CIRCULAR CYLINDERS UNDER CERTAIN PRACTICAL SYSTEMS OF LOAD. 203 
Thus we see we need only work out the series 
where .s has integral values ranging from 1 to 12. 
These series are easily calculated, and, to them, the sum-fornnda is quite 
applicable. 
By this means it was found that 
(1-000,0027 + (-1)'-000,0598) 
cos — 
6 
- cos2iV/6 (-031,2519 + (-1)' -000,0308) 
-f cos3i7r/6 (-004,1165 -f (-1)^' -000,0171) 
- cos477r/6 (-000,9776 + (-1)' -000,0102) 
+ cos 5t7r/6 (-000,3207 + (-1)^’ -000,0064) 
- coszV (-000,1291 + (-1)* -000,0041) 
and 
= cosiV/O (1-000,5611 + (- 1)‘-003,1246) 
- cos 2i7r/6 (-125,4607 d- (-1)*-002,1368) 
+ cos3i7r/6 (-037,4212 + (-1)'- -001,5343) 
- cos4i7r/6 (-015,9496 + (-1)' -001,1448) 
-h cos 5t7r/6 (-008,2777 -f (-1)' -000,8811) 
- costTT (-004,8694 + (-1)' -000,6956), 
and the calculation of the stresses on the boundary then became a simple matter. 
