64 ON MAGNETISM. 



Disturbing needle broadside-on. 



l'O foot. 



4. 29'. 20". 



c = 1*5 foot. 



Disturbing needle end-on. 



= 



I'D foot. 



'2 



< 2 = 2.29'.52". 

 It is to be remarked that 



c =r5foot. 



3.375 . ? = 5-0625. 



Now first, dividing the first equation above by the 

 second, we get the approximate equation 



Substituting the numerical values of sin d l and sin 9 V 

 this becomes 3*4490 = (l'5) m+1 . Looking at the powers 

 of 1*5 placed above, it is impossible that m + 1 can be 

 2 or 4, but the equation is so nearly true when m+l=3, 

 (that is, 3*4490 approaches so near to 3'375) as to afford 

 strong presumption that m + 1 = 3. 



Secondly, we obtain in the same way -: -j 1 ap- 



sin < 2 



(0 \m+l . 

 J . Substituting the numerical va- 

 lues of < x and < 2 , this becomes 3*4115 = (l*5) m+1 . This 

 is very nearly correct if m + 1 = 3. 



Thirdly, if we divide the equation for ^ by that for 



0, we obtain . 7 = m. Substituting the numerical 



1 ein H w 



