8 



ART. 9. S. KU8AKABE. 



In all cases, we have between the four values the following 

 functional relation. 



L.L. + K.U.=E.L. + L.U. 

 Thus, the difference of the two sums indicates an error of observa- 

 tion : whence it gives the means of rejecting from numerous 

 observations those which are incorrect. For instance, in the 

 case of a piece of sandstone w^e had : 



TABLE II. 



To calculate the amount of bending, we have four equations 

 containing four unknown quantities. There is, however, one 

 functional relation between the four equations. At the same 

 time, the unknown quantities also may be reduced to three, as 

 d and Y appear always in one and the same combination. 

 Put x=L.L. 



x + y=L.U. 



x + z=E.L. 

 then x+y + z = K.U. 



Taking any three of the four equations, we may solve them. . It 

 is preferable, however, to use all equations, since none of them 

 is strictly correct. Applying the method of least squares we 

 have 



x = i[3L.L. + L.U. + R.L.-K.U.], 



