set the circuit C into oscillatory movement, and that this oscillatory movement continues long after the exciting blow has ceased. A careful study of many photographs of this nature shows that a circuit containing capacity and selfinduction acts at the first instant as if no capacity were in the circuit. It then begins to oscillate with a higher period than it afterwards reaches, acting at first like a closed organ-pipe and subsequently like a pipe open at both ends.

In fig. 3, S' represents an oscillating primary discharge. S represents the photograph of the spark produced in the circuit B from which the capacity had been removed. The movements in this circuit B exactly follow those of the exciting circuit A. S" is the photograph of the oscillating movement produced in the circuit C. It is of a different period from that of the exciting circuit S' and continues much longer. A secondary circuit without capacity acts like a sensitive plate, and accurately follows every movement of the exciting circuit.

In fig. 4 S' represents again the oscillating primary circuit, S the oscillating secondary circuit C. The circuits are nearly in geometrical resonance. Slight beats, however, can be observed. The duration of the secondary is nearly the same as that of the primary.

Fig. 5 shows clearly the phenomena of beats. In this case the secondary circuit was 20 centim. from the primary circuit.

Fig. 6 also shows the phenomenon of beats, and also the rise to a maximum in the oscillations of the secondary circuit, S. In this case an iron wire constituted a portion of circuit C. It seemed as if the effort to magnetize the iron diminished the power to produce the initial movement in the secondary circuit with as much energy as was the case when a copper wire of inductance equal to the iron wire was introduced in its place.

Î have stated that Stefan has given a theory of electrical oscillations, and in his interpretation of his equation points out the necessity of supposing under certain conditions an aperiodic movement superimposed upon an oscillatory movement, in conductors containing self-induction and capacity. In regard to this latter point, my experiments seem to support his theoretical conclusions. I am inclined to believe, however, that the behaviour of condensers in secondary circuits, which are suddenly submitted to electrical disturbances, cannot properly be explained by the theory in Stefan's paper. Moreover, it results from his theory that electrical oscillations * Ann. der Physik und Chemie, xli. 1890, p. 422,

on an iron circuit of the same geometrical form and dimension as a copper circuit have the same period as oscillations on the copper circuit, supposing the capacity in the two circuits to be equal. I am led to suspect that there is a change of the period of electrical oscillations when an iron wire is substituted for a copper wire of the same geometrical form. I shall return to this subject of the change of period on iron wires in a following paper.

Oettingen has given some beautiful examples of the interference of electrical oscillations of different periods when they are led, so to speak, to the same spark-gap. I believe that my photographs are the first ones, however, which show the existence of such electrical beats or interference between independent circuits.

In order to present electrical beats between two secondary circuits both of which were excited by a unidirectional movement in a primary, I employed in certain cases two primary coils of one turn each, connected in series, and placed these primaries at right angles to each other; the secondaries corresponding to these two primaries were thus also at right angles to each other. This disposition of my apparatus enabled me to study the effect of two secondaries on each other; for on varying the angle between the planes of the primary coils and their accompanying secondaries, the beats can be made to appear or disappear.

It seems to me that we have in these photographs evidence of what may be termed the electrokinetic momentum of electricity. Something very like inertia is certainly shown by the gradual rise to a maximum and the behaviour of secondary circuits to unidirectional impulses from a primary circuit. A mental picture of the disturbance produced in secondary circuits can be produced in my mind by analogies drawn from the subject of the motion of fluids. In such analogies, to my mind, the idea of inertia is always present. I remarked in the opening of this paper that the formula t=2π VLC does not apply at the instant of starting an oscillating current in a secondary conductor by means of a unidirectional flow in a primary circuit. This formula is true only after the full effect of the capacity of the oscillating circuit comes into play. My photographs show that at first neighbouring secondary circuits act like circuits without capacity, the oscillations in such circuits rise to a maximum in intensity and then fall, after the rate is established. This is true also when aircondensers are employed, and cannot therefore be attributed to the action of a solid or liquid dielectric.

* Ann. der Physik und Chemie, xxxiv. 1888.

Bjerknes has shown* that the oscillations in a Hertz resonator are not damped out so quickly as those in the primary exciting circuit. My photographs also show that the oscillations in all neighbouring circuits continue long after the unidirectional spark in the primary or exciting circuit has ceased. This is true whether there is resonance or not, and is more marked when the circuits are not in tune, except so far as electrical beats tend to damp the oscillations of the secondary circuit.

I am inclined to believe, therefore, that the conclusions of Bjerknes are true only for open circuits or circuits in which no sparks occur. When sparks occur in two circuits which are in resonance the duration of time-sparks appears to be the same. With periods ranging from 00001 to 000001 of a second, I have found it impossible to tune two circuits in which sparks occurred to perfect resonance. There were always indications of beats due, I believe, to the capacity not rising immediately to its full value.

