HELIOMETEK.] MICEOMETER 255 following) for the elimination of the effect of flexure on the position angles. There is very little left to criticize in this instrument. It embraces the results of all knowledge and experience on the subject to the present time. In one point, however, modern heliometers have a disadvantage compared with the older forms. A great advance in accuracy was, no doubt, made when the screw was abandoned as a means both of moving and measuring the displace ment of the slides. 1 But it is obviously much quicker to read and record the indication of one screw-head than to bisect two or four scale-divisions and enter the corresponding readings. Auwers, in his researches on the parallax of 61 Cygni, 2 was able, with the Kb nigsberg heliometer, to make forty pointings in about an hour ; it is quick work to make sixteen pointings (reading two divisions on each scale at each pointing) with the modern heliometer in the same time, when attention is paid to the desirable reversals of the segments and of the position circle and the resettings in right ascension and declination. Now time during opportunities of good definition (or otherwise) 3 is too precious to be sacrificed, if it can be saved even by ten-fold labour afterwards. Carrington 4 has suggested the possible use of photography to record the readings of astro nomical circles, and since his day "Swan lights" and "sensitive dry plates" seems to have brought his suggestion within the range of practice. A special microscope, fitted with an aplanatic photo graphic objective and a well-contrived carrier, might be made automatically to expose a different part of a narrow dry plate, by mere pressure or turning of a button after each bisection. Each plate might easily record the sixteen bisections which constitute a complete measure of two pairs of stars (as in a parallax determina tion). As it is only necessary to photograph two divisions of each scale, the photographic enlargement of these divisions need only be limited by the sensitiveness of the plates and the power of the illumination to produce a picture in a conveniently short space of time. The plates employed at night could be conveniently developed the following day and measured with a special apparatus at any convenient time and with almost any desired accuracy. Were such a system reduced to practice it would at least double, perhaps treble, an observer s possible output of work. Gill has introduced a powerful auxiliary to the accuracy of helio meter measures in the shape of a reversing prism placed in front of the eye-piece, between the latter and the observer s eye. If measures are made by placing the image of a star in the centre of the disk of a planet, the observer may have a tendency to do so systematically in error from some acquired habit or from natural astigmatism of the eye. But by rotating the prism 90 the image is presented entirely reversed to the eye, so that in the mean of measures made in two such positions personal error is eliminated. Similarly the prism may be used for the study and elimination of personal errors depending on the angle made by a double star with the vertical. The best plan of mounting such a prism has been found to be the following. I , I 2 (fig. 37) are the eye lens and field lens respectively of a Merz positive eye-piece. In this construction the lenses are much closer together and the diaphragm for the eye is much farther from the lenses than in Ramsden s eye-piece. The prism Fig. 37. p is fitted accurately into brass slides (care has to be taken in the construction to place the prism so that an object in the centre of the field will so remain when the eye-piece is rotated in its adapter). There is a collar, clamped by the screw at S, which is so adjusted that the eye-piece is in focus when pushed home, in its adapter, to this collar. The prism and eye-piece are then rotated together in the adapter. On the theory of the heliometer and its use consult Bessei, Aslronomische Untersuchungen, vol. i.; Hansen, Ausfiihrliche Methode mil ilem Fraunhoferschen Heliometer anzitstellcn, Gotha, 1827; Chauvenet, Spherical and Practical Astro nomy, vol. ii. pp. 403-436. Philadelphia and London, 1876; Seeiiger, Theorie des Heliometers, Leipsic, 1877 ; Lindsay and Gill, Dunecltt Publications, vol. ii., Dunecht (for private circulation), 1877; Gill, Memoirs of the Royal Astronomical Society, vol. xlvi. pp. 1-172. Micrometers which Involve the Employment of tlie Diurnal Motion. Advantage is often taken of the diurnal motion to measure the relative positions of stars. The varieties of reticules and scales that have been employed are far too numerous even for mention in detail. The, following are the means and methods by which most work has been done, and they are typical of all the others. In the focus of his meridian telescope Lacaille had a brass diaphragm in 1 Screws, as Auwers s discussion of Bessel s observations (" Parallax e von 61 Cygni," Abhandlungen der KQnigl. Akad. der Wissenfchaften zu ISerlin, 1868) has shown, are apt to wear and change their errors. It is, besides, undesirable to apply force and friction to a delicate standard of measure. 2 Astron. Xuchrichten, No. 1416. 3 For example, in determining the diurnal parallax of a planet the most favourable conditions are limited on the one hand by the uncertainties of refrac tion at large zenith distances, and on the other by the small parallax factors of small zenith distances. It would probably be best to secure all the observations between 50 and 60 ZD, and this would only be possible with special facilities for reading the scales. 