The extent of the jump, taken at every 5th turn of the plate, was now the fringe-width; and at every 10th or 15th turn, it was clearly. I find in my notes that this large jump of the fringes impressed me here, again and again, as a thing peculiarly beautiful.

Fourth Set, the same again as the second. The only question in this case was, whether it might still be possible, by the most careful work and under the best conditions attainable, to detect a very small jump of the fringes at the instant of discharge. Many observations were taken at high potential, some at the highest, but without a trace of effect of that kind.

Fifth Set, the same again as the first. The results of first and third sets were recovered regularly. Sparks were then taken, sometimes at every turn of the plate, sometimes oftener. At every spark there was a very small downward jump of the fringes, so small sometimes as to be barely caught, but quite regular and beautifully distinct.

Remarks.-The jump of the fringes was chosen as the principal object of observation, because it was never quite concealed, nor even much obscured, by the mechanical disturbance of the liquid; but I should add that the contrary motion, the gradual ascent of the fringes during the process of charging, was generally evident enough in the experiments, though not often undisturbed or quite regular in its course.

:

The best observations were got when the fringes happened to continue at rest through a sensible interval of time, including the instant of discharge. The contrast between the two cases was then very remarkable, especially at high potential in the one case, the beautifully clear jump so often mentioned; in the other case, no trace of a jump in either direction, generally not even a perceptible shiver of the fringes at the instant of strongest discharge. Instances of this kind occurred not very rarely in the experiments; and there could be no contrast more striking than that between the phenomena in the two cases.

From what I know of the apparatus and its performance, I am sure that no regular and abrupt retardation or acceleration amounting to as much as the hundredth part of an average wave-length could have escaped observation in the experiments. It will be remembered also that the jump of the fringes at high potential extended to four fifths of the fringe-width. With reference, therefore, to the dielectric CS2, and the two principal vibrations parallel and perpendicular to the line of force, it appears that the regular effect of the electric strain upon one of the vibrations is a positive retardation, while upon the other vibration there is very probably no effect

whatever, and certainly no effect as large as the eightieth part of the former.

Second positive dielectric: a paraffin oil, specific gravity 845. This liquid was far inferior to CS2 electrically and also as an optical medium. The method of experiment finally adopted as the best was a little different from that with CS2. The prime conductor had its capacity enlarged by connexion with a Leyden jar; the machine was kept working at a constant rate, and the prime conductor was partially discharged, at short and regular intervals, by spark upon the knob of the first internal conductor, which was of course discharged in each interval. The phenomenon looked for was a quick motion of the fringes at the instant of the spark; that is, at the instant of electric charging of the liquid.

(1) Plane of polarization of the pencil BF (through the electric field) vertical: rise of fringes indicates relative retardation of this pencil. At the instant of the spark there was a quick upward jump of the fringes through something like of the fringe-width, generally followed by a set of large and comparatively slow disturbance-movements. In most cases also, immediately after the spark, the observer was able to detect the contrary jump quite clearly, by laying his finger on the knob of the first conductor. Through a long set of observations taken at different potentials, the upward jump of the fringes at the instant of charging was obtained with perfect regularity; and-amplitude excepted—the effect was not inferior to that in CS2.

(2) Plane of polarization of the pencil BF horizontal : rise of fringes indicates relative retardation of BF. Many observations were taken at different potentials, high and low. There were sluggish and irregular disturbance-movements, great and small, but no trace of a regular jump of the fringes in one direction or the other at the instant of the spark. There could be no doubt as to the true meaning of these results. In this positive dielectric, as in CS2, the vibration along the line of force is retarded by electric strain, and the perpendicular vibration is unaffected.

First negative dielectric oil of colza. This liquid also was far inferior to CS2, especially as an optical medium. The method of experiment followed with paraffin was retained here as the best: the first internal conductor was charged by spark from the prime conductor at regular intervals, and was put to earth for a moment in each interval.

(1) Plane of polarization of the pencil BF vertical: rise of fringes indicates relative retardation of BF. The fringes were generally curved and very imperfect at the beginning

of an experiment; but a few successive charges brought them, after some disturbance, into permanently good form, and then there was a quick downward jump seen always at the instant of the spark. And, as in the contrary case of paraffin, this jump was a thing as distinct as possible from the sluggish and irregular disturbance-movements by which it was generally followed. When the spark was taken at every 10th turn of the plate, the potential was about as high as the liquid could bear, and the extent of the jump was fully of the fringewidth. In the course of a long set of observations, this downward jump of the fringes at the instant of charging was seen with perfect regularity, and always distinctly. In this case, therefore, the regular optical effect of electric strain was an acceleration.

