284 A. TAN AK AD ATE 



also 





(- 



-l)"[«^.sin 



(n + l) 



(■ 





tail = — as before 



V 



Thus, taking only the increment of force, we get from equation (2) 

 A'2u s;^ / sinS . „ sinS ^ „ _ \ 



â^B ^-^^{^—^-ix^ — j—^y+ ; 



but when Ix and I y are each small p becomes very nearly r, and may 



be regarded as measured from the center of the rectangle [ 2a, 2b ]. 



We may then dispense with the sign ^ in discussing the configuration. 



Thus if 



3Ö = TT or nir 



IT n% 



or 5 = _ or -3- 



the coefficients of {ixf and {^yY vanish simultaneously. In other 

 words if the magnets are arranged occupying any four opposite 

 corners of a regular hexagon, that is if a/& be nearly 4/7,* the error 

 due to a sn-;all displacement will be eliminated up to the third order 

 of the displacement inclusive. 



The simultaneous disappearance of the coefficients of (ixf and 

 {itlY might indeed have been anticipated from the general equation 

 VW = since V is here function of only x and y we have 



ox ox^ ex oy- dx 



now IV/lx is F. Hence when either of Tt^F/lx'^ or yF/ly^ vanishes 

 the other must do so too. 



Practically it will be fouud better to make a/b somewhat larger tliau 4/7, so to obtain a 



I' rn.lKrfi nf niiifnt-iviif \r ii-i flin f'lnlil 



greater rauge of uuiformity ia the lield. 



