192 



On the Stienglii of Beayns 



point of support. After it had remained in this state about half 

 an hour, without being any more depressed than it was five mi- 

 nutes after the weight was hiid on, I subjected the fixed end to 

 a considerable pressure, and the depression increased in propor- 

 tion to the pressure, and ultimate]} tiie bar was broken without 

 any additional weight at the other cud. The experiment vvas 

 repeated with the same results. 



When a beam is supported in the middle, and a weight sus- 

 pended at each end ; the weights and the extending forces an- 

 10 each other as BD : AB ; the compressing forces will be nearly. 



if not exactly, equal to the extending forces, because there is a 

 considerable degree of pressure transmitted to the lower part of 

 the beam D, bv the exertion of the parts of the upper side to 

 retain their rectilineal position. Now the effect of the extending 

 forces to compress the beam is measured by BE, and this force 

 is resisted by the compressing forces AD, and A'D, and by the 

 support at D : therefore, BD : BE : : W (= the weight at A or 



A') : ^-^ , equal the force compressing the beam at B j and 



the strength of the beam is inversely as this pressure. 



Put L = the length, D = the depth, B = the breadth, anr' 



2E = BE = twice the deflexion 5 then the weight the bear.. 



.,, . . BD' , D , . 



will sustam, is as -r— , and as ,^,,, , that is as 



■iEW 



BD3 

 2EWL ' 



w 





If the deflexion is equal to the depth, the proportion becomes 

 W : -J— j ^"^ when it is less than the depth, we may safely 



neglect it, and make the proportion W : — r— . 



In order to compare the rule with Buffon's experiments, I 

 have taken the first experiment on the beams five inches square 

 as a standard, and the following Table shows how far it agree- 

 with the longer lengths. 



Tlic 



