258 Mr. L. F. Richardson on a Freehand Graphic way 
the length of one turn is 
+ 
4ttV 2 
Therefore we may satisfy the equation V 2 «=0 by making 
a proportional to \/ l-\ ^— as the radius varies. A 
H 
I 2 
47T 2 ?' 2 
table giving the values of \ / 1 4 ™ — for a number of 
P 
values of j is annexed. 
r 
/ 4ttV 2 
A / 1+— 77- 
For standard chart. 
I 
T 
I times this equals arc 
2irr 
equals tangent of angle 
of one turn of thread. 
H a' 
%• 
between helix and circle. 

1-0000 
•5507 
1-8157 
CO 
•05 
1-0482 
•5639 
1-7735 
3-1831 
•10 
1-1811 
•5985 
1-6707 
1-5916 
•15 
1-3741 
•6456 
1-5490 
1-0610 
•20 
•30 
1-6060 
•6979 
1-4328 
•7958 
2-1338 
•8045 
1-2430 
•53052 
•40 
2-7049 
•9058 
1-1040 
•39789 
•50 
3-2969 
1-0000 
10000 
•31831 
•60 
3-9003 
1-0877 
•9194 
•26526 
•70 
4-5105 
1-1697 
•8550 
•22736 
•80 
5-1251 
1-2468 
•8021 
•19894 
•90 
5-7426 
1-3198 
•7577 
•17684 
1-00 
6-3623 
1-3892 
•7199 
•15916 
1-5 
9-478 
1-6955 
•5898 
•10610 
20 
12-606 
1-9554 
•5114 
•07958 
25 
15740 
2-1850 
•4577 
•06366 
30 
18-876 
2-3928 
•4179 
•05305 
35 
22-014 
2-5840 
•3870 
•04547 
oc 
GO 
00 

oo 
It is hoped that these values are correct to les 
half a unit in the last place. 
than 
As there is no surface normal to the screw-threads, it is 
not possible to draw standard rectangles of the appropriate 
chequer ratio for each distance from the axis. But as the 
whole distribution of Y is determined when the section of it 
by a plane passing through the axis of the screw is known, 
