Beiträge zur Fixsternenkunde. 1. Methode, die scheinbaren Durchmesser sammtlicher Fixsterne in Bogenmass zu bestimmen. 2. Gedanken über die Möglichkeit, die absoluten Entfernungen und absoluten Durchmesser der Fixsterne auf rein optischem Wege zu bestimmen. 3. Methode, die Geschwindigkeit, mit der die Lichtmolekel bei der Wahrnehmung der Fixsterne am Orte des Beobachters schwingen, zu bestimmen.

Prague: Gottlieb Haase & Sons, 1846.

First edition, very rare separately-paginated offprint, of this important complement to Doppler’s epoch-making discovery in 1842 of the principle named after him. The three articles comprising this offprint contain extensions of the Doppler principle, as well as the first suggestion to use photographic and photometric methods for the determination of the sizes and distances of stars. “Doppler’s scientific fame rests on his enunciation of the Doppler principle, which relates the observed frequency of a wave to the motion of the source or the observer relative to the medium in which the wave is propagated. This appears in his article ‘Ueber das farbige Licht der Doppelsterne und einiger anderer Gestirne des Himmels’ (read 25 May 1842). The correct elementary formula is derived for motion of source or of observer along the line between them; the extension to the motion of both at the same time appears in an article of 1846 … Since then the technique has provided the science of astrophysics with one of its most important tools for measuring the size and the structure of the universe” (DSB). “From 1845 onwards, Doppler deals intensely with photography and photometry, which in fact constitute the tools of evidence that would reach great importance for the confirmation and applications of his principle, yielding fresh impetus to astronomy to such an extent as only the invention of the telescope had previously brought about. In his paper written in 1846, Doppler proposes to use photography, photos then still being named daguerreotypes, for measuring applications since ‘the iodized Daguerre plate exhibits a considerably higher susceptibility to light than out human eye.’ This unpretentious formulation anticipates the idea for an instrument, called a measuring-projector of spectra, that until the mid-20th century was being used for photometric evaluation of photographic data that were recorded by spectrographs. Yet, in 1846, Doppler constructs a simple photometer to determine the pattern and distribution of brightness of very remote so-called fixed stars. This in fact was carried out at a time 15 years prior to the leading work of Zöllner and four years prior to Humboldt’s anticipating remark: ‘Every laborious work concerning the relative brighness of stars will not gain in reliability until one is finally able to replace the classification according to mere estimation with measuring methods that are based on the progress of modern optics. The feasibility of attaining such a goal is not to be doubted by astronomers and physicists’” (Schuster, p. 77). OCLC lists 6 copies (BL, Edinburgh, Strasbourg, Heidelberg, Basel, Hamburg). Only one copy located in auction records (in a modern binding without wrappers).

Born in Salzburg, Christian Doppler (1803-53) attended the Polytechnic Institute in Vienna from 1822 to 1825, but returned to Salzburg and pursued his studies privately. He completed the Gymnasium and subsequent philosophical courses in an unusually short time, while tutoring in mathematics and physics. From 1829 to 1833 he was employed as a mathematical assistant in Vienna, and wrote his first papers on mathematics and electricity. In 1835 Doppler was on the point of emigrating to America; he had sold his possessions and had reached Münich when he obtained a position as professor of mathematics and accounting at the State Secondary School in Prague. In 1841 he became professor of elementary mathematics and practical geometry at the State Technical Academy there, during the tenure of which he enunciated his famous principle (1842). He had become an associate member of the Königliche Böhmische Gesellschaft der Wissenschaften in Prague in 1840 and was made a full member in 1843.

“Apart from that annus mirabilis 1842, the period that lasted for only half a year, from January until June 1846, will doubtless remain the most productive period in the life of the physicist. During these few months, Doppler delivered at the sessions of the Prague Society of Science an unbelievable eleven scientific treatises” (Hiebl & Musso, p. 26). It was during this period of intense scientific activity that Doppler presented to the Königliche Böhmische Gesellschaft der Wissenschaften the three papers contained in the present offprint.

