val we find the average of each of the six sets of differences to be respectively 1.78, 170, 1-64, 156, 1.54, 139, and the aver age of all the differences to be 1·59.

Several hypotheses have occurred to me in explanation of this phenomenon, but as I have not as yet been able to put them to the test of experiment I am not prepared to submit any of them, though I intend to test them as opportunity offers. As, however, the objects for which this station is created does not embrace the carrying on of researches for purely theoretical purposes, it may be some time before the desired opportunity for experiments occurs, and hence I desire to place on record this preliminary observation. I ought to add however that the idea has suggested itself to me that we may possibly find in this phenomenon a means for distinguishing between and perhaps measuring the effects of different detonating explosives.

I am deeply indebted to Commander C. F. Goodrich, U. S. N., Inspector in charge of the Torpedo Station, for permission to publish this account, and to Mr. Arendt Angstrom, C. E., for the precise drawings used in figs. 1 and 3. Torpedo Station, Newport, R. I.

ART. VI.-Mode of Reading Mirror Galvanometers, etc.; by R. W. WILLSON, Ph.D.

IN physical work which requires the observation of small angles of deflection, such as the reading of a reflecting galvanometer, it is sometimes found that the use of telescope and scale is inconvenient or trying to the eye, while the method with lamp and scale has other disadvantages beside that of requiring a darkened room.

In many such cases a method of reading may be used, which I do not remember to have seen described, but which I have found so useful that I think it merits description. Though often more convenient than the telescope and scale it does not compare with the latter in accuracy; but in this respect it is not much inferior to the spot of light, while it is free from some of the most objectionable features of that method.

Replacing the telescope by a peep hole gives for many purposes a very convenient means of reading, where the magnifying power of the telescope can be dispensed with, a vertical line being drawn on the surface of the mirror to fix the sight line. A better plan, however, consists in placing in front of the movable mirror, and as near it as possible, a good-sized piece of thin plate mirror, from half of which the silvering has been removed, so that the silvered and unsilvered portions meet in a

horizontal line which crosses the center of the movable mirror; usually the reflecting portion is placed above, as shown in fig. 1, where a and b represent the silvered and unsilvered portions of the fixed mirror and c the movable mirror.

The instrument is so adjusted that the movable mirror when in its position of rest is nearly parallel to the fixed mirror. The scale used, as shown in fig. 2, has its middle division line prolonged downward to form an index; this scale being brought in front of the mirror, the eye is placed at the proper height to see, as in fig. 3, the image of the scale in the upper fixed mirror, the lower ends of the divisions coincident with the lower edge of the silvering, while the index is seen nearly continuous with the middle line of the scale, but reflected from the movable mirror; any deflection of the latter causes the image of the index to move along the lower edge of the reflected scale by an amount corresponding to the double angle of deflection.*

It is obvious that this construction does not interfere with the use of the instrument with lamp, or telescope and scale, the lower portion of the fixed mirror acting as the usual covering glass; it is then desirable, however, to give the latter a slight forward inclination to avoid double reflection; a sufficient inclination may be given with the leveling screws, without interfering with the mode of reading, above described, unless the lines of the graduation are very short.

* A simple geometrical consideration shows that if the scale reading be n, the angle of deflection a, the distance of the scale from the fixed mirror A, and the distance between the two mirrors d, tan 2α= ; A and d, if necessary, cor

η

A-d'

The advantage of the method arises mainly from the natural and easy use of the eye; to secure this it is desirable that the scale should be sufficiently open to be read without straining the eye.

The fixed mirror should be as large as possible, especially in the horizontal direction, to facilitate the bringing of the eye into the proper position without effort.

It is also important if the movable mirror is round that the line of division between the silvered and unsilvered surfaces shall cross it nearly in a diameter in order that the position of the eye may not be too much restricted, as is the case if the line is very short in which the fixed and movable mirrors overlap. Where it is practicable a rectangular mirror is to be preferred.

Jefferson Physical Laboratory, April, 1888.

ART. VII.-Bertrandite from Mt. Antero, Colorado; by SAMUEL L. PENFIELD.

THIS rare mineral was first identified as a new species by M. E. Bertrand* from the study of a few small crystals collected from a pegmatite vein at Petit Port, near Nantes, France. M. Des Cloizeauxt has also identified the mineral at the gneiss quarries at Barbin, near Nantes, while M. A. Damourt has analyzed it and determined its composition to be H,Be,Si,O,; he also gave to it the name Bertrandite. The mineral has since been identified by R. Scharizers at a feldspar quarry near Pisek, Bohemia, where it occurs lining cavities left by the decomposition and disappearance of beryl crystals. At all of these localities the crystals are minute and are found only in small quantities. The crystalline form determined by Bertrand and Des Cloizeaux is orthorhombic, while Scharizer finds grounds for believing that the crystals are monoclinic with close approximation in form and optical properties to orthorhombic symmetry.

