity of electricity upon the plate under the same electrometer indication. 5. On a further investigation of the laws of electrical charge, the quan tity which any plane rectangular surface can receive under a given intensity is found to depend not only on the surface, but also on its linear boundary extension. Thus the linear boundary of 100 square inches of surface under a rectangle 37.5 inches long by 2.66 inches wide, is about 80 inches; whilst the linear boundary of the same 100 square inches of surface under a plate 10 inches square is only 40 inches. Hence the charge of the rectangle is much greater than that of the square, although the surfaces are equal, or nearly so. 6. The author finds, by a rigid experimental examination of this question, that electrical charge depends upon surface and linear extension conjointly. He endeavours to show that there exists in every plane surface what may be termed an electrical boundary, having an important relation to the group. ing or disposition of the electrical particles in regard to each other and to surrounding matter. This boundary, in circles or globes, is represented by their circumferences. In plane rectangular surfaces, it is their linear extension or perimeter. If this boundary be constant, their electrical charge (1) varies with the square root of the surface. If the surface be constant, the charge varies with the square root of the boundary. If the surface and boundary both vary, the charge varies with the square root of the surface multiplied into the square root of the boundary. Thus, calling C the charge S the surface, B the boundary, and μ some arbitrary constant depending on the electrical unit of charge, we have C=μS.B, which will be found, with some exceptions, a general law of electrical charge. It follows from this formula, that if when we double the surface we also double the boundary, the charge will be also double. In this case the charge may be said. to vary with the surface, since it varies with the square root of the surface, multiplied into the square root of the boundary. If therefore the surface and boundary both increase together, the charge will vary with the square of either quantity. The quantity of electricity therefore which surfaces can sustain under these conditions will be as the surface. If 7 and 6 represent respectively the length and breadth of a plane rectangular surface, then the charge of such a surface is expressed by μ2lb (1+b), which is found to agree perfectly with experiment. We have, however, in all these cases to bear in mind the difference between electrical charge and electrical intensity (1). 7. The electrical intensity of plane rectangular surfaces is found to vary in an inverse ratio of the boundary multiplied into the surface. If the surface be constant, the intensity is inversely as the boundary. If the boundary be constant, the intensity is inversely as the surface. If both vary alike and together, the intensity is as the square of either quantity; so that if when the surface be doubled the boundary be also doubled, the intensity will be inversely as the square of the surface. The intensity of a plane rectangular surface being given, we may always deduce therefrom its electrical charge under a given greater intensity, since we only require to determine the increased quantity requisite to bring the electrometer indication up to the given required intensity. This is readily deduced, the intensity being, by a well-established law of electrical force, as the square of the quantity. 8. These laws relating to charge, surface, intensity, &c., apply more especially to continuous surfaces taken as a whole, and not to surfaces divided into separated parts. The author illustrates this by examining the result of an electrical accumulation upon a plane rectangular surface taken as a whole, and the results of the same accumulation upon the same surface divided into two equal and similar portions distant from each other, and endeavours to show, that if as we increase the quantity we also increase the surface and boundary, the intensity does not change. If three or more separated equal spheres, for example, be charged with three or more equal quantities, and be each placed in separate connexion with the electrometer, the intensity of the whole is not greater than the intensity of one of the parts. A similar result ensues in charging any united number of equal and similar electrical jars. A battery of five equal and similar jars, for example, charged with a given quantity =1, has the same intensity as a battery of ten equal and similar jars charged with quantity =2; so that the intensity of the ten jars taken together is no greater than the intensity of one of the jars taken singly. In accumulating a double quantity upon a given surface divided into two equal and separate parts, the boundaries of each being the same, the intensity varies inversely as the square of the surface. Hence two separate equal parts can receive, taken together under the same electrometer indication, twice the quantity which either can receive alone, in which case the charge varies with the surface. Thus if a given quantity be disposed upon two equal and similar jars instead of upon one of the jars only, the intensity upon the two jars will be only one-fourth the intensity of one of them, since the intensity in this case varies with the square of the surface inversely, whilst the quantity upon the two jars under the same electrometer indication will be double the quantity