THE COMPASS-NEEDLE ON THE DEVIATIONS OE THE COMPASS. 
• 169 
3. The effective power of each needle in correcting a quadrantal deviation is inversely 
proportional to the horizontal force of the earth at the place. A quadrantal deviation 
completely corrected in England, would therefore reappear to nearly half its amount 
near the magnetic equator ; the correction would, however, become again perfect as the 
vessel went further to the south. In lower magnetic latitudes, or more accurately when 
the horizontal force is greater than in the place of correction, the correction, though 
insufficient, would be beneficial. In higher magnetic latitudes, the quadrantal deviation 
would be over-corrected. These defects admit of beiug remedied by a provision for 
adjusting the mutual distances of the compasses, and it is probably only in very high 
magnetic latitudes that this mode of correction would have to be abandoned. 
On the whole, we venture to anticipate that this mode of correcting the quadrantal 
deviation will be found of advantage in the case of corrected steering compasses in large 
hon-built ships. 
Mathematical Investigation of the Effect of the Length and Arrangement 
of the Needles. 
In the following part of the paper it has not been thought necessary to give the details 
of the mathematical operations. Those expressions only are given which are directly 
apphcable in illustration of the experiments described in the preceding part. 
In this investigation a bar magnet, and likewise a compass needle, is supposed to 
consist of two particles of N. and S. magnetism, separated by a finite interval. 
Let A be a magnetic particle whose force at the unit of distance on a 
unit of the opposite magnetism 
=M 
B be the extremity of a needle whose force 
If C be the centre of the needle, the force of A to turn B round C is 
BC . BC.AC . 
Mm sin ABC = Mm - ^3 sin ACB. 
Let BC=a, CA=5, AB=c, ACB=^'. 
Then, since 
cos 
going as far as terms involving 
The force to turn B round C is therefore 
{(^+8 3 ") 
2 B 
MDCCCLXI. 
