336 MR. L. F. RICHARDSON: APPROXIMATE ARITHMETICAL SOLUTION 



It should, of course, be negative for a pressure. Therefore we will write 



. (25). 



I have also arrived at this result by an independent method. 



We must next consider the stretch s x . For on the surface a great way in front or 

 behind the dam one would expect s z to vanish on account of the uniformity of the 

 surface pressure. Now in MICHELL'S solution for a finite loaded portion AB all the 

 stresses vanish at an infinite distance, and therefore the stretches also. But when A 



moves off to infinity we find from (25), after differentiation, that p.s z = - 



8 



= 1 -1- -{20 4 cos 9 sin 6} . Here s z vanishes when 6 = |-TT, that is, behind 



the tail. But not when 9 = +^ir in front, under the water. 



4 - 2. T/ie detailed ivorking for a particular shape of contour. 



4'2'L The form chosen fur investigation is shown in fig. 7. It was the best 

 representation of the Assuan dam, as drawn in PEARSON'S papers, which I was able 



Fig. 7. Contour chosen for investigation. 



to obtain with so few as six co-ordinate differences to the height, without inter- 

 polation on the boundary. As a real structure it would be liable to crack at the 

 points opposite the re-entrant angles on the flank, somewhat as the unfortunate 

 Bouzey dam did, but that tendency will not affect the stresses lower down, with 

 reference to which PEARSON has given warning, and to which attention will here be 

 directed. The height, p, is 6 metres. The area of the cross-section above? the line, 



