22 



CIECULAE NO. 131, BUREAU OF PLAXT INDUSTRY. 



of a large pan, narrower at the bottom than at the top. The upper 

 part varies in outhne from a cone at one extreme to half a sphere 

 at the other. The upper row of outlines in figure 2 represents these 

 two extreme forms of top and a form intermediate between them. 

 The lower row of outluies m figure 2 represents the two common 

 shapes of the bottom part of round stacks. It is necessary to cal- 

 culate the volume of the top and bottom parts separately and then 

 add them together. 



V».0 8 HO^- 



V= .08 HCc 



Fig. 2. — Diagram showing various shapes of round haystacks: 1, 2, and 3, Upper part of stacks (above the 

 bulge); 4 and 5, lower part of stacks (below the bulge). Formulas for calculating the volume are given 

 in each figure. 



Formulas ^ for making these calculations are given on the outline 

 drawings in figure 2. Thus, in drawing No. 1, the formula for finding 

 the volume of a perfectly conical top is — 



F=0.027 EC\ 



In these formulas H represents the height of that portion of the 

 stack being measured (not the full height of the stack), while C 

 represents the circumference of the bottom portion of the top — that 

 is, the circumference at the bulge or shoulder of the stack — and the 

 small superior figure "-" to the right of Vindicates that this circum- 

 ference is to be squared. 2 The formulas for outlines Nos. 2, 3, and 4 



1 The method of deriving the formulas for determining the volume of round haystacks will be apparent 

 from the following equations, 7r=3.1416: 



Solid. 



Cone 



Paraboloid 

 Spheroid . . 

 Cylinder.. 

 Frustrum . 



V^olume. 



Jsi?2/7=0.027 IJC": 



*;r/f2//=O.04O HC": 



iffie3= 0.053 i/C2. 

 gi?2 g= 0.08 HC"-. 

 HV;rjR%r2= 0.080 HCc. 



2 This formula is obtained as follows: 



^ 2\i2 



v^^ 



.; F=0.08 HC^. 



[Cir. i:;i] 



