By comparing these dimensions with those of the four times larger Ertel vertical circle of the Central Observatory, it is evident that the portable instrument, for which the actual probable accidental error of a meridian zenith distance resulting from two pointings, one circle east and one circle west, is ±05, has derived a decided advantage from its small size and proportionately higher magnifying power. Recognizing the principle that in an astronomical measurement the fewest possible assumptions must be made,—and that computed probable errors give a very unreliable or perhaps no indication of the extent to which the constant or systematic errors introduced by assumptions as to the condition of the instrument, &c., may have vitiated our results, it is necessary not only to examine thoroughly the instrument itself, but also in using it to still farther reduce the influence of its imperfections. Therefore a zenith distance is made to depend upon eight pointings of the telescope (or 4x8 pointings of the microscope micrometers), the four in one position of the circle being preceded and succeeded by two in the opposite position; the whole series requiring from sixteen to twenty-four minutes for its complete observation. A latitude or a time determination depends upon a pair of stars observed on opposite sides of the zenith at the same zenith distance; or upon sixteen pointings whose result is sensibly free from any assumption as to the zenith point, flexure or refraction. The examination of the instrument used by Colonel Smyssloff leads to the following results. The error of bisecting the interval between the two wires of either pair in the field of view of the microscope by a division of the limb of the circle, the error arising from accidental errors of the screw and the divisions of the screw head, and the error of reading these divisions, combine to affect the mean of four measurements with the microscopes, The probable accidental error of a division of the di- 10" 17 +0"-23 +0"-12 The combination of these gives ✅(0’·17)2+(0 ́ ́·23)2+(0′′·12)2=±0′′·31. The probable accidental error of pointing on a star may be afterward investigated,-but if we assume that it equals an apparent visual angle of 1', this will correspond to an arc of 1067. Whence (0·31)2+(067)2 =±0.74. A zenith distance depending on one pointing, circle right, and one, circle left, may therefore be expected to be affected with an accidental error of and for one depending on eight pointings we have a probable accidental error, +0"-26. A latitude or time determination depending on two such zenith distances has accordingly the probable accidental error of observation, ±0"-18. The influences of refraction, clock correction, flexure, periodic errors of division, still remain. The latter have not, to my knowledge, as yet been specially investigated,-the circles are divided with the same machine used in dividing the small circles investigated by Struve in Dorpat. See his "Beschreibung. der Breite Gradmessung," and the "Description de l'Observatoire Central." The combined influence of all disturbing causes can be investigated by a series of determinations of the latitude of any known station,-the zenith point of the divided circle being successively altered by arcs of 30° or 45°. Sixteen determinations of the latitude of Poulkova afford an example of this investigation which should be entered into by each observer for his own instrument. Using the declinations given in the British Nautical Almanac, there results the following series of values of the latitude of the station, which was the northeast small dome on the grounds at Poulkova, and whose latitude, by reference to that of the Ertel vertical circle as deduced by Dr. Peters, is +59° 46′ 2002. Each of the following values of ❤ results from one observation consisting of eight pointings upon the respective stars. Assuming the 16 values resulting from the 16 pairs to be free from flexure, there results a probable error of latitude from one pair = ±0.35. The difference of the latitudes resulting from the two stars of each pair depends upon the flexure of the tube and the error in the declinations, as well as upon any systematic error in the refraction or the graduation, though this is probably insensible. Assuming the latitude to be 59° 46' 20"00, we find the differences from this to be represented by the formula +316 siu (z-30°·3); (A.) applying this to each of the thirty-two observations, there results a probable error of a latitude from two stars 10"34. From the sixteen values of the flexures we derive a probable error resulting from the error in the ephemeris and the error of pointing and reading; this is ±0"-31. And subtracting the latter source of error, there results +0"-25 as the, probable error of the declination in the British Nautical Almanac. The investigation of flexure might also be made by means of observations in the prime vertical, but here we probably have a complicated combination of flexure and personal equation. Eight determinations of time made by Colonel Smyssloff (each depending upon eight pointings on each of a pair of stars observed in the prime vertical), compared with simultaneous observations by Wagner at the Ertel transit gave Wagner-Smyssloff 0·02 0·03; the probable error of a single determination resulting =±0.09; or, if we allow equal accuracy to each instrument, the probable error of a clock correction given by the vertical circle ±0.06. = A series of comparisons between Messrs. Smyssloff, Bolscheff and Demetrieff, in which each observed four of the eight pointings gave, S.-D.-0098, S.-B.-05-046, B.