98 LECTURE XII. 



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 determined are large, the scale 

 becomes very much contracted, and the instrument requires to be levelled 

 with great accuracy. A counterpoise acting on a spiral or conical barrel 

 has also been applied to a similar purpose ; it is capable of a scale some- 

 what 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 sup- 

 ported by the hook. This instrument is called a spring steelyard. Mr. 

 Hanin's * spring steelyard has a long index, which revolves on a centre, 

 and shows at once the weight according to the standards of different coun- 

 tries. 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 curvature 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 equal 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 about one 

 part in five thousand from the apparent weight indicated by the spring 

 steelyard. (Plate IX. Fig. 114.) 



The spring steelyard affords us the most convenient method of measur- 

 ing 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 animal which is employed in drawing a distant boat or car- 

 riage, by the inclination of the rope or chain to the horizon, compared 

 with the weight of that portion of it which the animal supports, that is, of 

 the part which extends to the point where the curve becomes horizontal.*!* 



All animal actions, or, at least, all the external actions of animals, are 

 ultimately dependent on the contractions and relaxations of the fleshy 

 parts, which are called muscles. The operation of the particular muscles 

 belongs properly to the science of physiology ; but their mechanism may 

 in general be understood from the properties of the lever and of the 

 ^ centre of gravity. The bones are the levers, the joints the fulcrums, and 

 the force is applied by the muscles, which are usually attached to the bones 

 by the intervention of tendinous cords. When a muscle contracts in the 

 direction of its fibres, it becomes at the same time thicker, and its total bulk 



* Hist. etMem. de Paris, 1765, H. 135. 



f Consult Morin, Description des Appareils Chronometriques, et des Ap. Dyna- 

 mometriques. Metz, 1838. 



