19:^0] New Metpiod for Laying Out Circular Curves 



47 



The resident engineer can more easily pick np the P. I., than any 

 other point and he would find it convenient to realign the curve by 

 deflections from this position while construction is going on, since it 

 is apt to be beyond the grade stakes and not disturbed. 



The points on the curve established by deflections according to 

 the proposed new method are at equal and integral distances apart, 

 but they are not full stations. The writer believes the advantages 

 of full station points are largely imaginative. However, the chain- 

 men can easily locate full station points on their return trip from 

 the P. C. to the P. T., as is explained in Example 1. The middle or- 

 dinate of the equal chords can be found in Table III which has been 

 compiled by the writer for the purpose. In this connection, it should 

 be remembered that middle ordinates vary practically as the square of 

 the chords ; and for any chord, the ordinates vary practically as those 

 of a parabola. See Fig. 3. Thus if the middle ordinate is 1 ft. the ordi- 

 nate (or offset) at a point 2/5th of the chord-length from the end of 

 the chord is 0.6 ft. The middle ordinate in practice is usually less 

 than 1 ft. as will be seen later. 



Before proceeding with an illustration, Table II will be explained. 

 This table gives the Externals, Tangents, Radii, and Degrees of Curve 

 for circular Arcs of 100 feet in length according to values of the deflec- 

 tion angle ranging from 1° to 128°. It is offered as a substitute for 

 the tables giving the functions of a 1° curve. The following formulas 

 were used in computing the values in Table II : 



100 A 100 A 



D = 



L 100 



5729.578 



5729.578 



T = E tan V., A = tan i/> A , 



A 

 5729.578 

 E = K tan M.. A = exsec i/,A, 



