REPORT ON THE STRENGTH OF MATERIALS. 99 



confident that no one would have been more happy than him- 

 self to have been enabled to substitute fact for hypothesis, had 

 he possessed the means of adopting the former. But unfor- 

 tunately such a series of experiments are too expensive and 

 laborious to be undertaken by an individual situated as he was, 

 having a family to maintain by his industry, and whose close 

 and unremitting application to these and similar inquiries, in all 

 probability shortened his valuable life*. 



At present I have referred principally to experiments made 

 with a view of determining the ultimate strength of materials ; 

 and with data thus obtained practical men have been enabled 

 to pursue their operations with safety, by keeping sufficiently 

 within the limits of the ultimate strain the materials would bear, 

 or rather with which they would just break, some working to a 

 third, others to a fourth, &c., of the ultimate strength, according 

 to the nature of the construction, or the opinion of the con- 

 structor. 



But it is to be observed, that although we may thus ensure 

 perfect safety as far as relates to absolute strength, there are 

 many cases in which a certain degree of deflection would be 

 very injurious. It is therefore highly necessary to attend also 

 to this subject, particularly as the deflection of beams and their 

 ultimate strength depend upon different principles, or are at 

 least subject to different laws. Hence most writers of late date 

 give two series of values, one exhibiting the absolute or relative 

 strength, and the other the absolute or relative elasticities. 

 These values will of course be found to differ in different au- 

 thors, on account of the uncertainty in the strength of the ma- 

 terials already referred to, but amongst recent experiments the 

 difference is not important : they will also be found differently 

 expressed, in consequence of some authors deducing these 

 numbers from experiments differently made. Some, for ex- 

 ample, have drawn their formulae for absolute strength from 

 experiments made on beams fixed at one end and loaded at the 

 other, using the whole length ; some, again, from experiments 

 on beams supported at each end and loaded in the middle, 

 using the half length. Some take the length in feet, and the 

 section in inches ; others all the dimension in inches ; and a 

 similar variety occurs in estimating the elasticity. Also, in the 

 latter case, some authors employ what is denominated the mo- 

 dulus of elasticity, in which latter case the weight of the beam 



* Mr. Tredgold's Principles of Carpentry, and his Treatise on the Strength 

 of Iron, ought to be in the possession of every practical builder; besides which 

 two works, he published many separate articles on the same subject in different 

 numbers of the Philosophical Magaziiie. 



H 2 



