94 THIRD REPORT — 18"3. 



the guidance of practical men ; and by tabulating such results 

 in a subsequent part of this article, I shall endeavour to answer 

 the leading questions of the Committee of the British Associa- 

 tion, as far, at least, as relates to experimental results. In re- 

 ference to theory, it must also be admitted that some uncer- 

 tainty still remains ; but this likewise is in a great measure to 

 be referred to the nature of the materials, which is such as to 

 offer resistances by no means consistent with any fixed and 

 determinate laws. 



Hence some authors have assumed the fibres or crystals 

 composing a body to be perfectly incompressible, and others 

 as perfectly elastic ; whereas it is known that they are strictly 

 neither one nor the other, the law of resistance being difl^er- 

 ently modified in nearly every different substance ; and as it is 

 requisite theoretically to assume some determinate law of action, 

 it necessarily follows that some doubt must also hang over this 

 branch of the subject. It is, however, fortunate that whatever 

 may be the uncertainty on these points, the relative strength 

 of different beams or bolts of the same material, of similar forms 

 and submitted to similar strains, is not thereby affected ; so that 

 whatever may be the law which the fibres or particles of a 

 body observe in their resistance to compression or extension, 

 still, from the result of a well conducted series of experiments, 

 the absolute resisting force of beams of similar forms, of the 

 same materials, of any dimensions, submitted to similar strains, 

 may, as far as the mean strength can be depended upon, be 

 satisfactorily deduced. An examination of these different views 

 taken of the subject by different writers will, it is hoped, be 

 found to furnish a reply to the other queries of the Committee. 

 The first writer who endeavoured to connect this inquiry with 

 geometry, and thereby to submit it to calculations, was the ve- 

 nerable Galileo, in his Dialogues, published in 1633. He there 

 considers solid bodies as being made up of numerous small 

 fibres placed parallel to each other, and their resistance to se- 

 paration to a force applied parallel to their length, to be pro- 

 portional to their transverse area, — an assumption at once ob- 

 vious and indisputable, abstracting from the defects and irre- 

 gularities of the materials themselves. He next inquired in 

 what manner these fibres would resist a force applied perpen- 

 dicularly to their length : and here he assumed that they were 

 wholly incompressible ; that the fibres under every degree of 

 tension resisted with the same force, and, consequently, that 

 when a beam was fixed solidly in a horizontal position, with one 

 end in a wall or other immoveable mass, the resistance of the 

 integrant fibres was equal to the sum of their direct resistances 



