HELIOMETER (from Gr. ἥλιος, sun, and μέτρον, a measure), an instrument originally designed for measuring the variation of the sun’s diameter at different seasons of the year, but applied now to the modern form of the instrument which is capable of much wider use. The present article also deals with other forms of double-image micrometer.
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| Fig. 1. | Fig. 2. |
The discovery of the method of making measures by double images is stated to have been first suggested by O. Roemer about 1768. But no such suggestion occurs in the Basis Astronomiae of Peter Horrebow (Copenhagen, 1735), which contains the only works of Roemer that remain to us. It would appear that to Servington Savary is due the first invention of a micrometer for measurement by double image. His heliometer (described in a paper communicated to the Royal Society in 1743, and printed, along with a letter from James Short, in Phil. Trans., 1753, p. 156) was constructed by cutting from a complete lens abcd the equal portions aghc and acfe (fig. 1). The segments gbh and efd so formed were then attached to the end of a tube having an internal diameter represented by the dotted circle (fig. 2). The width of each of the portions aghc and acfe cut away from the lens was made slightly greater than the focal length of lens × tangent of sun’s greatest diameter. Thus at the focus two images of the sun were formed nearly in contact as in fig. 3. The small interval between the adjacent limbs was then measured with a wire micrometer.
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| Fig. 3. |
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| Fig. 4. |
Savary also describes another form of heliometer, on the same principle, in which the segments aghc and acfe are utilized by cementing their edges gh and ef together (fig. 4), and covering all except the portion indicated by the unshaded circle. Savary expresses preference for this second plan, and makes the pertinent remark that in both these models “the rays of red light in the two solar images will be next to each other, which will render the sun’s disk more easy to be observed than the violet ones.” This he mentions “because the glasses in these two sorts are somewhat prismatical, but mostly those of the first model, which could therefore bear no great charge (magnifying power).”
A third model proposed by Savary consists of two complete lenses of equal focal length, mounted in cylinders side by side, and attached to a strong brass plate (fig. 5). Here, in order to fulfil the purposes of the previous models, the distance of the centres of the lenses from each other should only slightly exceed the tangent of sun’s diameter × focal length of lenses. Savary dwells on the difficulty both of procuring lenses sufficiently equal in focus and of accurately adjusting and centring them.
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| Fig. 5. |
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| Fig. 6. |
In the Mém. Acad. de Paris (1748), Pierre Bouguer describes an instrument which he calls a heliometer. Lalande in his Astronomie (vol. ii. p. 639) mentions such a heliometer which had been in his possession from the year 1753, and of which he gives a representation on Plate XXVIII., fig. 186, of the same volume. Bouguer’s heliometer was in fact similar to that of Savary’s third model, with the important difference that, instead of both object-glasses being fixed, one of them is movable by a screw provided with a divided head. No auxiliary filar micrometer was required, as in Savary’s heliometer, to measure the interval between the limbs of two adjacent images of the sun, it being only necessary to turn the screw with the divided head to change the distance between the object-glasses till the two images of the sun are in contact as in fig. 6. The differences of the readings of the screw, when converted into arc, afford the means of measuring the variations of the sun’s apparent diameter.
On the 4th of April 1754 John Dollond communicated a paper to the Royal Society of London (Phil. Trans., vol. xlviii. p. 551) in which he shows that a micrometer can be much more easily constructed by dividing a single object-glass through its axis than by the employment of two object-glasses. He points out—(1) that a telescope with an object-glass so divided still produces a single image of any object to which it may be directed, provided that the optical centres of the segments are in coincidence (i.e. provided the segments retain the same relative positions to each other as before the glass was cut); (2) that if the segments are separated in any direction two images of the object viewed will be produced; (3) that the most convenient direction of separation for micrometric purposes is to slide these straight edges one along the other as the figure on the margin (fig. 7) represents them: “for thus they may be moved without suffering any false light to come in between them; and by this way of removing them the distance between their centres may be very conveniently measured, viz. by having a vernier’s division fixed to the brass work that holds one segment, so as to slide along a scale on the plate to which the other part of the glass is fitted.”
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| Fig. 7. |
Dollond then points out three different types in which a glass so divided and mounted may be used as a micrometer:—
“1. It may be fixed at the end of a tube, of a suitable length to its focal distance, as an object-glass,—the other end of the tube having an eye-glass fitted as usual in astronomical telescopes.
“2. It may be applied to the end of a tube much shorter than its focal distance, by having another convex glass within the tube, to shorten the focal distance of that which is cut in two.
“3. It may be applied to the open end of a reflecting telescope, either of the Newtonian or the Cassegrain construction.”
Dollond adds his opinion that the third type is “much the best and most convenient of the three”; yet it is the first type that has survived the test of time and experience, and which is in fact the modern heliometer. It must be remembered, however, that when Dollond expressed preference for this third type he had not then invented the achromatic object-glass.
Some excellent instruments of the second type were subsequently made by Dollond’s eldest son Peter, in which for the “convex glass within the tube” was substituted an achromatic object-glass, and outside that a divided negative achromatic combination of long focus. In the fine example of this instrument at the Cape Observatory the movable negative lenses consist of segments of the shape gach and acfe (fig. 1) cut from a complete negative achromatic combination of 814 in. aperture and about 41 ft. focal length, composed of a double concave flint lens and a double convex crown. This was applied to an excellent achromatic telescope of 314 in. aperture and 42 in. focal length. In this instrument a considerable linear relative movement of the divided lens corresponds with a comparatively small separation of the double image, so that simple verniers reading to 11000 in. are sufficient for measurement.
With one of these instruments of somewhat smaller dimensions (telescope 212 in. aperture and 312 ft. focus), Franz von Paula Triesnecker made a series of measurements at the observatory of Vienna which has been reduced by Dr Wilhelm Schur of Strasburg (Nova Acta der Ksl. Leop.-Carol. Deutschen Akademie der Natursforscher, 1882, xlv. No. 3). The angle between the stars ζ and g Ursae maj. (708″.55) was measured on four nights; the probable error of a measure on one night was ±0″.44. Jupiter was measured on eleven nights in the months of June and July 1794; from these measures Schur derives the values 35″.39 and 37″.94 for the polar and equatorial diameter respectively, at mean distance, corresponding with a compression 1/14.44. These agree satisfactorily with the corresponding values 35″.21, 37″.60, 1/15.59 afterwards obtained by F. W. Bessel (Königsberger Beobachtungen, 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, Schur finds the mass of Jupiter = 1/1048.55 ± 1.45, a result which accords well within the limits of its probable error 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.
Considering the accuracy of these measures (an accuracy far surpassing that of any other contemporary observations), it is somewhat surprising 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 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 possession of Bessel at Königsberg during the time when his new observatory there was being built. In 1812 Bessel measured with it the angle between the components of the double star 61 Cygni and observed the great comet of 1811. He also observed the eclipse of the sun on May 4, 1818. In the discussion of these observations (Königsberger Beobacht, Abt. 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
