MICROMETERS.] 251 35" 21, 37" 60, 1/15 69 afterwards obtained by Bessel (Kb nigsbcrgcr Bcobachtungen, xix. 102). From a series of measures of the angle between Jupiter s satellites and the planet, made in June and July 1794 and in August and September 1795, Scliur finds the mass of Jupiter = , a result which accords perfectly with the received value of the mass derived from modern researches. The probable errors for the measures of one night are 0"-577, 0" 889, 0"-542, 1" 096, for Satellites I., II., III., and IV. respectively. It is probable that Triesnecker deduced the index error from his measures of the diameter of Jupiter, as, in 1794, the measures of diameter are made on the same nights with those of the measures of distance of the satellites, and it is possible that measures of diameter may have been made in 1795 but not pub lished. Considering the accuracy of these measures (an accuracy far sur passing that of any contemporary observations), it is somewhat sur prising that this form of micrometer was never systematically used in any sustained or important astronomical researches, although a number of instruments of the kind were made by Dollond. Probably the last example of its employment is an observation of the transit of Mercury (November 4, 1868) by Mr Mann, at the Royal Observatory, Cape of Good Hope (Monthly Notices R. A. S., vol. xxix. p. 197-209). The most important part, however, which this type of instrument seems to have played in the history of astronomy arises from the fact that one of them was in the posses sion of Bessel at Konigsberg during the time when his new obser- Bessel s vator y tnere Avas being built. In 1812 Bessel measured with it the observa- an S^ e between the components of the double star 61 Cygni and tions. Frauu- hofer. observed the great comet of 1811. He also observed the eclipse of the sun on May 4, 1818. In the discussion of these observations (Kb nigsberger Beobacht., Abth. 5, p. iv) he found that the index error of the scale changed systematically in different position angles by quantities which were independent of the direction of gravity relative to the position angle under measurement, but which depended solely on the direction of the measured position angle relative to a fixed radius of the object-glass. Bessel attributed this to non-homogeneity in the object-glass, and determined with great care the necessary corrections. But he was so delighted with the general performance of the instrument, with the sharpness of the images, and the possibilities which a kindred construction offered for the measurement of considerable angles with micrometric accuracy, that he resolved, when he should have the choice of a new telescope for the observatory, to secure some form of heliometer. Nor is it difficult to imagine the probable course of reasoning which led Bessel to select the model of his new heliometer. Why, he might ask, should he not select the simple form of Dollond s first type ? Given the achromatic object-glass, why should not it be divided ? This construction would give all the advantage of the younger Dollond s object-glass micrometer and more than its sharp ness of definition, without liability to the systematic errors which may be due to want of homogeneity of the object-glass ; for the lenses will not be turned with respect to each other, but, in measurement, will always have the same relation in position angle to the line joining the objects under observation. It is true that the scale will require to be capable of being read with much greater accuracy than nnnrth of an inch for that, even in a telescope of 10 feet focus, would correspond with 2" of arc. But, after all, this is no practical diffi culty, for screws can be used to separate the lenses, and, by these screws, as in a Gascoigne micrometer, the separation of the lenses can be measured ; or we can have scales for this purpose, read by microscopes, like the Troughton 1 circles of Piazzi or Pond, or those of the Carey circle, with almost any required accuracy. Whether Bessel communicated such a course of reasoning to Fraunhofer, or whether that great artist arrived independently at like conclusions, we have been unable to ascertain with certainty. The fact remains that before 1820 2 Fraunhofer had completed one or more of the five heliometers (3 inches aperture and 39 inches focus) which have since become historical instruments. In 1824 the great Konigsberg heliometer was commenced, and it was com pleted in 1829. To sum up briefly the history of the heliometer. The first appli cation of the divided object-glass and the employment of double images in astronomical measures is due to Savary in 1743. To Bouguer in 1748 is due the true conception of measurement by double image without the auxiliary aid of a filar micrometer, viz., by changing the distance between two object-glasses of equal focus. To Dollond in 1754 we owe the combination of Savary s idea of the divided object-glass with Bouguer s method of measurement, and the construction of the first really practical heliomoters. To Fraunhofer, some time not long previous to 1820, is due, so far as we can ascertain, the construction of the first heliometer with an 1 The circles by Ruichenbaeh, then almost exclusively used in Germany, were read by Temiers only. 2 The diameter of Venus was measured with one of these hcliometcrs at the Observatory of Bres .iu by Drundes in 1820 (Berlin Jahrbuch, 1824, p. 1(>4) achromatic divided object-glass, i.e., the