Schmidt's Lunar Map

by John Birmingham

Part 1

CLOSELY following the appearance of Lohrmann’s complete sections, edited by Dr. Schmidt, we have this author’s own lunar map published by the Prussian Government. Dr. Schmidt’s great work, which he calls a chart of the lunar mountains, is, like Lohrmann’s, in 25 sections, which would form a map of six French feet diameter, about 6 feet 6 inches English. The sections, however, are intended to remain separate, each one forming a map in itself, graduated at the edges, and they are thus evidently more convenient for reference than if joined together. They are in photo-lithograph, made from the original chart at the office of the Prussian General Staff.

It redounds highly to the honour of his Imperial Highness the Crown Prince of Prussia that it was at his request, and under his auspices, that the publication of the work was undertaken by the Government, which has thus been the means of giving to the world a performance which must be placed among the greatest feats of astronomical science and observation, while it must rank among the most distinguished achievements of German capability and perseverance.

In the volume accompanying the map, Dr. Schmidt gives a history of his labours, which may here be briefly referred to.

In the autumn of 1839, when of the age of 14 years, and at his own home at Eutin in Oldenburg, a copy of Schröter’s work on the Moon came into his hands, and he was so struck with the figures of the shadow-throwing hills and craters, that the effect in a great degree fixed the bias of his after life. His own first observations were made with a small telescope, the work of his father; and with the instrument steadied by a lamp-post, he made his first attempts at sketching. The study of Schröter’s work, together with observing and sketching, now became his chief employment, and it was not long before he had constructed a rough wooden stand for his telescope, which greatly facilitated his observations. At length, owing to the kindness of a gentleman, who noticed the industry of the young astronomer, he procured, early in 1841, the loan of a 4-foot Dollond, with a power of 15 to 20. In July of the same year he saw, for the first time, the Moon in a larger telescope. This was at the Altona Observatory, where Petersen showed him the craters Bullialdus and Gassendi; and now he got a fair idea of the rich abundance of lunar objects, both by his observations with the large instrument, and still more by what he saw in Mädler’s chart, which he found at the observatory. In 1842 he came to Hamburg, and through the goodness of the director of the observatory, he had the use of several telescopes from 1842 to 1845. In 1845 he came to the Bilk Observatory, where he made but little progress in his lunar sketches.

It seems worthy of remark that the scientific ardour of the worthy director of this observatory, Herr Benzenberg, was just sufficient to allow the young astronomer the use of only a wretched instrument, while the principal telescope was rigidly tabooed, so that its outward good looks and polish might not suffer by handling! Very different was the conduct of those able men, Galle and Bruhns, who subsequently placed the great Berlin refractor at Herr Schmidt’s disposal on several occasions. From 1845 to 1853 he was employed at the Bonn Observatory, where, on account of other work, he was not able to pursue his lunar studies in the usual manner, though still he succeeded in making many useful sketches. From 1853 to 1858, at the Olmütz Observatory, he made not many drawings, but numerous micrometrical measurements. In the interim, in March 1855, he sketched at the great Roman refractor, and in April at the observatory at Naples.

On December 2, 1858, Herr Schmidt came into his present position as director of the Athens Observatory, where the condition of things prevented all observing for a whole year, until the 6-foot refractor by Plössl was again set up. From February 1860 to the beginning of 1865 considerable progress was made in lunar observations, although the greater part of the time was occupied with other work.

At length Dr. Schmidt determined to lay down all his fragmentary surveys on a 6-foot map, for the purpose of seeing what parts of the Moon had been neglected in his work, which was principally expended on certain favourite areas. All this time, however, he had no notion of completing any general chart, not seeing that he could ever bring to an end the delineation of the lunar surface as it appeared in the 6-foot Plössl. Simultaneously with this, in 1865, he seems to have begun a map of 1 metre diameter, in 4 sheets, in which the principal objects were laid down from Mädler, and the details of his own observations added in. He now very soon found how much he wanted and how little he possessed; and he was obliged so to extend and repeat his observations, that the older ones became at length of little importance.

Nine years longer were devoted to this work, until, in July 1874, he determined on concluding it, as it became manifest that for an exhaustive representation of all the details of lunar features, visible in a 6-foot refractor, would be required more powers of endurance and a longer lifetime than are allotted to mortals.