The single theme linking these three contributions is Doppler’s desire to measure the sizes and distances of the fixed stars. He begins the first article, Methode, die scheinbaren Durchmesser sammtlicher Fixsterne in Bogenmass zu bestimmen’ [‘Methods of determining the apparent diameter of the fixed stars in radians’] by noting that, although this problem may be beyond our present abilities to solve, nevertheless it is worth making the attempt as in doing so useful discoveries and techniques may appear (he compares the situation with the failed attempts to create perpetual motion, or to square the circle). He notes that, although Bessel has proposed the use of parallax to determine stellar distances, using the Earth’s orbit as a baseline, this method cannot succeed for any but the nearest stars. Doppler then suggests a new method of determining stellar sizes and distances which he accepts is only provisional and will require refinement. He makes the assumption that most stars have approximately the same absolute luminosity because of their common origin. The different apparent luminosities of stars are therefore due to their different sizes and distances from us. Doppler then describes a simple instrument that allows an observer to view simultaneously two stars that are nearby in the sky. By fitting the two eye-openings with variable apertures, they can be adjusted until the apparent luminosities of the two stars are perceived to be the same. This allows the relative apparent luminosities of the stars to be found, and hence their relative size/distance, i.e., angular diameter in radians. To determine the actual angular diameter of a star, Doppler suggests using his method to compare a nearby star, say Sirius, with the Sun (using a projection method rather than direct observation to avoid blinding the observer), the angular diameter of the Sun being known. This would allow one to determine the angular diameter of Sirius, and from that the angular diameter of other distant stars could be found.

It is in the second paper, ‘Gedanken über die Möglichkeit, die absoluten Entfernungen und absoluten Durchmesser der Fixsterne auf rein optischem Wege zu bestimmen’ [‘Thoughts on the possibility of determining the absolute distances and absolute diameters of the fixed stars by purely optical means’], that Doppler first suggests the use of photography in astronomical observation. We quote from an anonymous review of the article in TheCivil Engineer and Architect's Journal (vol. 10 (1847), p. 102).

“Professor Doppler of Prague says that for the ascertaining of the diameters of the fixed stars, the telescope has been hitherto mainly depended upon, and that the instrument has been so far improved as it possibly ever can and will. The susceptibility of the human eye for the the minutest objects has been hitherto considered paramount; but M. Doppler asserts that the susceptibility of the human retina is surpassed many thousands of times by that of a prepared (iodized) Daguerreotype plate. Physiological experiments have shown that objects which appear to us under an angle of vision less than 50 or 40 inches are no more seen in extenso, but as amorphous simple points. On the other hand, physiological researches of such men as Müller, Weber, &c., have shown that the diameter of one of the nerve-papillae of the retina is no more than 1/2400 or 1/3000 of an inch. But, comparing the susceptibility of the retina papillae with the microscopic experiments made with Daguerre’s plates, it will follow that the single globules of mercury are of such extreme minuteness that they only become visible by an 800-fold magnifying power; and, therefore, that on the space of a Daguerre plate, equal to one retina papilla, more than 40,000 single minute globules of precipitated mercury are to be met with. Each of these is capable of producing the image of well-defined objects – which would merge on the human retina in single, indiscernible luminary points. Thence, Professor Doppler argues, that Daguerre’s plates are 40,000 times more susceptible for impressions than the human eye.

“Considering, moreover, that a great improvement in microscopes is very probable, M. Doppler thinks that instead of telescopes, microscopes will come into use. At the ecat point, therefore, where the image of a celestial body is formed before the object lens of a telescope of considerable length, an apparatus is to be placed whereby a silver plate (iodized, brome-iodized, or otherwise prepared) can be securely inserted. As the place of the images is the same for all celestial objects, a plate of a well-defined, constant thickness can be inserted with great accuracy. In this way, Dauguerreotype images of all, even the smallest, fixed stars can be obtained, if (as is to be supposed) the light will be sufficient to affect the plates. It is also to be taken into account that the images of the fixed stars, obtained by an object lens of from 10 to 12 inches, will possess a light 10,000 times stronger than they present to the naked eye. Plates thus affected are to be treated with mercurial vapours and laved and then viewed by a good microscope. As these images will have been magnified (through the action of an object-lens – say of 110 inches focal length) to the extent of 14 times their natural appearance, and being again magnified 1,200-fold, the angle of vision under which they are now to be viewed will have been increased 16,800-fold.”

