represents point from average of crystals taken at random.
represents point from average of selected crystals.

represents probable actual rate of growth.

represents equation D3-kt.

represents equation D2=kt.

The unit of time is the time of one revolution of the shutter, or 125 seconds. The substance was potassic iodide.

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either almost as large as the second image, or very small compared with it. It will appear almost as large as the second image when the preceding exposure has just not caught the beginning of the crystal, which has thus had a whole interval for growth; or very much smaller than the second image when the first impression has registered a crystal only a very small fraction of a second old. Marked examples of the former case are to be found in fig. 11, and of the latter in the largest crystal in fig. 9, and the smallest

crystal in fig. 15. The times of revolution represented by figs. 9 and 11 are the same, 1.25 seconds, and the other conditions also were identical, hence we may compare these with accuracy. Careful measurements of the sizes in fig. 9 showed the first large impression of the crystals to be about eighty per cent. of the diameter of the next impression, and approximately the same relationship appears in fig. 11. In order to find if this relationship corresponds with the equation D3=kt, the larger diameter is assumed to be 0.93, the theoretical value corresponding to two intervals of time, if that corresponding to two and one half intervals is taken as unity. Hence the smaller one becomes 0.75, corresponding to one interval of time; a value, marked in a circle on the diagram, which is surprisingly near the cubic curve. Hence the equation D3kt is confirmed. That the same curve holds approximately for the further growth of the crystal is manifest by a quantitative study of fig. 9 (Plate VIII.).

In this connexion it is interesting to note that the crystal seems often to grow at first in the same proportion in all directions. Even the very minute image in the centre of the second exposure, given in fig. 9, shows itself under the microscope to be elongated like the crystal which grows from it. In the next exposure this crystal had the proportions 0.02 mm. x 0.0125 mm., and after four more exposures it still had almost exactly the same proportions, being 0.035 mm. × 0.022 mm. After two or three more seconds the form given in fig. 9 began to change slightly, the crystal becoming slightly less elongated in shape; but by this time the neighbouring crystals had grown so much as to approach it, and hence to alter the conditions. A similar constancy in proportion may be observed in many other series here given.

The diagram shows how exceedingly fast the diametric growth of the crystal must be in the first tenth of a second of its existence. Hence we have an explanation for the suddenness of its appearance to the eye of an observer, and for the blurred edges of its photographic image. It is true that another cause may contribute to the blurred effect; namely, the irregular refraction caused by the convection of the lighter solution which has just deposited part of its load; but the speedy growth alone is capable of explaining the observed indistinctness.

Interesting as the rapid initial growth in diameter may be, it places a serious bar in the way of more precise study of the birth of crystals. One clearly needs not only high magnifying power, but also great speed; and these two together require

very intense light. Whether or not we shall be able to obtain more positive knowledge with the present apparatus, is a questionable matter. In the near future the attempt will be made here to carry further the work herein described; but it is doubtful if any more definite results will be obtained. The great speed of initial growth casts a measure of doubt over some of the observations of Link and his followers. Is is not possible that the subjective effect of the rapidly growing crystal might be mistaken for that of a globule of liquid? Even upon the photographic plate there is a slight resemblance, and in one or two cases deliberate study is needed to detect evidence of structure in the smallest crystals. In conclusion, the report of the foregoing pages may be summarized as follows:-It has been found possible to take very frequent photomicrographs of crystals during their birth and growth. An enlargement of over four thousand diameters was obtained, and both common and polarized light were used. Only substances with high melting-points were examined, and the crystallization was always from aqueous solution. No properly focussed image on any of the plates seemed to be devoid of crystalline structure. The growth in diameter during the first second of the crystal's life was found to be vastly greater than during the subsequent period. Not the diameter itself, but a power of the diameter, was proportional to the time under the conditions used in our experiments. This exceedingly rapid initial diametric growth accounts for a lack of definition noticed in the first images,a lack of definition sufficient to have misled the eye, but not enough wholly to obscure the photographic evidence of crystalline structure.

Hence we may conclude that whatever theoretical reason there may be for believing that crystals always develop from a transitory liquid phase, the present experimental evidence is inadequate to prove that these globules attain a size visible in the microscope, except in the case of substances which melt at temperatures not far from the temperature of crystallization. The present paper is to be regarded rather as the suggestion of a mode of study than as a finished treatment of the subject, however.