-D. +0.132; and the probable error of a determination of time 006, which in the latitude 60° corresponds to a vertical angle of 10"-45. As in the determination of latitude so in that of time, a pair of stars equally distant from the zenith is always observed, each being pointed upon four times in each position of the circle, the eight pointings requiring twenty minutes or less. The stars are of course observed near the prime vertical. [To be concluded.] ART. XXVI.-On Cryophyllite, a new mineral species of the Mica Family, with some associated minerals in the granite of Rockport, Massachusetts; by JOSIAH P. COOKE, Jr. IN a paper published in a recent number of this Journal* I described a new mineral species allied to Helvin, to which I gave the name of Danalite. Associated with Danalite in the granite ledges forming the extremity of Cape Ann, Massachu setts, are two remarkable micas, one of which is the new species to which on account of its easy fusibility and foliated structure I have given the name Cryophyllite. Mineralogical Characters. The mineralogical characters of cry. ophyllite are as follows. Like other varieties of mica it crys tallizes in six-sided prisms, which are frequently of considerable size, from one to two inches in length and of proportionate diam. eter. The basal cleavage is highly perfect, yielding thin flexible and transparent lamina, which when examined with a polarizing microscope give a biaxial image, the angle between the optical axes varying from 55° to 60°. The angles 55°, 57° 30', and 60°, were all measured on different specimens. The dispersion of the axes, if any, is so slight that its character could not with certainty be determined, the color of the mineral tending to obscure any such effect. The perfect uniformity of the two systems of rings both as to form and to color indicates that the mica belongs to the trimetric system. Nevertheless, the angle between the prismatic planes measured with an application goniometer 120° as accurately as is possible with this instrument, and in one instance the planes of an hexagonal pyramid terminating the prism were distinctly seen. Considering, however, these crystals as belonging to the trimetric system, in accordance with the gen erally received opinion of mineralogists as to crystals of the mica family, all of which present essentially the same crystallographic characters, we must regard the six-sided prism of cryophyllite as formed by the union of the planes I of the rhombic prism with the brachydiagonal basal planes . The plane of the optical axes coincides with the shorter diagonal of the rhomb base, and the crystals are frequently much elongated in this direction, so that the form of the cleavage face was as shown in the accompanying figure, the line ab indicating the position of the plane of the optical axes. Further more, the crystals were frequently twinned together on the plane it, and it was observed that in such cases the planes Vol. xlii, No. 124, July, 1866. of cleavage of the two crystals were absolutely coincident, proving that the rhombic prisms are rectangular and not oblique, as De Senarmont has previously shown to be true of other crystals of the mica family. The color of cryophyllite in axial directions is dull emerald green, not unlike glass colored with protoxyd of iron, and so deep that the lamina are opaque unless quite thin, but like other colored micas it is dichrous and appears brownish-red in the direction of the lateral axes. The color of the streak is light gray with a tint of green. The luster is brilliant on the cleavage face inclining to resinous. The hardness is from 2 to 2-5 and the specific gravity 2.909. Before the blowpipe cryophyllite very easily fuses with some intumescence to a greyish enamel bead, and it even fuses in flakes of considerable size in the flame of a candle, so that its fusibility is from 15 to 2 of von Kobell's scale. It imparts to the flame of a Bunsen's lamp a most brilliant lithia reaction, and by examining the colored flame with a spectroscope the presence of potassium, sodium and rubidium may also be readily discovered. The amount of sodium however must be exceedingly small as it does not sensibly modify the lithia flame as seen by the naked eye, and the same is true to a still greater degree of rubidium. The presence of rubidium is best recognized by mixing the pulverized mineral with pure pulverized sulphate of lime, exposing a small bead of this mixture supported by a loop of fine platinum wire to the flame of a gas blowpipe and examining the flame with a spectroscope. The characteristic double blue line of rubidium is then seen very distinctly for a few moments, but soon disappears. No trace of cæsium could be discovered, either by the mode of experimenting just described or by examining the platinum salt obtained in the course of the analysis, by the partial precipitation of the alkalies with chlorid of platinum. Heated alone in a closed glass tube cryophyllite slightly changes color, but gives no sublimate, although when heated in the same with bisulphate of potash it gives a strong reaction of fluorine. When in fine powder, it is completely decomposed after some time even by the dilute mineral acids, the silica separating as a fine powder. From this description it is evident that in its mineralogical characters cryophyllite closely resembles other members of the mica family, especially the lepidolites, dif fering from these chiefly in the ease with which it is decomposed by acids and in a somewhat greater fusibility. Method of Analysis. In analyzing the mineral the fine powder was decomposed in a closed glass flask in the same way as described in my paper on Danalite, using dilute hydrochloric or sulphuric acids as the case required. Each complete analysis was made with three portions of the same powder. From the first |