ON THE STRENGTH OF PILLARS. 
455 
Explanation of the Plates. 
Fig. I. Plate XIII. represents the lever and other apparatus used for breaking the 
pillars : it has been described in the commencement of this paper (Art. 2.). 
Fig. 2. Plate XIV. shows the manner in which the pillars were subjected to a 
constant strain, to try the effect of time upon them (Art. 53.). 
Figs, a, b, c, &c. to n, Plate XV. are the forms of the fractures from some of the 
solid pillars with rounded ends in Table I., the pillars as they appeared after frac- 
ture being drawn and placed over the forms of the fractures. 
Figs, o, p , q, r, s, t, u, v, Plate XV. are the forms of the fractures from the shorter 
pillars with flat ends in Table II. ; and the figures over them represent the appearances 
after fracture of the pillars they were obtained from, with marks upon the pillars, 
showing the places where they broke. All these sections are referred to in Tables I. 
and II. In many of these pillars there was a crack after fracture, showing the posi- 
tion of the neutral line ; and in some, the compressed part broke off as a wedge, the 
form of which may be seen from the marks upon the pillars. 
The groups of pillars, designated as No. 1, No. 2, No. 3, &c. Plate XV. are intended 
to represent the forms of the different cast-iron pillars broken, with marks upon 
them, showing where they usually broke. Those in No. 1, which may be considered 
as including the longer pillars in Tables I., II., V., represent three pillars of the same 
material, length and diameter, whose relative strengths are as 1, 2, 3, nearly. 
No. 2. are pillars differing from those of No. 1, in having discs upon the flat ends, 
to give them a larger bearing ; the results showing that a small increase of strength 
is obtained by that addition. 
No. 4. represents the forms of the pillars in Tables VI. and VII., which generally gave 
strengths about one-seventh or one-eighth above those obtained from uniform solid 
pillars of the same length and weight. The marks upon them show where they usually 
broke. 
No. 5. includes pillars formed to show the effect of defective fixing; a pillar so 
placed that the pressure would pass through the diagonal, bearing only about one- 
third of what it would have done if the ends had been pressed upon through their 
whole surface (Table XI.). 
No. 6. The second pillar in this group is intended, by its section in the middle, to 
represent the connecting rod of a steam-engine ; and experiment shows that it is very 
weak compared with a hollow cylinder of the same length, weight, and lateral dimen- 
sions (Table XL, Art. 48.). The first form of pillar in No. 6. gave strengths greater 
than the second, but still less than a hollow cylinder would. 
No. 7- shows the relative diameters of the hollow pillars in Table VIII., broken 
with rounded caps upon the ends, the caps being shown near to the pillars. 
No. 8. represents the hollow pillars in Table IX., broken, with their ends flat ; the 
rings round the three first pillars given, show the manner in which some of these 
