Beer and Maedler also measured the heights of one thousand and ninety-five lunar mountains and crater-summits: the resulting measures are given in a table contained in the comprehensive text-book which accompanies their map. These heights are found by one of two methods, either by measuring the length of the shadow which the object casts under a known elevation of the sun above its horizon, or by measuring the distance between the illuminated point of the mountain and the “terminator” in the following manner. In the annexed figure ([Fig. 15]) let the circle represent the moon and M a mountain upon it: let S A be the line of direction of the sun’s rays, passing the normal surface of the moon at A and just tipping the mountain top. A will be the terminator, and there will be darkness between it and the star-like mountain summit M. The distance between A and M is measured: the distance A B is known, for it is the moon’s radius. And since the line S M is a tangent to the circle the angle B A M is a right angle. We know the length of its two sides AB, AM, and we can therefore by the known properties of the right-angled triangle find the length of the hypothenuse BM: and since BM is made up of the radius BA plus the mountain height, we have only to subtract the moon’s radius from the ascertained whole length of the hypothenuse and we have the height of the mountain. MM. Beer and Maedler exhibited their measures in French toises: in the heights we shall have occasion to quote, these have been turned into English feet, upon the assumption that the toise is equal to 6·39 English feet. The nomenclature of lunar features adopted by Beer and Maedler is that introduced by Riccioli: mountains and features hitherto undistinguished were named by them after ancient and modern philosophers, in continuance of Riccioli’s system, and occasionally after terrestrial features. Some minute objects in the neighbourhood of large and named ones were included under the name of the large one and distinguished by Greek or Roman letters.
Fig. 15.
PLATE IV.
PICTURE MAP OF THE MOON.
PLATE V.
Skeleton Map of Moon
To Accompany Picture Map, [Chap. VII]
The excellent map resulting from the arduous labours of these astronomers is simply a map: it does not pretend to be a picture. The asperities and depressions are symbolized by a conventional system of shading and no attempt is made to exhibit objects as they actually appear in the telescope. A casual observer comparing details on the map with the same details on the moon itself would fail to identify or recognize them except where the features are very conspicuous. Such an observer would be struck by the shadows by which the lunar objects reveal themselves: he would get to know them mostly by their shadows, since it is mainly by those that their forms are revealed to a terrestrial observer. But such a map as that under notice indicates no shadows, and objects have to be identified upon it rather by their positions with regard to one another or to the borders of the moon than by any notable features they actually present to view. This inconvenience occurred to us in our early use of Beer and Maedler’s chart, and we were induced to prepare for ourselves a map in which every object is shown somewhat, if imperfectly, as it actually appears at some period of a lunation. This was done by copying Beer and Maedler’s outlines and filling them up by appropriate shading. To do justice to our task we enlarged our map to a diameter of six feet. Upon a circle of this diameter the positions and dimensions of all objects were laid down from the German original. Then from our own observations we depicted the general aspect of each object: and we so adjusted the shading that all objects should be shown under about the same angle of illumination—a condition which is never fulfilled upon the moon itself, but which we consider ourselves justified in exhibiting for the purpose of conveying a fair impression of how the various lunar objects actually appear at some one or other part of a lunation.
The picture-map thus produced has been photographed to the size convenient for this work: and in order to make it available for the identification of such objects as we may have occasion to refer to, we have placed around it a co-ordinate scale of arbitrary divisions by which any object can be found as by the latitude and longitude divisions upon a common geographical map. We have also prepared a skeleton map which includes the more conspicuous objects, and which faces the picture map (Plates [IV.] and [V.]) The numbers on the skeleton map are those given in the second column of the accompanying table. The table also gives the co-ordinate positions of the various craters, the names of which are, for convenience of reference, printed in alphabetical order.
