Longitude

“ The situation of any place is known by its latitude and longitude. As charts of every ocean and sea are furnished to the sailor, in which are laid down the latitudes and longitudes of every point of land, whether on the shores of islands or the main, he has, therefore, only to ascertain his latitude and longitude at any particular place on the ocean, in order to find where he is, with respect to the nearest point of land, although this may be, and may always have been, entirely out of sight to him. ”

“ As regards the counting of longitude in two directions, and the degree of advantage or disadvantage that may arise in starting from zero and treating east longitude as positive or plus, and west longitude as negative or minus, let me ask the attention of the Congress to the fact that longitude is already counted in these two directions, and that, as a matter of fact also, latitude is counted in the same way, in both directions from the equator, north latitude being plus and south latitude minus. ”

“ The Moon’s longitude is always taken geocentrically. When approximate longitudes are required, the employment of a mean vector, which is equal to half the minor axis of the planet, is found convenient. For the convenience of astronomical students I may here give the constant logarithms of the values of the tangent, which, being added to the logarithm of the tangent of half the distance of the planet from the Sun in longitude, will give the tangent of the complement. ”

“ It is regretable that geographers lost the excellent opportunity offered by the Vienna Weltausstellung of 1873, to determine in congress a single point de départ of longitude for the civilised world. Now each nation has the pretension of making a first meridian of its own, consequently whilst geographical readers have a fair conception of latitude, that of longitude is especially hazy. ”

“ Of two places on this globe whose direction from one another you are desirous of knowing, that is in what part of the heavens the one diverges from the other, first of all note the difference of latitude and longitude. This ascertained turn the globe until some one rhumb cuts the meridian in the latitude of the first place, then turn to the east or to the west as is required, until the degrees of the equator through which the meridians of the places pass equal in number the difference in longitude of the two places. ”

“ In sailing East or West, however, your problem is more difficult. Only on the equator is a minute of longitude and a nautical mile of the same length. As the meridians of longitude converge toward the poles, the lengths between each lessen. We now have to rely on tables to tell us the number of miles in a degree of longitude at every distance North or South of the equator, i.e., in every latitude. ”

“ The latitude of any point being determined directly by observation, and independently of the latitude of any other place, is less likely to be in error than the longitude, which can only be ascertained with reference to the meridian of some other place; being measured by time, is determined by the comparison of the local time with the time at some other place, the longitude of which is known. ”

“ Since (if not certain) it is at least probable, that the latitude itself, or rather the effect of the latitude, can be found (even in very dark weather) much more accurately from that declination alone, than can either the longitude or the effect of the longitude from the variation, though the sun itself is shining brightly or all the stars are visible, with the most skilful employment likewise of all the most exact instruments. ”

“ But in order to compare ob servations made at different places on the surface of the earth a knowledge of their difference of longitude becomes necessary, as the local time varies proportionally with the longitude, one hour corresponding to 15. Longitude can be determined either geodetically or astronomically. The first method supposes the earth to be a spheroid of known dimensions. Starting from a point of departure of which the latitude has been determined, the azimuth from the meridian (as determined astronomically) and the distance of some other station are measured. ”

“ Even with the larger and more accurate instruments used in astronomical observatories on shore the means of ascertaining latitude were far in advance of those by which longitude could be obtained, and this equally applied to the various heavenly bodies themselves upon which the terrestrial positions depended, the astronomical element of declination (corresponding to latitude) being far more accurately determined than that of right ascension (corresponding to longitude) . ”

“ The longitude and latitude of a planet being ascertained from an almanac, we can find with what degree it ascends. For example, given that the longitude of Venus is 6° of Capricorn, and her N. latitude 2°. Set the one leg of a compass upon the degree of longitude, and extend the other till the distance between the two legs is 2° of latitude, from that point inward, i.e. northward. The 6th degree of Capricorn is now to be set on the horizon, the label (slightly coated with wax) to be made to point to the same degree, and the north latitude is set off upon the wax by help of the compass. ”

