Surface-Loading on the Flexure of Beams. 



483 



to be found in a more recent work by Professor Boussinesq, 

 published in 1885*. The following is a brief account of the 

 results obtained. 



Fiff. 1. 



S S / being the surface of the solid (infinite below in length, 

 width, and depth), M a point within, situate at a distance 

 MN=^ below the surface, K any element of the surface, 

 situate at the distance K M = r from the point M, and subject 

 to a given exterior pressure KP = 2?, having the component 

 K ~P / =p / along K M, the pressure which a plane element E E' 

 taken through M parallel to the surface S S' will support, per 

 unit of area, in consequence of the pressure p, will be found 

 directed along the direction of K M produced, and will be 

 equal to 



MF. 



If, as a particular case, the pressure KP —jp be normal, then 



pi —p cos NMK=p -, and 



MF 



_ 3px 2 



(2) 



If, further, it is required to find the vertical component of 



MF, we have (MF) -, or 



3p% 3 



2irr 5 



(3) 



The treatment of this particular problem is not pursued any 

 further in this work ; but Professor Boussinesq has kindly 

 furnished me with a solution more nearly applicable to the 



* Application des Potentiels a Vetude de FEquilibre et du Mouvement 

 des Solides elastiques (Gautkier-Villars, Paris, 1885). 



See also Theorie de VElasticite des Corps solides, Clebscli ; translated and 

 annotated by MM. de Saint- Venant and Flamant. (Paris : Dunod, 1883, 

 p. 374, note to art. 46.) 



2 K 2 



