UNIT OF MEASURE FOE A AND E. 65 



values of the sines, this becomes 1*8996 m. This 

 affords a strong presumption that m = 2, agreeing with 

 the deductions above. 



Fourthly, if in like manner we divide the equation 

 for < 2 by that for 2 , the numerical equation becomes 

 1-9205 = . 



It is impossible that any integer but 2 can represent 

 the value of m : and, remarking that, in the omission of 

 small terms, the equations above are not rigorously 

 correct, the value m = 2 is at once assumed for further 

 investigations ; and this gives the Final Law of Magnet- 

 ism, that attractions and repulsions of magnetic masses 

 are inversely as the square of their distance. 



29. Inference as to the numerical value of ike pro- 

 portion of A to E. Remark on the unit of measure for 

 A and E. 



Considering the law of inverse square of distance to 

 be established, unless following phenomena should con- 

 tradict or modify it (none of which do so), it has been 

 usual for experimenters to restrict themselves, for finding 

 the ratio of AB to EB, to observations with disturbing 

 needle end-on : partly because the apparatus is more 

 convenient, partly because the deflexion with a given 

 separation of needles is greater. The observations of 

 deflexion being then taken with the needles at the two 

 distances c t and c 2 , we have the two following equations, 

 which possess all the accuracy that is required for com- 

 parison with observation ; 



5 