Dr. Schmidt seems not very clear on the subject of these maps. For two years, he says, he worked at the first great map already referred to, and added from time to time all the results of the Athens Observations [sic], until it became evident that this would lead to no satisfactory conclusion. The division into four parts was inconvenient for several reasons; and Dr. Schmidt finally determined on a 6-foot map as before, but divided into 25 sections, corresponding with Lohrmann’s, but of course, on double the scale. The graduation was copied from Lohrmann; but it was afterwards discovered that it would have been better if this work had been done specially for the new map. If Lohrmann’s sections contained faults of graduation, on account of the paper suffering unequal pressure in the printing, the errors in Schmidt’s would be somewhat greater, as not alone adopting the faults of the original, but suffering from imperfections of their own, induced by the unequal expansions of the different papers on which the sections were drawn. But this, after all, was of little import. Although the margins of the sections might not close so well together as was desired, still the delineation of details succeeded in the main as intended, and greater faults were happily avoided. The construction of this second map was continued without intermission, except from August 1869 to April 1870, and in July and August in each year, and meanwhile every favourable time for observation was made use of. In 1873 and 1874 the non-topographical part of the map (that is, the colouring) was added.

It was found that in the course of eight or nine years’ working at the sections, the parallel and meridian lines were obliterated, and an attempt in 1874 to restore them was unsuccessful, because in the mean time the surface of the paper had become too rough. Each section has, however, the graduation at the margins, so that approximate positions can be determined. For several considerations, it was decided to write no names in the sections, but to confine them, in number over 500, to the descriptive letterpress.

In 1874 the author brought his chart to the observatory at Berlin, where it excited so much interest that it was determined to publish it under state patronage. At the instance of his Imperial Highness the Crown Prince, the 25 sections were photographed at the General Staff Office, under the direction of Count von Moltke; and Dr. Schmidt, having received proof-sheets in April 1875, was thus assisted in proceeding with the descriptive text, which he had commenced in 1873. Only the observations from 1842 to 1874 have been made available for the chart. The sketches of previous years were considered imperfect, and were rejected.

J. BIRMINGHAM

Part 2

WHILE the author, like Lohrmann and Mädler, adopted a modified style of Lehmann’s method of delineation, it appears that the various declivities of the hills are not represented with angles of inclination so true as they might be. To explain this Dr. Schmidt says that he knew that in process of time his sketched shadings would become faded; and as he was determined, since 1868, to have the work photographed, it seemed necessary to have faint heights and ridges in the Mares much more strongly marked than their real steepness required. Hence the author explains that this chart does not give the correct impression of the individual characters of the lunar mountains which, he admits, are better represented by Mädler. He could easily have made his drawings nearer the truth if he had intended to have the work lithographed; but with photography it was different, and his object was that every feature should be sharply delineated.

The correct representation of the several forms of lunar mountains belongs to a higher department of art, and can have been hitherto but in a few instances attained. With all his industry Lohrmann failed in this design, while he made the ridges too broad, and almost entirely misrepresented the character of the crater walls. Mädler was more fortunate, and his chart contains remarkable illustrations of individual forms. In Schmidt’s chart the shadings present a general uniformity, and the desire to show characteristic differences was sacrificed on account of other considerations. Lunar drawings require for sufficient exactness several repetitions; and to spend the necessary time for a close portraiture of the various objects in a map like Dr. Schmidt’s was obviously out of the question.

With regard to the colouring of the Moon, to show it properly in a topographic chart is impossible; and Dr. Schmidt, like his predecessors, confined himself to representing the grey tints of the flats and several dark spots. Light-rays he shows only in the Mares , and light-spots where they appear within dark areas. By photography alone we can fairly picture the full Moon, where the endless modifications of brightness are beyond the art of the draughtsman. The mountains about the limb occupied Dr. Schmidt’s attention less than the interior formations; and with regard to the former, his map appears as defective as the maps of Lohrmann, and Beer and Mädler, though it is in reality more comprehensive. When the selenographic positions of the limb-mountains are accurately known, they can then, more properly than at present, be included in some future general chart.

Dr. Schmidt adopts the positions of the first and second order from Lohrmann, but he has laid down the intermediate detail altogether from his own measurements. He has excluded all written names from the chart, using only letters and numerals instead; but the nomenclature, old and new, is found in the descriptive text. In this he has omitted all mathematical explanations and formulæ such as appear in the works of Schröter, Lohrmann, and Mädler, as he regards it as essentially no other than a descriptive volume and an index to the objects that he has delineated. He explains, however, the methods of measuring lunar heights; and an original expedient of his own, where, for want of a micrometer, he measured by time , appears especially ingenious, and was well applied in those cases where the shadows ran parallel with the Moon’s motion. Her increase in R.A., which would obviously affect the angle deduced from the time, was, of course, taken into account, and conveniently found in the duration of her meridian passage as it appeared in the ‘Nautical Almanac.’ The heights ascertained by this method number 109 in his list, while he records no less than 2894 as taken with the micrometer; and it may be added that for these results no less than 57,000 observations were made from 1853 to 1858, which, of themselves, would be sufficient to give a fair idea of the untiring patience with which Dr. Schmidt pursued his immense task.

