In order to measure very small rotations, e.g. of the suspended parts of a galvanometer or magnetometer, two methods are commonly employed. We may either observe with a magnifier the motion of a material pointer; or, following Gauss, cause the rotating parts to carry round a mirror in which a scale is seen by reflection. In a modification of Gauss's method, well known from Sir W. Thomson's galvanometers, the image of a dark or bright line is thrown objectively upon the scale. In deciding which arrangement to adopt in any particular case, various circumstances would have to be taken into account, but still a comparison of capabilities from a purely optical point of view is not without interest.

In the mirror method the optical limit depends upon the horizontal breadth of the mirror itself. The easiest road to the desired conclusion, as well as the most instructive, is by a direct application of the principles of the wave theory. To take the simplest case, we will suppose the mirror rectangular. Consider, then, a luminous point, and its image after reflection, whether in the focal plane of a telescope, or formed directly upon a scale. The optical work being perfect, the secondary rays from every part of the mirror agree in phase at the focal point. Now suppose that the mirror rotates through such an angle that one vertical edge advances a quarter of a wave-length (¼λ), while the other retreats to the same amount, and consider the effect on the phase-relations at the point in question.

§ 1. In former communications to the Royal Society we have investigated the absolute unit of electrical resistance, and have expressed it in terms of the b.a. unit and of a column of mercury at 0° of known dimensions. The complete solution of the problem of absolute electrical measurement involves, however, a second determination, similar in kind, but quite independent of the first. In addition to resistance, we require to know some other electrical quantity, such as current or electromotive force. So far as we are aware, all the methods employed for this purpose define, in the first instance, an electrical current; but as a current cannot, like a resistance, be embodied in any material standard for future use, the result of the measurement must be recorded in terms of some effect. Thus, several observers have determined the quantity of silver deposited, or the quantity of water decomposed, by the passage of a known current for a known time. In this case the definition relates not so much to electric current as to electric quantity. A more direct definition of the unit current, and one which may perhaps be of practical service for the measurement of strong currents of 50 ampères or more, would be in terms of the rotation of the plane of polarisation of sodium light, which traverses a long column of bisulphide of carbon enveloped by the current a given number of times.

1. The phenomenon, to which the present investigation relates, is Faraday's discovery of the “Magnetisation of Light,” or in more usual language the rotation of the plane of polarisation of light in traversing certain media exposed to powerful magnetic force. One of the characteristics of this rotation is that it takes place in the same absolute direction whichever way the light may be travelling, differing in this respect from the rotation which occurs without the operation of magnetic force in quartz and many organic liquids. Advantage of this property has been taken by Faraday and others in order to magnify the effect. By reflecting the light backwards and forwards it is possible to make it traverse several times a field of force whose length is limited.

A consequence remarkable from the theoretical point of view is the possibility of an arrangement in which the otherwise general optical law of reciprocity shall be violated. Consider, for example, a column of diamagnetic medium exposed to such a force that the rotation is 45°, and situated between two Nicols whose principal planes are inclined to one another at 45°. Under these circumstances light passing one way is completely stopped by the second Nicol, but light passing the other way is completely transmitted. A source of light at one point A would thus be visible at a second point B, when a source at B would be invisible at A; a state of things at first sight inconsistent with the second law of thermodynamics.

Smoke-jets by Intermittent Vision

In the second series of these observations (Phil. Mag. 1879 [vol. I. p. 406]) I proved that when stationary sonorous waves occupy the region surrounding a sensitive flame, the action of sound in causing the flame to flare manifests itself when the burner is situated at a loop, but not when the burner is situated at a node; from which we infer that the effects are due to a lateral disturbance causing the issuing jet to bend from its course. During the same year I made a stroboscopic examination of a jet of phosphorus-smoke issuing from a drawn-out glass nozzle, and disturbed by the neighbourhood of a vibrating tuning-fork of pitch 256. So much light is necessarily lost in this method of observation that some precaution is required in illuminating the jet. Two points should be especially attended to. In the first place, the eye must be so situated that the scattered light by which the jet is seen is but slightly deflected from its original course; and, secondly, the background must be thoroughly dark. By carrying out adequately this system of illumination, and by so choosing the revolving disk that the apertures bore a not too small proportion to the entire circumference, I was able to see tolerably well by the light of a good gas-flame. When the coincidence of periods was nearly approached, the serpentine motion of the jet previous to rupture was clearly observable.

