MU. L. N. G. FILON ON THE ELASTIC EQUILIBRIUM OF 
l>28 
Table of Q, and 5;,. 
■«. 
Sn- 
r = - 2 ( 1 . 
r = •4a. 
'/• = • 6«. 
r = a. 
r = •2a. 
r = • 4a. 
r = -Oa. 
r = a. 
0 
•036956 
• 149306 
•341554 
1-000000 
•740348 
1-502982 
2-310929 
4-16.3295 
1 
•006884 
‘030078 
•078098 
•333333 
•046574 
•106104 
• 195552 
•586933 
2 
•001551 
•007871 
•025651 
•200000 
•006457 
•018173 
•045167 
•278032 
3 
•000331 
•002073 
•009064 
•142857 
•001021 
•003803 
•013485 
•179752 
4 
•000068 
•000547 
• 003339 
•mill 
•000169 
•000813 
•004522 
•132502 
5 
•000013 
•000145 
•001266 
•090909 
•000029 
•000212 
•001619 
•104848 
6 
•000003 
•000039 
•000492 
•076923 
• 000005 
•000053 
•000604 
•086720 
/ 
•000001 
•000011 
•000195 
•066667 
•000001 
•000014 
•000232 
•073927 
8 
•000000 
•000003 
•000078 
•058824 
•000000 
•000004 
•000091 
•064419 
9 
•000000 
■000001 
•000032 
•052632 
•000000 
•000001 
•000036 
•057075 
Fig. 4. 
Table of v^. 
7- = • 2a. 
r = •4a. 
r = -Qa. 
•740348 
1-502982 
2-310929 
4-163295 
•015525 
•035368 
•065184 
• 195644 
•001291 
•003635 
•009033 
•055606 
•000146 
•000543 
•001926 
•025679 
•000019 
•000097 
•000502 
•014722 
•000003 
•000019 
•000147 
•009532 
•000000 
•000004 
•000046 
•006671 
•000000 
•000001 
•000015 
•004928 
•000000 
•000000 
•000005 
•003789 
•000000 
•000000 
•000002 
•003004 
From these, using the formulae of approximation given in the last section, when 
r = a, we obtain the values of v and the two stresses. I have tabulated them in the 
form vji>Q and (stress) /T^ where i’q, Tq are the greatest values of the displacement and 
of the shear respectively in a cylinder of the same length, subject to a uniform 