upon one of them only; in which case the charge varies with the surface, the intensity being constant. If therefore as we increase the number of equal and similar jars we also increase the quantity, the intensity remains the same, and the charge will increase with the number of jars. Taking a given surface therefore in equal and divided parts, as for example four equal and similar electrical jars, the intensity is found to vary with the square of the quantity directly (the number of jars remaining the same), and with the square of the surface inversely (the number of jars being increased or diminished); hence the charge will vary as the square of the quantity divided by the square of the surface; and we have, calling C the charge, Q the quantity, Q2 and S the surface, C= ; which formula fully represents the phenomenon S2 of a constant intensity, attendant upon the charging of equal separated surfaces with quantities increasing as the surfaces; as in the case of charging an increasing number of equal electrical jars. Cases, however, may possibly arise in which the intensity varies inversely with the surface, and not in versely with the square of the surface. In such cases, of which the author gives some examples, the above formula does not apply. 9. From these inquiries it is evident, as observed by the early electricians, that conducting bodies do not take up electricity in proportion to their surfaces, except under certain relations of surface and boundary. If the breadth of a given surface be indefinitely diminished, and the length indefinitely increased, the surface remaining constant, then, as observed by Volta, the least quantity which can be accumulated under a given electrometer indication is when the given surface is a circular plate, that is to say, when the boundary is a minimum, and the greatest when extended into a right line of small width, that is, when the boundary is a maximum. In the union of two similar surfaces by a boundary contact, as for example two circular plates, two spheres, two rectangular plates, &c., we fail to obtain twice the charge of one of them taken separately. In either case we fail to decrease the intensity (the quantity being constant) or to increase the charge (the intensity being constant), it being evident that whatever decreases the electrometer indication or intensity must increase the charge, that is to say, the quantity which can be accumulated under the given intensity. Conversely, whatever increases the electrometer indication decreases the charge, that is to say, the quantity which can be accumulated under the given intensity. 10. If the grouping or disposition of the electrical particles, in regard to surrounding matter, be such as not to materially influence external induction, then the boundary extension of the surface may be neglected. In all similar figures, for example, such as squares, circles, spheres, &c., the electrical boundary is, in relation to surrounding matter, pretty much the same in each, whatever be the extent of their respective surfaces. In calculating the charge, therefore, of such surfaces, the boundary extensions may be neglected, in which case their relative charges are found to be as the square roots of the surfaces only; thus the charges of circular plates and globes are as their diameters, the charges of square plates are as their sides. In rectangular surfaces also, having the same boundary extensions, the same result ensues, the charges are as the square roots of the surfaces. In cases of hollow cylinders and globes, in which one of the surfaces is shut out from external influences, only one-half the surface may be considered as exposed to external inductive action, and the charge will be as the square root of half the surface, that is to say, as the square root of the exposed surface. If, for example, we suppose a square plate of any given dimensions to be rolled up into an open hollow cylinder, the charge of the cylinder will be to the charge of the plate into which we may suppose it to be expanded as 1:2. In like manner, if we take a hollow globe and a circular plate of twice its diameter, the charge of the globe will be to the charge of the plate also as 1:2, which is the general relation of the charge of closed to open surfaces of the same extension. The charge of a square plate to the charge of a circular plate of the same diameter was found to be 1: 1∙13; according to Cavendish it is as 1 : 1∙15, which is not far different. It is not unworthy of remark that the electrical relation of a square to a circular plate of the same diameter, as determined by Cavendish nearly a century since, is in near accordance with the formula CS above deduced. 11. The author enumerates the following formulæ as embracing the general laws of quantity, surface, boundary extension, and intensity, practically useful in deducing the laws of statical electrical force. Symbols. Let C= electrical charge; Q= quantity; E= intensity, or electrometer indication; S= surface, B= boundary extension, or perimeter; A= direct induction; d= reflected induction; F= force; D= distance. Formulæ. CS, when S and B vary together. Εα Εα S.B S (Q being constant), for all plane rectangular surfaces. 1,8 being constant, or equal 1. B' In square plates, Ca with side of square. In circular plates, C x with diameter. In globes, Ca with diameter. ▲, or induction & S, all other things remaining the same. The same for 8, or reflected induction. In circular plates, globes, and closed and open surfaces, |