The method which I have outlined in this paper seems to offer a fruitful one for investigation; for a large number of comparative photographs can be taken with far greater ease than by the arrangement of apparatus employed by Feddersen.

Jefferson Physical Laboratory,

Harvard University, Cambridge, Mass., U.S.

XX. The Attraction of Unlike Molecules.-II. The SurfaceTension of Mixed Liquids. By WILLIAM SUTHERLAND†.

HE most direct method of measuring the attractions of

to

obtaining a

expression for the surface-tension of mixed liquids involving the attractions of the unlike molecules of the liquids as well as the attractions of the like molecules for one another, and then by experimental determinations of the surface-tensions of mixtures to obtain the data wherewith to calculate the attractions of the unlike molecules from the theoretical expression. The present paper contains both a theoretical and an experimental part, of which the theoretical had better come first as indicating the lines on which the experiments are to be discussed.

In a paper on the Law of Molecular Force (Phil. Mag. [5] vol. xxvii. p. 305), which has been largely superseded by * Ann. der Physik und Chemie, xliv. 1891; xlvii. 1892.

† Communicated by the Author.

a later one on the Laws of Molecular Force (Phil. Mag. March 1893, [5] vol. xxxv. p. 211), there is given the establishment of an expression for the surface-tension of a liquid whose molecules attract one another with a force inversely as the fourth power of the distance between them. If 3Am2/pt denotes the molecular attraction between two molecules of mass m at distance r apart in a liquid of density p, then it is shown that the surface-tension

where e is a length of the order of magnitude of the average distance of a molecule from its nearest neighbours and proportional to that distance; for it represents the distance to be left between two continuous distributions of matter on opposite sides of a plane in order that the attraction between them may be the same as that between two molecular distributions, the density and law of attraction in the continuous and molecular distributions being the same.

Suppose we have a gramme of a mixture of which a fraction p is a liquid of density p1 and molecular mass m1, and 1 the fraction p2 a liquid of density p2 and molecular mass m2, producing a liquid of density p; if there is no shrinkage on mixing the liquids 1 and 2, then

Now in the mixture p1 grammes of liquid 1 are distributed through a volume 1/p, and by themselves form a medium of density

Pip, to be denoted by p1';

similarly the other liquid 2 has in the mixture a density

P2P, to be denoted by p'.

Thus, then, if we draw a plane in the mixed liquid and seek to represent the attraction between the molecules on the opposite sides of the plane, the problem reduces itself to that of finding the attraction between a liquid 1 of density pi on one side (say the left side) on the liquid 1 of density pi on the right side, and the similar attraction between the parts of liquid 2 of density p' on the left and right sides, and the attraction of liquid 1 of density pi on left on liquid 2 of density pa on right, and the attraction of liquid 2 of density P2 on the left on liquid 1 of density pi' on the right. The last two attractions are equal; thus in place of the expression Ap❜e in the surface-tension of a single liquid we shall have for

where e, eg, and eg are distances corresponding to e and representing the distances to be left between continuums which may be supposed to replace the molecular mediums whose attractions have just been enumerated. For a single liquid, for instance liquid 1 for which the value of e may be denoted by e, e is proportional to (m1/p1); and then for its surface-tension relation (1) may be written

=

where k is the same for all liquids. Similarly for liquid 2,

(4)

(4)

Now if e̟ is taken as represented by (m1/p1)3, we cannot take e as represented by (m/p'); because if we did so and then in (3) put p1=P2 and suppose liquid 2 to become identical with liquid 1, in which case e'=e2=1e2', we should find that (3) would not reduce to 1A1 pie, as it ought. The most appropriate way in which to represent e' is to take it as given by (m1/p') reduced in the ratio of the cube root of the P1/P1 occupied by liquid 1 to the cube root of the total space 1/p. Thus e' is represented by (m1/p1')*(P1P/P1)3, eg by (m2/p2') (P2P/P2), and 2 by (e+e)/2; so that for the surface-tension of the mixture we get

space

which is an equation for determining the ratio 1A2/(1A1 2A2)† by a measurement of the surface-tension of a mixture of the liquids 1 and 2 of known surface-tensions a1 and a2. In these expressions, if we put pi=p2=1/2 and suppose liquid 2 to become identical with 1, we get the identity 11=a1 as we ought; also if we put p2=0 and p1=1 we get the same identity. There is doubtless something arbitrary in the manner in which we have fixed the values of e', eg, and ¡e,', but we must remember that, in the original establishment of the relation a=kAp2e, there is an arbitrary step in the