BALANCE 281 



surface of the earth are constantly solicited by a force which tends to bring them to- 

 wards its centre, and that they fall to the earth when they are free to move. This 

 force is called gravity. Though the bodies be not free, the effort of gravity is still 

 sensible, and the resultant of all the actions which it exercises upon their material 

 points constitutes what is called their weight. Weights are, therefore, forces which 

 may be compared together, and by means of machines may be made to correspond or 

 be counterpoised. 



To discover whether two weights be equal, we must oppose them to each other in a 

 machine where they act in a similar manner, and then see if they maintain an equi- 

 librium ; for example, we fulfil this condition if we suspend them at the two extremities 

 of a lever supported at its centre, and whose arms are equal. Such is the general idea 

 of a balance. The beam of a good balance ought to be a bar or double cone of metal, 

 of such strength as to secure perfect inflexibility under any load which may be fitly 

 applied to its extremities. Its arms should be quite equal in weight and length upon 

 each side of its point of suspension ; and this point should bo placed in a vertical line 

 over the centre of gravity ; and the less distant it is from it, the more delicate will 

 be the balance. Were it placed exactly in that centre, the beam would not spon- 

 taneously recover the horizontal position when it was once removed from it. To 

 render its indications more readily commensurable, a slender rod or needle is fixed to 

 it, at right angles, in the line passing through its centres of gravity and suspension. 

 The point, or rather edge, of suspension, should be made of perfectly hard steel, and 

 turn upon a bed of the same. For common uses the arms of a balance can be made 

 sufficiently equal to give satisfactory results ; but, for the more refined purposes of 

 science, that equality should never be presumed nor trusted to ; and, fortunately, exact 

 weighing is quite independent of that equality. To weigh a body is to determine how 

 many times the weight of that body contains another species of known weight, as of 

 grains or pounds, for example. In order to find it out, let us place the substance, sup- 

 pose a piece of gold, in the left hand scale of the balance ; counterpoise it with sand 

 or shot in the other, till the index needle be truly vertical, or stand in the middle of 

 its scale, proving the beam to be horizontal. Now remove gently the piece of gold, 

 and substitute in its place standard multiple weights of any graduation, English or 

 French, until the needle again resumes the vertical position, or until its oscillations 

 upon either side of the zero-point are equal. These weights will represent precisely 

 the weight of the gold, since they are placed in the same circumstances with it, and 

 make the same equilibrium with the weight laid in the other scale. 



This method of weighing is obviously independent of the unequal length as well as 

 the unequal weight of the arms of the beam. For its perfection two requisites only are 

 indispensable. The first is that the points of suspension should be rigorously the same 

 in the two operations ; for the power of a given weight to turn the beam being unequal, 

 accordingly as we place it at different distances from the centre of suspension, did that 

 point vary in the two consecutive weighings, we should require to employ, in the 

 second, a different weight from that of, the piece of gold, in order to form an equi- 

 librium with the sand or shot originally put in the opposite scale ; and as there is 

 nothing to indicate such inequality in the states of the beam, great errors would result 

 from it. The best mode of securing against such inequality is to suspend the cords 

 of the scales from sharp-edged rings, upon knife-edges, at the ends of the beam, both 

 made of steel so hard-tempered as to be incapable of indentation. The second condition 

 is, that the balance should be very sensible that is, when in equilibrium and loaded, 

 it may be disturbed, and its needle may oscillate, by the smallest weight put into 

 either of the scales. This sensibility depends wholly upon the centre of suspension ; 

 and it will be the more perfect the less friction there is between that knife-edge surface 

 and the plane which supports it. Both should therefore be as hard and highly 

 polished as possible ; and should not be suffered to press against each other, except 

 at the time of weighing. Every delicate balance of moderate size, moreover, should 

 be suspended within a glass case, to protect it from the agitations of the air, and the 

 corroding influence of the weather. In some balances a ball is placed upon the index 

 or needle (whether that index stand above or below the beam), which may be made 

 to approach or recede from the beam by a fine-threaded screw, with the effect of varying 

 the centre of gravity relatively to the point of suspension, and thereby increasing, at 

 will, either the sensibility or the stability of the balance. The greater the length of 

 the arms, the less distant the centre of gravity is beneath the centre of suspension, 

 the bettor polished its central knife-edge of 30, the lighter the whole balance, and 

 the loss it is loaded, the greater will be its sensibility. In all cases the arms must bo 

 quite inflexible. A balance made by Kamsdon for the Royal Society is capable of 

 weighing ten pounds, and turns with one hundredth of a grain, which is the seven- 

 millionth part of the weight. Seo WEIGHING MACHINE. 



