44 Journal of the Mitchell Society [September 



— e, = 90° + y^A — Gi. 



It should be noted that the following pairs of deflections add up 

 to 180° + A°; (1) + (9), (2)'+ (8), (3) + (7) and (4) + (6). 



Using the above formulas, tables have been computed for all values 

 of the deflection angle A varying by 1° from 3° to 128°. This covers 

 all cases that are likely to occur in locating curves for roads and 

 streets. 



Fig. 2 is a graphical verification of the fact that for a fixed A, 

 the deflections to the points of equal division on a curve remain con- 

 stant for any length of the curve. This makes the method perfectly 

 general. 



The order of procedure in laj'ing out a curve is as follows : ( 1 ) 

 set up the instrument at the P. I., backsight on the first tangent witii 

 vernier reading 0°, transit the telescope, unclamp the vernier and fix 

 the line of sight on the second tangent, the vernier giving the de- 

 flection angle A°; (2) decide what length of curve to use (deter- 

 mined usually either by the desired external distance E or the tan- 

 gent length T) ; (3) compute T and E, using either the well-known 

 table of tangents and externals for a 1° curve, or preferably the tan- 

 gents and externals for a 100-ft. curve (Table II) ; (4) lay ofl^ the 

 tangent length locating the end of the curve (the P. T.) ; (5) di- 

 vide the length of curve by 10 and locate each of the ten points, or 

 every other one, or every third one, etc., depending upon how many 

 are needed to properly define the curve, by starting at the P. T., and 

 getting the intersection of the end of the chord with the line of sight 

 from the P. I., according to deflections read directly from the tables 

 (Table I). 



The middle point, or the 5th point of the curve, cannot be located 

 very precisely by intersections, since the end of the chord would be 

 moved in an arc tangent to the line of sight. This point can be lo- 

 cated exactly by measuring the external distance E from the P. I., 

 and this serves as a check. If only the 2d, 4th, 6th, 8th, and 10th 

 points are located, then it is not necessary to know E. 



