Determination of Differences of Longitude by Rockets.—Another mode of ascertaining differences of longitude is that of conveying the time from one point to another by fire-signals or rockets. Thus, if a rocket is fired from a station between two observatories, and the explosion noted in the time proper to each place, the difference between the times will be the difference of longitude. A chain of such signals may be extended a considerable distance thus :—Let the two points to be con nected be A and a, and let an observer with a chronometer be placed at a, and others with rockets at a, $, thus : A, a, a, $, a. Then the observers at A and B note the rockets from a and $ in times of their respective observatories. The person stationed at a notes by his chro nometer the rockets at a and $ (suppose $ at 10 minutes after a), and as lie observes a at the same physical moment with A, A would see /3, if it were visible, just 10 minutes Later than he does actually see a, and therefore the explosion of $ is known in time proper to A's observatory; but it is also seen by B at the same moment in his time, and therefore the difference of longitude is obtained. In like manner, any number of intermediate stations of observers and rockets may be interpolated between two distant points, A and B. The relative personal equation of the observer at A and n must be taken into account [EQUATION, PER SONAL] both as astronomers and observers of signals ; but the personal equation of the intermediate .observer does not affect) the observation. In this way the longitude of Paris from Greenwich wa.s:determined. (` Phil. Trans.') Determination of Differences of Longitude by Galvanic Signals.—The beat method hitherto devised for determining differences of longitude, is founded on the transmission of signals by galvanic electricity. This method was first successfully practised in the United States of America. The most obvious mode of its application consists in despatching from one of the two stations to the other, a definite number of signals by the telegraphic wire, the observer at the one station recording the times of transmission of the signals, and the observer at the other station recording the times when they are received. The opera tion is then repeated by the transmission of signals from the second station to the first. The velocity of the electrie fluid being supposed to be sensibly instantaneous, a comparison of the local times at the two stations will indicate their difference of longitude. The application of this method, which has been found to give the best results, consists in receiving the signals upon Saxton's recording apparatus.
Finally, the longitude and latitude ofsone place from another may be determined by measurements on the earth's surface, if the figure of the earth be sufficiently well known. The geodesical Latitudes and longitudes are in many caeca found not to agree with those found astronomically, owing, as it is supposed, to some variations in the density of the earth in the neighbourhood of the place of observation. It is however a convenient way of finding the latitude and longitude of points near a well-established observatory, and connected by trigono metrical survey.
Let the distance T. a In feet and the bearing K 0 P of the point P from the observatory o be known by survey, and o N be an arc of the meridian. Then drawing P K a perpendicular to o N, r K =P 0 x sin of o x and o x=r a x cos P ox, when P x and si x are known, in feet.
Find the value of o in seconds of latitude approximately by supposing 1" to be =100'8 feet, and add or subtract this, as the case may be, to the latitude of o, which will give the latitude of m, the middle point ; call this A. Then the value in English feet of a degree of latitude at is is 3627471+ number the logarithmof which = 3'5634881 +2 log sin A and the value of a degree of longitude at the same parallel in English feet= { 1 3'0863668 number, log= + Jog cos A f + number, log= + log cos +2 log sin A Witli these values of a degree of latitude and longitude the distances o K and r lc are readily converted into arcs of latitude and longitude. On this subject the reader may consult the article GEODESY, and the Encyclopcodia Netropoliatana,' art. Figure of the Earth.' The solution of the problems assumed to be known in the foregoing article may be found in all treatises on astronomy and in most col lections of tables of navigation. We have recommended Thomson's as very convenient, and sufficiently accurate for the traveller and navigator, but any tables and methods which a man has become accustomed to will do. It would require too much space to give reasons and explanations for the opinions here advanced, but we will give two or three recommendations which few observers will regret to have followed. The first is to make, when practicable, large masses of careful and unhurried observations, and especially to observe the rules given above for nullifying instrumental error, by making such observa tions that a given error will have contrary effects in the result. Secondly, to be very careful in selecting their instruments and their timekeepers, which should come from good makers, and he carefully tried before starting, especially at such temperatures as the traveller may expect to meet with. A chronometer which is excellent for a polar expedition may be an indifferent watch on the Tigris or in the interior of Africa, and vice vend. For any overland expedition three pocket chronometers should at least be taken, and the number must be increased according to the length, the difficulty, and the importance of the journey, and a liberal allowance made for stoppages, changes of rate, accidents, &c. : a belt of half a dozen chronometers would scarcely be felt to be an inconvenience. Lastly, if the traveller's object be chiefly that of determining exact positions, he should be careful to determine the longitudes of all his principal points by solar eclipses or occultations of fixed stars by the moon, if he cannot carry and fix a transit. At these points he should determine the rates of his chrono meters for a new departure, and determine as much of the country as circumstances will allow by journeys of ten days or a fortnight, returning to the same place. When the principal points are well fixed (we speak of longitudes, for good latitudes may be got with almost any instrument, or by any person), the chronometers will fix every halting place where the time is observed, and this may be got in a few minutes any fine night or morning or afternoon ; and then the itineraries, compass bearings, marches, &c., and all the loose information on which too much of our geography is founded, will furnish valuable details in the proper place. The necessary apparatus is not very expensive or cumbrous, and with a little practice can be managed by a moderately intelligent and methodical person.
LOOM. [WEArrso.]