| Name. | Number. | Map Ordinates. | |
|---|---|---|---|
| Abulfeda | 107 | 30·0 | 120·7 |
| Agrippa | 151 | 31·2 | 110·0 |
| Airy | 93 | 34·7 | 123·0 |
| Albategnius | 109 | 35·5 | 119·7 |
| Aliacensis | 61 | 35·8 | 131·0 |
| Almanon | 94 | 29·0 | 122·3 |
| Alpetragius | 92 | 40·8 | 122·4 |
| Alphonsus | 110 | 39·6 | 120·9 |
| Apianus | 62 | 33·6 | 129·3 |
| Apollonius | 154 | 6·5 | 109·5 |
| Arago | 152 | 24·7 | 108·7 |
| Archimedes | 191 | 40·3 | 95·8 |
| Aristarchus | 176 | 62·3 | 99·2 |
| Aristillus | 190 | 37·0 | 93·3 |
| Aristotle | 209 | 30·0 | 84·6 |
| Arzachael | 84 | 39·5 | 124·0 |
| Atlas | 228 | 20·7 | 86·6 |
| Autolycus | 189 | 36·8 | 95·5 |
| Azophi | 76 | 30·7 | 126·8 |
| Bacon | 17 | 32·5 | 142·0 |
| Baily | 207 | 26·0 | 85·4 |
| Barocius | 34 | 31·8 | 138·5 |
| Bessel | 179 | 27·4 | 100·1 |
| Bettinus | 11 | 48·8 | 144·9 |
| Bianchini | 215 | 51·6 | 86·3 |
| Billy | 121 | 64·3 | 121·4 |
| Blancanus | 12 | 43·7 | 144·8 |
| Bonpland | 110 | 48·5 | 117·6 |
| Borda | 56 | 15·2 | 131·0 |
| Boscovich | 160 | 31·1 | 106·8 |
| Bouvard | 40 | 66·6 | 134·3 |
| Briggs | 196 | 68·0 | 97·2 |
| Bullialdus | 86 | 50·1 | 125·5 |
| Burg | 206 | 25·5 | 87·5 |
| Calippus | 199 | 32·4 | 90·3 |
| Campanus | 71 | 52·3 | 129·0 |
| Capella | 104 | 17·8 | 118·0 |
| Capuanus | 43 | 50·5 | 132·8 |
| Casatus | 7 | 43·7 | 147·0 |
| Cassini | 200 | 35·5 | 89·7 |
| Catherina | 95 | 24·7 | 124·0 |
| Cavalerius | 144 | 71·2 | 109·5 |
| Cavendish | 88 | 63·5 | 127·4 |
| Cichus | 44 | 47·3 | 132·8 |
| Clavius | 13 | 41·8 | 143·5 |
| Cleomides | 183 | 10·7 | 97·0 |
| Colombo | 98 | 12·8 | 122·7 |
| Condamine | 214 | 48·7 | 84·2 |
| Condorcet | 164 | 4·5 | 104·7 |
| Copernicus | 147 | 49·8 | 107·0 |
| Cyrillus | 96 | 23·5 | 121·3 |
| Damoiseau | 124 | 69·2 | 117·2 |
| Davy | 113 | 43·2 | 119·8 |
| Deambrel | 129 | 26·8 | 113·5 |
| Delisle | 195 | 55·7 | 95·2 |
| Descartes | 106 | 28·5 | 119·3 |
| Diophantus | 194 | 55·5 | 96·3 |
| Doppelmayer | 70 | 58·6 | 129·6 |
| Encke | 140 | 59·7 | 110·6 |
| Endymion | 227 | 20·6 | 83·8 |
| Epigenes | 223 | 39·0 | 79·5 |
| Erastothenes | 168 | 44·6 | 104·0 |
| Eudoxus | 208 | 29·7 | 88·0 |
| Fabricius | 35 | 20·0 | 136·8 |
| Fernelius | 37 | 35·1 | 134·8 |
| Firmicus | 156 | 5·8 | 107·7 |
| Flamsteed | 126 | 62·8 | 114·5 |
| Fontana | 122 | 65·9 | 123·0 |
| Fontenelle | 221 | 43·0 | 81·3 |
| Fourier | 67 | 62·5 | 130·7 |
| Fracastorius | 78 | 20·5 | 127·0 |
| Furnerius | 52 | 11·7 | 133·0 |
| Gambart | 138 | 47·2 | 112·2 |
| Gartner | 224 | 26·5 | 82·3 |
