and Mathematics to Seismology. 183 



It will frequently be possible to divide nearly the whole of 

 a loaded area, not itself rectangular, into a small number of 

 rectangles, so that the results obtained above could doubtless 

 be utilized for obtaining approximate values of the slope in 

 many cases where the loaded area is not rectangular. 



Subcases when one Dimension of Loaded Rectangle small. 



§ 11. In iig. 4, AB represents an elongated loaded area 

 symmetrical about Ooc. If we suppose the breadth .26 small 



Fig. *. 



B 



... i' H --f --q? 



compared to the distance OA=c, and denote the length AB 

 by 2a, we easily deduce from (17) as a first approximation 



^(at'0) = (l-iy)P-r-2™()A.OB, . . . (19) 

 ax 



where PE/> .2ax2b is the total load over the area. 

 If, further, c be small compared to 2a, we have 



d £^{fitO) = (l- V )pb/irnc={l-*i)?+tonac. . (20) 



When (20) applies, the slope along the axis of symmetry 

 varies inversely as the shortest distance from the loaded area. 



§ 12. In fig. 5, AB represents an elongated area perpen- 

 dicular to the axis of symmetry Oy. 



1 



/ 



Fig. 5. 



1 



\A 





O 



Supposing first that OD( = c) and the breadth 2b are com- 

 parable, but both small compared to the length 2a, we easily 

 find from the formula corresponding to (17) 



^ (at0 )=ii^)??iog C ±^. . . , (21) 

 dy v ' nn & c v 



