MAGNETISM. 



77 



M m be drawn at right angles to S N, senting therefore the axis of motion. If 

 and passing through the centres of the the needle were truly balanced, its 

 cylindrical ends of the axis, and repre- centre of gravity would coincide with 



Fig. 68. 



the intersection of these lines at c. But 

 supposing this not to the be case, and that 

 in consequence of an error in the sus- 

 pension the centre of gravib is aig ; 

 draw gf perpendicular to S N, cutting 

 it in n, and make nf equal to g n. 

 When the instrument is turned half way 

 round, so that the opposite face of the 

 needle is presented to us, the edge S M N 

 will now be in the place before occu- 

 pied by S m N, and the centre of gravity 

 will be situated at that part where 

 point /was before ; therefore the mean 

 between the forces by which the needle 

 is drawn out of its true position in these 

 two situations, in consequence of its not 

 being truly balanced, is accurately the 

 same"; and the mean between the two 

 observed dips is very nearly the same as 

 if the centre of gravity had been at n. 

 But if the centre of gravity were at n, 

 the dip would be very nearly as much too 

 great in the one position of the needle, 

 or it would be too little when the poles 

 are reversed ; or vice versa. Therefore 

 the mean of the observed dips in these 

 four situations will be very nearly the 

 same as if the needle were truly ba- 

 lanced. 



(297.) In the second place, if the 

 planes on which the axis rolls are not 

 horizontal, the dip will be very nearly 

 as much greater than it would otherwise 

 be, when one face is turned to the west, 

 as it is less when the other is ; for if 

 these planes dip towards the south in 

 one case, they will dip as much towards 

 the north in the other, supposing the 

 levels by which the instrument is set to 

 remain unaltered. Consequently, the 

 mean of the two observations will be 

 very nearly the same as if they had 

 been placed in a truly horizontal plane. 



(298.) The same method of reasoning 

 will show, in the third place, that the 

 mean of the two observations above- 

 mentioned will not be altered, although 

 the index-line joining the mark by 

 which we observe with the axis of mo- 

 tion be not parallel to the axis of the 

 needle ; that is, although the index line 

 do not coincide with the continuation of 



the line SN ; or although the line join- 

 ing the two divisions of 90 be not per- 

 pendicular to the horizon ; or although 

 the axis of motion do not pass through 

 the centre of the divided circle, pro- 

 vided it be in the same horizontal plane 

 with it. Should it happen, indeed, that 

 the axis of motion is not in the same 

 horizontal plane with the centre of the 

 divided circle, the error thence arising 

 will not be compensated by this me- 

 thod of observing ; unless the position 

 of both ends of the needle be taken as 

 checks upon one another. This, how- 

 ever, is of no consequence, since it is 

 easy to examine whether or not they 

 are in the same horizontal plane. 



(299.) But the error that is most dif- 

 ficult to be avoided in the construction 

 of the instrument, is that which arises 

 from the ends of the axis not being truly 

 cylindrical. It is, accordingly, essential 

 that the parts of the axis which rest in 

 the agate planes should be exactly the 

 same. The instrument, however, is so 

 contrived as to admit, on occasion, by 

 giving the axis a little liberty in the 

 notches by which it is lifted up and 

 down, of our making these planes bear 

 against a part of the axis distant about 

 a hundredth or a fiftieth of an inch from 

 their usual point of bearing. Mr. Ca- 

 vendish found that, when the axis is con- 

 fined, so as to have no such liberty, 

 and when care is taken, by previously 

 making the needle stand at nearly 

 the right dip, that it shall vibrate in 

 very small arcs when let down on the 

 planes : that then, if the needle be lifted 

 up and down any number of times, it 

 will commonly settle exactly at the same 

 point each time ; at least the difference 

 is so small as to be scarcely sensible. 

 But if it be not so confined, there will 

 often be a difference of twenty minutes 

 in the dip, according as different parts 

 of the axis rest on the planes ; and that, 

 although the greatest care be taken to 

 free the axis and planes from dust; 

 which can be owing only to some irre- 

 gularity in the axis. If the needle 

 vibrate in arcs of live degrees, or more, 



