CURVE FORMULAS 
T = R tan i I 
50 tan i I 
T = 
Sin. 
Sin. 
Sin. 
| D = 
D 
50 
R 
1 D = 50 tan 
2 
R = T cot. i I 
5° 
Sin. § D 
E = R ex. sec £ I 
E = T tan i I 
Chord def. = 
R 
No. chords = ^ 
Tan. def. = J chord def. 
The square of any distance, divided bv twice the radiys, will equal 
the distance from tangent to curve, very nearly. 
To find angle for a given distance and deflection. 
Rule 1 . Multiply the given distance by .01745 (def. for T for 1 ft.) 
and divide given deflection by the product. 
Rule 2 . Multiply given deflection by 57 - 3 , and divide the product by 
the given distance. 
To find deflection for a given angle and distance. Multiply the angle 
by . 01745 , and the product by the distance. 
GENERAL DATA 
Right Angle Triangles. Square the altitude, divide by twice the 
base. Add quotient to base for hypotenuse. 
Given Base 100, Alt. io.io 2 ^200 = .5. 100-fi. 5 = 100.5 hyp. 
Given Hyp. 100 , Alt. 25 , 252 -=-200 = 3 . 125 . 100 - 3. 125 = 96.875 = Base. 
Error in first example, . 002 ; in last, . 045 . 
To find Tons of Rail in one mile of track: multiply weight per yard 
by 11 , and divide by 7 . 
Leveling. The correction for curvature and refraction, in feet 
and decimals of feet is equal to 0.574 d 2 , where d is the distance in miles. 
The correction for curvature alone is closely, §d 2 . The combined cor- 
rection is negative. 
Probable Error. If d t , d 2 , d 3 ,etc. are the discrepancies of various 
results from the mean, and if 2d “the sum of the squares of these differ- 
ences and n=the number of observations, then the probable error of the 
mean= _ r / 2d 2 
±0.6745 a 
\n(n-l) 
MINUTES IN DECIMALS OF A DEGREE 
1' 
.0167 
11' 
.1833 
21' 
.3500 
31' 
.5167 
41' 
. 6833 
51' 
. 8500 
2 
.0333 
12 
.2000 
22 
.3667 
32 
. 5333 
42 
.7000 
52 
.8667 
3 
.0500 
13 
.2167 
23 
.3833 
33 
. 5500 
43 
.7167 
53 
.8833 
4 
.0667 
14 
.2333 
24 
.4000 
34 
. 5667 
44 
.7333 
54 
. 9000 
5 
.0833 
15 
. 2500 
25 
.4167 
35 
. 5833 
45 
.7500 
55 
.9167 
6 
.1000 
16 
. 2667 
26 
.4333 
36 
. 6000 
46 
.7667 
56 
.9333 
7 
.1167 
17 
.2833 
27 
.4500 
37 
.6167 
47 
.7833 
57 
. 9500 
8 
. 1333 
18 
.3000 
28 
.4667 
38 
.6333 
48 
. 8000 
58 
.9667 
9 
. 1500 
19 
.3167 
29 
.4833 
39 
. 6500 
49 
.8167 
59 
.9833 
10 
. 1667 
20 
. 3333 
30 
. 5000 
40 
.6667 
50 
.8333 
60 
1 . 0000 
INCHES IN DECIMALS OF A FOOT 
1-16 
. 0052 
3-32 
.0078 
Vs 
.0104 
3-16 
.0156 
H 
. 0208 
5-16 
.0260 
Vs 
.0313 
.0417 
H 
.0521 
% 
.0625 
Vs 
.0729 
1 
.0833 
2 
.1667 
3 
. 2500 
4 
. 3333 
5 
.4167 
6 
.5000 
7 
. 5833 
8 
.6667 
9 
.7500 
10 
.8333 
11 
.9167 
