84 



MAGNETISM 



(3-22.) The preceding reasoning is 

 founded upon the supposition that 

 the axis of motion passed accurately 

 through the centre of gravity of the 

 magnet ; so that the effect of gravity 

 was removed, and could not in any way 

 interfere with the rotatory force of mag- 

 netism. This, however, is a condition, 

 which it is next to impossible practically 

 to fulfil ; and if it be not exactly fulfilled, 

 then, whenever the centre of gravity is 

 not in the precise line passing vertically 

 through the centre of suspension, the 

 effect of gravity is to impart to that 

 side of the magnet, on which the centre 

 is found, a tendency to preponderate ; 

 and its oscillations are no longer pro- 

 duced by the simple action of the mag- 

 netic forces, nor directed to the exact 

 line of their action. The only method 

 of correcting this source of error, when 

 it is not very considerable, is to reverse 

 the polarities of the magnet, and make 

 a new set of observations on the incli- 

 nation and intensity in this state of the 

 magnet ; and then to take the mean of 

 the corresponding observations, which, 

 in consequence of the compensation of 

 the opposite errors existing in the two 

 modes of estimation, will express the 

 true value of the quantity sought. 



(323.) In order to compare the re- 

 sults of two sets of observations on 

 magnetic intensity in different parts of 

 the world, it is necessary to employ the 

 same needle in both cases ; since the 

 application of the various formulae ne- 

 cessary to be employed for comparing 

 the action of the same force on two dif- 

 ferent needles would be attended with 

 great difficulty and uncertainty. 



(324.) The oscillations of the com- 

 pass-needle, which moves in a hori- 

 zontal plane, furnish data for the calcu- 

 lation of the intensity of that part only 

 of the terrestrial force which acts in that 

 plane; whereas those of the dipping- 

 needle, moving on a horizontal axis and 

 consequently in a vertical plane, when 

 that plane coincides with the magnetic 

 1 meridian, indicate the full amount of the 

 force of the terrestrial magnetism at the 

 place of observation. The ratio be- 

 tween these two quantities is that of the 

 base and hypothenuse of a right-angled 

 triangle, inclined at an angle equal to 

 the dip ; that is to say, the intensity of 

 the horizontal force is to the intensity 

 of the whole force as the cosine of the 

 angle of the dip is to the radius. Let 

 SN, fig, 73, be the horizontal needle ; 



Fig. 



NE the line of dip ; NR a horizontal 

 line perpendicular to SN. The force 

 NE is resolved into RE, perpendicular 

 to RN, and which being out of the plane 

 of motion, and perpendicular to it, does 

 not contribute to the motion of the 

 needle, and NR the horizontal force ; 

 which latter is to NE as the cosine of 

 the angle ENR is to the radius. This 

 force, NR, is constant in all positions 

 of the needle in the horizontal plane ; 

 and acts always in parallel directions. 

 Its rotatory action, however, will, of 

 course, depend upon the deviation of 

 the needle from the position of equili- 

 brium, that is, upon the angle which it 

 makes with the plane of the meridian ; 

 being proportional to the sine of that 

 angle. The oscillations are therefore 

 isochronous, that is, performed in equal 

 times, whether the arc be large or 

 small, like those of a pendulum ; and 

 are governed by the laws above stated 

 as applying to those of pendulums ; and 

 the same remark applies equally to the 

 oscillations of the dipping-needle per- 

 formed in the plane of the magnetic me- 

 ridian. 



(325.) When the position of the axis 

 of the dipping-needle is changed, so that 

 the plane in which the needle moves is 

 no longer that of the magnetic me- 

 ridian, though still vertical, the force by 

 which it is actuated is in like manner to 

 be estimated by that portion of the ter- 

 restrial force which, on being resolved, 

 has the direction of that plane ; that 

 portion which is perpendicular to the 

 plane being of no effect. 



Let the circle SANB, fig. 74, repre- 

 sent the plane of the motion of the 

 needle SN ; NE being the line of dip, 

 or the direction of the terrestrial forces. 

 The force represented by NE may be 

 resolved into the two forces NV and 

 NH, the one perpendicular to the ho- 

 rizon, and the other parallel to it. Let 

 the former be denoted by the letter v, 

 and the latter by h; and let us call the 



