“ If we regard as a constant magnitude, the relation of the electroscopic forces and to each other depends solely upon the magnitude of the space which the electricity occupies in the circuit; we can therefore bring the electroscopic force of the body nearer to its greatest value solely by increasing the capacity of the circuit, either by a general increase of its dimensions, or by attaching anywhere to it foreign masses. ”

“ Imagine, for instance, a ring everywhere of equal thickness and homogeneous, having, at any one place, in its whole thickness, one and the same electrical tension, i.e. inequality in the electrical state of two surfaces situated close to each other, from which causes, when they have come into action, and the equilibrium is consequently disturbed, the electricity will, in its endeavour to re-establish itself, if its mobility be solely confined to the extent of the ring, flow off on both sides. ”

“ We may, to render our assertion intelligible by an example, undoubtedly imagine bodies in nature which consist only of homogeneous elements, but whose position to each other, taken in one direction, might be different than when in another direction; such bodies, as our mode of representation immediately shows, might conduct the electricity in one direction in a different manner than in another, notwithstanding that they might appear uniform and equally dense. ”

“ Experience, as yet, leaves us in uncertainty respecting the change of conductibility, which occurs when two fluids are mixed in various proportions with one another, and likewise with respect to the law of tensions, which is followed by different mixtures of the same constituents in various proportion; for, if we do not err, no experiments have been instituted relatively to the latter law, and the law of the change produced in the conducting power of a fluid, by the mixture of another, is not yet decidedly established by the experiments of Gay Lussac and Davy. ”

“ Another part of our theory on which there may exist a doubt is, the supposition that the agents of the terrestrial magnetic force are situated exclusively in the interior of the earth. If we seek for their immediate causes, partly or wholly, without the earth, and confine ourselves to known scientific grounds, we can only think of galvanic currents. But the atmosphere is no conductor of such currents, neither is vacant space; thus, in seeking in the upper regions for a vehicle of galvanic currents we go beyond our knowledge. ”

“ This new method of communicating such great attractive power to iron created in me the desire of repeating the experiments, and principally of taking into consideration the application of this attractive power, which it appears may be infinitely increased, to some useful purpose. I give these experiments to the public in the conviction that a force so easily evolved and so very powerful justifies repeated and varied experiments. ”

“ To begin with the most simple investigations, I have confined myself at the outset to those cases where the excited electricity propagates itself only in one dimension. They form, as it were, the scaffold to a greater structure, and contain precisely that portion, the more accurate knowledge of which may be gained from the elements of natural philosophy, and which, also, on account of its greater accessibility, may be given in a more strict form. ”

“ If we imagine one of the parts of which the galvanic circuit is composed to be a non-conductor of electricity, i. e. a body whose capacity of conduction is zero, the reduced length of the entire circuit acquires an indefinitely great value. ”

“ We have assumed, in accordance with the observations hitherto made, that when by any two exteriorly like constituted elements, whether they be of the same or of different matter, a mutual change in their electrical state is produced, the one loses just so much force as the other gains. Should it hereafter be shown by experiments that bodies exhibit a relation similar to that which in the theory of heat is termed the capacity of bodies, the law we have established will have to undergo a slight alteration, which we shall point out in the proper place. ”

“ In our theory it is assumed that every determinate magnetized particle of the earth contains precisely equal quantities of positive and negative fluid. Supposing the magnetic fluids to have no reality, but to be merely a fictitious substitute for galvanic currents in the smallest particles of the earth, this equality is necessarily part of the substitution; but if we attribute to the magnetic fluids an actual existence, there might without absurdity be a doubt as to the perfect equality of the quantities of the two fluids. ”

“ Let be a polygon on the surface of the earth, the sides of which are the shortest lines that can be drawn between their respective extremities, and are therefore portions of great circles, the earth being here considered simply as a sphere. ”

“ With respect to those circuits on which the atmosphere exercises some influence, and whose condition varies with time, without this change originating in a progressive chemical transformation of the circuit, and is thus distinguished from all the others by the magnitude of its current being different at different places,—I have been content, with respect to each of these, always to treat of only the most simple case, as they but rarely occur in nature, and in general appear to be of less interest. ”

“ The force which at each part of the earth imparts a certain direction to a magnetic needle suspended by its centre of gravity, (supposing it free from all extraneous influence, such, for example, as that of another artificial magnet, or the conductor of a galvanic current,) is termed the earth's magnetic force, in so far as the source whence it is derived is to be sought for in the earth itself. ”

“ Granting, which seems to be most natural, that the electricity is diffused proportionately to the mass over the space which these bodies then occupy, a complete analysis will show that the decomposing force of the circuit is in direct proportion to the energy of the current, and, moreover, that it depends on a coefficient, to be derived from the nature of the constituent parts and their chemical equivalents. ”

“ If the circuit, during its production, is exposed to no external deduction or adduction, the constant must be sought for in the circumstance that the sum of all the electricity in the circuit must be zero. ”

“ If we look away from the actual condition of the earth and take the question in its generality, there may certainly exist more than two magnetic poles; but it does not appear to have been noticed that if, for example, two north poles exist, there must necessarily be between them yet a third point, which is likewise a magnetic pole, but is properly neither a north nor a south pole, or is both if that expression be preferred. ”

