1904-5.] Mr T. Oliver on Diameters of Twisted Threads. 493 
Tables of Functions. 
e 2 
0 
•1 
•2 
•3 
•4 
•5 
■6 
■7 
■8 
1-571 
1-612 
1-660 
1-713 
1-777 
1-854 
1-950 
2-076 
2-257 
Fx+1 
2-571 
2-612 
2-660 
2-713 
2-777 
2-854 
2-950 
3-076 
3 257 
3-274 
3 326 
3-388 
3-455 
3-537 
3-634 
3-757 
3-917 
4-148 
l-<? 2 
1* 
•9 
•8 
•7 
•6 
•5 
■4 
•3 
•2 
-v/l-e 2 
1* 
•9487 
•8944 
•8367 
•7746 
•7071 
•6325 
•5477 
•4472 
1 +V /I_e2 
2' 
1-9487 
1-8944 
1-8367 
1-7746 
1-7071 
1-6325 
1-5477 
1-4472 : 
Vl-e 2 /(l+\/l-e 2 ) 
•5 
•4887 
•4722 
•4555 
•4364 
•4142 
•3875 
•3538 
•3091 ! 
Mean projection width 
1-637 d 
1 "619(2 
1*600(2 
1-574(2 
1-546(2 
1-505(2 
1-456(2 
1-387(2 
1-282(2 
(i+v'T 1 ^ 2 ) 2 
4- 
3-799 
3 J 587 
3-375 
3-150 
2-914 
2-662 
2-397 
2-094 ; 
•2500 
•2498 
•2493 
•2479 
•2459 
•2427 
•2375 
•2285 
•2136 
Sectional area of thd. 
7T(f 2 
•2500 
•2498 
•2493 
-2479 
•2459 
•2427 
•2375 
2285 
•2136 
tj -^2 j~y 
The sectional area of thread = irab = , - 7 rd 2 ^ v 
(1+Vl-e 2 ) 2 
Table showing the variation in the width of projection from 
e 2 = 0 to e 2 = '6 through J turn of twist (when a + b = d). 
Tallies of 9 
Values of 
<2 2 
I 
0 
•1 
*2 
•3 
-4 
•5 
•6 
0° 
2*000(7 
1-947(7 
1-889(7 
1-822(7 
1-746(7 
1-657(7 
1-550(7 
10° 
1 ‘985(7 
1-934(7 
1-877(7 
1-815(7 
1-739(7 
1 -652(7 
1-545(7 
20° 
1 "940(7 
1-894(7 
1-843(7 
1-784(7 
1-716(7 
1 -633c7 
1-532(7 
30° 
1-866(7 
1 -830(7 
1-786(7 
1-737(7 
1-676(7 
1-604(7 
1-512(7 
40° 
1-766(7 
1-740(7 
1-710(7 
1-671(7 
1-624(7 
1-565(7 
1-486(7 
50° 
1*643(7 
1 629(7 
1-613(7 
1 -590(7 
1*559(7 
1-518(7 
1-460(7 
60° 
1-500(7 
1-499(7 
1-497(7 
1-490(7 
1-480(7 
1-463(7 
1 -432(7 
70° 
1 -342(7 
1-351(7 
1-362(7 
1-375(7 
1-384(7 
1-393(7 
1-395(7 
80° 
1-174(7 
1-194(7 
1-217(7 
1-241(7 
1-268(7 
1 -299(7 
1-333(7 
90° 
1-000(7 
1-026(7 
1-055(7 
1-091(7 
1-127(7 
1-172(7 
1-225(7 
Mean Values 
1-637(7 
1-619(7 
1-600(7 
1-574(7 
1 -546(7 
1-505(7 
1*456(7 
Maximum Value 
Minimum Value 
2*00 
1-90 
1-79 
1-67 
1-55 
1-41 
1-26 