In common with some of my predecessors in this chair, I recognise that probably the most useful form which a presidential address could take, would be a summary of the progress of physics, or of some important branch of physics, during recent years. But the difficulties of such a task are considerable, and I do not feel myself equal to grappling with them. The few remarks which I have to offer are of a general, I fear it may be thought of a commonplace character. All I can hope is that they may have the effect of leading us into a frame of mind suitable for the work that lies before us.

The diversity of the subjects which come under our notice in this section, as well as of the methods by which alone they can be adequately dealt with, although a sign of the importance of our work, is a source of considerable difficulty in the conduct of it. From the almost inevitable specialisation of modern science, it has come about that much that is familiar to one member of our section is unintelligible to another, and that details whose importance is obvious to the one fail altogether to rouse any interest in the mind of the other. I must appeal to the authors of papers to bear this difficulty in mind, and to confine within moderate limits their discussion of points of less general interest.

The object of the present communication is to prove some general mechanical theorems, which may be regarded as in some sort extensions of that of Thomson relating to the energy of initial motions. The question involved in the latter may be thus stated:—

“Given any material system at rest. Let any parts of it be set in motion suddenly with any specified velocities possible, according to the connections of the system; and let its other parts be influenced only by its connections with these. It is required to find the motion.” And the solution is “that the motion actually taken by the system is that which has less kinetic energy than any other motion fulfilling the prescribed velocity conditions.” On the other hand, if the impulses are given, a theorem of Bertrand tells us that the kinetic energy is the greatest possible.

For our present purpose we suppose the system to be set in motion by an impulse of one particular type, which we may call the first. The impulse itself may be denoted by ∫ Ψ1dt, and the corresponding velocity generated by Ψ1. Under any given circumstances as to constraint, the velocity and the impulse are in proportion to one another; and the resulting kinetic energy T is proportional to the square of either, being equal to ½ Ψ1 ∫Ψ1dt.

In the course of his examination of atmospheric dust as rendered evident by a convergent beam from the electric arc, Professor Tyndall noticed the formation of streams of dust-free air rising from the summits of moderately heated solid bodies. “To study this effect a platinum wire was stretched across the beam, the two ends of the wire being connected with the two poles of a galvanic battery. To regulate the strength of the current a rheostat was placed in the circuit. Beginning with a feeble current, the temperature of the wire was gradually augmented; but before it reached the heat of ignition, a flat stream of air rose from it, which, when looked at edgeways, appeared darker and sharper than one of the blackest lines of Fraunhofer in the solar spectrum. Right and left of this dark vertical band the floating matter rose upwards, bounding definitely the non-luminous stream of air.”……

“When the wire is white hot, it sends up a band of intense darkness. This, I say, is due to the destruction of the floating matter. But even when its temperature does not exceed that of boiling water, the wire produces a dark ascending current. This, I say, is due to the distribution of the floating matter. Imagine the wire clasped by the mote-filled air. My idea is that it heats the air and lightens it, without in the same degree lightening the floating matter.

In some experiments with which I have lately been occupied a coil of insulated wire, traversed by an electric current, was suspended in the balance, and it was a matter of necessity to be able quickly to check the oscillation of the beam, so as to bring the coil into a standard position corresponding to the zero of the pointer. A very simple addition to the apparatus allowed this to be done. The current from a Leclanché cell is led into an auxiliary coil of wire, coaxal with the other, and is controlled by a key. When the contact is made, a vertical force acts upon the suspended coil, but ceases as soon as the contact is broken. After a little practice the beam may be brought to rest at zero at the first or second application of the retarding force.

