1884.] Determination of Pressures of Granular Substances. 237 



height, greater than 60 lbs. on the square foot of side surface, and 

 that this pressure is nearly uniform between the bottom and 6 ft. off 

 the top, about which point it diminishes gradually to the top. 



That the lateral or side pressure cannot be represented, like the 

 bottom pressure, by a parabolic figure, the respective weighings prove, 

 for with the aperture of 1 square foot, and a head of wheat 44 ft. 6 ins. 

 in height, the maximum dormant pressure was 47 lbs. With the 

 aperture of 4 square feet, the maximum dormant pressure with a head 

 of 45 feet was 59 '5 lbs. on each square foot. With the aperture of 

 9 square feet and a head of 45 ft. 6 ins. the maximum dormant pres- 

 sure was 40*8 lbs. on each square foot. 



With the data given in the foregoing pages,we are now in a posi- 

 tion to compute both the vertical and lateral pressures, and to deter- 

 mine the distribution of the pressures of the wheat contained in a 

 bin of the dimensions given. They are as follows : — 



Length of bin, 6 ft. 9 ins. ; breadth of the bin, 6 ft. ; height of the 

 wheat, 51 ft. 9 ins. ; weight of the wheat, per cubic foot, 53 lbs. ; 

 weight of the wheat contained in the bin, 111,080 lbs. 



Bottom pressure computed by the formula, ax dx cXw=p, or the 

 bottom area in square feet into the diameter of the inscribed circle in 

 feet, into the constant, into the weight of wheat in pounds per cubic 

 foot, equal the pressure upon the bottom in pounds. If we substitute 

 the dimensions we shall have (6 ft. in. X 6 ft. 9 ins.) = 40 ft. 6 in. X 

 6 ft. 5 ins. x 0-84x53 lbs.=ll,569 lbs., the pressure upon the 

 bottom. 



The side pressure will be the superficial area in feet of the inside 

 of the walls of the bin multiplied by 43 lbs., or, 25 ft. 6 ins. X 

 51 ft. 9 ins. x43 lbs. = 56,744 lbs., the pressure on the four sides. I 

 adopt 43 lbs., the constant of pressure as shown by the weighings 

 with the 9 square feet aperture, in this calculation, for the reason 

 that it more closely approximates the size of the bin than the smaller 

 apertures do. The difference between the sum of the vertical and lateral 

 pressures and the whole of the weight of the wheat contained in the 

 bin would be 42,767 lbs., and this would represent the friction of the 

 wheat against the sides. This frictional pressure added to the lateral 

 pressure would represent the weight sustained by the side walls. 

 The wheat is formed into an elastic 'plug, fitting closely to the shape of 

 the bin, and each grain is held in sensitive equilibrium by the 

 resultants of the vertical, lateral, and frictional resistances. 



If a slide valve were opened in the bottom or side of the bin when 

 it is full of wheat, the equilibrium of the grains would be disturbed 

 to the extent of a vertical column having a sectional area somewhat 

 larger than the aperture of the valve, and its height equal to the head 

 of wheat. It would be a vortex column fed mostly by the wheat at 

 the top of the bin sliding into it down slopes formed by the angle of 



