put in communication with the earth, the wire a becomes charged with free negative electricity, as was established by means of Thomson's electrometer; the deflection of the electrometer may become as great as if its poles had been connected with a Daniell's element. It is at the same time observed that the depression of the mercury in the glass tube is greater than when the circuit is closed; in other words, the constant of capillarity is greater than before. Now the increase of the electromotive force between mercury and dilute acid, with a simultaneous increase of the constant of capillarity at the common surface, is just what is called polarization by hydrogen: the phenomena can then be thus represented :

If by mechanical means the surface of contact between mercury and acid water be increased, the mercury thereby becomes polarized with hydrogen.

On this may be based a very striking experiment which may be made with the capillary electrometer. If by blowing or by suction with the mouth the atmospheric pressure over the mercurial column be varied, the column of mercury in the fine point can be moved without exertion-this, however, only so long as there is metallic contact between a and B. If this contact be suddenly broken, the column of mercury at once becomes immovable, as if it were frozen. This may be thus explained. On blowing, for instance, the surface of mercury begins to increase; it thereby becomes polarized, and the increase of the capillary constant produces an increase of the capillary pressure which cannot be overcome by the lungs. The exact opposite is the case with suction.

On the same phenomena is based an apparent disturbance observed in capillary experiments, namely a slow decrease of the constant of capillarity, as has been shown by Quincke for mercury in water. If, for instance, mercury be allowed to ascend in a moistened capillary tube, the surface of the mercury in the tube is increased and is thereby polarized. Now polarization, as is well known, diminishes with time, first rapidly, afterwards continually more slowly. In accordance with this a decrease of the constant of capillarity is observed. A similar thing happens when a drop of mercury is brought into water: in flattening on the bottom it increases its surface and assumes a slowly decreasing polarization.

With the electrometer or galvanometer it can be directly shown that when mercury is contained in a glass vessel under dilute sulphuric acid, dipping a glass rod into it or merely inclining the vessel is sufficient to produce a change of the capillary and electrical conditions. Similarly any agitation produces an alteration of the capillary constant. But when a

circuit is closed, the polarization, capillary constant, and depression are constant.

By "increase of the surface of contact" of mercury and dilute acid two things might be understood―(1) moistening fresh parts of the mercury which had hitherto been dry, or (2) further recession from each other of parts already wetted. In all the above phenomena the second is to be understood. This can be shown by the following simple experiment.

On a dry surface of mercury a broad drop of dilute sulphuric acid is placed, which is then removed by a pipette, so that only a wet spot remains. If this spot be perforated by an iron point it polarizes and contracts immediately. But we only see a distortion of the entire surface, such as would take place upon the surface of a stretched caoutchouc balloon upon which was a damp spot and from which air emerged. The individual details at what is ordinarily the jagged edge of the spot, as well as the outlined part of the dry surface, remain separately recognizable during the distortion, as if they had been drawn upon a caoutchouc membrane; and after the polarization has ceased they return to their old position.

On Young's view, according to which the constant of capillarity is regarded as a superficial tension, the result last adduced (namely, that when the circuit is open the constant increases on expansion) would be simply expressed thus-that the surface of mercury behaves like an ordinary elastic membrane, the tension of which increases when the membrane is stretched.

XXXV. On the Measure of Work in the Theory of Energy. By ROBERT MOON, M.A., Honorary Fellow of Queen's Colelge, Cambridge*.

То

my former remarks on this subject† I desire to add the following.

1. I cite the following sentences of Professor Maxwell as expressing generally accepted views:

"Work is done when resistance is overcome; and the quantity of work done is measured by the product of the resisting force

* Communicated by the Author.

† See Philosophical Magazine' for September 1873.

and the distance throughout which that force is overcome (Theory of Heat, 1871, p. 87).

"Fs is the work done by the force F acting on the body [M] while it moves in the direction of F through a space s" (ibid. p. 89).

Interpreting the latter of these sentences by the former, it is clear that in the case considered the resistance offered to the action of the force F is treated as exactly equivalent to, and as capable of being represented by, F. The question arises, therefore, What is F?

The phrases "the absolute force," "the force acting at a point," are so constantly in use among us that we are apt to lose sight of their purely conventional character.

Force can only be measured by its effects; and in order that force may produce any effect, it must operate throughout an interval of time. As a matter of fact F is the amount of momentum generated by a force acting uniformly during a unit of time; and what F truly represents is the force acting on a body during a unit of time*. If, therefore, F can be accepted in any degree as the representative of the resistance offered in the above case, it must represent the resistance offered in a unit of time. Thus, if we adopt the above definition of work, it follows from the simple rules of arithmetic, not less than I trust that I have already shown it to result from sound mechanical principles, that the work done by the force F acting during the time T is FT2 FT, and not as, if the measure of work above proposed

2

were admissible, it would be, supposing the body to move from rest under the influence of the uniform force F throughout the time T.