4 Monthly Notices R. A. S., vol. xxx. p. 46. which was cut a hole, having parallel, sharp, straight edges of the La- shape shown in fig. 38. The longer diagonal of the rhomboid caille s so formed was at right angles, and the shorter parallel, to the rhom- diurnal motion. The method of observation consisted in noting bold, the instant of ingress and egress of each star which presented itself. The mean of the times thus noted for each star gave the time of its transit over the imaginary line ab, whilst the difference between the instant of ingress and that of egress (converted into arc by the known approximate declination) gave the length of the chord traversed by the star parallel to the imaginary line cd. Hence (the dimensions of the rhomboid being known) the differ- c- ence of the star s declination from the line cd became known (the ob server was of course careful to note whether the star passed to north or south of cd). Thus every star that crossed the field was observed, all their right ascensions were referred to the clock-time of passing ab, and all their declinations to that of cd ; hence their mutual differ ences of right ascension and declination were known. In this way, in the short space of ten months, Lacaille observed nearly ten thousand stars at the Cape of Good Hope in the years 1751-52. 5 Fraunhofer s ring micrometer consists of a ring of steel, very truly Ring mi- turned, mounted in a hole cut in a circular disk of glass. The ring is crometer placed in the focus of a telescope, and viewed by a positive eye-piece. The observer notes the instants when the two objects enter and emerge from each side of the ring. The only data required for com puting the difference of right ascension and declination of the two objects are the times above mentioned, the diameter of the ring, and the approximate declination of one of the objects. The latter is always known. The methods of determining the former and of reducing the observations are to be found in every work on practical astronomy. The ring micrometer has been largely used in observ ing comets. Argelander, in making his famous survey of the northern heavens, 6 Arge- employed a semicircle of glass, the straight edge of which (truly lander s ground) crosses the centre of the field of view at right angles to the scale, diurnal motion of the stars. Differences of right ascension were directly observed at this edge, whilst differences of declination were noted by strong dark lines drawn at right angles to the edge at each 10 of arc. A telescope of 3 inches aperture with a magnifying power of 10 diameters commanded a field of 3 20 in declination. One observer was placed at the telescope, another at the clock. The telescope observer marked the instant when the star touched the glass edge, by calling sharply the word "eight" or "nine," &c., which also indicated the magnitude ; the same observer also noted and recorded the reading of the declination scale (where the star crossed it), without removing his eye from the telescope. The clock observer wrote down the magnitude called out by the telescope observer, and the instant by the clock when the word was given. The two records were then compared after the observations of the night were over. In this way Schbnfeld and Krueger (Argelander s assistants) observed and catalogued about three hundred thousand stars. The probable error of an observation is about 7 sec. in right ascension and "4 in declination. Bond 7 employed a very similar arrangement, differing only from Bond s Argelander s in having the scale cut on a sheet of transparent mica mica nnrtfth of an inch in thickness. Very oblique illumination was declino- employed, and the divisions and figures were seen bright upon a meter, dark background. The range of declination was limited to 10 , the scale was divided to 10", the right ascensions were observed by chronographic registration, and the great refractor of the Cambridge II. S. Observatory (with an aperture of 15 inches and power of 140) was employed. The probable errors in right ascension and declina tion were found to be 06 sec. in right ascension and 0" 6 in declination results of marvellous accuracy considering the amount of work accomplished in a short time and the faintness (eleven to twelve magnitudes) of the stars observed. We were on the point of criticizing Bond s programme as some- Peters s what too ambitious for realization without cooperation (it would zones, take about twenty-six thousand hours of observing to carry out the scheme for the northern hemisphere alone) when we received from Peters of Clinton, U. S., the first twenty maps of a series which will include the whole of the sky between declination + 30 and - 30. If we consider that all the stars in these maps of the eleventh magni tude or brighter have been observed by a method similar to Bond s, that the enormous additional labour of frequent revision has been undertaken, and all stars visible with a power of 80 in a telescope of 13 inches aperture (about fourteenth magnitude) have been filled in 5 Lacaille, Ccelum Australe Stelliferum, Paris, 1763, and A Catalogue of 9766 Stars, from t/ie Observations of Lucail/e, London, 1847. 6 Atlas des Niird!i<-hen Gestirnffii Ilimmels, Bonn. 1863, Introduction.
7 Annals of the Astronomical Observatory, Harvard College, vol. i. part ii.