CALIBRATION OF A GLASS TUBE. 313 



As the corrections a o and a n are zero, we have the values of 

 aj and <*> n -i directly, and therefore those of all the other principal 

 points. 



The calculation presents several verifications on which it is useless 

 to insist here. The curve constructed with these different values of 

 a will show by its continuity whether the subdivision of the tube has 

 been carried so far that we could deduce the corrections for the 

 intermediate points. For more details we must refer to the memoir 

 published by M. Benoit on this subject. 



923. The mean capacity v of one division of the tube at zero is 

 then determined by observing the number n of divisions corrected 

 for errors of calibration, and for the spherical curvature of the ends, 

 which a weight p of mercury occupies in melting ice, and the experi- 

 ment will be repeated as a control with columns of different lengths. 

 If d is the specific gravity of mercury, and e the length of a division 

 at zero, we have 



md' 



If, lastly, p is the specific resistance of mercury that is to say, 

 the resistance of a column of unit length and of unit section, s the 

 section of the tube corresponding to any given division, the total 

 resistance of the tube is 



-. 



It is not really necessary to calculate the section at each point. 

 If we consider the column comprised between two divisions a and , 

 the corrections for which are a and /?, the mean section of this 

 column is 



/3-a\ 

 *-/ J 



and the corresponding resistance 



r= p 



J. R. BENOIT. Travaux et Memoires du bureau international des poids 

 et mesures. Vol. n., Part i., p. C. 35, 1883. 



