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to obtaining the final result many different dispositions of the apparatus were tried, and the method tested in most of its features. Experiments were also made upon a block of paraffin smaller than the large plate; but it was found that the results were incorrect in this case, which fact makes it necessary to use blocks of the same size as or larger than the plates of the apparatus.
In obtaining the final values, the apparatus was adjusted so that d2+d=3.51 centim., and D was changed until the capacities of the two sides were nearly equal. In all cases superior and inferior readings were taken as previously described, and the mean taken as the true reading. The following characteristic set of ten readings, taken with slow fields, are given to illustrate the accuracy with which the plate may be adjusted. One scale-division
The final values obtained for paraffin are embodied in the following table. The value for slow fields differs a trifle from that published in a preliminary article; further experience with the apparatus having led to the present value.
Thus K for paraffin is 3 per cent. less in oscillating fields than in slowly varying fields.
Observations upon Glass.
Plate-glass seems to be the most important substance upon. which to experiment, as its specific inductive capacity has been found very different by different observers, and because the values of K found for it are much greater than the square of its index of refraction. The greatest pains were taken to obtain certain results for this substance; and as the values obtained differ considerably from those found by other observers, it is hoped my readers will pardon the mention of some tedious details.
The second method was employed as described under Case II. Twelve plates of American plate-glass were used, six plates being placed in each half of the apparatus. By making the proper selection of plates for each side, the two piles were made of the same thickness. The density of this glass was determined with a Jolly balance and found to be 2.678. All measurements of dimensions were made with an excellent pair of vernier calipers and repeated a large number of times. Referring to fig. 4 for the meaning of the letters, the following dimensions were employed. These are all given in scale-divisions which equal one half the metric system :P=1021, d1=11.964, d2=5·010, d=x
In order that there might be no springing of the plates after all had been adjusted, eight ebonite posts were placed at the corners as shown in fig. 4. The plate N was supported upon three thin tubes of ebonite. All surfaces where there could be any harmful leakage of electricity, such as along the supports to the plates M and N, were covered with a thin coating of paraffin. The small plates were connected to the spark-gap or transformer with two No. 36 bare copper wires,
each 2 feet long. These wires were supported near the spark-gap at the ends of glass rods covered with paraffin. The transformer and spark-gap were also carefully insulated by glass and paraffin. These precautions are necessary by reason of the fact that a small leakage of electricity from the surface of the small plates changes the reading in a marked manner. Leakage of electricity, however, could be seen by darkening the room, and could also be detected by a peculiar manner in which the sparks went out. This was carefully looked for and avoided. In making the test with oscillating fields, half of the readings were taken with the transformer in one position and then the other half were taken with the ends of the transformer reversed, and the mean of the two series taken as the true reading. This becomes necessary unless the primary and secondary of the transformer are symmetrically arranged in reference to each other. Indeed it was found that the readings could be perceptibly changed by sliding the secondary coil over the primary into different positions. It is easily seen, however, that if the primary and secondary always have the same relation, and the connexions to the primary are reversed after half the readings are taken, the error is eliminated in the mean of all the readings. The current through the coil was at times large and again small, and also occasionally reversed; but these changes, as expected, did not affect the results. The length of the indicator spark-gap could also be changed without affecting the mean reading. Readings for slow fields were taken in sets of ten and averaged. The mean of twenty such sets, taken with slow fields, was 3.097. The greatest departure from the mean was+09. Finally, from (17), when d=11·964, d2=5010, d=3.097, we obtain K=6.254.
The value was next obtained for oscillating fields, no change being made in the apparatus, except to connect in the transformer and approach the balls to the proper distance for sparks to pass and cause oscillations. Readings were taken in sets of twenty each. Following is the average of each of the sets taken :
The connexions to the transfor.ner were now reversed :
d=5010, d=11.964, and hence K'-5-861.
These results, then, give the specific inductive capacity of plate-glass 6.2 per cent. less in oscillating than in slowly changing fields.
Though the relative values of K for glass under these two conditions seemed to be undoubtedly correct, it was not expected to find such a low value for slow fields; and so, to verify the results obtained, the apparatus was taken apart and put together again with the dimensions changed and the experiment repeated for slow fields. The distances chosen were P=6401, d=3.524, d1=11.964; and as the result of thirty readings d4=1.574. Whence K=6·14, or 1.8 per
cent. less than before.
These results show that there is a decrease in the value of K for paraffin and glass when the alternations of force are rapid, but that the change is much smaller than several observers have stated. M. Blondlot found K for glass in oscillating fields to be 2.84. J. J. Thomson obtained for glass the value 2.7 (see 'Recent Researches in Electricity and Magnetism,' by J. J. Thomson, p. 471 and following). Ewing found the value of mirror-glass by a method of oscillations (Physical Review, July and August 1894, p. 51) to be 5.84. His calculated value for glass was 6.24.
The above method, it is believed, is capable of giving accurate results if the apparatus be well made, and it is hoped that the detailed description given above will enable anyone to readily repeat the experiment. Should this be done, I would suggest that the apparatus might with advantage be made considerably smaller.
I desire to say, in conclusion, that I am greatly indebted to Professor Henry A. Rowland for suggestions, and especially for the opportunity of performing the experiment*.
*The entire original idea of this method and all its details are due to Mr. Northrup, and only one or two very minor points are my own.HENRY A. ROWLAND.
Densities in the Earth's Crust."
N the seventeenth chapter of his 'Physics of the Earth's
ment of the densities and thicknesses of the different layers composing the Earth's crust, which would give, to a high degree of approximation, a uniform value for gravity over the Earth's surface. As attempts have recently been made, in the pages of this Journal and elsewhere, to criticise the method of investigation, it occurred to me that it might be desirable to give an independent investigation of the equations obtained by Mr. Fisher. This might possibly serve to render the meaning of the work clearer than is done in the book.
In the chapter referred to above the central nucleus is supposed to consist of concentric spherical shells of uniform density, so that it will only be necessary to consider the portion outside this, which we will hereafter refer to as the crust." We will suppose this portion to consist of m layers, whose densities, commencing from the outermost, are respectively P1, P2, P We will also use the symbols P2,···, Pm2. ki, k2,..., km, to denote the distances of the lower surfaces of the respective layers from the Earth's surface, these distances being measured along a radius of the Earth. This will be more convenient than taking symbols to denote the thicknesses of the layers. Since we suppose the layers forming the crust to be of varying density and thickness, we see that the p's will vary from one radius to another, as also will the k's, with the single exception of k We must suppose km constant, as we have laid down that the inner surface of the Earth's crust shall be a sphere concentric with the outer
Let O be the Earth's centre, and P a fixed point on its surface. We will take OP as the axis of polar coordinates, and consider the vertical component of the attraction at P of a polar element taken somewhere within the crust. If ρ be the density of the element we are considering, this will be represented by the expression
r2 sin (a—r cos 0)
a being the Earth's radius.
*Communicated by the Author.