96 THIilD REPORT 1838. 



my expei'iments showed very distinctly after the fracture the 

 line about which the fracture took place, I thought of availing 

 myself of this datum, and that which gave the strength of direct 

 cohesion, in order to deduce the law of resistance ft-om actual 

 experiment, instead of using any assumed law whatever. 



The result of this investigation implied that the resistance 

 was nearly as first assumed by Galileo, and although very dif- 

 ferent from what I had anticipated, yet, as an experimental re- 

 sult, I felt bound to abide by it, attributing the discrepance to 

 the imperfect elastic properties of the material. Mr. Hodgkin- 

 son, however, in a very ingenious paper read at the Manchester 

 Philosophical Society in 1822, has pointed out an error in 

 my investigation, by my having assumed the momentum of 

 the forces on each side the neutral axis as equal to each other, 

 instead of the forces themselves ; consequently the above de- 

 duction in favour of the Galilean hypothesis fails. This paper 

 did not come to my knowledge till the third edition of my Essay 

 was nearly printed off, and the correction could not then be 

 made; but being made, it proves that the law of actual resistance 

 approaches much nearer to that of perfect elasticity than from 

 the nature of the materials there could be any I'eason to expect ; 

 so that in cases where the position of the neutral axis is known, 

 and also its resistance to direct cohesion, a tolerably close ap- 

 proximation may be made to the transverse strength of a beam 

 of any form, by assuming the resistance to extension to be pro- 

 portional to the quantity of extension, and the centre of com- 

 pression as the fulcrum about which that resistance is exerted. 

 But I have before observed, and beg again to repeat, that by 

 far the most satisfactory data will always be obtained by ex- 

 periments on beams of the like form (however small the scale,) 

 and of the same material as those to be employed, because then 

 the law of resistance forms no part of the inquiry, and does not 

 necessarily enter into the calculation, the ultimate strengths 

 being dependent on the dimensions only, whatever may be the 

 absolute or relative resistance of the fibres to the two forces 

 we have been considering. 



At present I have only considered the resistance of a beam 

 to a transverse strain ; but there is another mode of application, 

 in which, again, the law of resistance necessarily enters, and 

 has led to many curious and even mysterious conclusions. This 

 is when a force of compression is applied parallel to the length. 

 In the case of short blocks, the resistance of the material to a 

 crushing force is all that is necessary to be known ; and in the 

 Philosophical Transactions for 1818 we have a highly valuable 

 table of experimental results on a great variety of materials, by 



