CHAP, i.] OSCILLATIONS OF THE PENDULUM. 29 



acting at the extremities of two unequal arms of a lever are, when 

 equilibrium is established, in the inverse ratio of the lengths of the 

 arms of the lever. 



In the Roman steelyard, the beam A B (Fig. 9) may be divided 

 into two parts, the shorter of which (o A) forms one arm of the lever 

 of constant length ; at the extremity is suspended a hook or scale- 

 pan intended to support the body to be weighed. On the longer part 

 (OB), graduated properly into kilogrammes and fractions of a kilo- 

 gramme, or in England to pounds, &c., moves a collar M, which sup- 

 ports a constant weight P: and it is this weight which, placed more 

 forward or drawn back along the graduated rod, produces equilibrium 

 with the heavy bodies placed in the pan Q, or hung to the hook. The 



FIG. 9. The Roman steelyard. 



equilibrium is established when, after many oscillations, the beam 

 retains a horizontal direction. 



The steelyard is usually constructed so that the centre of gravity 

 (o) of the whole instrument lies in the vertical which passes through 

 the edge of the suspension knife and a little above it. Then, in the 

 absence of the movable weight and of any weight placed in the pan, 

 the beam remains in equilibrium and takes a horizontal position. 

 The zero of the graduation is then at the point of suspension itself. 

 The different divisions are ascertained by placing a known weight 

 one kilogramme or pound, for instance in the pan and finding the 

 point of the beam where the movable weight produces equilibrium : at 



