all these circles, till then convergent, cut each other, that is, BOOK at the pole there is no more longitude. The reckoning of the latitudes begins at the equator. This commencement is naturally determined by the circumstances of the earth's motion. It is otherwise with the longitude; for all the meridians being great circles, nature furnishes no motive for choosing one in preference to any other, as a term from which to begin to count, or as first meridian. We need First menot be surprised, therefore, that geographers have varied much in their choice. Ptolemy fixed his first meridian at the Fortunate Isles, (now the Canaries,) because it was the most western limit of the countries known in his time; and as their extent from cast to west was more considerable than from south to north, the former received the name of longitude, or length, the latter that of latitude, or breadth, which they still bear. This first meridian of the ancients is not known with certainty, as its position depends on the precise meaning of the appellation Fortunate Isles, a point which we shall discuss in the history of geography. In order to render the manner of expressing longitudes in French geography uniform, Louis XIII. ordered, by an express declaration, that the first meridian should be placed in the Isle of Ferro, the most western of the Canaries. Delisle, one of the first who endeavoured to give precision to geographical determinations, fixed the longitude of Paris 20 degrees east of that meridian. When, by more rigorous observations, it was known that the difference of longitude between Paris and the principal town of the Isle of Ferro was 20° 5' 50", it was necessary to advance the first meridian 5' 50" to the cast of that point, so that it is now a circle of mere convention, which passes through no remarkable point. The Dutch had fixed their first meridian at the Peak of Teneriffe, a mountain situated in the island of that name, and then esteemed the highest in the world. Gerard Mercator, a famous geographer of the 16th century, chose the meridian which passes through the island ridian. BOOK Del Corvo, one of the Azores, because in his time it was the line on which the magnetic needle suffered no variation. It must be confessed, that it is the most natural and the most commodious point of departure with respect to maps of the world. Geographers have only agreed together in maintaining an abuse, that is in understanding by the name of the meridian. of a place, only the half of the great circle corresponding Meridian with the celestial meridian; the other half, which is in the meridian. opposite hemisphere, with respect to the poles, is sometimes called the anti-meridian. and anti Longitudes counted after the According to the custom of geographers, the longitudes begin to be counted from the eastern side of the first meridian, and are reckoned in the same direction over the whole circumference of the equator, till they return to the western side of the meridian. In this way of counting the longitudes may rise to 360.° These conventional arrangements have not been adopted by mariners. Astronomical observations having become of custom of general use in navigation, and the tables which indicate the navigators. moment of the celestial phenomena, and the position of the heavenly bodies at different epochs, being always calculated for the meridian of the principal observatory of each nation, navigators found it more convenient to refer to this meridian the points of the routes they followed. Thus French mariners count from the meridian of the observatory at Paris; the English from Greenwich; the Spaniards from Cadiz. Let us observe, moreover, that mariners estimate the longitude from the difference of the time which elapses between the passage of the meridians through the same heavenly body, or from the difference of hours counted at the same moment in two different places. If one has advanced towards the cast, one counts more than under the meridian from which one set out; the contrary happens when one advances towards the west. It is necessary, therefore, when we convert a difference of time into a difference of longitude, to indicate if it be oriental or occidental. In this way of counting, the longitude is always marked by the side near est the first meridian, so that the longitudes only embrace BOOK the semi-circumference, or do not rise beyond 180° and the globe is divided into two hemispheres with respect to the first meridian; in the hemisphere situated to the west, the longitudes have the denomination of occidental; and in the other oriental. All marine charts are established according to this system of numeration. of geogra These diversities in the manner of estimating the longi- Reduction tude necessitate calculations of reduction. We are obliged, phical lonbefore using a map, to examine what is the meridian adopt-gitudes. ed by the geographer, "which often embarrasses even learned persons."