188 Prof. E. Bouty's Studies on Magnetism. 



In this formula, A is a constant depending only on the nature 



of the steel, and /3 a quantity of the form — , B being a second 



constant. The diameter of the needles is represented by a. 



The formula is conformable to the results of Coulomb's expe- 

 riments*. I propose to verify it for the particular case of needles 

 of very slight diameter and little length. 



I. Needles of the same diameter. — The temper of the needles 

 compared should be identical; the breaking of a saturated, 

 quite regular cylindrical needle furnishes saturated needles in 

 that condition. They are saturated; for the primitive needle 

 possesses in every point of it a higher degree of magnetism than 

 corresponds to the saturation of the fragment which belongs to it 

 after the breaking. The breaking itself has, according to the 

 preceding, no other effect than that which would result from the 

 separation of the parts which were in precise juxtaposition. 

 Finally, the temper is as identical as possible ; we shall even see 

 that employing the results eliminates the minute differences of 

 local temper which cannot be entirely avoided. 



The mother needle is magnetized to saturation, by at least 

 four Bunsen elements, in a coil of 25 centims. length, very 

 regular, and formed of three superposed layers of wire. In order 

 to make an experiment, the length and magnetic moment of the 

 entire needle are measured; the two ends are then removed by 

 breaking them off at 3J or 4 centims. distance from the extre- 

 mities, preserving the end fragments ; the length of the middle 

 fragment and its magnetic moment are measured, and by suc- 

 cessive breakings, each accompanied by two measurements, it is 

 reduced to a length of 1 or 2 millims. The experiment is finished 

 by measuring the length and magnetic moment of the two ends, 

 entire and reduced to successively shorter lengths. 



It is rare that all the measurements can be accomplished with 

 one and the same apparatus; two are therefore employed : — one 

 less delicate, for the greater lengths ; the other more delicate, 

 for the shorter ones. The ratio of the two apparatus is deter- 

 mined with the greatest care by a number of measurements taken 

 from both. 



In order to be clear of all accidental irregularities, the results 

 of the experiments are represented by a curve — the lengths x of 

 the needles being taken for the abscissae, and the corresponding 

 magnetic moments for the ordinates. This curve is traced with 

 extreme care by means of the measurements made on the middle 

 fragments of the mother needle. If this needle is saturated, the 



* Coulomb, " Determination des forces qui ramenent differentes aiguilles 

 aimantees aleur meridien magnetique," Mem. de VInstitut, vol. lii. 



