356 Analysis of Scientific Books and Memoirs. 



The first experiments we meet with, were made on slips of yellow pine 

 and Baltic fir, with a view to ascertain the law observed between the de- 

 flections or extensions, and the weights or forces employed to produce 

 them ; and in order to avoid compression, an artificial fulcrum was con- 

 trived for the beam to turn about, whereby all the fibres might act by ex- 

 tension only. The following are the results in one of those cases. 



Weights. 



5 - 



10 - 



15 - 



20 - 



25 - 



30 - 



35 - 



40 - 



45 - 



50 - 



55 - 



minute, and then broke. 



" The two first of these experiments are the concluding ones of a series of 

 a similar kind, and were made with great care. Previous to their com- 

 mencement, a considerable weight, but still such as would not injure the 

 elasticity of the wood, was laid upon it, to make the iron recede as much 

 as possible. The weight was then taken off, and a small slip of thin tin 

 forced in between the ends of the iron. 



" The deflections in both of them, and consequently the extensions are, 

 through their whole ranges, very nearly in the proportion of the forces. 

 The same may be said of the last experiment, and of every other we made, 

 during the earlier stages of flexure ; but as we continued the experiment, 

 and arrived nearer to fracture, the extensions always increased faster than 

 the forces. — We will seek for the ultimate value of the index v in the last 

 experiment, and for that purpose shall select one of the earlier weights, as 

 20lb., with its deflection 28, and the last weight it bore or 105lb., with its 

 deflection 241 ; and since the forces were supposed to be as the v power of 



the extensions, we have 20lb. : (28) v : : 105lb : (241)"' But v in the two 

 cases is different, and in the former is = 1 (since then the extensions were 



as the forces,) and hence we haye 20 : 28 : : 105 : (241)"' or (241 ) v = 



28 X 105 



— 3q = 147. And by taking the Logarithms we have v X Log. 241 



Log. 147 2.1673173 9098 



= Log. 147, and v = f^^ x = 2 .3820170 = ToOOO = >91 nearl y- 



And pursuing the same mode with respect to the two former experi- 

 ments, and considering the tabular deflections as integers, since the result 

 will be the same, we shall have — 

 In the first, 



„ 19X240 Log. 76 



COlb. : 19 : : 240lb. : (83) = — 35 — = 76. Whence v = j e 3 = 



1.8808136 



1.9190781 



.98. 