The apparatus might be used to obtain a series of kinetoscopic pictures of insects or other small animals or plants, and is now being used for the study of the change in structure of steel at high temperatures. We are indebted to the Rumford Fund of the American Academy of Arts and Sciences for some of our apparatus.

Cambridge, Mass., October 1898 to October 1900.

XLIX. On the Resistance of Dielectrics, and the Effect of an Alternating Electromotive Force on the Insulating Properties of Indiarubber. By A. W. ASHTON, B.Sc., Royal Exhibition Scholar*.

1. TN undertaking the following research an endeavour has 1. IN undertaking the following

First. What relation exists between the resistance of different dielectrics and the electromotive force at which the resistance is measured.

Secondly. What form is taken by the curves showing the variation of the current with the time when (a) a condenser is charged by a battery of given E.M.F., (b) the condenser is discharged by placing it directly on to the terminals of a galvanometer.

Thirdly. What effect is produced on the insulating properties of indiarubber by the continued application of a high alternating pressure.

2. The question whether dielectrics can be said to strictly obey Ohm's law in regard to electrical conductivity has been considered by previous observers, but at present very definite conclusions do not appear to have been reached. The variation in the insulation resistance of several cables was examined by Heim (see Electrician,' vol. xxv. p. 751). The method of measurement used was that known as the "direct deflexion" method, in which the current is measured by the deflexion of a sensitive galvanometer joined in series with a battery and the plates of the condenser formed by the cable tested. Readings were taken after one or two minutes' electrification, and after a reading at any one pressure the inner and outer conductors of the cable were connected for one or two hours in order to get rid of the slowly disappearing "residual charge." From these experiments, Heim concluded that the dielectrics tested showed a decided deviation from Ohm's law, the conductivity being greater at the higher pressures. In the discussion on a paper by Preece (see Journal Institute of Electrical Engineers, Dec. 1890), some results were given by Alexander Siemens of tests taken on cables with cores of different materials, viz., guttapercha, indiarubber, and impregnated fibre. The charging pressure was varied over a wide range (from 100 to 1200 Leclanché cells), and it was found that the resistance calculated from the current after one minute's electrification became less as the pressure increased. Leick (Wiedemann's Annalen, No. 13,

* Communicated by the Physical Society: read May 31, 1901. Phil. Mag. S. 6. Vol. 2. No. 11. Nov. 1901.

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1898) has tested certain dielectrics, viz., guttapercha, paraffin, and sulphur, and has found an increase of conductivity at the higher voltages.

3. In all the above experiments, the resistance of the dielectrics examined has been calculated from the values of the current obtained at not more than a few minutes' electrification. Unfortunately these values of the current are those which are most affected by the previous electrical treatment of the dielectric. In a paper by Ayrton and Perry, "On the Viscosity of Dielectrics" (see Proc. Roy. Soc. vol. xxxvi.), it is suggested that more accurate values of the true conductivity of a dielectric might be obtained by taking readings of the current when it has become steady. An attempt has been made to examine certain dielectrics by this method in order to ascertain the conductivity at different pressures. In the above paper, Professors Ayrton and Perry also drew attention to the analogy existing between the behaviour of bodies under mechanical stress and that of dielectrics under electrical stress; it is further pointed out that careful distinction must be drawn between that part of the energy absorbed by the dielectric which is afterwards recoverable, and the portion which is converted into heat, and which determines the amount of true conduction taking place. The form of the "residual charge" curves has been examined in the case of glass by Hopkinson (Phil. Trans. vols. clxvi. & clxvii.). In these experiments the condenser was charged for a definite time and then discharged for an instant. The plates of the condenser were then joined to an electrometer, and readings of the residual potential were taken from time to time. Amongst other results, Hopkinson found that this residual potential was proportional to the exciting potential.

4. In the experiments which are now described these residual charge effects have been examined in the case of several dielectrics by means of curves showing the current (1) when the condenser is charged with a battery having a galvanometer in series with it; (2) when the condenser is discharged by connecting directly to a galvanometer. The examination of rubber for deterioration in insulating properties when subjected to the continuous action of alternating pressure, has been suggested by the failures which have sometimes occurred when rubber has been used as the insulating material for alternating-current mains. The dielectrics upon which experiments have been made are indiarubber, paraffined paper, and mica. The indiarubber tested consisted of three different kinds of sheet-rubber called Nos. 1, 2, and 3, and an "Okonite " cable,