% 



^38 THE STRENGTH 



ments 23 and 26, to what they would have 

 been if the depth had been 5| inches, the 

 deflections from both these would have been 

 .91 ; for li^^i = .91 and '-^ = .91. The 

 lengths of the beams here being 7 feet, as in 

 experiment 24, the deflections are about | higher 

 than .71, the quantity that we have just found 

 they should have had, if the deflections had 

 been as the lengths. Comparing likewise the 

 length and deflection in experiment 28, or 

 31, with those in experiment 32, where the 

 depth was the same, we find that double the 

 length gave there more than three times the 

 deflection. 



From these different experiments w^ find, that 

 the ultimate deflections are in a higher ratio 

 than as the lengths, but are not as the square 

 of the lengths, as is generally assumed. 



3rd. — The ultimate deflections, we see, are 

 in a ratio somewhat higher than as the length; 

 and comparing those in experiments 30 and 

 33, with that in experiment 32, they appear 

 sometimes to increase faster than the depths 

 decrease. If, however, the ultimate deflections 

 were directly as the length and inversely as the 

 depth, or were higher than in both of these 

 ratios in an equal degree, we should conclude 



