Lieut.-Col. A. R. Clarke on the Elasticity of Brass. 133 



II., III., IV. ; and the flexure was measured with each face up ; 

 so that each bar gives four values of E : the round rod was 

 also observed in four positions. In the case of this rod, 



~, wl z ,^ . x 



where k is its radius. 



To combine the four values of E in each case, we should 

 proceed as follows : — if dw, dl, ... be the corrections necessary 

 to the observed values of these quantities, we must express the 

 consequent corrections to the computed values of E. Let the 

 first two (that is, the values of E resulting from the opposite 

 faces I. and III.) be multiplied each by a factor ^(1 + #), and 

 the other two by J(l — 0) ; then it is easy to express the pro- 

 bable error of the resulting value of E in terms of the probable 

 errors of the observations ; and the value of 6 to be used is that 

 which renders this expression a minimum. In the present 

 case, however, the first two rods are very nearly square in sec- 

 tion ; and the third rod giving identical values (or nearly) for 

 E, the multipliers are immaterial. We therefore take the 

 mean of the four computed values with a probable error 



E 





+ 4 



&*i) 



BA 2 +^^ 2 



for the square rods, and 



±e{^ 



+ 9 



'dl 2 , iP B^ 



l- 



*16^ + 



25 



1 



^rf+^de 3 



2 



r 



V 



*<!■ 



} 



for the round rod, where 



f ~~ \§\e\ + e\ + e\ + e\P 



the symbol B meaning probable error ; ~dh is taken to be the 

 probable error of either h or k ; and the four e's are assumed to 

 be determined with the same accuracy, 



This last supposition is not, however, quite exact. In the 

 following Table the values of e are given for each face of each 

 rod, the probable error being that resulting from the agreement 

 of the eight determinations made with each face up. 



Rod. 



Face I. up. 



Face II. up. 



Face III. up. 



Face IV. up. 







in. 



in. 



No. 1. 



{ 



0-20670+3 

 020716 + 4 



0-21328+2 

 0-21342+2 



„ 2. 



1 



0-20913 + 1 



0-20885+4 



0-20831+2 

 0-20803+2 



„ 3. 



I 



0-26910+3 

 0-26910 + 1 



0-14719 + 1 

 014715+2 



„ 4. 



I 



014875 + 2 

 0-14853 + 5 



0-14882 + 2 

 014912 + 1 











