748 Mr. Charles E. S. Phillips [Feh. 11. 



Let us now turn to some experiments upon the flow of sand 

 through a tube. 



This long glass barrel is filled and ready. I free the nozzl^ and 

 collect the powder which flows out during 10 seconds. The quantity 

 so obtained is placed in one pan of a balance. AVhen the height of 

 sand in the tube has fallen to only a few inches above the outlet, I 

 repeat the operation, placing the second amount collected in the 

 opposite one. You see that the pans again stand level. It is there- 

 fore clear that the sand pours out at the same rate irrespective of its 

 lieight in the tube. 



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

 destroyed ? This may l)e answered by a further experiment. 



A glass cell 2 feet high, 1-4 inches wide and h inch deep, is closed 

 in at the sides only (Fig. 10). A movable section of a cone 0, 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 Y, remains wedged between the 

 glass back and front of the cell. A 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, we 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 remove the wood section the sand remains in position. 

 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, h, 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 h = r tan 35". If we consider an element of 

 the section just referred to, it is evident that a vertical downward 

 force applied to the top of the sand becomes resolved 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=T,; ••■■<.) 



where H is the horizontal thrust, W the load, / the span, and h the 

 height. 



