ON THE STEENGTH OF PILLAES OF CAST lEON. 
809 
the length being constant, then 
w 
=in{w 
r — r 
(V 
(K) 
for pillars of variable texture, as above. If the pillar be hollow r' = 0, and 
w=m(D" — fZ”), (C.) 
as before found. 
The falling otf in the strength of solid pillars from that of hollow ones of the same 
external diameter, and of the same kind of iron, may be seen very evidently from the 
results of the experiments in Tables I. and II., and made the subject of further investi- 
gation, if the principles assumed be admitted. 
Example I. If in a hollow pillar, n, in equation C, be 3-6, and d be taken of different 
values as below, we shall have w=77i(T)^'^—d^'^); and 
if d= j , w=m(D=’“--0078D^'=)=wX -9922 
if fZ= w=:w2(D^-^--0884D®-^)=mx-9II6 
if fZ=^, w=w(D^-^--242 D=*^)=mx-758 
if fZ=|D, w=m(D^-®--365 D^®)=mx-635 
if 6 Z=|d, w=m(D^-^~-458 D=*'*)==mx '542 
if d=~B,iv=m(D^'^--b2S D^'=)=wx-472 
Example 2. In the formula (B.), for metals of variable texture, ^ — -d'’ \, 
j.' 39—294 1 
and supposing, for example, as in Low Moor iron, — 3^ — ^”4 
if fZ= w=m(^D'-®-ix -00781 D^''^)=m(D® ®--00I9D^'®)=mx -998 D®-^=22-954 IP^; 
if d= y , w=m(^D3-^-ix -0884- =m(D=*-®--022I D3'^)=mx -9779 1^^=22-492 
if fZ=^, w=m(^D'-^-^X-242 D3'^)=m(D^'^--0605 D^'^)=mx -9395 D^-®=2I-608 
if fZ=^, ^(;=?>^(^D^•=-ix•365 =m(D^'^- -091 D^'^)=mx-909 D=’-^=20-907 
if rZ=^, w=m(^D^*-jX-458 D'®) =m(D^'®--II45 D^-^)=mx -8855 D^''^=20-366 
CO 
0^1 
The mean value of x obtained from the first six pillars in the summary (page 861) is 
2174 lbs., the power being 3-55 ; and for solid pillars it is 2029 lbs. (Exp. II and 12). 
These values for a power 3-5, as assumed in the problem above, are 2322 and 2126 lbs. 
MDCCCLVH. 5 X 
m being assumed as 
as below. 