“ Disregarding however the great certainty and distinctness which accompany our manner of representation, there might still be something more to say, and perhaps with some justice, against Laplace's mode of treatment in favour of ours, in this respect, that the former takes not the least account of the possible nature of the given elements of bodies, but merely has to do with imaginary elements of space, by which the physical nature of the bodies is almost entirely lost sight of. ”

“ For it is placed beyond all doubt, both from theoretical considerations, as well as from experiments, that electricity in motion penetrates into the interior of bodies, and its quantity accordingly depends on the space occupied by the bodies; while, on the other hand, it is no less ascertained that static electricity accumulates at the surface of bodies, and its quantity therefore is dependent on the extent of surface. ”

“ I have distinctly separated the consideration of such galvanic circuits in which no portion undergoes a chemical change, from those whose activity is disturbed by chemical action, and have devoted a separate part to the latter in the Appendix. This total separation of two parts forming a whole, and, as might appear, the less dignified position of the latter, will find in the following circumstance a sufficient explanation. A theory, which lays claim to the name of an enduring and fruitful one, must have all its consequences in accordance with observation and experiment. ”

“ By Professor Carl Friedrich Gauss, of the University of Göttingen.
[Translated by Mrs. Sabine, and revised by Sir John Herschel, Bart.]
The unwearied zeal with which, in recent times, endeavours have been made to examine the direction and intensity of the magnetic force of the earth, at all parts of its surface, is the more worthy of admiration, as it has been prompted by the pure love of science. Great as is the importance to navigation of the most complete attainable knowledge of the lines of declination, more than this is scarcely required for its purposes. ”

“ The mode in which electricity makes its appearance at the place of contact of two different bodies, or the electrical tension of these bodies, I have thus expressed: when dissimilar bodies touch one another, they constantly maintain at the point of contact the same difference between their electroscopic forces. ”

“ Though electro-magnetism from its intrinsic importance certainly is one of the most remarkable and interesting discoveries of modern times, yet it would create a much higher interest, and gain in popularity, if it could be rendered practically useful. For some time past I had been occupied with the idea, whether the power of electro-magnets, which without doubt might be infinitely increased, could be applied as a motive power for machinery. ”

“ We need now no longer hesitate about allowing the electrical action of an element not to extend beyond the adjacent surrounding elements, so that the action entirely disappears at every finite distance, however small. The extremely limited circle of action with the almost infinite velocity with which electricity passes through many bodies might indeed appear suspicious ”

“ However, it must not be forgotten that we have not here to deal with mathematical, but with physical determinations; for, strictly taken, does not represent a surface, but that portion of a disc of the circuit on which the atmosphere has direct influence, and in fact signifies nothing more than that part of a disc of the circuit which is traversed by the electricity continually passing through the circuit. ”

“ We have, it is true, constantly endeavoured to conceive the nature of the action in question, in its connexion with those with whose properties we are better acquainted; but, nevertheless, we wish the determinations given to be regarded as nothing more than fictions, which are only to remain until we become by experiment in possession of the true law. ”

“ Nor can a smaller quantity of electricity be imparted from the one body to the common surface than it is deprived of by the other, as this circumstance would be evinced by an infinitely high degree of negative electricity. ”

“ The motion of electricity is effected in most bodies so rapidly that we are seldom able to determine its changes at the various places, and on that account we are not in a condition to discover by observation the law according to which they act. ”

“ A physical foundation can only be allowed to such attempts as have considered the earth as a real magnet, and have employed in the calculation only the demonstrated mode of action of a magnet operating at a distance. ”

“ If for instance we consider that for infinitely small masses at infinitely short distances all particular relations must necessarily have the same weight as for finite masses at finite distances, it is not directly evident how the method of the immortal Laplace—to whom we are indebted for so many valuable explanations respecting the nature of molecular actions,—according to which the elements must be constantly treated as if they were placed at finite distances from each other, could nevertheless still afford correct results ”

“ The simplest hypothesis of this kind is that which supposes a very small magnet in the centre of the earth; or rather (as it is not likely that any one ever believed in the actual existence of such a magnet) supposes magnetism to be so distributed in the earth, that its collective action at and beyond the surface is equivalent to the action of an imaginary infinitely small magnet; much as gravitation towards a homogeneous sphere is equivalent to the attraction of a sphere of equal mass condensed in its central point. ”

“ We represent to ourselves magnetization as a separation of the magnetic fluids. Admitting this representation, the mode of action of the fluids (repulsion of similar and attraction of dissimilar particles inversely as the square of the distance) belongs to the number of established physical truths. No alteration in the results would be caused by changing this mode of representation for that of Ampère, whereby, instead of magnetic fluids, magnetism is held to consist in constant galvanic currents in the minutest particles of bodies. ”

“ When two electrical elements, and , of equal magnitude, of like form and similarly placed with respect to each other, but unequally powerful, are situated at the proper distance from each other, they exhibit a mutual tendency to attain electric equilibrium, which is apparent in both constantly and uninterruptedly approaching nearer to the mean of their electric state, until they have actually attained it. ”