26 
TRANSACTIONS OF THE TEXAS ACADEMY OE SCIENCE. 
©•o d 
S2S 
'C bD . 
03 I 
I 
© d 
Distances from vertex in feet. 
Algebraic 
ence ol 
ents— pi 
Rate of 
per stati< 
0 
50 
100 
150 
200 
250 
300 
350 
400 
0.3 
0.075 
0.15 
o.os 
0.04 
0.01 
0. 
0.4 
.1 
.20 
.11 
.05 
.01 
0. 
0.5 
.125 
.25 
.14 
.06 
.02 
0. 
0.6 
.15 
.30 
.17 
.08 
.02 
0. 
0.7 
.175 
.35 
.20 
.09 
.02 
0. 
0.8 
.20 
.40 
.23 
.10 
.03 
0. 
0.9 
.225 
.45 
.25 
.11 
.03 
0. 
1.0 
.25 
.50 
.28 
.13 
.03 
0. 
1.1 
0.1833 
.83 
.57 
.37 
.21 
.09 
.02 
0. 
1.2 
.20 
.90 
.63 
.40 
.23 
.10 
.03 
0. 
1.3 
.2167 
.98 
.68 
.44 
.24 
.11 
.03 
0. 
1.4 
.2333 
1.05 
.73 
.47 
.26 
.12 
.03 
0. 
1.5 
.25 
1.13 
.78 
.50 
.28 
.13 
.03 
0. 
1.6 
.2667 
1.20 
.83 
.53 
.30 
.13 
.03 
0. 
1.7 
.2833 
1.28 
.89 
.57 
.32 
.14 
.04 
0. 
1.8 
.30 
1.35 
.94 
.60 
.34 
.15 
.04 
0. 
1.9 
0.2375 
1.90 
1.46 
1.07 
.74 
.48 
.27 
.12 
.03 
0. 
2.0 
.25 
2.00 
1.53 
1.13 
.78 
.50 
.28 
.13 
.03 
0. 
2.1 
.2625 
2.10 
1.61 
1.18 
.82 
.53 
.30 
.13 
.03 
0. 
2.2 
.275 
2.20 
1.68 
1.24 
.86 
.55 
.31 
.14 
.03 
0. 
2.3 
.2875 
2.80 
1.76 
1.29 
.90 
.58 
.32 
.14 
.04 
0. 
2.4 
.3 
2.40 
1.84 
1.35 
.94 
.60 
.34 
.15 
.04 
0. 
2.5 
.3125 
2.50 
1.91 
1.41 
.97 
.63 
.35 
.16 
.04 
0. 
2.6 
.325 
2.60 
1.99 
1.46 
1 .02 
.65 
.37 
.16 
.04 
0. 
Instead of a parabola, we might employ a flat circular curve to unite 
the two grade lines, and it may he of some interest to see what the equa- 
tions to he employed will he like. There would he this advantage, that 
the rate of change per station would he uniform, and if need he the radius 
of curvature may he made constant for all differences of gradients, the 
length of curve varying with the intersection angle. If we let l, r and d 
have the same significance as before, the length l will he given by (6) as 
soon as r has been fixed upon. 
