The summer of 1870 was unusually cool; but the winter has been extremely gloomy, with torrents of rain, and occasionally such thick fogs, that I could see neither to read nor to write. We had no storms during the hot weather; but on the afternoon of the 21st December, there was one of the finest thunderstorms I ever saw; the lightning was intensely vivid, and took the strangest forms, darting in all directions through the air before it struck, and sometimes darting from the ground or the sea to the clouds. It ended in a deluge of rain, which lasted all night, and made us augur ill for the solar eclipse next day; and, sure enough, when I awoke next morning, the sky was darkened by clouds and rain. Fortunately, it cleared up just as the eclipse began; we were all prepared for observing it, and we followed its progress through the opening in the clouds till at last there was only a very slender crescent of the sun's disc left; its convexity was turned upwards, and its horns were nearly horizontal. It was then hidden by a dense mass of clouds; but after a time they opened, and I saw the edge of the moon leave the limb of the sun. The appearance of the landscape was very lurid, but by no means very dark. The common people and children had a very good view of the eclipse, reflected by the pools of water in the streets.

Soon after my dear husband's death, we went to Spezia, as my health required change, and for some time we made it our headquarters, spending one winter at Florence, another at Genoa, where my son and his wife came to meet us, and where I had very great delight in the beautiful singing of our old friend Clara Novello, flow Countess Gigliucci, who used to come to my house, and sing Handel to me. It was a real pleasure, and her voice was as pure and silvery as when I first heard her, years before. Another winter we spent at Turin. On returning to Spezia in the summer of 1861, the beautiful comet visible that year appeared for the first time the very evening we arrived. On the following, and during many evenings while it was visible, we used to row in a small boat a little way from shore, in order to see it to greater advantage. Nothing could be more poetical than the clear starlit heavens with this beautiful comet reflected, nay, almost repeated, in the calm glassy water of the gulf. The perfect silence and stillness of the scene was very impressive.

I was now unoccupied, and felt the necessity of having something to do, desultory reading being insufficient to interest me; and as I had always considered the section on chemistry the weakest part of the connection of the “Physical Sciences,” I resolved to write it anew.

407. We naturally divide Statics into two parts–the equilibrium of a Particle, and that of a rigid or elastic Body or System of Particles whether solid or fluid. The second law of motion suffices for one part–for the other, the third, and its consequences pointed out by Newton, are necessary. In the succeeding sections we shall dispose of the first of these parts, and the rest of this chapter will be devoted to a digression on the important subject of Attraction.

408. By § 221, forces acting at the same point, or on the same material particle, are to be compounded by the same laws as velocities. Therefore the sum of their resolved parts in any direction must vanish if there is equilibrium; whence the necessary and sufficient conditions.

They follow also directly from Newton's statement with regard to work, if we suppose the particle to have any velocity, constant in direction and magnitude (and § 211, this is the most general supposition we can make, since absolute rest has for us no meaning). For the work done in any time is the product of the displacement during that time into the algebraic sum of the effective components of the applied forces, and there is no change of kinetic energy. Hence this sum must vanish for every direction.

604.] In our theoretical discussion of electrodynamics we began by assuming that a system of circuits carrying electric currents is a dynamical system, in which the currents may be regarded as velocities, and in which the coordinates corresponding to these velocities do not themselves appear in the equations. It follows from this that the kinetic energy of the system, so far as it depends on the currents, is a homogeneous quadratic function of the currents, in which the coefficients depend only on the form and relative position of the circuits. Assuming these coefficients to be known, by experiment or otherwise, we deduced, by purely dynamical reasoning, the laws of the induction of currents, and of electromagnetic attraction. In this investigation we introduced the conceptions of the electrokinetic energy of a system of currents, of the electromagnetic momentum of a circuit, and of the mutual potential of two circuits.

We then proceeded to explore the field by means of various configurations of the secondary circuit, and were thus led to the conception of a vector 21, having a determinate magnitude and direction at any given point of the field. We called this vector the electromagnetic momentum at that point. This quantity may be considered as the time-integral of the electromotive force which would be produced at that point by the sudden removal of all the currents from the field.

391. Until we know thoroughly the nature of matter and the forces which produce its motions, it will be utterly impossible to submit to mathematical reasoning the exact conditions of any physical question. It has been long understood, however, that an approximate solution of almost any problem in the ordinary branches of Natural Philosophy may be easily obtained by a species of abstraction, or rather limitation of the data, such as enables us easily to solve the modified form of the question, while we are well assured that the circumstances (so modified) affect the result only in a superficial manner.

392. Take, for instance, the very simple case of a crowbar employed to move a heavy mass. The accurate mathematical investigation of the action would involve the simultaneous treatment of the motions of every part of bar, fulcrum, and mass raised; and from our almost complete ignorance of the nature of matter and molecular forces, it is clear that such a treatment of the problem is impossible.

It is a result of observation that the particles of the bar, fulcrum, and mass, separately, retain throughout the process nearly the same relative positions. Hence the idea of solving, instead of the above impossible question, another, in reality quite different, but, while infinitely simpler, obviously leading to nearly the same results as the former.

241.] If by means of an electrometer we determine the electric potential at different points of a circuit in which a constant electric current is maintained, we shall find that in any portion of the circuit consisting of a single metal of uniform temperature throughout, the potential at any point exceeds that at any other point farther on in the direction of the current by a quantity depending on the strength of the current and on the nature and dimensions of the intervening portion of the circuit. The difference of the potentials at the extremities of this portion of the circuit is called the External electromotive force acting on it. If the portion of the circuit under consideration is not homogeneous, but contains transitions from one substance to another, from metals to electrolytes, or from hotter to colder parts, there may be, besides the external electromotive force, Internal electromotive forces which must be taken into account.

The relations between Electromotive Force, Current, and Resistance were first investigated by Dr. G. S. Ohm, in a work published in 1827, entitled Die Galvanische Kette Mathematisch Bearbeitet, translated in Taylor's Scientific Memoirs. The result of these investigations in the case of homogeneous conductors is commonly called ‘Ohm's Law.’

Ohm's Law

The electromotive force acting between the extremities of any part of a circuit is the product of the strength of the current and the Resistance of that part of the circuit.

On Electrostatic Instruments

The instruments which we have to consider at present may be divided into the following classes:

1. (1) Electrical machines for the production and augmentation of electrification.

2. (2) Multipliers, for increasing electrification in a known ratio.

3. (3) Electrometers, for the measurement of electric potentials and charges.

4. (4) Accumulators, for holding large electrical charges.

Electrical Machines

207.] In the common electrical machine a plate or cylinder of glass is made to revolve so as to rub against a surface of leather, on which is spread an amalgam of zinc and mercury. The surface of the glass becomes electrified positively and that of the rubber negatively. As the electrified surface of the glass moves away from the negative electrification of the rubber it acquires a high positive potential. It then comes opposite to a set of sharp metal points in connexion with the conductor of the machine. The positive electrification of the glass induces a negative electrification of the points, which is the more intense the sharper the points and the nearer they are to the glass.

When the machine works properly there is a discharge through the air between the glass and the points, the glass loses part of its positive charge, which is transferred to the points and so to the insulated prime conductor of the machine, and to any other body with which it is in electric communication.