Page:Encyclopædia Britannica, Ninth Edition, v. 3.djvu/280

impossible to name the inventor of the more perfect form of the instrument. But taking the precision balance in what is now considered its most perfected form, we may safely say that all which distinguishes it from the com mon balance proper is, in the main, the invention of the late Mr Kobinson of London. In Robinson s, as in most modern precision balances, the beam consists of a perforated flat rhombus or isosceles triangle, made in one piece out of gun-metal or hard-hammered brass. The substitution for either of those materials of hard steel would greatly increase the relative inflexibility of the beam, but, unfortunately, steel is given to rusting, and, besides, is apt to become magnetic, and has therefore been almost entirely abandoned. The perforations in the beam are an important feature, as they considerably diminish its weight (as compared with what that would be if the perforations were filled up) without to any great extent reducing its relative solidity. In fact, the loss of carrying power which a solid rhombus suffers in consequence of the middle portions being cut out, is so slight that a very insignificant increase in the size of the minor diagonal is sufficient to compensate for it. Why a balance beam should be made as light as possible is easily seen ; the object (and it is as well here to say at once, the only object) is to diminish the influence of the unavoidable imperfections of the central pivot. To reduce these imper fections to a minimum, the beam in all modern balances is supported on a polished horizontal plane of agate or hard steel fixed to the stand, by means of a perfectly straight " knife-edge," ground to a prism, of hard steel or agate, which is firmly connected with the beam, so that the edge coincides with the intended axis of rotation. In the best instruments the bearing plane is continuous, and the edge rests on it along its entire length ; in less expensive instru ments the bearing consists of two separate parts, of which the one supports the front end, the other the hind end of the edge. Every complete balance is provided with an " arrest- ment," one of the objects of which is, as the name indi cates, to enable one to arrest the beam, and, if desired, to bring it back to its normal position ; but the most impor tant function of it is to secure to every point of the central edge a perfectly fixed position on its bearing. So far all modern precision balances agree ; but the way in which the point-pivots A and B of our fictitious machine are sought to be realised varies very much in different in struments. In Robinson s, and in the best modern balances, the beam is provided at its two extremities with two knife- edges similar to the central one (except that they are turned upwards), which, in intention at least, are parallel to, and in the same plane as, the central edge ; on each knife-edge rests a plane agate or steel bearing, with which is firmly con nected a bent wire or stirrup, provided at its lower end with a circular hook, the plane of which stands perpendicular to the corresponding knife- edge ; and from this _ hook the pan is sus- pended by means of a second hook crossing the first, mat ters being arranged so that, supposing both end-bearings to be in their proper places and to lie horizontally, the work ing points A and B of the two hook-and-eye arrangements are vertically below the intended point-pivots A and B on the edges. In this construction it is an important func tion of the arrestment to assign to each of the two ter minal bearings a perfectly constant position on its knife- edge. How this is done a glance at figs. 3 and 4 (of which the former is taken from an excellent instrument constructed by L. Oertling of London, and the latter from an equally good balance, represented in fig. 5, made by Messrs Becker & Co., of New York) shows better than any verbal explanation. But what cannot be seen from thesa sketches is that the range of the arrestment is regulated, and its catching con trivances are placed, so that when the arrestment is at its highest place, the cen tral edge is just barely lifted from its bearing, and the terminal bear ings are similarly lifted from their re spective knife-edges, so that the beam is now at rest in its normal position. In other bal ances, as, for instance, in the justly celebrated instru ments of Mr Staudinger of Giessen, Robinson s plane terminal bearings are replaced by roof-shaped ones (fig. 6), so that their form alone suffices to secure to them a fixed position on their knife-edges. Another A construction (which offers the great advantage of being easy of execution and facilitating the adjustment of the instrument) is to give to the terminal edges the form of circular rings, the planes of which stand parallel to the central edge, and from, which the pans are suspended directly by sharp hooks, so that the points A and B coincide with A and B respectively. In either case the terminal bearings are independent of the arrestment, which must consequently be provided with some extra arrangement, by means of which the beam, when the central edge is lifted from its support, is steadied and held fast in its normal position. In second and third class instruments even the central edge is made independent of the arrest ment, by letting it work in a semi-cylindrical or, what is better, a roof-shaped bearing, which, by its form, assigns

to it (in intention at least) a definite position.

Fig 3 "" Oe " lhlg s Balar - ce " End of Beam.

Fw- 4._Becker s Balance. End of Beam.

Fig. 5. Becker s Balance.

Fig. 6.

In order now to develop a complete theory of the precision

balance, let us first imagine an instrument, which, for distinctness, we will assume to be constructed on Robinson s model, the knife-edges and bearings, &c., being exactly and absolutely what they are meant to be, except that tho terminal edges, while still parallel to the axis of rotation, are slightly shifted out of their proper places. Supposing such a balance were charged with P = p + p from the left, and P" = p + p" from the right knife-edge, and. it is clear that in this case also the charges may be assumed

to be concentrated, P in a certain fixed point A on the