There is no sea-level in the Moon from which to measure the mountain-heights, and the datum-plain must be found in the low lands adjacent. In the method of measuring by shadows, the land at the end of the shadow is taken as level with the base of the mountain. The height is then simply the difference between the land referred to and the summit. The altitude of the Sun above the horizon of the mountain is, of course, a chief factor in the question; and though this may be ascertained by calculation, it is not found practically much more advantageous than the method of directly measuring the distance from the terminator. The uncertainty, however, of defining the true terminator on a broken surface like that of the Moon must then be regarded as presenting a serious obstacle in such measurements; and while these seem sufficiently difficult even in the Mares , it is not easy to see how they can give much hope of a fair approximation in other districts where the serrated outlines of the grouped hills rise in all confusion from the darkness. Mädler recommends those measurements to be taken when the distance of the terminator from the mountain is from 10 to 12 times the length of its shadow, as the uncertainty of the terminator becomes less important according as it recedes from the object. Penumbral effects must render the definition of the true shadow less certain; and altogether it would seem necessary to leave a wide margin for error in those measurements of lunar mountains. Indeed this view seems justified by the various measures of the same objects over and over again, surveyed with inexhaustible diligence by Dr. Schmidt. The differences are startling; and as examples may be given the mountain Huyghens, where one measure gives double the height of another, and Curtius (of which Dr. Schmidt took no less than 80 measures), where the height by one measure over another is more than quadrupled. In cases of such extreme differences, a mean can scarcely be much relied on. Mountains, when precisely on the limb, can be measured by their addition to the angular diameter of the moon at the time of observation. Whatever this diameter is calculated to be, the measure will give the height of the mountain above it. It is plain that a position within or on the other side of the limb must subtract from the apparent height, and great care on this account is necessary. Some of these mountains are of great size, and may be compared to the loftiest of the Andes, or even the Himalayas. Yet their heights over the valleys are not so considerable as the height of the mountains of the earth above the depths of the oceans, though the difference seems not very great, as Schmidt found examples along the eastern limb and at the south pole, where the hills rose about 6000 toises, or over 38,000 English feet, above the adjacent hollows, and Schröter measured heights of 4000 toises and depressions of 3000, showing a difference of level equal to near 45,000 English feet. Yet the aspect of those limb-mountains is not imposing. Only one of them might be compared in form to Chimboraço, while it was far from exhibiting the steepness of Cotopaxi and other volcanoes of the earth. There are no striking elevations on the N.E. or S.W. limbs. On the N.W. there are some visible at times of favourable libration.

Dr. Schmidt gives a list of light-rays , including light-spots and craters surrounded with bright or dark nimbi . The bright borderings will be found to be formed of close and delicate rays, or, at least, they give rise to an efflux of rays that widen as they advance. The nimbus may be of a dark shade, like those surrounding Tycho, Aristarchus, and Dionysius; and it is easy to conceive that its light-reflecting qualities depend on the nature of the stuff ejected by the crater. Dr. Schmidt regards the nimbi as volcanic ash distributed, as in terrestrial eruptions, round about the orifice. The ash may be of various colours; but it is possible, and, in the case of Linné , very probable, that the deposited stuff was in a fluid condition.

When the light-formations are of small extent, they may not be inaptly referred to eruptions similar to those that are seen on the earth. Dr. Schmidt observed, in the innumerable eruptions of the Santorin volcano in 1866 and 1868, that bright-coloured pumice and light grey ash were deposited on the dark surface of the hill in most remarkable radial streaks; and the matter being ejected on all sides, the streaks traced upwards coalesced into a uniform covering towards the summit, while lower down the hill they remained in separate lines of over 100 metres in length and from 2 to 10 metres wide. Here they consisted of the coarser materials, which rolled towards the foot of the mountain. Thus the crater, looked down on from a certain height, would appear surrounded by a bright nimbus, from which issued bright rays or streaks all round.

