526 



4^, 3i, 2i, 11, '\o, 2^„ 3o, 4o pulling 011 the chain in a vertical direction, 

 perpendicularly to AB, then a diagram is drawn in the following 



X 



Fig. 4. 

 manner. Parallel to AB a line OM is drawn representing the longi- 

 tudinal strain of the chain. Perpendicularly to (he end of OM 

 OB is drawn, and on this line parts 0(t, GF, i<'^ 'are taken repre- 

 senting the pulls 4i, 3i etc. to 4„ on the same scale as has been* 

 used with OAI. The points of division in the line DC are joined 

 with M. From B a line is drawn, parallel to ilfC, till it intersects with 

 H^. From there a line is drawn, parallel to ME, till it intersects 

 with K3a etc. In this way we finally get the line BNA, which 

 represents the shape of the chain. 



Theoretically this construction would also be correct, if the number of 

 the lateral loads were infinitely great and their distances infinitely small. 



If we regard this method of construction more closely, we imme- 

 diately see that the line OC represents the sum of all the lateral 

 forces, if we start in the middle of the chain. We may consequently 

 consider the distance from every point of that line to the point O 

 as the integral of the lateral forces. If these be represented by the 

 expression f{Z) and if the forces act at distances dl from each 



other, then \f{Z)dl is an expression for the length of each part of 



the line OC, reckoned from the point O. 



