498 Prof. C. A. Carus Wilson on the Influence of 



To find k the beam is placed on two supports and centrally 

 loaded ; the two points where the black bands cross the 

 normal are observed (the span being longer than four depths) , 

 and plotted, and an hyperbola drawn through them ; a tangent 

 is then drawn to this curve from the centre of the section 

 and its intercept on the upper edge measured, the span giving 

 coincidence of the black bands can then be calculated. 



Experiment 8. For a beam 128 millim. x 19 millim. deep 

 x 5*5 millim. I find this span to be 73 millim. ; hence 



73 

 19 



Q 



Taking 6 at 0*04 millim., j— 0*002 millim., and neglecting 

 i-K we nave 



p =~=3'8±. 



A = f x 3-84 x 0-252 = 0-726. 



Proposition VI. 



To verify the equation to the curve of loading. 



Experiment 9. Beam 128 millim. x 19 millim. x 5*5 millim. 



The stress corresponding to the blue fringe with this beam 

 was found, as already explained, by loading the beam over a 

 span of 120 millim., until the blue fringe appeared at the 

 bottom of the beam ; the load required was 55 lb. ; hence the 

 corresponding stress is 1*436 tons per square inch*. 



When laid on the base of the steel frame, the same fringe 

 was observed at 1*7 millim. from the top with a load of 65 lb. 



From the equation to the curve of loading, taking k = 0*726, 

 = 0*04 millim., we ought to have a stress at 1*7 millim. 

 from the top equal to 



25-42 g5 1 



y — 0*726 X . . x —^2 X kT? = 1*419 tons per square inch. 



The lines of Principal Stress afford a convenient means of 

 studying the condition of strain in a bent beam. 



In a memoir published in 1838 f Lame discussed the 



W 



* From the equation y=k — there is a compressive stress of 0*121 ton 



per square inch here due to the load. I have not added the effect of this 

 to that of the bending, as there is no proof that the superposition of small 

 strains holds when the strains themselves are so unequal. 



t Comptes Rendus, vol. vii. p. 778: "Memoire sur les surfaces iso- 

 statiques dans les corps solides en equilibre d 'elasticity." 