The single hand-specimen in the author's possession was selected by Mr. W. B. Smith, of Denver, Col., from a lot of material collected during the past summer at Mt. Antero in the search for specimens of phenacite. The crystals of bertrandite are attached to quartz which is associated with beryl.

*Bull. Soc. Min. de France, iii, 1880, p. 96.
Bull. Soc. Min. de France, v, 1882, p. 176.
Bull. Soc. Min. de France, vi, 1883, p. 252.
Zeitschr. Kryst., xiv, 1888, p. 33.

Other minerals occurring at the locality are phenacite, orthoclase, muscovite and fluorite.

The crystals are little rectangular blades 5mm long, 2mm wide and 0.2-0.4mm thick. The largest faces, 5×2mm, correspond to the basal plane of Bertrand lengthened out in the direction of the brachy-axis, ă, and marked by slight striations parallel to the shorter diameter or macro-axis, 7. Opposite this flat basal plane the crystals have a curved surface composed of the basal plane and brachydomes in oscillatory combination. The curved surface either joins the basal plane directly, forming a sharp, thin edge along the whole length of the crystal, or a narrow brachypinacoid is present between them. This curious development gives to the crystals a hemimorphic aspect which is very characteristic and not accidental; for all of the eight or ten crystals on the specimen were of this same character. The general shape of the crystals is that of a thin slice cut from the side of a cylinder parallel to its axis. The crystals are attached at one end and are terminated at the free end by a macropinacoid. The observed planes are therefore the three pinacoids, one of the basal planes being rounded by oscillatory combinations parallel to the brachy-axis. The faces have a good luster, that of the basal plane being pearly, the others vitreous. They are not well suited for measurement. was one V-shaped twin in the specimen, the twinning plane being the brachy-dome 031 (3-2) of Bertrand. The flat basal planes formed the outside limbs of the V and made an angle of 61° 52′ with one another, the curved surfaces formed the reentrant angle. Similar twins are described by Bertrand with re-entrant angle of about 60°. Two cleavages were identified, prismatic and basal, both highly perfect. The measured angles are as follows:

There

These values differ quite widely from the calculated values of Bertrand, but if we regard the cleavage angle m^m= 59° 34' as good (it was certainly free from disturbing influences such as striations) and couple with it the angle of the twin cxc=118° 8', we obtain the axial ratio for orthorhombic axes

c:b;a=0·5953 : 1· : 0·5723.

The important measurements of Des Cloizeaux and Scharizer, with the values calculated from the above axes, are:

The above measured angles agree very well with the calculated values, and where the difference is large the reason may be found in the uncertainty of the measurements made on so small crystals. Scharizer's measurements agree about as well with these orthorhombic values as with his own calculated values for monoclinic axes.

I cannot give a reason for the hemimorphic development of the basal plane. If Scharizer is correct in assuming that the crystals are monoclinic with the brachy-axis of Bertrand as the ortho-axis, such a development might result from twinning about an orthopinacoid, one basal plane being converted into a curved surface by oscillations with hemi-orthodomes, symmetrically situated on either side of the twinning plane. This would require for B-90° 28' 34" (Scharizer's value for the inclination of the a and c axes) a salient angle along the twinning line on the base of 180° 57′ which could not be detected. A section across the crystals, parallel to Scharizer's clino-pinacoid, should also show an inclined extinction which would be especially marked along the twinning limit; a section thus prepared shows perfectly normal orthorhombic symmetry in polarized light.

The optical properties point most decidedly to orthorhombic symmetry. The obtuse bisectrix is normal to the basal plane, the plane of the optical axes is the brachypinacoid. The divergence of the optical axes measured with a large Fuess apparatus in the Thoulet solution (n=1.6503 for yellow, Na, flame), is

2H=101° 10′ for yellow.

Using Bertrand's mean index of refraction ẞ=1·569 we get 2V=108° 42′ for yellow.

Bertrand determined 2V=105° 8', and Scharizer 2V=108° 31'. The dispersion about the obtuse bisectrix is marked p> v and therefore about the acute bisectrix p <v. A section parallel to the macropinacoid showed the acute bisectrix in the