“ To find the latitude of a place is not so difficult—the length of the day at different times of the year will by itself be almost enough to determine this, as we have seen in the very earliest history of Greek Page 163 geography—but to determine the longitude was a much more difficult task, which in the earlier stages could only be formed by guesswork and dead reckonings. ”

“ Neither Charmian nor Martin knew as much as I knew about navigation. And all the time the Snark was rushing madly along toward Tanna, in the New Hebrides. Something had to be done.
How it came to me I know not - call it an inspiration if you will; but the thought arose in me: if southing is latitude, why isn't westing longitude? Why should I have to change westing into longitude? And then the whole beautiful situation dawned upon me. The meridians of longitude are 60 miles (nautical) apart at the equator. At the poles they run together. ”

“ Do you wish to go from east to west, or vice versâ, in the same latitude? always proceed on the same parallel. Do you wish to go from one place to another as many degrees distant in longitude as it is different in latitude? Then take the course of 45 degrees either to the south-west or south-east, or north-west or north-east. If the latitude is greater than the longitude, then add to the 45 degrees as many degrees towards the nearest pole, as the number of degrees by which the latitude exceeds the longitude. ”

“ Though the problem of finding the longitude be, in fact, one of geography rather than astronomy, it is an application of astronomical science which has so materially affected the progress of our knowledge, that it deserves the notice we have bestowed upon it. ”

“ Mr. Green also demands special notice.
One great question of the day amongst seamen and geographers was the discovering of some ready and sure method of ascertaining the longitude. Half the value of the explorations made up to this time had been lost from this want. The recognised means of finding longitude was by the observation of lunars; that is, accurately measuring the angular distance between the centres of the moon and of the sun, or of the moon and some star. ”

“ What is really determined is the longitude from some intermediate point, generally in the same country, and in telegraphic communication with the place whose longitude we wish to know. This intermediate point would, for the time, be the practical prime meridian. But the longitude of this point itself must always be uncertain. Science is continually advancing in accuracy, and we find that we continually need to correct the longitude of our intermediate meridian, and hence of all points determined from it. ”

“ Assuming the earth to be spheroidal, let A and B be two stations on its surface, and let the latitude and longitude of A be known, also the azimuth of B at A, and the distance between A and B at the mean sea-level ”

“ The up and down ones, from pole to pole, are meridians of longitude; the East-West ones are parallels of latitude. Now, since these are all numbered as degrees, the space between them being 1°, the latitudes from the Equator to the poles on either side of it as 1° to 90°, and the meridians [Pg 54] from Greenwich to its opposite point on the other side of the world 1° to 180°, it follows that if a seafarer can ascertain at the same time what particular degree of both latitude and longitude he is in, a glance at his chart or sea-map shows him the position of his ship. ”

“ The time sight was mathematically sound, but the navigator was not always aware that the longitude determined was only as accurate as the latitude, and together they merely formed a point on what is known today as a line of position. If the observed body was on the prime vertical, the line of position ran north and south and a small error in latitude generally had little effect on the longitude. But when the body was close to the meridian, a small error in latitude produced a large error in longitude. ”

“ By that resolution the longitude indicates the relation between the local time and the universal time in the simplest possible way. What can be easier than the method involved in the resolution of Mr. Rutherfurd? It is this: Local time at any place is equal to universal time plus the longitude of the place, plus being understood always in a mathematical sense. The longitude is to be added to the universal time if it is positive, and subtracted if it is negative. That is very simple, the whole being involved in one general formula. ”

“ Navigators are more interested in the question than mathematicians, and the longitudes must be engraved upon our hydrographic charts.
Now, as the learned Delegate of Great Britain, Prof. Adams, who has just spoken, has stated, the principle involved is the same, whether we reckon east or west, or reckon continuously in the same direction. It seems to me, however, that when we come to consider the reckoning of longitude in connection with the adoption of a universal day, we should then make a decided choice in favor of counting longitude from zero to 360 degrees. ”