all known Substances to the Magnetic Influence, ^c. lOT 



But the nature and extent of this disturbing influence will 

 be more evident, if we work out the case represented in Fig. 5, 

 exhibiting the effect of the first distance of a 12-inch magnet (C) 

 of 10 inches focal length, the powers of which, to the extent of 

 six lengths, are exhibited in the following Table. 



and FC common to both ; hence twice the squares of each must be equal. 

 Therefore the sum of the squares of F *, F n, and the sum of the squares of 

 F s\ F n' being each equal to the same thing, must be equal to one another. 

 Though, however, the sum of these several squares are equal — not so their 

 reciprocals, as is clearly shown by working out the case referred to in Fig. 5. 

 Or, take a more simple case : 



Let FC =6 4, and.C s = 3 ; then the fi- 

 gure F s C, being a right-angled triangle, 



2 2 2 



FC + C* =F«i whichgivesF* r= 5. 

 If the needle be now brought into the line 

 FC, then F«' will be (4 — 3) = 1 ; Fn' 

 = (4 + 3) = 7 ; and FC, as before, = 4. 

 Now, the sum of the squares F s and F n 

 = 25 + 25 is 50; which is equal to 



2FC +2C5 =32+18 being also 50. 



2 2 



In like manner, F ^ + F »' =, 1« + 7* 

 UK 50. Thus, as before stated, the sum of the squares of F s F n', and the sum 

 of the squares of F s' Fn' are equal, each amounting to 50, But not so the re- 



2 2 ^ 



eiprocals. The reciprocals of F s and F w 1 = 



2 ^ ^ 



and ^, their sum being ^. But the reciprocals of F s' and Fn' (» 1 and 49) 



are y- and - their sum being ^•^% = %' Hence, whilst the sums of the 

 two sets of squares are equal, their reciprocals are found to be in the relation 

 of ^ to 2, or as 1 to 12 nearly. 



25 and 25, or f and y) are ^ 



