84 THE LEVER. PRINCIPLE OF VIRTUAL VELOCITIES. 



The rod, made of hard wood, and well planed, may be obtained 

 from a joiner. The holes must be bored neatly, and clean through, 

 their positions having been previously marked on a pencil-line 

 ruled along the rod a little above the middle, about 6 mm below the 

 upper edge, so that the rod may hang horizontally without being 

 loaded. The readiest way of suspending the lever is to pass a thin 

 cord through the middle hole and fasten the ends to the crossbar of 

 the support, fig. 35 (p. 36). The weights are suspended, either imme- 

 diately or by a piece of thread, from forks provided with small rings, 

 One of these forks is shown in fig. 58 ; they are easily bent of thin 

 wire, and are fixed by a straight piece of wire which passes through 

 one of the holes. 



If a weight of 294 gr = O kgr '294, suspended at a dis- 

 tance of 8 cm from the fulcrum of the lever is to be kept 

 in equilibrium by a weight suspended on the other side 

 of the fulcrum, at a distance of 24 cm from it, we shall 



f 294 x 8 294 

 have to employ a weight of ^- = - .= 98 g . 



^j4: O 



If we suppose the lever to turn through any distance, 

 the force applied at a distance of 24 cm will act through 

 the space a b, which is three times as great as the 

 space c d through which the force acts that is applied 

 at a distance of 8 cm . But for equilibrium the work, 

 that is the product of the force into the space, must be 

 equal; one force must therefore be as much greatei 

 than the other as the space is less : in this case one 

 force must be a third of the other. This relation, 

 which is valid for aU kinds of machines, may be statec 

 thus : 



Two forces applied to a machine will be in equilibrium 

 if the first force is to the second as the space througl 

 which the second force acts, if motion takes place, is to th( 

 space through which the jirst force acts ; or more shortly 

 if the forces are inversely proportional to the spaces. 



