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



*»$-„£ +2 =o, ,i4±^/T3- 



For the neutral points to be real and different, we must have 



. , R 2a 40 

 m>lG, — > — - . 



When the neutral points coalesce into one, we have m equal 

 16,?/ equal -v*, and for the ratio of the span to the depth, 



y- equal — , equal 4*245, or, say, the span is 4J times the 



depth. 



" As regards the horizontal tension at points along A D, 

 you take a linear function of y as I do, and your condition of 

 moments is the same as my (2), but in lieu of my (1) you 

 do what is equivalent to taking the total tension nil. You 

 further omit the correction to the vertical pressure when we 

 pass from a solid of infinite depth to one terminated by a 



P 



plane below. You further take the coefficient of— as k. a 



V 



2 

 constant to be determined by the observations, instead of — . 



" Taking the place of the neutral point (at one fourth of the 

 depth) and the ratio of span to depth as given by my formulas, 

 and then treating them as if they had been the results of 

 experiment, and substituting in your formulae for the deter- 

 mination of k, I got 0*7947 instead of 0*64. The largeness 

 of your coefficient is I think fully accounted for by the 

 employment of the formulae which you used. 



" In your method you take the stress belonging to the solid 

 supposed infinitely deep, and superpose it on the stress corre- 

 sponding to a pure bend. 



*■ This comes to the same thing as retaining three terms 

 only in the equation I gave in my letter for determining the 

 y of the neutral points. 



" The equation thus becomes 



bira y 2 Zira y 



or 



P -6 +2 = °' 



9^ 



where 



Wi = 



b 2 b 



?>ira . , r dira , 



—, — instead of ^— —4, 



