August 25, 1910J 



NATURE 



259 



The question now is, how has the " head " been so 

 completely destroyed? This may be answered by a further 

 experiment. 



A glass cell 2 feet high, 14 inches wide, and \ inch 

 deep, is closed in at the sides only (Fig. 10). A movable 

 section of a cone O, made of wood and imitating 

 one of sand, is pushed up through the lower 

 opening. Resting upon this, and fitting its 

 sloping sides, is a strip of felt D. If the wood 

 section be lowered (as shown in the figure), the 

 felt, resembling an inverted V, remains wedged 

 between the glass back and front of the cell. .^ 

 very small force, however, will dislodge it. 



Suppose we replace the wood model and hold 

 it in position by a strut S. Regarding this as a 

 section of a sand cone, wo see that its entire 

 weight would be carried upon the base of the 

 cell. Sand is now poured in from the centre of 

 the top opening, and rests upon the sloping felt. 

 The point to notice is that it supports its own 

 weight. When the particles are interlocked it 

 resembles the span of an arch, for if I now re- 

 move the wood section the sand remains in posi- 

 tion. When more is added, and the cell is nearly 

 filled, the net weight is considerable, yet the felt 

 bridge is not deformed in the least. Further, a 

 wooden plunger P, fitting the top opening, and 

 carrying heavy weights, may be inserted without 

 increasing the pressure upon the felt. 



Since the angle which the slope of a dry sand- 

 cone makes with the horizontal is 35°, the height. 

 /(, to which the particles will build in a tube of 

 radius r, so that the base of the cone corresponds 

 to the diameter of the tube, is fi = rtan35°. If 

 we consider an element of the section just re- 

 ferred to, it is evident that a vertical downward 

 force applied to the top of the sand becomes re- 

 solved in two directions, making an angle of 55° 

 with the vertical. Now, applying the well-known 

 formula for a symmetrical triangular frame loaded 

 at its apex, we have 



H = ^/ (.) 



where H is the horizontal thrust, W the load. 

 I the span, and h the height. 



Regarding the cell as the section of a tube, 

 l = ir and /i = rtan35°. Therefore, substituting 

 these values in (i), we have 



2 mn 35' i-i 



The ratio of the force applied vertically to that 

 oi_ the lateral thrust is thus equal to twice the 

 tangent of the angle which the slope of a cone 

 makes with the horizontal, viz. 1.4. 



For instance, if the vertical force due to a 

 weight placed on the sand is 100 lb., the lateral 

 pressure will amount to about 71 lb. A piston 

 resting upon a column of sand only a few 

 diameters high, contained in a strong tube closed 

 at its lower end by merely a thin membrane, is 

 capable, therefore, of sustaining very heavy 

 loads. 



In order to demonstrate thi> on a moderate 

 scale, I have arranged a sort of gallows, through 

 the projecting arm of which a flanged brass tube 

 is inserted vertically. This tube is 0-5 inch in 

 diameter, and closed at its lower extremity with 

 a piece of cigarette paper held in position by an 

 indiarubber band. A small quantity of sand is 

 tipped into the tube from above — enough to fill 

 it to a height of 3 inches. The column within 

 will therefore measure 6 diameters. The tube is 

 then well tapped to ensure normal piling of 

 the grains, and a loosely fitting iron plunger 

 is inserted so as to rest upon the sand, .\ttached 

 to the plunger is a cross-piece carrying a ring at each 

 end. which may be grasped with the hands. My 

 assistant (who weighs about 11 stonel thus suspends him- 



NO. 2130, VOL. 84] 



self safely, his weight being supported by the small sand 

 column. If the piece of cigarette paper is now removed, he 

 is let down with an unpleasant jerk. 



Some idea of the close arrangement of the particles 

 may be gathered by noticing that a long column of sand. 



moving downward within such a tube, will produce a 

 vacuum above it sufficient to lift water to a height of 

 about 6 feet. (E.xperimentally shown.) 

 These experiments upon loaded sand columns clearly 



