This distribution is not the same as that given by M Jamin; but as his method is so defective, and his "normal magnet" s indefinite, the agreement is sufficiently near.

The surface-density at any point of a magnet is

x b

which, for the same kind of steel, is dependent only on and d ď Hence in two similar magnets the surface-density is the same at similar points, the linear density is proportional to the linear dimensions, the surface integral of magnetic induction over half the magnet or across the section is proportional to the surface dimensions of the magnets, and the magnetic moments to the volumes of the magnets. The forces at similar points with regard to the two magnets will then be the same. All these remarks apply to soft iron under induction providing the inducing force is the same, and hence include Sir William Thomson's well-known law with regard to similar electromagnets; and they are accurately true notwithstanding the approximate nature of the formula from which they have here been deduced.

Our theory gives us the means of determining what effect the boring of a hole through the center of a magnet would have. In this case R' is not much affected, but R is increased. Where the magnet is used merely to affect a compass-needle, we should then see that the hole through the center has little effect where the magnet is short and thick; but where it is long, the attraction on the compass-needle is much diminished. Where the magnet is of the U-form, and is to be used for sustaining weights, the practice is detrimental, and the sustaining-power is diminished

in the same proportion as the sectional area of the magnet. The only case that I know of where the hole through the center is an advantage, is that of the deflecting magnets for determining the intensity of the earth's magnetism, which may be thus made lighter without much diminishing their magnetic moment.

In conclusion, let me express my regret at the imperfection of the theory given in this paper; for although the equations are more general than any yet given, yet still they rest upon two quite incorrect hypotheses; and so, although we have found these formulas of great use in pursuing our studies on magnetic distribution, yet much remains to be done. A nearer approximation to the true distribution could readily be obtained, but the results would, without doubt, be very complicated and would not repay us for the trouble.

In this paper, as well as in all the others which I have published on magnetic subjects, my object has been not only to bring forth new results, but also to illustrate Faraday's method of lines of magnetic force and to show how readily calculations may be made on this system. For this reason many points have been developed at greater length than would otherwise be desirable.

ART. IX.-On rifts of Ice in the rocks near the summit of Mt. McClellan, Colorado, and on the different Limits of Vegetation on adjoining summits in the Territory; by EDWARD L. BERTHOUD.

THE silver mines of Argentine District, a mining center about eight miles southwest from Georgetown, are located on the north slope of a high peak named McClellan Mountain, which forms a very prominent point of the main central range, and immediately facing a precipice fully 1500 feet high, the majestic mass of Gray's Peak; while 14 miles south is Argentine Pass, 13.100 feet in height.

This mountain, 13,430 feet* above the sea, is intersected in a northeast and southwest direction by a system of mineral veins, containing silver in large quantity with a little gold. The veins. seem generally to be nearly vertical, and occur at elevations varying from 12,300 feet to 13,400 feet. Three of them have been extensively mined, and two, the International and Belmont, have been developed and worked since 1867-68 with success, and with fair paying results; but with probably at a greater average cost per ton of mineral mined than any other similar mines in Northern Colorado. The Centennial Lode, the third mine examined, is now being well developed by its owners, who

* Vide Gardner, in Hayden's Report, 1873-74.

are working into the vein horizontally by excavating a drift. The ores found in these mines are galena rich in silver, decomposed quartz and honey-combed quartz, with sulphurets of silver, and some decomposed iron pyrites and a little carbonate of lead, with occasional small patches of sphalenite.

I have been thus particular in the description of these mines, merely to give a good general idea of their value and location. In a personal and critical examination of them, during a recent visit to the region, a peculiar feature was observed which excited much surprise.

The discovery-drift of the Centennial Lode runs into McClellan Mountain at an altitude above 13,100 feet, on a course southwest, at about 30 feet from the entrance of the tunnel. Intercalated in the vein, I found three or four well defined veins of solid ice, parallel with the bedding of the rock, and filling all its thinner side cracks and fissures; in fact, after further examination I found that the frozen stratum, and the congealed, hard earth, rock and gravel, began only a few feet below the accumulated rock and debris of the mountain slope, and continued as far as the excavation reached, some forty feet in depth.

From the Centennial Lode I went westward about 300 feet, and examined the drift that has been excavated into the mountain some 500 feet, upon the vein of the International Lode. Here there is repeated the same frozen substratum and the same rift or veins of ice in the country rock and in the vein. I went into the tunnel about 100 feet and found this glacial condition still existed; and the owner of the mine assured me that the ice and frozen rock continued all the way to the end of the tunnel and caused a good deal of extra expense in mining the ore.

The course of the "International Lode" is southwest, and its drift is about 50 feet in vertical elevation above the drift of the Centennial Lode.

The next "Lode" examined was the Belmont Lode, west and nearly parallel to the International. This mine is exploited by a system of horizontal galleries one above the other to the summit of the mountain, at 13,400 feet elevation. In the lower galleries the same frozen icy condition prevails as at the first two veins. But the summit drift, which was at the date of my visit about 60 feet long, does not show veins of ice in the wall-rock of the veins; this is probably due not only to the greater narrowness of the summit, here scarcely 200 feet where pierced by the tunnel, but also to the influence of wind and sun upon its western seamed and riven surface, and to its more perfect drainage and exposure.