2. Suppose a body whose mass is M to be moving in a certain direction with a velocity V1, and that the force F is applied to the body in the direction of its motion. Then, as before, if F be uniform we shall have

Fs=(MV2-MV2),

where s represents the space described by the body while the velocity changes from V1 to V; and putting V=V1+v, we shall have

work = Fs=M(v2+2vV1).

(a)

We thus arrive at the entirely inadmissible conclusion, that while the body moves through the space s, the work done upon it by the force F, and therefore, according to the above

* The test of uniformity, and necessarily the only test, being that the force generates equal amounts of momentum in equal times.

measure of work, the resistance offered by the body to the action of the force, will be greater when the body has an initial velocity V, urging it in the direction in which it is solicited by the force (in which case V, and v have the same sign), than it has when the body moves from rest,-nay, more, that when the space s through which the body moves (and therefore v) is indefinitely small, the resistance offered in the former case (which will be MvV) will be infinitely greater than in the latter, when it will be Mv2.

3. The vice, or rather one vice of the measure of work above proposed, is manifest from the formula (a) of the preceding article. In the production of what is there offered as the work done by the force, it is clear that the initial velocity (that which the body had before the force began its work) has been an agent.

This view of the subject may be further illustrated as follows. Suppose that V, is the velocity of the body at the beginning of the time T, and that throughout T the motion of the body is counteracted by the uniform force F, which is of such amount as to reduce the body to rest at the end of T. Under these circumstances two things will have been done during the time T:(1) Space will have been described.

(2) Velocity will have been destroyed.

The space manifestly has not been described by the agency of the force, the only product of which is the destruction of velocity; in other words, V, (in this case FT) measures the work done by the force.

=

4. It may be an object of curiosity to some of my readers to know how the above measure of work came to be adopted. On this point I am sorry to be unable to afford them very precise information. If my memory serves me rightly, Helmholtz, in his paper in Taylor's 'Scientific Memoirs' for 1852, treats it as a thing "well known;" and in Thomson and Tait's Natural Philosophy' it appears to be regarded in the same light. Professor Maxwell informs us that "If a body whose mass is one pound is lifted one foot high in opposition to the force of gravity, a certain amount of work is done, and this quantity is known among engineers as a foot-pound."

If this passage may be taken to afford the true clue, we can hardly fail to be struck with the originality of the suggestion that a great philosophical principle may be established by "engineering evidence."

5. I have already said that "force can only be measured by its effects," which in popular language is tantamount to the assertion that force is measured by the work it does. The establishment of the foregoing measure of work, therefore, is in

point of fact a rehabilitation of the Leibnitzian measure of forcea rehabilitation, indeed, of a very peculiar character; for the Leibnitzian measure is not supposed to supplant, but to stand pari gradu with its Newtonian rival.

If the views which I have endeavoured to unfold are correct, it will follow that the received measure of work, of whatever use it may be in simple cases (say when a body moves from rest) as affording within certain limits some rude indications, must be regarded as utterly inadmissible for every scientific purpose. 6 New Square, Lincoln's Inn, February 26, 1874.

XXXVI. Determination of the Absolute Value of the Siemens Mercury Unit of Electrical Resistance. By F. KOHLRAUSCH*.

THE

HE more firmly the general adoption of the Siemens Mercury Unit is established, the more desirable is it that the ratio which it bears to the scientific standard of resistance, the so-called Absolute or Weber's unit, should be known as accurately as possible. A determination of this ratio forms the subject of the present communication. It was carried out in the year 1869 in the Magnetic Observatory at Göttingen, by means of, on the one hand, the splendid instruments for galvanic and terrestrial-magnetic measurements which the Observatory and Physical Institute of Göttingen have acquired through the labours of W. Weber, and, on the other hand, of mercury units which Mr. Siemens kindly had prepared specially for this purpose.

I may be allowed to premise that I have shunned no labour in order to reach the degree of precision attainable with such means; and in assuming that this degree of precision has really been reached, I believe I am warranted by years of practice in observations of this nature, no less than by the final agreement of the results.

The outcome of the investigation is that the Siemens unit is equal, in absolute measure, to

or, expressing the same thing by a more convenient number, to

* Translated from Poggendorff's Annalen, Ergänzungsband VI. S. 1, an abstract having been communicated to the Göttingen Academy of Sciences on the 5th November, 1870.