Doppler concludes this paper by expressing the hope that, by means of the greatly increased sensitivity which the use of his proposed photographic and photometric methods would provide, it may become possible to determine the apparent angular diameters of the fixed stars. Although this has not proved to be possible, the daguerreotype process being too slow to record all but the brightest objects, “photography revolutionized the field of professional astronomical research, with longtime exposures recording hundreds of thousands of new stars and nebulae that were invisible to the human eye, leading to specialized and ever larger optical telescopes that were essentially big cameras designed to record light using photographic plates” (Wikipedia).

The third part, ‘Methode, die Geschwindigkeit, mit der die Lichtmolekel bei der Wahrnehmung der Fixsterne am Orte des Beobachters schwingen, zu bestimmen’ [‘Methods of determining the speed with which the light molecules vibrate in the perception of the fixed stars at the location of the observer’] returns to Doppler’s principle. Nowadays, discussions of the Doppler effect focus on the change of frequency of light (or other wave phenomena) due to the motion of the source or observer. But in his original formulation, Doppler also discussed the effect of this motion on the observed intensity of light. “In Doppler’s summary of his theory [in the 1842 paper], he said: ‘If a luminous object, regardless of whether it radiates light or is illuminate by it, is moving directly towards or away from the human eye with speed related to the speed of light, this movement necessarily results in a change of the color and intensity of the light … When the speed of a moving star changes, its color and intensity also change … nothing is easier to comprehend than that the distance and time interval between two successive waves must become shorter for an observer who is hurrying towards the oncoming waves and longer if he is moving away, and similarly, in the first case the intensity of the wave is stronger and in the second it must necessarily decrease’” (Mark, pp. 63-64). In the 1842 paper Doppler did not address the effect of motion on intensity in a quantitative theoretical manner, and in the present article he remedies that omission. At the beginning of the work he assumes that the source is stationary and the observer is in motiom; the case of a moving source is treated at the end of the paper.

Doppler’s analysis is based on his conception of the ether as composed of ‘ether molecules’, which are di-atomic, a combination of positively and negatively charged ‘ether atoms’ which themselves have no independent existence. The propagation of light takes place by means of oscillations of the ether molecules caused by compression and rarefaction of the ether. These oscillations of the ether molecules can cause oscillations of material molecules when the light impinges on a solid body, for eample when light impinges on the retina, and it is as a result of these secondary oscillations that the light is observed. In this article Doppler develops a mathematical theory of the oscillations of the ether molecules and the effect on these oscillations of the motion of the source or observer.

In modern (non-relativistic) treatments of this problem it is shown that when a light source moves towards an observer with speed v, the observed frequency increases by the factor

1 + v/c,

where c is the speed of light (this was Doppler’s result in the 1842 paper), and that the intensity increases by the fourth power of this factor.

The offered work is a separately-paginated offprint from Abhandlungen der königlichen böhmischen Gesellschaft der Wissenschaften, von den Jahren 1845-1846, V. Folge, Band 4, pp. 621-646. The journal volume carries the imprint ‘Prague: Calve, 1847,’ so the offprint preceded the journal appearance.

Hiebl & Musso. Christian Doppler: Life and Work, Principle and Applications: Proceedings of the Commemorative Symposia in 2003, Salzburg, Prague, Vienna, Venice, 2007. Mark, Optokinetics: A New System of Optics, 2011. Schuster, Moving the Stars: Christian Doppler, His Life, His Works and Principle, and the World After. 2005.

4to (280 x 218 mm), pp. [3], 4-26, with one lithographed plate. Original printed wrappers. Very fine.

Item #4936

Price: $3,500.00

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