96 HENRY A. KOWLAND 



the curve of distribution most often reproduced from his work, he used 

 a magnetized steel bar 27 French inches long and 2 lines in diameter 

 placed vertically; opposite to it, and at a distance of 8 lines, he hung 

 a magnetic needle 3 lines in diameter and 6 lines long, tempered very 

 hard; and the number of oscillations made by it was determined. The 

 square of this number is proportional to the magnetic field at that point, 

 supposing the magnetism of the needle to be unchanged; and this, 

 corrected for the magnetism of the earth, gives the magnetic field due 

 to the magnet alone. This for points near the magnet and distant from 

 the ends is nearly proportional to the so-called magnetic surface-density 

 opposite the point. At the end Coulomb doubled the quantity thus 

 found, seeing that the bar extended only on one side of the needle. 



It will be seen that this method is only approximate, and almost 

 incapable of giving results in absolute measure. The effect on the 

 needle depends not only on that part of the bar opposite the needle, 

 but on portions to either side, and gives, as it were, the average value 

 for some distance; in the next place, the correction at the end, by 

 multiplying by 2, seems to be inadequate, and gives too small a result 

 compared with other parts. For at points distant from the end the 

 average surface-density at any point will be nearly equal to the average 

 for a short distance on both sides, while at the end it will be greater 

 than the average of a short distance measured back from the end. To 

 these errors must be added those due to the mutual induction of the 

 two magnets. 



The next method we come to is that which has been recently used 

 by M. Jamin, and consists in measuring the attraction of a piece of 

 soft iron applied at different points of the magnet. In this case it 

 does not seem to have been considered that the attraction depends not 

 only on the magnetic density at the given point, but also on that around 

 it, and that a piece of soft iron applied to a magnet changes the distri- 

 bution immediately at all points, but especially at that where the iron is 

 applied. The change is of course less when the magnet is of very hard 

 steel and the piece of soft iron small. Where, however, we wish to 

 get the distribution on soft iron, it becomes a quite serious difficulty. 

 Another source of error arises from the fact that the coefficient of 

 magnetization of soft iron is a function of the magnetization: this 

 source of error is greatest when the contact-piece is long and thin, and 

 is a minimum when it is short and thick and not in contact with the 

 magnet. Hence this method will give the best results when the con- 

 tact-piece is small and in the shape of a sphere and not in contact with 



