146 Mr. H. A. Rowland on Magnetic Permeability, 



For the infinite electromagnet we have in the same way for 

 a circular section, 



Q' = 47rM/*(7rR 2 ) (7) 



When the section of the ring is thin, equation (6) becomes 

 the same as equation (7), and either of them will give 



X=47r ^ = KRW • " - ' • (8) 

 which is the same as equation (5). 



In all the rings used the last parenthesis of (6) is so nearly 

 unity that the difference has in most cases been neglected, the 

 slightest change in the quality of the iron producing many 

 times more effect on the permeability than this. Whenever 

 the difference amounted to more than ^io ^ was n0 ^ rejected. 



The apparatus used to measure Q' was based upon the fact 

 discovered by Faraday, that the current induced in a closed cir- 

 cuit is proportional to the number of lines of force cut by the 

 wire, and that the deflection of the galvanometer-needle is also, 

 for small deflections, proportional to that number. In the ex- 

 periments of 1870-71 an ordinary astatic galvanometer was 

 used; but in those made this year a galvanometer was specially 

 constructed for the purpose. It was on the principle of Thom- 

 son's reflecting instrument, but was modified to suit the case by 

 increasing the size of the mirror to § of an inch, by adding an 

 astatic needle just above the coil without adding another coil, by 

 loading the needle to make it vibrate slowly, and, lastly, by looking 

 at the reflected image of the scale through a telescope instead of 

 observing the reflection of a lamp on the scale. The galvano- 

 meter rested on a firm bracket attached to the wall of the labo- 

 ratory near its foundation. In most of the experiments the 

 needle made about five single vibrations per minute. The 

 astatic needle was added to prevent any external magnetic force 

 from deflecting the needle ; and directive force was given by the 

 magnet above. Each division of the scale was *075 inch long ; 

 and the extremities of the scale were reached by a deflection of 

 7° in the needle from 0. The scale was bent to a radius of 4 

 feet, and was 3 feet from the instrument. At first a correction 

 was made for the resistance of the air &c. ; but it was afterwards 

 found by experiment that the correction was very exactly pro- 

 portional to the deflection, and hence could be dispensed with. 

 This instrument gave almost perfect satisfaction j and its accu- 

 racy will be shown presently. 



The tangent-galvanometer was also a very fine instrument, 

 and was constructed expressly for this series of experiments. 

 The neeclle was 1*1 inch long, of hardened steel j and its deflec- 



