SURVEY OF MASSACHUSETTS. 55 
when precision is required, many altitudes of the sun, or, what is preferable, of stars, 
passing both to the north and south of the observer’s zenith, must be taken, and the cor- 
rections of the altitudes for refraction and parallax, and of the stars’ declinations, for 
aberration, nutation, and precession, must be carefully computed. The accurate solution 
of the problem, therefore, even by this method, is no longer easy, but requires much 
labour and time. Indeed, there is reason to doubt whether perfect accuracy can be 
obtained. In the Royal Observatory at Greenwich, which was established in 1675, are 
some of the largest astronomical instruments ever constructed, yet, within a few years, its 
latitude has been diminished one second; and the late director of that establishment has 
remarked, “that an error of half a second is even now not at all improbable, though it is 
rather unlikely that it should exceed that quantity.” In the latitude of Greenwich, one 
second is equivalent to one hundred and one feet and five inches, and in Massachusetts 
to one hundred and one feet and three inches; the length of a degree of latitude, 
increasing gradually, but constantly, as we recede from the equator, in consequence of 
the ellipticity or flattening of the earth. 
For the determination of the difference of the longitudes of two places there are many 
methods. But several of them, such as the eclipses of the moon, and of the satellites of 
Jupiter, and the distance of the moon from the sun or stars, are too uncertain to be 
resorted to when accuracy is requisite; and, indeed, no one of the various methods that 
have been proposed is altogether without its disadvantages. A single observation on the 
interval between the transit of the moon and a star may not give a result more accurate 
than a lunar distance, though the mean of several hundred of such observations, made in 
the course of several years, would probably be very correct. Eclipses of the sun, occul- 
tations of-stars, and transits of the two inferior planets, are of very rare occurrence; more- 
over, the longitude of the place of observations will be affected by the errors in the tables 
of the sun, moon, planet, or star, unless corresponding observations were made on the 
same eclipse, occultation, or transit, at some other place, whose longitude is known, 
whereby the amount of such error may be discovered and taken into consideration. The 
explosion of gunpowder or of rockets, or the sudden extinction of a bright light on some 
conspicuous eminence, (a method which was used with much success in the recent 
determination of the longitudes of Greenwich and Paris,) requires the services of several 
practical astronomers; and the last method, which, in theory, is equally simple and per- 
fect, that of transporting the time of one place to another by a chronometer, is liable to 
the objection, that although this is a beautiful, and even wonderful instrument, it is still 
not sufficiently perfect to be implicitly relied on. Such, however, is the comparative 
beauty and simplicity of this method, that it will hereafter be frequently adopted, espe- 
cially for the determination of the difference of the longitudes of places not remote from 
each other; whilst, in order to avoid the difficulty above mentioned, several of these instru- 
ments must be employed, and the comparisons between the places must be repeated until, 
from the mean of all the observations, a result shall be obtained, nearly as accurate as 
ean be hoped for. 
It is, therefore, obvious that the determination of the exact longitude is not less diffi- 
cult than of latitude. Indeed, it has been pronounced one of the most so of all the 
problems in practical astronomy. The astronomical observatories at Greenwich and 
Paris are not only two of the oldest, but perhaps the two most important in Europe: it 
