54 LECTURES TO SCIENCE TEACHERS. 



to it or not, and whether the pans he empty or equally 

 loaded. Such a "balance is wanting in proper action. 



(b) If the centre of gravity of the heam, when level, he 

 immediately above the centre of motion, the heam will upset 

 with the smallest action, that is to say the end which is 

 lowest will descend, and it will descend with the greater 

 velocity according as the centre of gravity is higher and the 

 points of suspension of the pans less loaded. 



(c) But if the centre of gravity of the heam be imme- 

 diately below the fulcrum, the heam will not rest in any posi- 

 tion hut when level ; and if disturbed from the level position 

 it will vibrate, and at last come to rest in a horizontal posi- 

 tion. Its vibrations will be quicker, and its tendency to the 

 horizontal position stronger, the lower the centre of gravity 

 and the less the weight upon the points of suspension of the 

 pans. 



Again, as to the relative position of the central knife-edge 

 with the line joining the two outer knife-edges from which 

 the pans are suspended, it is to be observed, 



(1.) That if the fulcrum be below the line joining the points 

 of suspension of the pans, and these be loaded, the beam will 

 upset, unless prevented by the weight of the beam tending 

 to produce a horizontal position, as shown in c. In such case 

 a small weight will produce an equipoise ; in the case of a, 

 a certain exact weight will cause the beam to rest in any 

 position, and all greater weights will cause the beam to upset, 

 as in b. 



(2.) If the centre of motion of the beam be above the 

 line joining the points of suspension of the pans, the beam 

 will come to its horizontal position, unless prevented by its 

 own weight, as in b. 



(3.) If the centre of motion of the beam coincide with the 

 line joining the points of suspension of the pans, and very 

 nearly with the centre of gravity, all the vibrations of the 

 loaded beam will be in lines nearly equal, unless the weights 

 be very small, when the vibrations will be slower. The higher 

 the fulcrum the slower will be the vibrations of the balance, 

 and the stronger the horizontal tendency. 



It thus becomes evident that the nearer the centre of 

 gravity is to the centre of motion, the more delicate will be 

 the balance, and the slower its vibrations. The tendency to 

 a horizontal position is therefore increased by lowering the 



