8 Wilson, Failure of certain Cast Steel Dies. 



plane, &c., &c., the maximum stress, at the inner edge of 

 the back is 



(4) 





where 2^= distance between the supporting edges in inches. 

 „ 2£ = ^= thickness of die. 

 „ 2f' = the projection on ox of the length of the arc 



of contact of the tube and die. 

 „ 3 = decrease in external radius of the tube. 

 „ 0' = decrease in radius of hole, and may be taken = c 



in formula (4) without serious error for the 



six dies in question. 

 „ /= coefficient of friction between copper and steel 



well oiled assumed '3. 

 2e' - If 



2e + 



(See Section II.) 



„ T — —, = average radial pressure over inner face. 



Equation (4) is so easily obtained by adding the 

 stresses due to bending and bursting as to need no further 

 explanation. Table I. (pp. 6, 7) gives particulars of six dies 

 which have failed during use. The stresses are shewn by (4) 

 and (i), first in terms of T, in order that any other value 

 of T may be inserted if necessary, and, secondly, with the 

 value of 7" given by (3). The last line gives the increment 

 of stress due to a variation of one inch in the distance 

 between the supporting edges. With the exception of 

 No. 6 all the dies seem too highly strained for the 

 irregular conditions under which they work. 



That they did not fail at once seems to show that 

 when in use they were in a condition such that a flaw or 

 disturbance might be sufficient to cause fracture. The 

 most obvious remedy seems to be that of thickening the 



