, 



MUTUAL CHANGES COMMON TO ALL MATTER 57 



particle on the other side, undergoing a displacement exactly 

 equal, but opposite, to its own. 



If, however, the position of the fulcrum is altered, there is 

 no longer equilibrium between the two opposing stresses, and 

 the heavier side descends. This may be prevented by attach- 

 ing a mass or restraint to the other side. Yarying masses may 

 be attached at varying distances and their effectiveness deter- 

 mined. By using a spring balance or dynamometer at different 

 positions the same results may be made apparent. 



If the mass of the rod be very small in comparison with the 

 adjustable masses kept in equilibrium by its agency, we may 

 pay attention to these masses alone. We shall then find that, 

 in cases of equilibrium, the vertical distances through which 

 each mass moves, if the rod is displaced, are inversely pro- 

 portional to the masses themselves. This may be shown by 

 fixing to each mass a pencil, so that their displacement may 

 be marked on two sheets of paper placed in position behind 

 the lever. From these and similar observations it is known 

 that the lever will be in equilibrium if the sum of the products 

 of the numerical values of the vertical displacements and of 

 the masses for all the particles of matter on the one side of the 

 fulcrum be equal to the sum of the same products for every 

 particle on the other side the fulcrum. If any considerable 

 displacement occurs some of the matter on one side may change 

 to the other side, and equilibrium be destroyed. 



The beam of a good balance will be found to exhibit all 

 the properties of 

 a lever balanced r 

 at its centre on 

 the smallest area 

 which is practic- 

 able. Hence if 

 the pans and the 

 masses in them 

 are together equal the lever is in equilibrium. 



It may be shown by geometry that the vertical displace- 

 ment will always be proportional to the horizontal distance 

 from the fulcrum that is, DF : GE : : BD : BE. (See fig 16.) 