This control over the oscillations has been found so convenient that I have applied a similar contrivance in the case of ordinary weighings, and my object in the present note is to induce chemists and others experienced in such operations to give it a trial. Two magnets of steel wire, three or four inches long, are attached vertically to the scale-pans, and underneath one of them is fixed a coil of insulated wire of perhaps 50 or 100 turns, and of 4 or 5 inches in diameter. The best place for the coil is immediately underneath the bottom of the balance-case.

In Grove's well-known gas battery it would seem that the only efficient part of the platinum surface is where it meets both the gas and the liquid, or at any rate meets the liquid and is very near the gas. In order to render a larger area effective I have substituted for the usual platinum plates platinum gauze resting upon the surface of the liquid in a large trough in such a manner that the upper surface is damp but not immersed. One piece is exposed to the oxygen of the air; the other forms the bottom of an enclosed space into which hydrogen is caused to flow. The area of each piece is about 20 square inches.

To test the efficiency, the current was passed through an external resistance of about 6 ohms, including a galvanometer. Under these circumstances the permanent current was about one-fourth of that obtained when a large Daniell cell was substituted for the gas element. An inferior, but still considerable, current was observed when coal gas was used instead of hydrogen prepared from zinc.

InSilliman's Journal for 1881 Mr E. S. Holden, after quoting observations to a like effect by Sir W. Herschel, gives details of some observations recently made with a large telescope at the Washburn Observatory, from which it appears that distant objects on a dark but clear night can be seen with the telescope long after they have ceased to be visible with the naked eye. He concludes, “It appears to me that this confirmation of Herschel's experiments is important, and worth the attention of physicists. So far as I know there is no satisfactory explanation of the action of the ordinary Night glass, nor of the similar effect when large apertures are used.”

It is a well-known principle that no optical combination can increase what is called the ‘apparent brightness’ of a distant object, and indeed that in consequence of the inevitable loss of light by absorption and reflection the ‘apparent brightness’ is necessarily diminished by every form of telescope. Having full confidence in this principle, I was precluded from seeking the explanation of the advantage in any peculiar action of the telescope, and was driven to the conclusion that the question was one of apparent magnitude only,—that a large area of given small ‘apparent brightness’ must be visible against a dark ground when a small area would not be visible. The experiment was tried in the simplest possible manner by cutting crosses of various sizes out of a piece of white paper and arranging them in a dark room against a black back-ground. A feeble light proceeded from a nearly turned-out gas-flame. The result proved that the visibility was a question of apparent magnitude to a greater extent than I had believed possible.

Perhaps the simplest way of measuring a current of moderate intensity, when once the electro-chemical equivalent of silver is known, is to determine the quantity of metal thrown down by the current in a given time in a silver voltameter. According to Kohlrausch the electro-chemical equivalent of silver is in c.g.s. measure 1·136 × 10−2, and according to Mascart 1·124 × 10−2. Experiments conducted in the Cavendish Laboratory during the past year by a method of current weighing described in the British Association Report for 1882 have led to a lower number, viz. 1·119 × 10−2. At this rate the silver deposited per ampere per hour is 4·028 grams, and the method of measurement founded upon this number may be used with good effect when the strength of the current ranges from ampere to perhaps 4 amperes. It requires however a pretty good balance, and some experience in chemical manipulation. [See Art. 112.]

Another method which gives good results and requires only apparatus familiar to the electrician, depends upon the use of a standard galvanic cell. The current from this cell is passed through a high resistance, such as 10,000 ohms, and a known fraction of the electro-motive force is taken by touching this circuit at definite points. The current to be measured is caused to flow along a strip of sheet German silver, from which two tongues project.

Galvanometers suitable for currents of an ampère or two are most accurately standardised by means of the silver voltameter, but this method ceases to be convenient when the current to be dealt with rises above five ampères. The present instrument is a kind of differential galvanometer, provided with two electrically distinct coils, whose constants are in ratio of ten to one. A current of one ampère through one coil thus balances a current of ten ampères through the other. If the first be measured in terms of silver, the second serves to standardise an instrument suitable for the larger current.

