OF AETS 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 H is half the length of the needle 



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



— m ' wi 



a: = sm . or sm ce = — . 



R ^ 



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 frjam 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. 8. III.) 14 



