or other Articles from Mines. 1 93 



to the top of the pit, it is suspended from the larger pe- 

 rimeter of one frustum, whilst the descending part of the 

 opposite chain is hanging down the pit from the smaller 



perimeter of the other, and in that position a --■ -^ j= the 

 counterpoise required at the same radius. 



Consequenilv, by supposing a, the weight of the basket 

 of coal, to be SOOlbs. and h, the weight of the descendino 

 part of the chain, 400lbs. (these are the weights which we 

 have adopted lierc), we have the counterpoise required upon 

 the cylindrical barrel, at 24 inches radius, IQOOibs. when 

 the basicet of coals is at the bottom of the pit, and 400lbs. 

 when it is at the top ; but upon the barrel formed of frus- 

 tums of right cones, the counterpoise r^-quired at 32 inches 

 radius is 600lbs. in each position. And as the counterpoise 

 required is in inverse proportion to the length of the radius 

 at which it is applied, we have 24 : 32 : : 600 : SOOlbs. the 

 counterpoise required upon the barrel formed of frustums of 

 right cones, at 24 inches radius. Again, as the descending 

 part of a chain + a basket of coal of double its weight, un- 

 bending out of equi-distant grooves from the base of a frus- 

 tum of a right cone, towards its smaller perimeter, balances 

 in every revolution of the barrel, a chain of equal weight + 

 a basket of coal, of double its weight, bending into equi- 

 distant grooves from the smaller perimeter of a similar frus- 

 tum towards its base, the counterpoise required must be 

 equal in all parts of the descent. 



So that by making the weight of the basket of coal to that 

 of the chain, and the perimeters of the frustums of cones, 

 which form the barrel, to each other, in ilic proportion of 

 two to one, a maximum is obtained, by which a' barrel of 

 this description requires one- third less momentum, (and con-^ 

 sequent ly one- third less expence,) to work it than a cylin" 

 drical one. 



The barrels are made by nailing two to three inch planks 

 upon wooden or iron curves, as in the common way, and 

 afterwards iolded, spirally, with wrought iron tire, so as to 

 leave a vacancy of about half an inch between each fold, for 

 the lower part of the ellipses of those links of the chain 

 N S whicU 



