282 ELEMENTARY LESSONS ON [CHAP. v. 



its radius (if round), b its breadth, measured horizontally (if 

 rectangular). 



(ii.) Determination of -jj. The magnet is next caused to 

 deflect a small magnetic needle in the following manner, 

 " broadside on." The magnet is laid horizontally at right 

 angles to the magnetic meridian, and so that its middle point is 

 (magnetically) due south or due north of the small needle, and 

 at a distance r from its centre. Lying thus broadside to the 

 small needle its N.-pole will repel, and its S.-pole attract, the 

 N. -pole of the needle, and will exercise contrary actions on the 

 S.-pole of the needle. The total action of the magnet upon the 

 needle will be to deflect the latter through an angle 8, whose 



tangent is directly proportional to jj, and inversely propor- 

 tional to the cube of the distance r ; or 



M o , , 

 ~jj = r 6 tan o. 



Dividing the former equation by this, and taking the square root, 

 we get, 



M - 27r / K 



~- 7 V ^ta 



tan 5. 



NOTE ON INDEX NOTATION. 



325b. Seeing that electricians have to deal with quantities 

 requiring in some cases very large numbers, and in other cases 

 very small numbers, to express them, a system of index notation 

 is adopted, in order to obviate the use of long rows of cyphers. 

 In this system the significant figures only of a quantity are put 

 down, the cyphers at the end, or (in the case of a long decimal) 

 at the beginning, being indicated by an index written above. 

 Accordingly, we may write a thousand (=^iox lox 10) as 

 io 3 , and the quantity 42,000 may be written 42 x io 3 . The 

 British National Debt of 770,000,000 may be written ^77 x 

 io 7 . Fractional quantities will have negative indices when 

 written as exponents. Thus -^ ( o-oi), = I -f- io -j- 

 10 = io~ 2 . And so the decimal 0*00028 will be written 

 28 x io~ 5 (being = 28 x -ooooi). Trie convenience of this 

 method will be seen by an example or two on electricity. 

 The electrostatic capacity of the earth is 630,000,000 times 



