484 Dr. C. V. Burton on a Physical Basis 



uniformly from the position in which G coincides with E, 

 until H coincides with F. The chance of an error lying 

 between (m 1 + m 2 ) % and (m 1 + m 2 ) { x + &#) is equal to 



hos . . ("Fraction of its time of flight during"] 



GH ' L which G H includes the element §x.\ 



(i) 



In general the curve of error will take the form A B C D 

 (fig. 8) ; where A = D = unit length, and abscissas are 



rig. a 



to be multiplied by the constant coefficient m l + m 2 . If m l = m 2 , 

 B vanishes, B and C coinciding with N ; if w x and m 2 are 

 very unequal, B C preponderates, and A B, D C are nearly 

 vertical. 



7. Next to combine two independent sources of error, each 

 following any known law. In the rectangle A B D C (fig. 9) 



Fig. 9. 



letAM = MB = ON = ND = unit of length. Let the nume- 

 rical maxima of the errors be m x and m 2 , and the curves of 

 error yi=#i(#i) or ALU, and y 2 — ^> 2 {x 2 ) orVKD. Fol- 



