a ak a a a a a a pe 
THE CUBIC PARABOLA. 61 
Table 3. Extending over several pages, contains the angle 4 
for every ten links along the curve. Also other data necessary 
for the location of the parabola. The radius of curvature to the 
nearest chain is also tabulated. 
The following example will illustrate its use. 
Having decided upon the radius of the arc C C’, (See fig. 2.) 
compute the length LO = LO’ = tan o(R+H ) + (@_—@’). 
Say & = 10 chains 
Angle w = 50° 
“~L0= L10' = 66014 
Set instrument at O and for the further illustration, say that 
the mileage of the point O is 320 m. 4.¢. 14:51. The next chain 
to be set out is therefore at a distance 85:5 links from 0. 
Consulting the table we find at 80 links the angle is 9’ 48". 
To obtain the angle corresponding to 85-5 we must multiply the 
difference 15-6” by 5:5 = 1’ 25:8". Adding this to 9’ 48” we 
obtain 11’ 14”, neglecting the decimal, this is the angle to be laid 
out. In a similar manner we obtain the angles corresponding to 
the mileages 
320 m. 6c. = 52’ 43” 
320m. 7c. = 2° 4’ 33° 
320 m. 8c. = 3° 45’ 38” 
The angle 4° 4’ 40’, and the distance 401-818, brings us to the 
point C. 
It will now be more convenient to move the instrument to 4. 
(See fig. a) 
DA = Sec> (R+H)-R . 
The are C ’ can then be located in the usual manner. 
We may set out the arc C C’ from the point C. Having set 
the instrument at C, sight to 0. Revolve the telescope, towards 
the axis of X, through the angle = (¢—6), the telescope will 
then point in the direction of the tangent to C. The curve C Cc’ 
may then be located. 