But who could find analogies between such phenomena and those of lunar volcanos, from which, uninfluenced by hill or valley, the light-rays extend for hundreds of miles, and even, like those from Tycho, to a distance equal to a fourth of the lunar meridian or more? Even recollecting the far inferior gravitating power at the Moon’s surface, and admitting a much greater eruptive force, still much would remain unaccounted for, especially, among other matters, the excentric direction of many of the rays, which, traced backwards, run past on one side of the place from which they must have issued. And to this might be added other anomalies, such as the bendings and interlacings of the lunar streaks like those from Tycho, Kepler, and Copernicus. It has long been known that the rays run indifferently over hill and valley, that they are visible over a bright surface, that with a low Sun they are not apparent, and that they throw no shadow; but to observe them closely would require many years’ study with powerful means. This has never yet been accomplished, and instead of profitable observations, we seem content with hypotheses. Only in the 36th year of his observations did Dr. Schmidt devote some evenings to these features, and then only to make himself acquainted with the principal ones.

Many remarkable forms observed by Schmidt are not found in Mädler, who, on the other hand, has noticed some not seen by the former. With high powers a vast number of minute light-spots may be found, and in many of them, as in Linné, are little craters. It may be conjectured that here are the most recent of lunar formations, and that changes on the surface are by no means to be classed among the most infrequent phenomena. The great ray system must be mapped in detail, if in future times it may be ascertained whether changes occur there or not. It may be considered unlikely that any will be found; but to give up the search on account of such settled opinions, would be only yielding to a deplorable dogmatism, which, under the appearance of critical strictness, has been of little advantage to science.

Dr. Schmidt gives the positions of the light-rays, classed according to the 4 quadrants of Beer and Mädler’s map. He declares, however, the incompleteness of his list, which may be easily improved and enlarged by future observers.

The Rill formations seem specially to have attracted the attention of Dr. Schmidt, who in 1866 published a catalogue of no less than 425 of those objects. In the present work he includes new observations of many of them, and describes several not previously noticed.

The effects of the earth-light on the Moon, or “lumière cendrée,” are described by Dr. Schmidt in a series of interesting observations. None of these served to show the existence of a lunar atmosphere. He devotes a long description to the crater Boussingault when just reached by the terminator. A certain illumination of the interior should be referred either to the refractive power of the gaseous matter within, and reaching above it, or to the earth-light in addition to the direct sunlight striking the inside of the wall and reflected to the crater floor. Dr. Schmidt does not hesitate to adopt the latter explanation.

In comparing Lohrmann’s sections with Mädler’s list of positions in ‘Der Mond’ several differences will be noticed; and Dr. Schmidt seems always to agree with Lohrmann. In section XIV., for instance, the differences in the places of Mason, Plana, Eudoxus, Democritus, and Burg amount to about 2° both in latitude and in longitude. In Plana, indeed, there seems to be a difference of no less than 12° in latitude; but there is an evident misprint of 53° for 43° in Mädler’s list. In Eudoxus there appears a difference of some 5° in longitude.

It is well known to observers how an increase of power will alter the aspect of a lunar formation, breaking up into separate parts and irregular outlines what appears with inferior means as a single, sharply defined mass. For this reason it might be considered that the objects in Schmidt’s map might be more difficult of identification at first sight than those in Lohrmann’s; but it is quite the other way; for, notwithstanding the cutting up by a profusion of detail, the forms, as they appear with moderate powers, are, in general, more speedily recognized in Schmidt’s delineations. Take, for instance, the remarkable district in Section XVI. comprising Herschel II., Horrebow, South, Babbage, Pythagoras, Anaximander, &c. In Schmidt these are all identified at a glance, while in Lohrmann they are by no means so strikingly distinguished. In Lohrmann, and also in Beer and Mädler, South and Babbage are given very imperfectly. In Schmidt’s map it may be observed that the deep shading of the central ridge of Anaximander renders the eastern boundary less prominent than it appears in the telescope, and, indeed, Dr. Schmidt seems to confine the name to the western side of the ridge. Horrebow appears but as a single crater in Lohrmann, while in Schmidt it is nearly divided into two. It is composed of two in fact, with a low dividing lamina, seen only under favourable circumstances. The very remarkable double interior hill in Pythagoras, which has not been overlooked by Schmidt, appeared only single to Lohrmann, and so also to Beer and Mädler.

It may here be noticed that several remains of ancient craters, which have been more or less obliterated by newer formations, seemed to have escaped both observers, though some of them are more or less traceable in the maps.

