WEI 



a femicircular fteel fpring will be bent, when the weight is 

 applied to force the ends of the fpring to recede from eash 

 other. The quantity is (hewn by an index, which turns round 

 over a circular dial-plate, like a clock-hand. The principal 

 curiofity of this machine is, that the dial contains thirteen 

 concentric circles, each divided to {hew the weight in the de- 

 nominations of different countries ; -viz. on the two external 

 circles are divifions to fhew tioy and avoirdupois weight 

 in pounds ; within this is a circle to fhew the correfponding 

 number of Paris livres ; next Portuguefe arrobas, and Spa- 

 nj(h arrobas ; then Dutch, Swedifh, Danifh, and German 

 pounds ; fo that the inftrument becomes an univerfal table 

 for the ratios of thefe different weights. 



WBlGHlT^C-Machiiie, in ylgricullure and Rural Economy, 

 a fort of machine or contrivance made ufe of for the pur- 

 pofeof weighing neat cattle and fome other kinds of animals 

 alive, as well as different other ufes. It is a machine which 

 is perfeftly fimple and eafy in its manner of conftruftion. 

 It has a beam of the fteel-yard kind, at the top of which is 

 a pin, on which the fufpenfion of the beam is made. There 

 is a counterpoife which is moveable along the beam by 

 means of a Aiding focket, on which is raifed an iron arm, 

 fupporting a wooden box or fcale to receive the coimterba- 

 lancing weights m the operation of weighing. There are 

 different levers, which are hung on a projeding pin of the 

 beam by one end, the other refting on an iron fupport. 

 There is a lid or platform, on which is placed the fubjeft to 

 be weighed ; to the under fide of this, at each corner, are 

 attached blocks, from which proceed iron pieces, fimilar in 

 form to the fupporting piece, but reverfed in pofition : by 

 means of thefe four pieces the hd or platform ftands with 

 its whole weight entirely on the lever ; other pieces apply- 

 ing themfelves to the levers at a fmall diftance nearer to the 

 centre of the machine than to the fupporting piece. 



In the operation of weighing, the fubjeft to be weighed 

 being placed on the lid or platform, preffed by the different 

 pieces on the levers, which by their fufpenfion on the beam 

 determine it from its even pofition by a quantity propor- 

 tioned to the weight of the fubjeft, which is expreffed by 

 the counterbalancing weights required to be placed in the 

 box or fcale. See STt-l-h-Tard. 



A machine of this nature is of vafl utility and import- 

 ance in the different fyftems of grazing, feeding, and fat- 

 tening various forts of live-flock and domeflic animals, ef- 

 pecially where they are carried on to any confiderable 

 extent, not only in afcertaining and marking the progrefs 

 which is made by the different animals, and in {hewing how 

 they pay for the ufe of any particular kind of food, or 

 what power and property it may have in promoting the fat- 

 tening procefs, but in many other ways. 



Weighing-machines, conflrufted upon the fame plan as 

 thofe ufed on the public roads, are applicable, too, in the 

 above cafes, and many others of the rural kind, being ready 

 and convenient for fuch ufes. 



Weighing of the Air. See Weight of Air. 



Weighing Anchor, in Sea Language. See Anchor. 



WEIGHT, in Phyftrs, a quality in bodies by which 

 they tend towards the" centre of the earth, or in a line per- 

 pendicular to its furface. Or, weight may be defined, more 

 generally, a property inherent in all bodies, by which they 

 tend to fome common point, called the centre of gravity ; 

 and that with a velocity in proportion as they are more or 

 lefs denfe, or as the medium through which they pafs is 

 more or lefs rare. 



Weight and gravity are generally confidered as one and 

 the fame thing. Some philofophers, however, diflinguifh 

 gravity as the quality inherent in the body, and weight as 



WEI 



the fame quahty exerting itfelf according to its natural ten. 

 dency. See Gravity, Gravitation, and Density. 



Sir Ifaac Newton demonftrates, ill. That the weights 

 of all bodies at equal diftances from the centre of the earth, 

 are direftly proportional to the quantity of matter that 

 each contains : whence it follows, that the weights of bo- 

 dies have no dependence on their fhapes or textures ; and 

 that all fpaces are not equally full of matter. 



2dly, On different parts of the earth's furface, the 

 weight of the lame body is different, owing to the fphe- 

 roidical figure of the earth, which caufes the body on the 

 furface to be nearer the centre in going from the equa- 

 tor toward the poles : and the increafe in the weight is 

 nearly in proportion to the verfed fine of double the 

 latitude ; or, which is the fame thing, to the fquare of 

 the right fine of the latitude ; the weight at the equator 

 to that at the pole being as 229 to 230 ; or, the whole in- 

 creafe of weight from the equator to the pole, is the 229th 

 part of the former. 



.3dly, That the weights of the fame body at different 

 diflances above the earth, are inverfely as the fquares of 

 the diflances from the centre, fo that a body at the diftance 

 of the moon, which is fixty femi-diameters from the earth's 

 centre, would weigh only the 3600th part of what it weighs 

 at the earth's furface. 



4thly, That at different diflances within the earth or 

 below the furface, the weights of the fame body are di- 

 reftly as the diftances from the earth's centre : fo that, at 

 half way toward the centre, a body would weigh but half as 

 much, and at the very centre it.would have no weight at all. 

 5thly, A body immerfed in a fluid, which is fpecifically 

 lighter than itfelf, lofes fo much of its weight, as is equal to 

 the weight of a quantity of the fluid of the fame bulk with 

 itfelf. Hence, a body lofes more of its weight in a heavier 

 fluid than in a lighter one, and therefore it weighs more in a 

 lighter fluid than in a heavier one. 



The foregoing principles laid down by Newton are uni- 

 verfally admitted as correft, with the exception of the pro- 

 portional weight of bodies on different parts of the earth's 

 furface ; for it is important to obferve, that he founded bis 

 calculation of the earth's ellipticity on the hypothefis of 

 its being homogeneous, w»hicli is not the cafe ; and hence 

 he makes the equatorial diameter greater than the polar 

 axis, as 230 to 229. But from the numerous experiments 

 fince made on the pendulum in different parts of the world, 

 the ellipticity is found to be not fo great. 



By the inveftigations on this fubjeft by the marquis de 

 Laplace, (Mecanique Celefte, vol.ii. ) the ellipticity is found 

 to be ^4^; and the calculations and experiments of other 

 aftronomers concur nearly in this refult, making it on 

 an average about -^^-. lu our article Standard, we have 

 given tables of thofe determinations, and hkewife of the 

 principal experiments made on the pendulum in different 

 latitudes ; and we fhall here add fome further inveftigations 

 and new calculations, as effentially connefted with our fub- 

 jeft Weight, and of pecuhar intereft at the prefent 

 time. > 



The chevalier Delambre, in his " Aftronomie," vol. iii. 

 p. 585, gives the following fimple and elegant expofition 

 of the pendulum, with other ufeful formula for finding the 

 earth's elhpticity, &c. 



Let h be the height of the place of obfervation 

 above the level of the lea ; R, the radius of the earth ; 

 then the length of the pendulum is to be multiphed by 



R + M' f 2Kh + h^\ 2 b 



R 



— = I + 



R = 



-y- 



I + 



R 



Let 



