WEST VIRGINIA, the north-westernmost of the so-called Southern states of the United States of America, lying between latitudes 37° 10' and 40° 40' N., and longitudes 77° 40' and 82° 40' W.
VERMONT, a North Atlantic state of the United States of America and one of the New England group, lying between latitude 42° 44' and 45° o' 43' s N., and between longitudes 3° 35' and 5° 29' E.
This, of course, varies in different longitudes, while a further difficulty occurred in the attempt to fix the correct time of Easter by means of cycles of years, when the changes of the sun and moon more or less exactly repeat themselves.
NORTH CAROLINA, a South Atlantic state of the United States of America, situated between latitudes 33° 5 1 ' 37" (the southernmost point of the southern boundary-35° is the northernmost) and about 3 6 ° 34' 2 5.5" N., and between longitudes 75° 27' W.
Since 1890 further and more rigorous application of the telegraphic method of determining longitudes differentially with Greenwich has resulted in a slight correction (amounting to about 2" of arc) to the previous determination by the same method through Suez.
And between longitudes 80° 34' and 84° 49' W.
Latitudes from the observations of travellers may generally be trusted, but longitudes should be accepted with caution; for so competent an observer as Captain Speke placed the capital of Uganda in longitude 32° 44' E., when its true longitude as determined by more trustworthy observations is 32° 26' E., an error of 18'.
He moreover accuses Eratosthenes, (whose determination of a degree he accepts without hesitation) with trusting too much to hypothesis in compiling his map instead of having recourse to latitudes and longitudes deduced by astronomical observations.
A few latitudes had indeed been observed, but although Hipparchus had shown how longitudes could be determined by the observation of eclipses, this method was in reality not available for want of trustworthy time-keepers.
Latitudes and longitudes, and with their aid it is possible to reconstruct the maps.
Ptolemy knew but of a few latitudes which had been determined by actual observation, while of three longitudes resulting from simultaneous observation of eclipses he unfortunately accepted the least satisfactory, namely, that which placed Arbela 45° to the east of Carthage, while the actual meridian distance only amounts to 34°.
In France, in the meantime, an arc of the meridian had been measured (1669-1670) by Jean Picard, numerous longitudes had been observed between 1672 and 1680 by the same, and by Phil.
These corrected longitudes were not yet available for the maps produced by Nicolas Sanson of Abbeville, since 1627.
On the establishment of the Institute, Lagrange was placed at the head of the section of geometry; he was one of the first members of the Bureau des Longitudes; and his name appeared in 1791 on the list of foreign members of the Royal Society.
He was one of the first members, and became president of the Bureau of Longitudes, took a prominent place at the Institute (founded in 1796), professed analysis at the Ecole Normale, and aided in the organization of the decimal system.
The stars had been numbered and named at an early date, and we possess tables of lunar longitudes and observations of the phases of Venus.
And between longitudes 89° 5' and 96° 31' W.
And between longitudes 116° 57' and 124° 48' W.
In 1822 a commission of the Bureau des Longitudes made a series of experiments between Montlhery and Villejuif, I r m.
Formerly each nation took its own capital or principal observatory as the standard meridian from which longitudes were measured.
MONTANA, a north-western state of the United States, situated between latitudes 44 0 26' and 49° N., and between longitudes 27° and 39° W.
He became a member of the French Academy in 1860 and of the Bureau des Longitudes in 1878.
And longitudes 750 4' and 79° 33' W.
NEW HAMPSHIRE, a North Atlantic state of the United States, one of the New England group, and one of the Original Thirteen, lying between latitudes 42° 40' and 45° 18' 23" N., and between longitudes 70° 37' and 72° 37' W.
The inhabited islands lie between latitudes 18° 54' and 22° 15' N., and between longitudes 154° 50' and 160° 30 W., and extend about 380 m.
And between longitudes 74° 40' and 80° 31' 36" W.
From 1852 to 1867 he was in charge of the longitude department of the United States coast survey; he developed and organized the service, was one of the first to determine longitudes by telegraphic means, and employed the Atlantic cable in 1866 to establish longitude-relations between Europe and America.
Leverrier placed it on a totally new footing, freed it from the control of the Bureau of Longitudes, and raised it to its due rank among the observatories of Europe.
Most of the mechanical contrivances which made Tycho Brahe's instruments so superior to those of his contemporaries were adopted at Cassel about 1584, and from that time the observations made there seem to have been about as accurate as Tycho's; but the resulting longitudes were 6' too great in consequence of the adopted solar parallax of 3'.
FIe was created in that year a member of the Bureau des Longitudes and an officer of the Legion of Honour, in 1864 a foreign member of the Royal Society of London, and next year a member of the mechanical section of the Institute.
In 1808 he became astronomer to the Bureau des Longitudes; and when the Faculte des Sciences was instituted in 1809 he was appointed professeur de la mecanique rationelle.
He further became member of the Institute in 1812, examiner at the military school at St Cyr in 1815, leaving examiner at the Ecole Polytechnique in 1816, councillor of the university in 1820, and geometer to the Bureau des Longitudes in succession to P. S.
Through all these vicissitudes Arago had succeeded in preserving the records of his survey; and his first act on his return home was to deposit them in the Bureau des Longitudes at Paris.
And longitudes 82° 25' and 90 0 31' W., and consisting of two peninsulas - the upper or northern and the lower or southern - separated by a strait.
And between longitudes 32° and 37° W.
Cordovez Mauro, Reminiscencias Santafe y Bogota (Bogota, 1899); Norris and Laird (Bureau of Navigation), Telegraphic Determination of Longitudes in Mexico, Central America, the West Indies, and on the North Coast of South America (Washington, 1891); R.
And longitudes 8 4° 49' and 88° 2' W.
The longitudes and latitudes thus defined are geocentric, and the latitude is slightly different from that in ordinary use for geographic purposes.
Comparing the longitudes of the actual and the fictitious planet the former will sometimes be ahead of the latter and sometimes behind it.
The first depend on the mean longitudes of the planets, and always tend back to their original values when the planets return to their original positions in their orbits.
In the problems of celestial mechanics the angles within the parentheses are represented by sums or differences of multiples of the mean longitudes of the planets as they move round their orbits.
It follows that L the motions of the mean longitudes are nearly in the same proportion re versed.
The longitudes, latitudes and radii vectores of a planet, being algebraically expressed as the sum of an infinite periodic series of the kind we have been describing, it follows that the problem of finding their co-ordinates at any moment is solved by computing these expressions.
Assuming the mean motion of the moon to be known and the perigee to be fixed, three eclipses, observed in different points of the orbit, would give as many true longitudes of the moon, which longitudes could be employed to determine three unknown quantities - the mean longitude at a given epoch, the eccentricity, and the position of the perigee.
And between longitudes 78° 30' and 83° 20' W.
Of his Ephemerides (1755) practical rules for the employment of the lunar method of longitudes, proposing in his additions to Pierre Bouguer's Traite de Navigation (1760) the model of a nautical almanac.
Within two years of their first discovery, he had constructed approximately accurate tables of the revolutions of Jupiter's satellites, and he proposed their frequent eclipses as a means of determining longitudes, not only on land, but at sea.
The Ptolemaic catalogue embraces only those stars which were visible at Rhodes in the time of Hipparchus (c. 150 B.C.), the results being corrected for precession " by increasing the longitudes by 2° 40', and leaving the latitudes undisturbed " (Francis Baily, Mem.