(2) Plane of polarization of the pencil BF horizontal: rise of fringes indicates relative retardation of BF. When the fringes were imperfect at starting, the effects of a few successive charges were the same as in the first case, irregular displacements and changes of inclination, the fringes generally rising and falling in their lower and higher parts till they came into permanently good form. Afterwards there were smaller disturbances always present in this case as in the former; but neither there nor here were they such as to interfere ultimately with exact observation. The experiment was carried on for some time till the liquid was well mixed and the fringes good. Many observations were then taken, some of them at highest potential; but there was no trace of a jump ever seen at the instant of the spark. In this liquid, therefore, as in carbon disulphide and paraffin, the only one of the two principal vibrations which is affected by electric strain is that along the line of force; but as the present dielectric is of the negative class, the retardation produced is negative.

Second negative dielectric: seal oil. From want of homogeneity this liquid was very defective optically, the image of the slit L being much deformed and sometimes broken by streaks. The defect was remedied in a good degree by strong charges given to the liquid on both sides of the second conductor. The method of experiment was the same as with oil

of colza.

(1) Plane of polarization of the pencil BF vertical: rise of fringes indicates relative retardation of BF. At first, the electricity produced very large displacements and deformations of the fringes, in the midst of which there was no regular effect to be seen; but as the experiment went on, and the medium improved, the expected effect came out distinctly,

394 Mr. E. C. Rimington on an Air-Core Transformer

a quick downward jump of the fringes at or immediately after the instant of the spark. Under good optical conditions, and at potentials high and low, the effect was perfectly regular, and was as distinct and pure as that in oil of colza, though apparently not quite so large.

(2) Plane of polarization of the pencil BF horizontal : rise of fringes indicates relative retardation of BF. The disturbance of the fringes was greatly reduced as the experiment went on, till at last there was nothing left but a set of slow movements, very irregular and very small, sometimes invisible. In the midst of these as in their absence, and in a long set of observations taken at different potentials from low to highest, there was no trace ever seen of a jump of the fringes at the instant of the spark. It appears, therefore, that in this negative dielectric, as in oil of colza, the total optical effect of electric strain is an acceleration of the vibration which is directed along the line of force.

The conclusion to be drawn from the preceding experiments has been stated already by anticipation; but I repeat it finally in other terms as follows:

If light pass through an electrostatically strained medium at right angles to the lines of force, and be represented by two component lights whose planes of polarization are respectively parallel to the lines of force and perpendicular, then the proper and immediate optical effect of the electric strain is a change of velocity of the latter component *.

The use of the words proper and immediate in this statement may be thought objectionable; but some such words are required for the purpose here chiefly intended, which is, to exclude those undoubtedly remote effects of electric action that appeared as disturbances in all the experiments.

Glasgow, February 26, 1894.

XXXV. On the Behaviour of an Air-Core Transformer when the Frequency is below a certain Critical Value. By E. C. RIMINGTON.

IT

[Plates X., XI.]

T is usually supposed in the case of a transformer whose primary is connected to terminals having an alternating potential difference of constant value between them, that the

*The change of velocity in the case of any positive dielectric is of course a decrease.

+ Communicated by the Physical Society: read October 27, 1893.

ore Transformer
or immediately after
ptical conditions, and
was perfectly regular,
oil of colza, though

encil BF horizontal: -dation of BF. The reduced as the experihing left but a set of ery small, sometimes Their absence, and in a nt potentials from low een of a jump of the ppears, therefore, that colza, the total optical tion of the vibration

when the Frequency is below a certain Critical Value. 395 apparent impedance of the primary is diminished on closing the secondary. Under certain conditions, however, this is not the case, as the following investigation will show.

Let r be the resistance of the primary circuit;

L its inductance;

r the resistance of the secondary circuit;

N its inductance;

M the mutual inductance between the two coils.

The coefficients of induction are assumed constant in the following investigation, a result that can only be obtained in practice when coils not containing iron cores are employed. A pure sine-function alternating P.D. is also assumed."

Let p=2πn, where n is the frequency of alternation.

Let e be the value of the P.D. at any instant t, and E its maximum value.

Let c1 and c2 be the currents in the primary and secondary C1 circuits respectively, C1 and C, being their maxima.

and

Let I1= r2+p2L2, the impedance of the primary;
I= r2+pN2, the impedance of the secondary.
We have the well-known equations,

Differentiate (1) with respect to t, and multiply by N; differentiate (2) and multiply by M; then on subtraction we

Multiply (1) by r, and add to (3). This gives

a transformer whose aving an alternating tween them, that the

positive dielectric is of

d October 27, 1893.

Now it is obvious, if the P.D. be a pure sine function and the coefficients constants, that the currents must also be pure sine functions differing only in phase from the P.D.