ON STATICS. 127 



fectly vertical, since, in this position, the weight may be overpowered by 

 the minutest counterpoise acting on the other arm. The centre of gravity 

 being, in the common balance, very nearly in a right line between the weights, 

 in order that it may be immediately below the fulcrum, the arm must have a 

 very considerable angular motion for a slight inequality of the weights ; but 

 in the bent lever balance, the centre of gravity is at such a distance from the 

 fulcrum, that a moderate motion of the arms may bring it into the vertical 

 line. This motion is measured by an index on a graduated arc, which gives 

 the instrument a considerable range; and where expedition is particularly 

 desired, it may often be used with advantage; but if the weights to be de- 

 termined are large, tiie scale becomes very much contracted, and the instru- 

 ment requires to be levelled with great accuracy. A counterjioise acting on 

 a spiral or conical barrel, has also been applied to a similar purpose ; it is ca- 

 pable of a scale somewhat more extended than a bent lever balance, but it is 

 less simple, and scarcely more accurate. (Plate IX. Fig. 113.) 



A spring, which is usually of a spiral form, being made to support a hook 

 by the intervention of a graduated bar, the divisions of this bar, which are 

 drawn out beyond the fixed point, indicate the weight supported by the hook. 

 This instrument is called a spring steelyard. Mr. Ilanin's spring steelyard 

 has a long index, which revolves on a centre, and shows at once the weight 

 according to the standards of different countries. The divisions of the scales 

 in moderate flexures of the spring are nearly equal: hence it may be inferred, 

 that the space through which a spring is bent, and consequently its curva- 

 ture, or change of curvature, is simply proportional to the force which acts 

 on it, and that the vibrations of a weight supported by a spring, must, like 

 those of a cycloidal pendulum, be performed in ecpial times, whatever may be 

 their magnitude. The strength of all springs is somewhat diminished by 

 heat, and for each degree of Fahrenheit that the temperature is raised, we 

 must deduct abcmt one part in five thousand from the apparent weight in- 

 dicated by the spring steelyard. (Plate IX. Fig. 114.) 



The spring steelyard affords us the most convenient method of measunng 

 the immediate intensity of the forces exerted by animals of different kinds, 

 in the labour which they perform. When it is adapted for this purpose, it is 

 ■sometimes called the dynamometer. We may also estimate the force of an 