* When we have to do with longitudes reckoned according to the method of geographers, that is, by making the entire tour of the globe by the east, we must take the difference of longitude of the two meridians to be compared; and if the meridian from which we wish to set out is to the west of the other, this difference must be added to all the longitudes counted from the other; in the contrary case it must be retrenched. For example, Moscow is 35° 12' 45" from the meridian. of Paris, how many is it from that of Greenwich? Add the difference, which is 2° 20′ 15′′, and you will have the result 37° 33'. Here is another: Paris is 20° from the meridian of the Isle of Ferro, how many is it from the Dutch meridian of Teneriffe? This meridian being a degree more to the east than the other, retrench 1° from the given longitude, and you will have 19°. In this calculation there happen two particular cases. The result by addition may surpass 360°; for example, Madrid is 353° 57' 40" from Paris, counting in the manner of geographers, how many from the Isle of Ferro? You find, on adding the difference of the meridians, 373° 57' 40"; but as this sum exceeds the value of the whole circle, you see you have repassed a second time through the meridian of the Isle of Ferro. You must, therefore, retrench 360°, and you have * D'Alembert, dans l'Encyclopedie. BOOK III. of nautical 13° 57' 40'. In the same way it sometimes happens, that the given longitude is less than the difference of the meridians to be retrenched from it; in this case 360° are added to the longitude, the difference is then retrenched, and the sum required is found. For example, the isle Gomere is 32' from the isle of Ferro, you ask how much it is from the meridian of Teneriffe? Add 360° to 32', retrench the difference, and you have 359° 52', which is the longitude required. The reason of these operations is perceived on repeating them on the globe. Reduction The reduction of longitudes reckoned according to the longitudes. practice of navigators, is much more in use. In setting out from the same meridian, all the oriental marine longitudes, as far as 180°, remain the same as in the manner of reckoning adopted by geographers. With respect to the occidental marine longitudes, it is sufficient to deduct them from 360°, to bring them to the numeration of geographers. Here is an example: Venus's Point, in the island of Otaheite, has been determined by navigators to be 151° 50′ 30′′ of western longitude from the meridian of Paris. If from 360° we take off 151° 50' 30", the difference, which is 208° 9' So", will be the longitude according to geographers. It is evident that, by an inverse operation, we may transform into nautical longitude the geographical longitudes above 180°, by deducting them from 360°. If we set off from two different meridians, we must observe on what side the meridian to which we wish to refer the longitudes is placed with respect to the other. We must retrench their difference from all the longitudes of the same denomination as that side, and we must add to all those of a contrary denomination. An example will make this rule more easy. The meridian of the observatory of Paris being 2° 20′ 15′′ to the cast of that of Greenwich, all oriental longitudes with respect to Greenwich must be diminished by that quantity to be referred to the meridian of Paris, and the occidental longitudes must be augmented by that quantity. It is thus that the longitude of the Cape of Good Hope being 18° 23' 15" to the east of the meridian of Greenwich, becomes 16° 3' to the east of that of Paris; on the contrary, Cape Horn, placed by the English at 67° 21' 15" west of Greenwich, is 69° 41′ 30′′ west of Paris. In these reductions, as in those of the geographical longitudes, it may happen that the points to be reduced fall between two meridians, or between their opposite meridians. The place which is oriental with respect to one, then becomes occidental with respect to the other. In the first case, we can no longer retrench from the longitude to reduce the difference of the two proposed meridians; we must do the contrary, and change the denomination. In the second case, the number which results from the addition of the difference of the meridians, to the longitude. wanted from the meridian we wish to change, surpasses 180°, because it is beyond the meridian opposed to that to which the longitudes are referred; it must, therefore, be retrenched from 360°, or from the entire circumference, to make it go off from a side contrary to the same meridian; the longitude consequently changes its denomination again. Dover, for example, is 1° 18' 30" to the cast of Greenwich. Subtracting this longitude from the difference of the meridians 2° 20' 15", there will remain 1° 1' 45", which is the occidental longitude of Dover with respect to the meridian of Paris. Here is an example of the second case: At Turtle Isle, situated in the Pacific Ocean, the English count 177° 57' west longitude. Adding to this 2° 20', we find 180° 17'. The place is, therefore, 17' beyond the meridian opposed to that of Paris; and by retrenching 180° 17′ from 360°, we have 179° 43' of cast longitude with respect to the meridian of Paris. When the principal circles of longitude have been traced on the globe, and places known by observations have been marked on it, which are generally the capitals of states, the most frequented ports, and most salicut promontories, it only remains to fill up the intermediate spaces, by drawing from the best geographical maps the sinuosities of shores, the course of rivers, and the chains of mountains. But as all the materials of these designs must be taken from maps, of which we shall explain the construction in the BOOK III. |