first heliometer of the modern type. Double-Image Micrometers v-ith Divided Lenses. Various micrometers have been invented besides the heliometer for measuring by double image. Ramsden s dioptric micrometer consists of a divided lens placed in the conjugate focus of the inner most lens of the erecting eye-tube of a terrestrial telescope. The inventor claimed that it would supersede the heliometer, but it has never done anything for astronomy. Dollond claims the independ ent invention and first construction of asimilar instrument(Pearson s Practical Astronomy, vol. ii. p. 182). Of these and kindred instru ments only two types have proved of practical value. Amici of Modena (Mem. Soc. Ital., xvii. (1815) pp. 344-359) describes a micrometer in which a negative lens is introduced between the eye-piece and the object-glass. This lens is divided and mounted like a heliometer object-glass ; the separation of the lenses produces the required double image, and is measured by a screw. Dawes has very successfully used this micrometer in conjunction with a filar micrometer, and finds that the precision of the measures is in this way greatly increased (Monthly Notices, vol. xviii. p. 58, and Mem. R. A. S., vol. xxxv. p. 147). In the improved form 3 of Airy s divided eye-glass micrometer (Mem. R. A. S., vol. xv. pp. 199-209), the rays from the object- glass pass successively through lenses as follows. Lens. Distance from next Lens. Focal Length. a. An equiconvex lens b. 5 11 1 1 The lens b is divided, and one of the segments is moved by a micrometer screw. The magnifying power is varied by changing the lens a for another in which p has a different value. The magni fying pow r er of the eye-piece is that of a single lens of focus = ^p. In 1850 Valz pointed out that the other optical conditions could be equally satisfied if the divided lens were made concave instead of convex, with the advantage of giving a larger field of view (Monthly Notices, vol. x. p. 160). The last improvement on this instrument is mentioned in the Report of the R. A. S. council, February 1865. It consists in the introduction by Simms of a fifth lens, but no satisfactory descrip tion has ever appeared. There is only one practical published 4 investigation of Airy s micrometer that is worthy of mention, viz., that of Kaiser (Annalcn dcr Stcrmvarte in Leiden, iii. pp. 111-274). The reader is referred to that paper for an exhaus tive history and discussion of the instrument. 5 It is somewhat surprising that, after Kaiser s investigations, observers should con tinue, as many have done, to discuss their observations with this instrument as if the screw-value were constant for all angles. Steinheil(./OMTOaZ Savant dcMunich, 28th February 1843)describes Stein- a " heliometre-oculaire " which he made for the great Pulkowa re- lieil s fractor, the result of consultations between himself and the elder ocular Struve. It is essentially the same in principle as Amici s micro- micro meter, except that the divided lens is an achromatic positive instead meter, of a negative lens. Struve (Description dc I Obscrvatoire Central de Pulkowa, pp. 196, 197) adds a few remarks to Steinheil s descrip tion, in which he states that the images have not all desirable precision, a fault perhaps inevitable in all micrometers with divided lenses, and which is probably in this case aggravated by the fact that the rays falling upon the divided lens have consider able convergence. He, however, successfully employed the instru ment in measuring double stars, so close as 1" or 2", and using a power of 300 diameters, with results that agreed satisfactorily amongst themselves and with those obtained with the filar micro meter. If Struve had employed a properly proportioned double 3 For description of the earliest form see Cambridge Phil. Trans., vol. ii., and Greenwich Observations, 1840.
- We understand that a very thorough investigation of Airy s double-image
micrometer used by Dr Copeland at Mauritius on Lord Lindsay s expedition has been made by him, and will soon be published. 5 Dawes (Monthly Notices. January 1858, and Mem. R. A. S., vol. xxxv. p. 150) has suggested and used a valuable improvement for producing round images, instead of the elongated images which are otherwise inevitable when the rays pass through a divided lens of which the optical centres are not in coincidence, viz., " the introduction of a diaphragm having two circular apertures touching each other in a point coinciding with the line of collimation of the telescope, and the diameter of each aperture exactly equal to the semidiameter of the cone of rays at the distance of the diaphragm from the focal point of the object-glass." Practically the difficulty of making these diaphragms for the different powers of the exact required equality is insuperable; bur, if the observer is content to lose a certain amount of light, we see no reason why they may not readily be made slightly less. Dawes found the best method for the purpose in question was to limit the aperture of the object-glass by a diaphragm having a double circular aperture, placing the line joining the centres of the circles approximately in the position angle under measurement. Dawes successfully employed the double circular aperture also with Amici s micrometer. The present writer has success fully used a similar plan in measuring position angles of a. Centauri with the helio meter, viz., by placing circular diaphragms on the two segments of the cbject-
glass.