AND THE HYPERBOLIC LAW OF ELASTICITY. [189] 



This method seems to give more accurate values than the experiments on direct com- 

 pression detailed in the Report. For those experiments were made on bars enclosed in tubes 

 of which the sides resisted the flexure of the bars ; but this resistance had of necessity great 

 effect in sustaining the external force applied longitudinally at the ends of the bars. Also part 

 of the quantities set down for the compression of each bar is probably due to the two ends 

 approaching each other by its flexure. Moreover the numerical results are very irregular, for 

 instead of exhibiting the ratio of the weight to the compression as constantly diminishing as 

 the weight increases, they represent that ratio as alternately increasing and diminishing 

 several times. 



In the following computations, the coefficients 7 and $ in the hyperbolic formula for 

 compression are deduced by three independent calculations from experiments on three bars of 

 Blaenavon iron of different sizes compared with experiments on the direct extension of the 

 same material. 



We have seen that for the mean results of the direct extension of four different sorts of 

 iron in bars 10 feet long and 1 square inch in section 



w 



= 118156.424 "i- (- + 2.41 } . 



For Blaenavon iron alone the formula is nearly the same, and from the experiments will 

 be found to be 



w = 117106.5 



G + H 



Or if the length of the rod and the extension be both measured by the same unit of 

 length, 1 inch, 



10 



= 120 X 117106.5 -r (- + 2.47 x 120j . 



Hence a = 120 x 117106.5 and /3 = 2.47 x 120. 



We have seen that for the deflection (/) of a bar of the same material 3.066 inches bv 

 1.0522 inches in section, and supported on points 13^ feet asunder, 



w = 155.64 -r- (- +.081J , or /= iv -h (155.64- -081 w). 



The general formula for deflection was found to be 



[ 16 a + 7 J 



Comparing this with the above value of/, and remembering that w = ZP, we have 



155.64 = -—■ (a + 7) (1) 



Qi 



27 d a& + 7<5 



.081 = — - — — (2) 



16 a 2 a + 7 y ' 