This is certainly a singular phenomenon, when we consider that across the narrow valley north of McClellan Mt., not over

three-fourths of a mile distant and upon another high peak, the limit of tree growth exceeds 12,400 feet elevation on the south slope of that peak. Here can be seen Pinus aristata, some of the trees two feet in diameter and thirty feet high that retain their hold, and slowly increase in size, thus maintaining themselves in respectable numbers in spite of furious gales of snow and wind, and an extreme Arctic cold.

In Miscellaneous Publications, No. 1, U. S. Geological Survey of the Territories, which was published last year, under the direction of Prof. F. V. Hayden, the line of tree growth is given by Mr. J. T. Gardner in his report, as from 11,000 feet to 11,900 feet, between latitudes 39° and 40°. We believe this to be correct, and a fair general average. In Argentine District, which comprises McClellan Mountain, we have a very notable departure from this limit of from 500 to 1400 feet in elevation, and also about 1300 feet above timber line on Gray's Peak, three to four miles southwest, as given by Mr. Gardner. At the Equator and in the Torrid zone the limit of the growth of Pines is generally placed at 12,800 feet above the sea; how is it that, in lat. 39° 33' N., the limit of the growth of Pines has receded only 400 feet?

In McClellan Mountain and in Argentine District there are two antagonistic phenomena in immediate proximity; on one side of the valley, a mountain slope facing northeast, well grassed, totally devoid of shrubs and trees, where soil and rocky debris are underlain by a perpetual icy coat of hundreds of feet in depth, supporting on its surface a growth of plants strictly Alpine and Arctic, and abounding with Ptarmigan, Lagopus leucurus, and the tailless, earless marmot; and where on the 2d October, 1875, I found the following plants yet in bloom; Sedum stenopetalum, Potentilla norvegica, P. fruticosa, Sibbaldia procumbens, Astragalus alpinus, Silene acaulis, Draba aurea, Phleum alpinum, Primula Parryi, Gentiana, Heuchera, Castillera pallida, Ranunculus mvalis, Pedicularis, Cardamine and Crepis, while less than half mile distant, on the opposite slope of the vale, Pinus aristata of large size and a profuse growth of birches, willows, grasses and Arbutus, with flowing springs and small ponds, diversify its southwestern slope.

It has been suggested* that the frozen soil and rock of some mines examined by him, northwest from McClellan Mountain, on the west slope, have been thus left ice bound since the Glacial period; and that they thus retain their former ice-bound condition, from the excessive altitude of the mines there explored.

This may be the case, but it seems doubtful. There are in Colorado many mines at altitudes very nearly as high as the highest on McClellan Mountain, yet none have been exploited to the

* R. Weiser, in this Journal, III, viii, 477, 1874.

depth of from 100 to 500 feet in solid frozen soil and ice ribs. I am inclined to believe that the glacial condition of McClellan Mountain is due to local causes. Prominent among these would be the loose nature of the soil and deep rocky debris of the mountain, and the slow percolation of water exposed to excessive evaporation that is promoted and quickened by continued gales from the north and northwest that strike against the precipitous face of the mountain range in that direction. The opposite slope, on the contrary, which shows the abnormally high timber line, faces a Pass (Argentine Pass) 13,100 feet in height, which gives a way perfectly unobstructed for south-southwest winds. These prevail frequently in winter and spring, and are invariably temperate or even warm, and thus to their influence may be due the milder and more propitious character of this locality. In Colorado Territory it has been remarked that in our mountains, even in January, a southwest wind is invariably genial and warm; in two hours I have known a southwest wind to raise the thermometer from 13° below zero to 47 above. This abrupt change, however, is disastrous to tree growth, and destroys the quaking Asp, Cedar, and even Pines in more exposed localities; while the Cherry, Box Elder and the bitter Cottonwood (Populus angulata) have perished in the ensuing spring in our lower valleys and on the foot-hills.

I have presented this subject in order to secure for it further elucidation and discussion. The facts are of no little interest, since they conflict with accepted views as to the limits of growth of plant, and the influence of altitude on climate.

ART. X.-On a New Form of Lantern Galvanometer; by FRANCIS E. NIPHER, Professor of Physics in Washington University.*

IN the September number of this Journal, Prof. Barker has described a lantern galvanometer, which appears to possess many advantages over any heretofore described, and which is evidently a valuable addition to the apparatus of the public lecturer.

While meditating the construction of this instrument, the galvanometer now to be described was devised. A vertical section is shown in Fig. 1.

A square box (Y, Y), open at the top and bottom, is pierced on opposite sides to admit the wooden rods (b). To the inner extremities of these rods are attached coils (R), of covered cop* Read before the St. Louis Academy of Science, Oct. 18, 1875.