In Section XXIV. a large ancient crater including Fabricius and Argelander, and extending a long way to the east, is better defined in Schmidt than in Lohrmann; but the latter shows more distinct traces of two similar craters in Section VIII. The more southerly of these, extending from Lexell on the south, goes to Hell on the north-east, and quite includes that crater. It is bounded on the S.E. by a line of small craters given by both Schmidt and Lohrmann, and reaches Walter and Regiomontanus to the W. and N.W. Another ancient crater reaches from Purbachius to the northern end of “Straight Wall,” which runs nearly down its centre. Thebit lies within it on the west. Both these are of great size, like all the primitive craters, and, though not equalling those like the Mare Crisium, they are far larger than Hipparchus. A third smaller, situated between the two, cannot be traced in either Lohrmann or Schmidt; but it may be noticed at the short periods of illumination favourable for observing such wasted or nearly obsolete features.

The incipient formation of rills by inosculating craters may be well seen in Schmidt’s map. In Section III., about Römer and Posidonius, are found several good illustrations of crater rills; and in Section I. the single cleft of Hyginus shows, in its varied character, the relationship between rills with craters and those where craters are not distinguished.

Schmidt has added to his map a convenient epitome of the descriptive volume; and a valuable adjunct will be found in ‘Der Mond’ of Beer and Mädler, as their letters of reference are given by Schmidt in his sections. It must be said, however, that the letters are often obscure and not readily deciphered—a fault, perhaps, of the photography.

It is to be regretted that Schmidt does not give a list of positions, like Mädler in § 37 of ‘Der Mond’, with the addition of references to the sections in which the objects are to be found; neither does he give any comprehensive index. His list of points of the first order falls far short of ordinary requirements; nor are even these easily found in the map without any indication of the sections in which they appear. A small index map showing the sections, and containing the most prominent features with the names, would also be very desirable; and, in its absence, it may be suggested that a spare copy ( say from an old edition) of Webb’s excellent little map in the ‘Celestial Objects’ can be well utilized as an index by dividing it into sections corresponding with those of Lohrmann and Schmidt, and adding with pen or pencil the names to a selection of the principal formations.

In even a cursory examination of Schmidt’s map its completion by a single observer must seem almost incomprehensible to a man of ordinary powers; but it requires protracted study to well realize the extent of the work. Any person who tries with the aid of a 6-feet telescope to give a closely detailed delineation of even a small area of the Moon, will soon conclude that a period of thirty-three years was comparatively a very short one for the accomplishment of Dr. Schmidt’s great task. It is, in all truth, a performance highly creditable to the age in which we live, and to Teutonic intellect and perseverance. It is a splendid example of great results from small beginnings. We have, first, the astronomer, as a youth of 14, viewing the Moon with a little telescope steadied by a lamp-post, and probably the laughing-stock of many a passer by; afterwards he is found, in maturer years, pursuing his favourite study under more or less difficult circumstances and in different countries, until, at length, as director of a national observatory, he completes the wonderful production of his truly inimitable labours. For this it required all the unswerving persistence that is ever a chief attribute of genius; and the pages of the ‘Astronomische Nachrichten’ and other scientific publications can testify to the large amount of other astronomical work performed by Dr. Schmidt simultaneously with his lunar researches.

It is to be hoped that his map will soon be well known and justly appreciated in this country. To every person interested in lunar topography it is certainly indispensable; and the observer who sees something in the Moon not shown by Lohrmann, or Beer and Mädler, may be saved from imagining a new discovery by finding that the object is represented by Schmidt. This may be easily understood when it is known that the number of craters shown by Lohrmann is 7177, and by Mädler 7735, while in Schmidt’s map they reach the extraordinary amount of 32,856. The rills number in Lohrmann 77, in Mädler 71, and in Schmidt 348. As regards other objects, such as hills, ridges, banks, crater-terraces, &c., Schmidt’s map easily surpasses the others in comprehensiveness. Still, of course, the survey cannot be considered exhaustive even within the range of a 6-feet telescope; and although, by referring to Schmidt’s map, an observer may find an object which otherwise, by its absence in other maps, he might be led to suppose was new, it would be plainly wrong to infer that a formation must necessarily be recent because it is not noticed even by Schmidt. In a work of such magnitude as his it would be manifestly senseless to imagine that even sufficiently obvious objects might not, in some instances, have escaped him. With a telescope not superior to the Athenian refractor I have observed a few things not indicated by him,—such as a second large crater in Gruithuisen’s Schröter, a dilapidated diaphragm dividing Endymion into two, &c.; I should, however, be far from concluding on that negative evidence that they were not old formations. I believe the instances of Schmidt’s oversights of rather obvious objects to be wonderfully rare; but at the same time, it is, I should say, in change of aspect in what he represents, rather than in the detection of something not shown in his chart (unless something very striking), that we are to seek for sure indications of continued action affecting the topography of the Moon.

J. BIRMINGHAM