Surface-Loading on the Flexure of Beams. 



503 



" When the two neutral points merge into one, we have in 

 both cases alike y equal J b, and the only difference is that 



Sw y equals m instead of m plus 4. 



"If you had supposed the coefficient for the infinite solid to 

 be an unknown quantity k, and had applied your observations 

 to determine it, using my formulae instead of your own, you 

 would have got something very close indeed to 0*64. 



" It is noteworthy that in your problem, taken as one in 

 two dimensions, the theoretical stresses in the planes of dis- 

 placement are independent of the ratio between the two 

 elastic constants ; in other words, independent of the value 

 of Poisson's ratio." 



I have calculated the positions of the neutral points from 

 Sir George Stokes's formula 



4 _ V 16 m 



for spans of §§, 100, and 120 millim. in a beam 128 millim. 

 long x 5*5 millim. wide x 19 millim. deep. These are given 

 in the following Table in the 2nd and 3rd columns. The 

 results of actual observations (see p. 494) are given in columns 

 4 and 5 ; while columns 6 and 7 give the same points as found 

 by plotting the intersection of the curves of pure bending and 

 loading (infinite solid assumed) : — 



Span. 



Distance of Neutral Points from 



top edge, by 



Sir George Stokes's 

 formula. 



Observation. 



Intersection of 

 curves. 



88 



63 3-2 

 70 25 



7-7 1-8 



64 33 

 7-2 25 



7-8 1-8 



6-9 2-7 

 7'3 2-3 



7-8 1-75 



100 



120 





The error by the intersection method is greater in pro- 

 portion as the span is smaller, as might have been expected. 



If the observed positions of the neutral points are inserted 

 in Sir George Stokes's formula, the value 0'64 is obtained for 



2P 1 



the constant h in the equation x — — .-. 



it y 



M'Gill University, Montreal, 

 October 12, 1891. 



