For the case of oblique vibration (Fig. 2), call mx =x (x being an abscissa of the dial circle), and the ordinate rm'=y.

The point of the dial m' will have a velocity

R"+r sin. V = R'

(being the latitude) and the difference of rotary velocities be

(1–

tween it and C will be V1

R" + sin
R'

and the distance

om" gained, in the direction of rotation, by the pendulum, will

But the increment of abscissa om' corresponding to the increment of ordinate om" will be determined by the equation of the circle, these increments (being very small) being as the differentials of y and x.

om': om"::dx dy::√2rx-x2: r-x; hence om=om".

R" + sin √2rx − x2

an expression the same as obtained for the case of vibration in the plane of the meridian, and constant for all positions of the plane of vibration.

It is then proved that, at each vibration, the plane of vibration will shift on the dial through an angle whose arc, on the dial circumference, will be equal to the difference between the arcs of rotation described during the same time by the centre and extremity of the meridional diameter of the dial.

of

After a complete revolution of the earth, the length of the arc of the dial passed over, or which measures the angular change plane of vibration will be, evidently, equal to the difference be

tween the total circumferences of the two small earth's circles, just mentioned.

3.

R"-2TR cos(+).

We have proved that the length of the arc of the dial moved over by the pendulum in 24 hours is equal to the difference between these circumferences

where

circ R'-circ R"-27R (cos - cos (+1)) =

2πR (cos cos cos + sin sin )

(as is actually the case) is extremely minute, cos' is sensibly 1 and the above expression becomes

circ R'-circ R"-27R sin sin '.

But R sin Cm and 27R sin is therefore equal to the circumference of the dial circle.

2R sin sin is therefore equal to the dial circumference, or 360° multiplied by the sine of the latitude.

a result

In other words the plane of oscillation will move in 24 hours through an angle equal to 360° × sine of the latitude :arrived at by other methods and proved by observation.

The foregoing demonstration is rigid; it is based upon the simple fact that the pendulum has (with its point and axis of suspension) a rotary motion of its own, around the axis of the earth; and that while this rotary movement is preserved unchanged, the oscillation of the pendulum is governed by the same laws in reference to its axis of suspension as if both were motionless in space; a supposition on which all the investigations of the phenomena of gravitation, as applied to the earth and heavenly bodies, are based. It assumes nothing unless it be, that the mere angular motion which the direction of the axis of suspension and of gravity together undergo, will not permanently alter the direction of the chord of the arc of oscillation.*

*This assumption is capable of proof but it is not worth while to complicate the subject by introducing it here.

SECOND SERIES, Vol. XX, No. 59.-Sept., 1855.

81

ART. XXIV.-Reëxamination of American Minerals: PART V.. -The Minerals of the Wheatley Mine in Pennsylvania.— Anglesite; Cerusite; Wulfenite; Vanadate of Lead; Pyromorphite; Mimetene; Galena; Copper; Copper Pyrites; Malachite; Azurite; Blende; Calamine; Hematite; Fluor Spar; Calc Spar; Sulphur, &c.; by J. LAWRENCE SMITH, M.D., Prof. Chem. Med. Depart. University of Louisville.*

(Communicated to the Am. Scientific Association, August, 1855.)

BEFORE describing the minerals of this mine, it is well to say a word with reference to its location, and also to quote some remarks on the geology of the surrounding country by Prof. H. D. Rogers. Although this is departing from the plan usually adopted in this series of papers, still the occurrence of all the minerals, here described, at one locality, cannot but render the geology of the place interesting to mineralogists.

This mine is situated in Chester Co., near Phoenixville, Pennsylvania, and is one of several interesting developments of a thorough and very able exploration of this region by Mr. Charles M. Wheatley. At the request of Mr. Wheatley, Prof. Rogers made a geological examination of the metalliferous veins of this district, and the following remarks are taken from his report.

"These veins belong to a group of lead and copper-bearing lodes of a very interesting character, which form a metalliferous zone, that ranges in a general east and west direction across the Schuylkill River, near the lower stretches of the Perkiomen and Pickering Creeks in Montgomery and Chester Counties, and bids fair to constitute at no distant day a quite productive mineral region.

"The individual veins of this rather numerous group, are remarkable for their general mutual parallelism, their average course being about N. 31° 35° E. by compass, and not at all coincident with that of the belt of country which embraces them. They are true lodes or mineral injections, filling so many dislocations or fissures, transverse to the general direction of the strata which they intersect. The metalliferous belt ranges not far from the boundary which divides the gneissic or metamorphic rocks of Chester County from the middle secondary red shale and sandstone strata."

"This vein varies in thickness from a few inches to about two and a half feet, and we may state its average width at not less than eighteen inches. It is bounded by regular and well-defined, nearly parallel walls, the prevailing material of which is a coarse, soft granite, composed chiefly of white feldspar and quartz.

