114 



APPLICATION OF THE PRELIMINARY RESULTS 



turn towards the meridian, in order to compare the results with 

 the table of COULOMB'S observations, given by M. BIOT (Traitt 

 de Phy. Tome 3, p. 84). Now we have before proved that this 

 force for any wire may be represented by 





where, for abridgment, we have supposed 



It has also been shown that for any steel wire 



aj3 = .0548235, 



the French inch being the unit of space, and as in the present 

 case a = , there results /3 = .657882. It only remains there- 



fore to determine K from one observation, the first for example, 

 from which we obtain K= 5 8. 5 very nearly ; the forces being 

 measured by their equivalent torsions. With this value of K 

 we have calculated the last column of the following table : 



The last three observations have been purposely omitted, be- 

 cause the approximate equation (a) does not hold good for very 

 short wires. 



The very small difference existing between the observed and 

 calculated results will appear the more remarkable, if we reflect 

 that the value of /3 was determined from an experiment of quite 

 a different kind to any of the present series, and that only one 

 of these has been employed for the determination of the constant 



