184 



Dr. 0. Chree on Applications of Physics 



If, further, the breadth be small compared to the shortest 

 distance from 0, we reduce (21) to 



■f?(atO)=2(l-iy)^/7rnc = (l-i7)P/29rwac, . (22) 

 ay 



where P denotes as before the total load. Comparing (20) 

 and (22) we observe that for equal distances c, the position 

 of the loaded area in fig. 5 is twice as effective as the position 

 in fig. 4. 



' Fig. 6. 



M Q 













JC 



§ 13. In fig. 6 the elongated loaded area has its centre at 

 the origin of coordinates, and the axes of Ox andO?/ are along 

 its length 2a and breadth 2b respectively. The slope is 

 required at a point Q(#, y) whose shortest distance from the 

 area is considerable compared to b. 



Draw through Q a parallel to AB cutting in M and N the 

 lines AM and BN drawn perpendicular to AB. 



From (15) and the corresponding equation we have as first 

 approximations to the components of slope 



_dw _ {l—rj)pb ( 1 1 \ 



~dx~ irn VQA QB/ 



(23) 



Jkw _ (1-77>£AM f 1 I I , 9± . 



\ QA(QA + QM) QB(QB + QN) J ^> 



dy 



irn 



In (24), QM and QN are to be treated algebraically, and 

 the formula must not be applied to cases in which either 

 QA+QM or QB + QN tends to become very small (cf. § 11). 



Numerical Illustrations. 



§ 14. Suppose in the case of symmetry, illustrated by fig. 3, 

 that the loaded area is a square 100 metres in the side, and 

 that OM, its shortest distance from ; is 1 metre. 



