224 ON A NEW MAGNETICAL INSTRUMENT. 



and, when the bar has no permanent magnetism, will vanish alto- 

 gether. In this latter case, in fact, it appears from (1) and (2) 

 that u' = u ; so that the preceding equation is reduced to 



A-5L|A. (7) 



We must remember that, since the angle u in the preceding for- 

 mulas is the deviation of the suspended magnet from the position 

 which it would assume under the action of the earth alone, its 

 changes are the differences between the observed changes of position 

 of the suspended magnet and the corresponding changes of decli- 

 nation. Let a denote the deviation of the suspended magnet, 

 measured from some fixed line, and a' the corresponding angle 

 when the iron bar is removed ; then 



., u = a - a', AM = Aa - Aa'. 



But Aa = &w, Aa' = k'n' ; in which n denotes the number of divi- 

 sions of the scale of the instrument corresponding to the angle Aa, 

 n the number corresponding to the angle A a' as shown by the de- 

 clinometer, and k and k f the arc- values of a single division in each 

 instrument. Hence 



Aw - 1m - k'n. (8) 



I now proceed to the construction of the apparatus employed 

 in these measurements. 



The magnet is cylindrical ; its length is three inches, and dia- 

 meter one-fourth of an inch. A mirror is attached to the stirrup 

 by which it is suspended, by means of which the varying position 

 of the magnet may be observed with a telescope at a distance, after 

 the method of Gauss. This mirror is of course vertical ; and it has 

 a motion round a vertical axis, by means of which it may be ad- 

 justed to any desired position of the observing telescope. The 

 mirror is circular, and is three-fourths of an inch in diameter. The 

 moveable part, the stirrup to which it is attached, has the form of a 

 cross ; and it is rendered vertical by means of three screws, near 

 the ^xtremities of three of the arms of the cross, the heads of which 

 project and hold it. The mirror is maintained in contact with 

 these heads by springs at the back. 



The box is octagonal : the interval between the opposite sides is 

 four mches, and that between the top and bottom two inches. The 



