APPLIED GEOMETRY. 31 
| i ahve AC DE py i 
sured, the height desired will = —G@p_ ; or (substituting c for AC, a for DE, 
and d for CD) = aa If the foot of the object cannot be reached, the same 
process may be repeated with the same staff, at another place, D’, and the 
height will = = if C’D'= d’, AC’=c’'. If now, CC’= b, and consequently, 
lat ) (cla. by a bd’ | 
c=c'+8, then Wor Gea whence Ca) and the height required 
Ea 
oo a 
The describing of a part of the earth’s surface, 7. e. making a perfect 
representation of it on a reduced scale, is to be considered as one of the prin- 
cipal problems in surveying. Three methods may be employed when only a 
small part, easily overlooked, is in question: in these the plane table is the 
most convenient instrument to be employed. 1. By sighting forwards and 
measuring. Sight from a given station A (pl. 4, fig. 9), situated in the 
inside or in the circumference of the figure, towards all its corners, which 
are to be indicated by signals or other marks ; measure also the distance of 
this point from all the corners, determine the sight lines on the plane table 
by means of a diopter ruler, and mark off, according to a scale, the propor- 
tional lengths of the distances above mentioned. By connecting the 
extremities of the lines thus obtained, we shall have a figure similar to that 
of the field. 2. By going round the figure, or sighting backwards. All the 
sides of the figure (except two) must be measured, and sights taken from 
one corner to the others. This is also called surveying the figure from the 
circumference. The method is inconvenient, but. oftentimes the only one 
practicable (fig. 11). 3. Surveying from two stations. Measure a base 
line, AB (fig. 9), and sight from its ends to all the corners of the figure ; 
transfer this base, reduced, to the paper, and draw from its extremities the 
lines of sight : the intersections of these two sets of lines will determine the 
corners of the figure. This method, when it can be employed, is always 
preferable to the other two. It is more fully illustrated in pl. 5 (fig. 57). 
Klere 2b is the base, which may be 100 or 1000 feet long. After it has been 
measured, the plane table is set up at A, and from a, sights taken to the 
other extremity of the line, as also to all the principal points visible from A, 
as C, D, E, F, &c. The corresponding sight lines are then to be drawn on 
the table by means of the sight or diopter ruler. The length of the base 
line is then to be marked off on the sight line running towards 0, on a 
reduced scale, as >> or sa5a; and the table removed to B. It is here 
to be set up in such a manner that the point b lies directly over that 
part of the base answering to b. It is furthermore erected so that the 
sight line to @ corresponds with the line ab drawn on the table. The 
points C, D, E, F, &c., already sighted from A, are to be sighted from B, and 
the corresponding sight lines drawn upon the plane table. Their intersec- 
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