Prof. E. Bouty's Studies on Magnetism. 195 



rated needles. Indeed the asymptotes of all the curves corre- 

 sponding to needles of the same diameter cut the axis of x m 

 exactly the same point. This has been verified 



On 3 curves for needles of 0'551 millim. 

 „ 2 „ „ 0-398 „ 



„ 3 „ „ 0282 „ 



„ 2 „ „ 0175 „ 



Further, in the case we are considering, the complete curve is 

 only a proportional reduction of the curve for saturated needles. 

 It i's exactly represented, within the same limits, by the equation 



2e *- e ~*\ .... (9) 



y=mAa 2 x- 



e* +e 



in which m is a factor whose value is less than 1, depending on 

 the degree of magnetization of the mother needle. 



Table VI. 







Curve R. 





1 



Curve S. 





Difference. 



Observed. 



Calculated. 



millim. 











3 



5-60 



4-40 



4013 



+0-387 



4 



1200 



8-60 



8-597 



+0003 



5 



2000 



1415 



14-317 



-0167 



6 



3000 



2100 



21-492 



-0-492 



7 



4200 



29-50 



30-088 



-0-588 



8 



55 50 



39-60 



39-760 



-0 160 



9 



70-20 



5050 



50-290 



+0-210 



10 



85-60 



61-20 



61-323 



-0123 



The above Table refers to a needle of 0*551 millim. diameter. 

 The second column contains the moment of saturation of the needles 

 as furnished by the experimental curve, and the third the moment 

 of the rupture-needles ; the numbers in the fourth column were 

 obtained by multiplying those in the second by the ratio m of 

 the angular coefficients of the two asymptotes ; the fifth column 

 gives the differences between the observed and the calculated 

 numbers. 



Above 10 millims. the curves approach very closely their 

 asymptotes, and the comparison which forms the object of this 

 Table ceases to be of interest. 



Note that the poles of short rupture-needles are situated the 

 same as if the needles were saturated. 



II. These different results do not apply to thicker needles (of 

 1 to 2 millims. diameter for example). In the first place, the 

 asymptotes to the different curves corresponding to needles of 



02 



