ON THE STRENGTH OF PILLARS. 
425 
Hereof = 1" : 1-47” : : 1754 : 7888. Reducing gives n = 3’902. 
Whence the strength is nearly as the fourth power of the side of the square. 
I made no experiments to ascertain the inverse power of the length to which the 
strength is proportional in timber. The great flexibility of such long and slender 
pieces as would have been necessary to give sufficient variety in their length, — and for 
the length of the shortest to be a sufficient number of times the thickness, that it 
would not be sensibly crushed by the breaking weight, — convinced me that it would 
be as well to seek for this power hypothetically, as to endeavour to obtain it by ex- 
periments, which would probably be unsatisfactory. 
I therefore assumed (after trying some other hypotheses less successfully,) the 
d 4 
strength of timber to be as - p , which is the simple conclusion of Euler. 
ci d * 
Whence b = —p, where the constant a must be obtained from experiment, for any 
particular kind of wood. 
Dantzic Oak. 
The experiments in Table XIII. upon square pillars of this wood flat at the ends, 
give as below : 
1st. From a mean of the results of four experiments, a pillar 60| inches = 
5’04166 feet long, and T75 inches square, required 9625 lbs. to break it. Whence, 
taking the length in feet and the lateral dimensions in inches, w r e have ^in the for- 
a d 4 \ b P 
mula b = -p) b = 9625, d= 175, 1= 5'04166 a = = 26085. 
2nd. From a mean of three experiments upon pillars 46T inches = 3 - 84 166 feet 
long, and T50 inches square, the breaking weight was 7888 lbs. ; which gives a, ob- 
tained as above, = 22999 lbs. 
d 4 
A mean between these two values of a is 24542 lbs. ; whence b = 24542 ~p- 
Here the length is in feet, the side of the square in inches, find the weight in lbs. ; 
and the rule is only applicable to cases where the pillar is in length so many times 
the thickness that it is not crushed, as in Articles 6. and 59, by the breaking weight. 
These remarks apply to the following cases : 
Red Deal. 
The results from two experiments upon square pillars of this wood, each four feet 
d 4 
ten inches long, and two inches square, Table XIII., give b =17511 ; the different 
values being as above. 
3 i 
MDCCCXL. 