| Gassendi | 90 | 59·7 | 123·3 |
| Gauricus | 46 | 43·5 | 132·5 |
| Gauss | 201 | 10·3 | 90·3 |
| Gay Lussac | 169 | 50·1 | 103·8 |
| Geber | 83 | 29·6 | 124·8 |
| Geminus | 187 | 13·0 | 93·0 |
| Gérard | 218 | 63·7 | 88·8 |
| Goclenius | 101 | 11·8 | 118·5 |
| Godin | 135 | 31·3 | 111·7 |
| Grimaldi | 125 | 70·8 | 116·3 |
| Gruemberger | 6 | 41·4 | 145·8 |
| Gueriké | 114 | 46·5 | 119·6 |
| Guttemberg | 102 | 13·9 | 118·3 |
| Hainzel | 39 | 52·3 | 136·7 |
| Hansteen | 123 | 65·5 | 119·9 |
| Hase | 54 | 9·8 | 129·5 |
| Heinsius | 88 | 45·5 | 136·0 |
| Helicon | 212 | 48·0 | 89·6 |
| Hell | 47 | 41·7 | 131·6 |
| Hercules | 229 | 22·3 | 86·7 |
| Herodotus | 175 | 63·2 | 99·6 |
| Herschel | 112 | 39·3 | 116·2 |
| Hesiodus | 64 | 45·8 | 130·0 |
| Hevelius | 141 | 71·5 | 111·3 |
| Hippalus | 87 | 54·0 | 127·0 |
| Hommel | 20 | 26·8 | 140·0 |
| Hyginus | 158 | 33·6 | 108·0 |
| Inghirami | 27 | 61·3 | 138·9 |
| Isidorus | 103 | 16·7 | 118·0 |
| Kant | 105 | 25·8 | 118·5 |
| Kepler | 146 | 60·0 | 108·0 |
| Kies | 72 | 49·7 | 128·8 |
| Kircher | 10 | 47·5 | 145·8 |
| Klaproth | 8 | 43·5 | 146·7 |
| La Caille | 74 | 37·5 | 126·8 |
| Lagrange | 68 | 67·0 | 131·3 |
| La Hire | 177 | 54·3 | 99·3 |
| Lalande | 117 | 43·4 | 115·3 |
| Lambert | 193 | 49·6 | 97·8 |
| Landsberg | 127 | 54·0 | 113·0 |
| Langreen | 100 | 6·3 | 117·7 |
| Letronne | 120 | 62·0 | 119·0 |
| Licetus | 21 | 34·1 | 139·6 |
| Lichtenberg | 197 | 66·5 | 94·9 |
| Linnæus | 188 | 31·7 | 95·7 |
| Littrow | 185 | 20·5 | 99·4 |
| Lohrman | 143 | 71·3 | 112·8 |
| Longomontanus | 23 | 45·7 | 140·6 |
| Lubiniezky | 91 | 51·3 | 123·5 |
| Macrobius | 182 | 13·7 | 100·2 |
| Maginus | 22 | 40·0 | 140·4 |
| Mairan | 217 | 56·7 | 89·5 |
| Manilius | 167 | 32·2 | 103·9 |
| Manzinus | 4 | 31·3 | 146·0 |
| Maraldi | 181 | 18·6 | 100·8 |
| Marius | 171 | 65·0 | 105·5 |
| Maskelyne | 132 | 19·5 | 111·0 |
| Mason | 204 | 23·7 | 88·8 |
| Maupertius | 213 | 48·7 | 85·8 |
| Maurolycus | 33 | 31·8 | 137·0 |
| Menelaus | 165 | 28·3 | 103·0 |
| Mercator | 65 | 51·4 | 130·2 |
| Mersenius | 89 | 61·7 | 125·7 |
| Messala | 202 | 14·0 | 90·5 |
| Messier | 131 | 10·8 | 114·0 |
| Metius | 36 | 18·8 | 105·9 |
| Moretus | 5 | 39·5 | 146·5 |
| Moesting | 128 | 41·6 | 113·2 |
| Neander | 57 | 18·7 | 131·0 |
| Nearchus | 18 | 26·8 | 142·0 |
| Newton | 1 | 41·0 | 147·7 |
| Nonius | 49 | 36·5 | 133·2 |
| Olbers | 172 | 73·0 | 107·7 |
| Pallas | 149 | 38·6 | 109·5 |
| Parrot | 108 | 35·8 | 121·6 |
| Petavius | 80 | 9·5 | 127·5 |
