MAGNETISM 



NS through C, in O. Let the circle with O as centre and radius 

 ON or OS meet PN in Q. Since the circle touches PS at S 



PQ . PN = PS 2 



PQ PN 



PS 2 ~ PN 2 



or PQ and PN are inversely as the squares of PN and PS 

 respectively. Produce NT to Q' so that PQ = PQ', and PS to N" so 



that PN =PN'; PQ', PN'are proportional to and in the di ruction 

 of the intensities due to the two poles, and PR, the diagonal 

 of the parallelogram PQ'RN', is the line of their resultant. 



To verify this construction for a given magnet, the magnet 

 should be laid on a sheet of paper and the direction of PR 

 determined. The sheet should be turned round till PR is in the 

 line of the magnetic meridian. On placing a compass needle at P, 

 the needle will remain in the line PR if the construction has been 

 correctly made, since the force due to the magnet is in the same 

 line as the earth's force. The agreement of experiment with calcula- 

 tion of course verifies the inverse square law. 



Gauss's proof of the inverse square law. The most 

 exact proof of the law is due to Gauss.* The general nature of 

 his method is as follows: If two points D and E be taken at 

 equal distances from the centre C of a small magnet NS, D in the 

 axis and E in the perpendicular to the axis through C, then the 

 intensity at D will be approximately double that at E if, and only 

 if, the inverse square law is true. Without entering into the full 



* Jutcnsltos I 'is Mtiynctivtv Tcrnstris (Werke, Bd. V). 



