254 C. F. GAUSS ON A NEW INSTRUMENT FOR OBSERVING 



cases, therefore, in the position of equilibrium, the two threads 

 and the centre of gravity are in one vertical plane. To give 

 precision to our ideas, it may be supposed that the two threads 

 are of equal length ; that the two upper points of connexion 

 are at the same height, and that their distance apart is the 

 same as that of the two lower points ; and lastly, that the two 

 latter form with the centre of gravity an equiangular triangle. 

 Under these suppositions, in a state of equilibrium, the two 

 threads will hang vertically, and a third vertical line, midway 

 between them, will pass through the centre of gravity of the 

 body. If we remove the body from this position by means of a 

 rotation around the last-named Une, the two threads will no 

 lono-er be vertical, nor will they be in one plane, and at the same 

 time the body will be somewhat raised. There arises conse- 

 quently a tendency to return to the former position, with a mo- 

 ment of rotation, which may, with sufficient accuracy, be re- 

 garded as proportional to the sine of the deviation from the 

 position of rest, and which is, therefore, greatest when the de- 

 viation amounts to 90 degrees. This maximum effect is always 

 understood when the moment of rotation is spoken of; it may 

 also be regarded as the force by which the body is retained in 

 equilibrium by its mode of suspension, and which, for shortness, 

 I shall call the directive force of suspension. The magnitude of 

 this force depends, 1 st, on the length of the suspending threads ; 

 2nd, on their distance apart; 3rd, on theweight of the body ; being 

 inversely proportional to the length of the threads, and directly 

 as the square of their distance apart, and as the weight of the 

 body. If the above suppositions are not fulfilled, the expression 

 for the directive force is more complicated, and the reaction of 

 the threads against the torsion also renders a small modification 

 necessary. Means are not wanting to enable us to determine 

 by experiment, with the greatest accuracy, the magnitude of the 

 directive force. If the body is left to itself, after having been 

 made to deviate fi-om its position of equilibrium, it will vibrate 

 with the greatest regularity, the middle of the vibrations co- 

 inciding with this position, and the duration depending on the 

 magnitude of the directive force and on the moment of inertia of 

 the body. 



If we further suppose a horizontal magnet bar to form a part 

 of the suspendf d body, a second directive force is exerted, and 

 the phaenomena depend on the combinations of the two forces, 