The novelty consists in the manner in which the ten to one ratio is secured. Twenty pieces of No. 17 cotton-covered wire, being cut to equal lengths of about eight feet, were twisted closely together, two and two, so as to form ten pairs, which ten pairs were again in their turn twisted slightly together so as to form a rope. In each of the two circuits there are ten wires. In one, that intended for the larger current, these wires are in parallel; in the other circuit the ten wires are in series. Of each of the original twists one wire belongs to the parallel and one to the series group. Now the two wires forming an original twist are equally effective upon a needle suspended in any reasonable situation with respect to them, and thus if the ten wires in parallel have the same resistance, the circuit formed by the ten wires in series will be precisely ten times as effective as the circuit formed by the ten wires in parallel.

Mit grossem Interesse habe ich aus einer neueren Mittheilung in den Annalen ersehen, dass Hr. Wild im Anschluss an einen Vorschlag von Dorn seine Zahl für diese Werthe der Siemens'schen Einheit in Ohme 0,9462 auf 0,94315 corrigirt hat, wodurch die Differenz zwischen seiner Zahl und der von mir gefundenen 0,9415 auf etwa ein Drittel reducirt wird. Die Untersuchung von Wild scheint sehr sorgfältig ausgeführt worden zu sein, indess möchte ich doch die Aufmerksamkeit derer, welche an die Vorzüge der Dämpfungsmethode glauben, auf einige Punkte lenken.

Bei der theoretischen Untersuchung wird die Wirkung des Magnets als identisch mit der eines Solenoids angesehen, durch welches ein constanter Strom geleitet wird, während sie in der That mehr mit der eines mit einem Eisenkern vorsehenen Solenoides verglichen werden kann. Mir scheint die Einführung einer grosscn Eisenmasse in den Multiplicator sehr sorgfältige Erwägungen zu verdienen. Selbst wenn man annimmt, dass der grössere Theil der Wirkung durch die Aenderungen gewisser Grössen, wie der Inductionscoëfficienten, compensirt werden kann, so kann doch ein kleines Residuum zurückbleiben infolge der Abweiehung der Magnetisirung des Eisens von den einfachen Gesetzen. Ich will nicht behaupten, dass dies in der That der Fall ist, indess müssen diejenigen, welche die Dämpfungsmethode benutzen, das Gegentheil beweisen.

Ferner ist der Magnet ein Leiter der Electricität. Es ist nicht erwiesen, dass nicht galvanische Ströme von erheblicher Stärke in einem 36 mm. langen und 12 mm. dicken Stabe erzeugt werden können, welcher in einer vom Strom durchflosscncn Spirale schwingt.

The accurate absolute measurement of currents seems to be more difficult than that of resistance. The methods hitherto employed require either accurate measurements of the earth's horizontal intensity, or accurate measurements of coils of small radius and of many turns. If in the latter measurement we could trust to the in extensibility of the wire, as some experimenters have thought themselves able to do, the mean radius could be accurately deduced from the total length of wire and the number of turns; but actual trial has convinced me that fine wire stretches very appreciably under the tension necessary for winding a coil satisfactorily. Kohlrausch's method, in which the same current is passed through an absolute galvanometer and through a coil suspended bifilarly in the plane of the meridian, is free from the above difficulty; but it is not easy so to arrange the proportions that the suspended coil shall be sufficiently sensitive, and the galvanometer sufficiently insensitive. In this method, as in that of the dynamometer, the calculation of the forces requires a knowledge of the moment of inertia of the suspended parts.

When the electromagnetic action is a simple attraction or repulsion, it can be determined directly by balancing it against known weights. In Mascart's recent determination a long solenoid is suspended vertically in the balance, and is acted upon by a flat coaxial coil of much larger radius, whose plane includes the lower extremity of the solenoid.