Now let us put: 



[s,,]^^ = the value obtained for ..upper reading minns lower reading" in com- 

 paring line n with the spider line at the point where lines n and m 

 intersect. 



The quantities [ä„] ^ will enable us to reduce readings on the reseau line 

 to what they would hâve been if the reseau line were a straight line, cor- 

 responding exactly with the spider line. But it is better to reduce the reseau 

 line to an ideal straight line differing as little as possible from the actual 

 reseau line. To acconiplish this we form a series of équations of the form: 



[s,:]„. + n„+b„ O;i-14) = 



and détermine by least squares the raost probable values of the constants a„ 

 and h„. We then adopt as the definitive sinuosity corrections the quantities 

 [s',,]^^^ , computed by the équation: 



[«'«]„. = [«"],„ + «■" + K (»« - 1 4) (1) 



The correspondiug équation for the m lines is: 



[*•'».]„ = [«"J„ + «». + b.n [n - 43) (2) 



The quantities [s'„]^_ and [s',,,]^ are the corrections which must be added to 

 micrometer readings on the réseau lines to reduce them to what they would 

 have been if the actual réseau lines were ideal straight lines. 



As an example we give here in extenso the results obtained for line 8, 

 expressed in microns as a unit. Each number in the table is the mean of 

 four comparisons for each observer. 



