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I have, in the main, used the nearest whole numbers, bracketed those values that might seem forced, and inserted a few numbers (possible blanks) to complete the series.

There is, I think, some other law or laws besides this simple one, effective in the matter, but there are many things justifying the view that this ideal arithmetical series, which on the whole is so closely attained (all things duly considered) expresses the chief of perhaps several laws, all jointly effective in limiting the mass of the elements.

One of the strongest objections thus far to the use of round numbers in such atomic theories, as well as to Prout's hypothesis in general, has been the irrationality of the ratio of H to 0. Now Lord Rayleigh has shown that at 13° C. water absorbs 4 per cent of its volume of Argon and that gases handled over water in the usual way almost invariably become containinated with the Argon held in solution. Moreover, it is quite likely that in reactions for the production of gases where water is used as a reagent (e. g. evolution of II by electrolysis of water or action of dilute acid on Zn), Argon contamination might result from the Argon so dissolved, and that such contamination once acquired, would not be removed by any ordinary reagents through which the gas was passed. A simple calculation will show that with hydrogen contaminated by only oths of one per cent of Argon, the ratio H to ( would be reduced from 1:16 to 1:15.879 which is about the latest values deduced from direct weighings of the two gases. And in those determinations based upon the synthesis of water, by passing H over red hot oxide of copper, with Argon in the water from which the H was evolved and contamination having occurred, the Argon, unabsorbed by any subsequent reagents, might finally turn up dissolved in the water formed by synthesis, and if this water were saturated with Argon the effect on the ratio would be to reduce it from 1:16 to 1:15.98.*

Probably it will be difficult to handle gases over the water bath without the risk of such contamination. In the case, however, of density determinations it would seem advisable after the weighing to absorb the gas by suitable reagents, and then if any residual gas, Argon or any other, be found, to apply the proper correction to the weights already obtained; I believe that when this has been done the ratio of H to () will be found nearer to the value 1 to 16 than is at present supposed.

It would be interesting to go more deeply into the question of the laws governing the masses of the elements to which I have barely alluded, and to which I have given attention for some years past, but this paper would then be extended far beyond all proper limits. At some future time I may discuss this matter also.

ART. XXXIII.-An Improved Rock Cutter and Trimmer ;

by EDGAR KIDWELL.

OVER a year ago the Michigan Geological Survey required a rock cutter, and consulted me regarding the matter. I therefore designed one, and as a year's use has shown this cutter to be fully capable of doing the work required of it, a detailed description may be of value to those having need of a similar machine.

The cutter had to be suitable for heavy and accurate work, hence ample strength of parts, power in the mechanisin, and freedom from lost motion were absolutely necessary. Previous experience in our shops had shown me that a No. 4 parallel swivel railway chipping vise, with wronght bar, as made by Merrill Brothers, possessed all these qualifications, and I therefore made in one of their vises such changes as were necessary to convert it into a cutter. The vise itself needed but few alterations, as it was necessary only to cut away the jaws to give the operator more room, and provide suitable openings for inserting the steel cutters. Provision was also made for holding cutters in place, and changing them quickly when necessary. Fig. 1 shows all necessary details.

* It is rather significant that the best determinations by these two different methods closely approximate to these two values of 15.88 and 15.98 respectively.

Two forms of cutter were made, and a duplicate set of each was provided. The working drawings, fig. 2, show the details of cutters so clearly that further description is unnecessary. The specification required that these cutters should be of the

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best quality Jessop's, Stubb's, or Mushet's steel, tempered very hard. It might be better for some kinds of work to have another form of cutter, with edges at an angle of 45° with top edge of jaws, but the two forms already mentioned have so far answered all requirements.

Fig. 2.

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A, B, Cutters with horizontal edge. C, D, Cutters with vertical edge. There should be also two pins, " diameter, 2" long, for holding cutters; one pin it" diameter, 4" long, for removing cutters.

Unless a large amount of work is to be done, it will be advisable to order only a single set of cutters. This will make a material reduction in the first cost of the machine, and one set of cutters, if properly cared for, will last for years.

If very rapid work is desired any of the various forms of quick-acting vise might be employed as a basis for the machine, but I do not think the change would be a good one. The quick-acting vises are provided with weaker screws, and the parallel bars are invariably of cast iron, cored hollow, and sadly deficient in strength, hence a cutter made from a vise of this kind would be liable to complete collapse when used for heavy work. No matter what form of vise is used, if the machine is to be satisfactory it is absolutely essential that the screw be accurately cut, to prevent lost motion, and that each cutter be carefully fitted to its seat, shaped so that cutting edges will exactly meet when brought together, and be made of the very best tool steel, properly tempered. If these precautions are taken, the result will be a machine that is free from every trace of ricketiness, and amply able to stand up to any work that can be put on it. During the last year the Michigan Geological Survey has made with one pair of jaws from 2500 to 3000 cuts, on such specimens as conglomerates, sandstones, amygdaloids, traps, felsites, porphyries, silicified tufas, prehnite and datolite veinstone with copper, and its jaws show practically no signs of wear on the cutting edges.

Fig. 3 shows the machine ready for use.

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In conclusion I would state that none of the features here mentioned are patented, and are free to all who may care to use them. The complete machine, from my drawings, can be got of Merrill Brothers, 465 Kent ave., Brooklyn, N. Y.

Michigan Mining School, Houghton, Michigan.

ART. XXXIV.- Relation of the plane of Jupiter's orbit to the mean-plane of four hundred and one minor planet orbits ; by H. A. NEWTON.

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ABOUT nine years ago (this Journal, III, xxxi, p. 319) I called attention in a brief note to the fact that the mean.plane of the orbits of the then known two hundred and fifty-one minor planets was inclined to the plane of Jupiter's orbit by a very sinal! angle. In fact no minor planet out of the whole 251 had its plane so near to the mean.plane as did the planet Jupiter. Since that time we have added to the list of planets between Mars and Jupiter one hundred and fifty newly discovered ones, and it seems worth while to find whether the same relation of the large planet to the entire group of four hundred and one small ones holds true.

The plane of an orbit is determnined by the longitude of the ascending node and the inclination, and its place inay be represented to the eye by a plot in which the inclination is the radius vector and the longitude of the node is the polar angle. The point thus plotted is of course the pole of the plane.

The mean-plane of the 401 planes, regarding each plane as a unit, may be determined with sufficient accuracy for the present purpose by the formulas for computing the center of gravity of the 401 points plotted, viz:

401 I cos ( = Eicos 8, and 401 I sin ( = Ei sin 82 : where i and 8 are the inclination and longitude of ascending node of any orbit, and I and 2 are the same functions of the mean-plane of all the orbits. Computing I and 2 for the 101 orbits as given in the Annuaire du Bureau des Longitudes for 1895, adding three later orbits from the Astronomische Nachrichten, we have

I= 0°.93, and l = 109°•3.

The corresponding quantities for Jupiter are

i = 1°:31, 8 = 98°•9,

so that the inclination of the mean plane to Jupiter's plane is 0°•43. The three minor planets whose planes are nearest to the mean-plane are 1893 Y, (27) and (149). These planes make angles with the mean-plane severally equal to 0°.65, 0°•74, and 09.77. The planet 1893 Y, was photographically discovered and has not yet a place in the numbered series of planets. Its plane will doubtless be much changed when the

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