OF ARTS AND SCIENCES. 209 



For small angles, this projection is very nearly equal to the arc 

 itself, for it is the sine of it; and if R is half the length of the needle 

 with its pointer, and M the projection on the mirror, then the angle 



. -^,( . m 



oc r= sin or sni « = — . 



R ^i 



This method obviates the difficulty of placing a plane mirror upon a 

 magnet, so that it shall be perpendicular to it, and also in a vertical 

 position in order that the image of a scale reflected from it can be seen 

 in a telescope, which is often a troublesome adjustment. It is true 

 that long pointers are needed, in order to magnify the indications of 

 the needle ; but a telescope pointed with a micrometer can be used, 

 which, after focusing on the vertical point at the end of the aluminum 

 pointer, one can focus on the deflection, and then read the fractions of 

 a division with extreme accuracy. In this case, very long pointers are 

 not necessary. The placing of the mirror perpendicular to the magnet 

 is an adjustment very easily made, for the pointer should coincide with 

 its image at the centre of suspension. A table of natural tangents is 

 therefore not necessary with this form of galvanometer. 



VOL. XI. (n. S. III.) 14 



