112 APPLICATION OP THE PRELIMINARY RESULTS 



from theory, and gives, for the determination of the constants A' 

 and fjf, the equations 



The chapter in which these experiments are related, contains 

 also a number of results, relative to the forces with which mag- 

 netized wires tend to turn towards the meridian, when retained 

 at a given angle from it, and it is easy to prove that this 

 force for a fine wire, whose variable section is s, will be propor- 

 tional to the quantity 



/ i u(p 

 I sdx 7 



j dx 



where the wire is magnetized in any way either to saturation or 

 otherwise, the integral extending over its whole length. But in 

 a cylindric wire magnetized to saturation, we have, by neglecting 

 quantities of the order a 2 , 



d<t> dX Zgf 



~f = -j- A 7T^ -* * ^~- ~ f an " s = 



dx dx 4-7T (1 ^ 



and therefore for this wire the force in question is proportional to 



( 



" 



The value of #, dependent on the nature of the substance of 

 which the needles are formed, being supposed given as it ought 

 to be, we have only to determine ft in order to compare this 



result with observation. But depends upon A = 2 log - , and 



on account of the smallness of a, A undergoes but little altera- 

 tion for very considerable variations in /u-, so that we shall be 

 able in every case to judge with sufficient accuracy what value of 

 p, ought to be employed : nevertheless, as it is always desirable 

 to avoid every thing at all vague, it will be better to determine 

 A by the condition, that the sum of the squares of the errors 



d*X' 

 committed by employing, as we have done, A , , 2 for the ap- 



