310 COMPARISON OF RESISTANCES. 



the expression 8 - 8 1 denoting the excess of any given measure 

 of length over the first. 



The correction a x being known, all the others will be successively 

 determined by equations (3). A further control would be obtained 

 by repeating the same series of observations with columns of different 

 lengths. The curve of the corrections obtained for a certain number 

 of points is finally traced, and from it we deduce the values for all 

 intermediate divisions. 



922. In order to obtain the best results from the control ex- 

 periments, they should be carried out systematically. 



As the first column occupies almost the th part of the total length 

 L of the scale, its extremities will always be near the n + i points 

 of division of the scale in n equal parts; these are the principal 

 points of the calibration. If X n is the excess of the reduced length 

 of the column of mercury over the th part of the length L, and 

 ^i> ^2> ^3 ---- ^n ^ e excess of the different lengths observed over 

 the same quantity, putting 



(')' ,, . L 



*,-,--, 



we might replace the n equations by the following 



J > 



in which # 15 8' 2 are quantities of the order of the corrections 



given by the readings, and A n a constant relative to this first 

 calibration. 