"It would seem to be a pretty general fact that such of these veins as are confined entirely or chiefly to the gneiss, bear lead as their principal metal; whereas, those which are included solely within the

* I am indebted to Prof. J. D. Dana for the figures and mathematical descriptions of the crystals given beyond.-J. L 8.

red shale are characterised by containing the ores of copper. But the zinc ores, viz., zinc blende and calamine, prevail in greater or less proportions in both sets of veins, existing, perhaps, in a rather larger relative amount in the copper-bearing lodes of the red shale."

"The gneissic strata of the tract embracing this group of lead-bearing veins, seem to differ in no essential features from the rest of the formation ranging eastward and westward through this belt of country. Here, as elsewhere, they consist chiefly of soft thinly bedded micaceous gneiss, a more dense and ferruginous hornblendic gneiss, and thirdly a thicker bedded granitic gneiss, composed not unfrequently of little else than the two minerals, quartz and feldspar.

Penetrating this quite diversified formation are innumerable injections of various kinds of granite, greenstone trap, and other genuine igneous rocks. The granites, as throughout this region generally, consist for the most part, of a coarse binary mixture of quartz and opaque white feldspar, tending easily to decomposition. This rock abounds in the form of dykes and veins, sometimes cutting the strata of gneiss nearly vertically, but often partially conforming with its planes of bedding for a limited space, and then branching through, or expiring in it in transverse or tortuous branches. A not uncommon variety of granitic dyke is a simple syenite composed of quartz, greenish semi-translucent feldspar, and a smaller proportion of dark green hornblende. A soft, white, and partially decomposed granite is a very frequent associate of the stronger lead-bearing veins, particularly in their more productive portions; but this material belongs, in all probability, not to the ancient granitic injections of the gneiss, but to those much later metalliferons intrusions which filled long parallel rents in that formation with the lead ores and their associated minerals."

"The gneissic strata and their granitic injections, throughout this district. display a softened, partially decomposed condition, extending in many places to a depth of twenty fathoms."

"Of the dozen or more lead and copper lodes of greater or less size brought to light in this quite limited region of five or six miles length and two or three miles breadth, the greater number are remarkably similar in their course, ranging N. 32°-35° E., and S. 32°—35° W.; and what is equally worthy of note, they dip, with scarcely an exception, towards the same quarter, or south-eastwardly, though in some instances so steeply as to approach the perpendicular.'

"There is no marked difference in the general character of the veinstones of the several mineral lodes, nor any features to distinguish as a class those of the red shale from those of the gneiss."

The minerals found in these veins are quite numerous, and among them, there are specimens of species hardly equalled by those coming from any other locality. Prof. Silliman, in his report on the minerals of this mine exhibited at the Crystal Palace, says, that the specimens of sulphate and molybdate of lead are the most magnificent metallic salts ever obtained in lead mining, and unequalled by any thing to be seen in the cabinets of Europe.

48. Anglesite.

This mineral is found abundantly and in beautiful crystals at this locality. The magnificence of many of the specimens can only be realized by seeing those in Mr. Wheatley's cabinet. The crystals are remarkable for their size and transparency;-in some instances, they weigh nearly half a pound being as transparent as rock crystal in nearly every part. Crystals with terminations at both ends have been obtained five and a half inches in length by one and a half in thickness; perfectly limped crystals an inch in length are quite common.

The following are some of the forms:

1.-0, ∞, 1-∞.

2.-0,·, -, 1, x, 1-2, 1-∞, ∞.. 0.00. 3.—0,-, -, ∞, 1-2, 2-4

4.—0, §.☎, ∞-☎, f-§, 1, ∞, 1-2, 2-4, 1-x.

Sometimes the crystals of this mineral are full of cavities, and of a milk-white color; but these do not differ in composition from the colorless and transparent forms. It also occurs in circular crystals.

It is sometimes colored. There is a black variety produced by the more or less perfect admixture of the sulphurets of lead and copper (coutaining traces of silver) in the mass of the crystals, whose form is not altered. There are crystals of a delicate green color arising from carbonate of copper, and others of a yellow color due to oxyd of iron.

The transparent and colorless variety is remarkably pure. Its sp. grav. is 6:35. On analysis it afforded,

1.

2.

according very precisely with the formula P3.

I would call attention to the method of analyzing this sulphate, as described in another paper, for it was analyzed in the moist way by dissolving it first in citrate of ammonia.

The anglesite of this mine is found variously associated. It is common to find it in geodic cavities in galena, the cavities being lined with hematite varying in thickness from to an inch or more, and often this hematite contains anglesite intimately mixed in the mass. It may occur in crystals occupying a portion of the geode, or it may fill its entire capacity, assuming the form of the cavity. It is also found compacted in the galena without the appearance of any cavity or the presence of any other mineral; acicular crystals occur diffused through the galena. Observed also on copper pyrites, with a thin layer of hematite inter