812
THEORY AND PRACTICE OF ENGINEERING.
Book 11.
CONFLANT
VAUCIRAl
.1V Rl
VILLE JUIFUE
BOURC DE>IA RHINE
another : N L, the original base from whence the triangulation commences, may representthe meridian line; but before we commence our computations we must correct any imper-fections in our instrument, or carelessness in taking our survey; we shall afterwards findmuch advantage by adopting the approximating theorem of Legendre, who first demon-strated that if each of the angles of a small spherical triangle be diminished by a third partof the spherical excess, their sines become proportional to the opposite sides of the triangle,considered as spherical. The situations of Paris and the several'towns in its neighbourhoodwere accurately laid down by the observations made from this base line, and hence com-menced the method now adopted in making a trigonometrical survey.
In 1784 the British government turned its attention to this interesting subject, and byMr. Fox’s direction, who was then minister, it was ordered that by means of a series oftriangles, the difference in the longitude between the observatories of London and Paris should be ascertained : the meridian of Paris having been already continued to Dunkirk,the Royal Spciety undertook, with the assistance of General Roy, to complete the task ;and he commenced laying down a base line, rather more than 5 miles in length, uponHounslow Heath.
To connect the triangulations between Taris and Dunkirk, Cassini, Meehain, andLegendre were employed by the French government, and, as a check on their operations,another base line was laid down in Romney Marsh in Kent, where a steel chain, constructedon purpose by the celebrated Ramsden, was made use of. Romney Marsh is 60 miles fromHounslow, and when the two bases were united, by calculating the sides of all the trianglestaken, so great an accuracy had been observed, that there was only the apparent error of28 inches : the junction of the two observatories of Paris and Greenwich was completedin 1788.
Heights may be mea-sured by the demicircle.
The height of the towerat A, the top of which wewill suppose is not to beapproached, may be mea-sured by placing the in-strument at C, in such a a c~ u k 1
manner that by elevating FIg . s73 . Fi „. 974 .
its plane perpendicular to
the horizon, through the pinnules of the diameter, which are parallel with the horizon,the tower A B is seen in some point, as at E. Then elevate the alhidade of the demi-circle until the top of the tower is visible through its pinnules : remark then on the demi-circle how many degrees are intercepted between the diameter and the alhidade, in orderto ascertain the angle E D B, which is here supposed to be 20°.
'1 lien measure on the ground the distance from the station to the tower, and afterwardsconstruct a scale and lay down a similar figure, the lines M, II, showing the plan of the