| Phocylides | 25 | 55·5 | 141·6 |
| Piazzi | 41 | 65·0 | 133·5 |
| Picard | 163 | 8·3 | 104·7 |
| Piccolomini | 58 | 21·7 | 131·0 |
| Pico | 211 | 41·9 | 87·3 |
| Pitatus | 63 | 44·1 | 130·2 |
| Plana | 205 | 24·8 | 88·8 |
| Plato | 210 | 41·8 | 84·8 |
| Playfair | 75 | 33·5 | 127·5 |
| Pliny | 165 | 24·2 | 103·4 |
| Poisson | 60 | 32·8 | 131·0 |
| Polybius | 82 | 24·5 | 125·6 |
| Pontanus | 59 | 29·0 | 130·2 |
| Posidonius | 186 | 22·2 | 94·3 |
| Proclus | 162 | 11·4 | 104·5 |
| Ptolemy | 111 | 39·5 | 118·2 |
| Purbach | 73 | 38·7 | 128·4 |
| Pythagoras | 220 | 53·0 | 81·2 |
| Pytheas | 178 | 49·7 | 100·4 |
| Ramsden | 42 | 52·9 | 132·5 |
| Reamur | 118 | 37·3 | 114·6 |
| Reiner | 145 | 67·3 | 108·5 |
| Reinhold | 139 | 51·5 | 111·2 |
| Repsold | 219 | 60·2 | 85·7 |
| Rheita | 51 | 16·1 | 134·2 |
| Riccioli | 142 | 72·7 | 113·8 |
| Riccius | 50 | 23·7 | 133·5 |
| Ritter | 134 | 26·0 | 111·6 |
| Roemer | 184 | 18·3 | 97·6 |
| Ross | 161 | 25·0 | 105·3 |
| Sabine | 133 | 25·0 | 112·0 |
| Sacrobosco | 77 | 27·5 | 127·7 |
| Santbech | 79 | 15·7 | 126·8 |
| Saussure | 31 | 39·6 | 137·7 |
| Scheiner | 14 | 45·5 | 143·5 |
| Schickard | 28 | 59·0 | 137·5 |
| Schiller | 24 | 51·3 | 141·0 |
| Schroeter | 137 | 42·3 | 110·7 |
| Schubert | 155 | 2·3 | 110·8 |
| Segner | 16 | 51·3 | 143·5 |
| Seleucus | 174 | 69·0 | 99·8 |
| Sharp | 216 | 54·2 | 87·7 |
| Short | 2 | 39·7 | 147·4 |
| Silberschlag | 157 | 32·0 | 108·1 |
| Simpelius | 3 | 35·8 | 147·7 |
| Snell | 55 | 11·3 | 129·6 |
| Soemmering | 136 | 42·8 | 112·2 |
| Stadius | 148 | 45·6 | 107·0 |
| Stevinus | 53 | 11·9 | 130·7 |
| Stoefler | 32 | 35·6 | 136·8 |
| Strabo | 226 | 23·2 | 81·6 |
| Struve | 203 | 18·3 | 88·7 |
| Taruntius | 153 | 11·7 | 109·0 |
| Taylor | 130 | 27·6 | 116·2 |
| Thales | 225 | 24·3 | 81·8 |
| Thebit | 85 | 40·8 | 126·8 |
| Theophilus | 97 | 22·3 | 120·0 |
| Timæus | 222 | 38·3 | 80·8 |
| Timocharis | 192 | 45·1 | 97·0 |
| Tobias Mayer | 170 | 54·5 | 103·0 |
| Triesnecker | 150 | 35·5 | 109·8 |
| Tycho | 30 | 43·0 | 142·3 |
| Ukert | 159 | 37·1 | 107·5 |
| Vasco de Gama | 173 | 72·8 | 104·9 |
| Vendelinus | 99 | 6·8 | 121·6 |
| Vieta | 69 | 64·3 | 129·7 |
| Vitello | 66 | 55·8 | 130·7 |
| Vitruvius | 180 | 20·1 | 102·0 |
| Vlacq | 19 | 25·0 | 140·1 |
| Walter | 48 | 37·8 | 131·9 |
| Wargentin | 26 | 57·5 | 140·2 |
| Werner | 62 | 36·4 | 129·3 |
| Wilhelm Humboldt | 81 | 5·7 | 127·8 |
| Wilhelm I. | 29 | 45·9 | 138·6 |
| Wilson | 9 | 45·7 | 146·4 |
| Wurzelbauer | 45 | 45·0 | 132·6 |
| Zuchius | 15 | 50·7 | 144·2 |