P VW X w; that is, the true weight is the geometric mean between W and w. In practice the arms of a It is evident that x will be increased as k is decreased, so that the sensitiveness of the bal ance becomes greater the nearer the centre of gravity of the beam is caused to approach to the centre of support. The balance should be provided with a thread and nut, D (see Fig. 1), to facilitate the vertical adjustment of the centre of gravity, in the same way that E is used in adjusting the horizontal position of that point. The centre of gravity of the beam must always remain below the centre of support, be cause when it is above that point the beam is unstable, and when it coincides with the centre of support the instrument will remain in equi libkium in any position. When a balance is made very sensitive, by bringing the centre of gravity close to the point of support or by in creasing the length of the arms of the beatn, the period of oscillation of the beam grows very long, so that the instrument is tedious to use. The experienced chemist or physicist therefore selects a balance whose sensitiveness and period of oscillation can be best adapted to the work he has in hand.
The ((precision balance is a delicate instru ment, and should be kept in a glass case, for protection, when not in actual use. The weigh tngs are also performed with the balance en closed in like manner, in order to avoid error from the effect of air-currents upon the beam. The knife-edges should be kept away from their bearings, and provision is always made for raising the pans from the ends of the beam, and the beam itself from the central support, by means of a system of stops and levers (not here shown) actuated by a conveniently situated lever or wheel The beam and pans should al ways be raised in this manner when changing the weights in the pans, in order to avoid giv ing the least shock to the knife-edges; for when these are dulled or otherwise injured the ac curacy and sensitiveness of the balance are materially lessened.
Weighings may be effected by two general methods. In the first method the position of the pointer, P (in Fig. 1), is noted on the scale at its extremity when the balance is at rest with the pans empty. The position so recorded is called the ((zero)) of the balance. The object to be weighed is then placed in one of the pans, and weights are added to the other pan until the balance will come to rest with its pointer at the same spot, or zero, as before. The weighing is then complete.
In the second method of conducting the ex periment (known as the ((method by oscilla tions))) the balance is not brought to rest at all, the necessary readings being taken while the beam is oscillating. The zero reading of the pointer is first obtained (with the pans empty) in the following manner: The empty balance is allowed to oscillate freely for a short time, and then the position attained by the pointer at one of its extreme positions toward the right is noted. The reading of the next following ex treme position to the left is then taken, and so on, observing the positions attained at the alter nate right and left swings, just as the pointer pauses and begins to return toward the mean position. The last reading is taken on the same side as the first, so that there is an odd num ber of observations on one side of the zero, and an even number on the other side. The read ings on the right are then averaged together, and those on the left are also averaged in the same way; after which the mean reading on the right is averaged with the mean reading on the left, and the result is taken as the position of the zero of the balance. The object to be weighed is then placed in one pan, and the weights in the other, the process of guess and trial being followed here just as in the preced ing method until an almost exact balance has been attained. The method of oscillations, with alternate readings to the right and left, is next repeated in precisely the same manner as when the pans were empty, and the reading obtained by the final averaging of these observations is taken as the reading of the balance for the loads that are in the pans at the time. A very
small weight is next added to one of the pans, and the oscillations are again observed, under the new conditions, precisely as before. The weight of the object under examination can then be determined by simple proportion. Thus, sup pose that the original zero reading of the pointer, with the pans empty, was 11.6. The object to be weighed being placed in one pan, and weights having a combined mass of W in the other, let the reading of the pointer (as de duced from the oscillations) be 10.4. The small mass, w, being then added to W, let the final reading of the pointer be 12.2. The following facts are now known: With empty pans the pointer reads 11.6. With the unknown mass (which may be denoted by P) in one pan, and a mass, W, in the other, the pointer reads 10.4. Finally, with P in one pan and W-Fw in the other, the pointer reads 12.2. The mass w has displaced the reading of the pointer by 1.8 divi sions. If it be assumed that a mass x when added to W, would have made the reading of the pointer precisely 11.6, as it was with the empty pans, we have the additional fact that a mass x would alter the reading of the pointer by 1.2 divisions. Hence the simple proportion — 2w whence x = —, and therefore the concluded 3 2w mass of P is W+ 3 The method of oscillations is favored by many physicists, in the belief that a better value of the zero of the balance can be obtained by studying the free swings in this way than by allowing the instrument to come to rest. In stead of adding very small weights to secure the last the "'rider)) is often used. This consists of a tiny weight made of wire, and suspended on the beam of the balance, as indi cated at R in Fig. 1. The beam is graduated when a rider is to be used, and the final step in the weighing consists in observing what posi tion the nder must have in order to make the balance perfect. The effect of moving the rider one division on the beam being known by previous experiment, the correction to be ap plied for any given position of the rider is easily calculated. Obviously the rider can be used with equal advantage whether the weigh ing is conducted by the•method of oscillations or not The weights used in connection with preci sion balances must be accurately compared among themselves if refined work is to be done, and a table of corrections prepared, by means of which the proper allowances may be readily found, for any minute inconsistencies that may exist among them. Reference must be made to the standard works on experimental physics for the details of the process by which these corrections are obtained. Crookes' classical paper on the atomic weight of thallium' 'Philo sophical Transactions' (1873, p. 277), may also be consulted with advantage, as it contains full details on this point, as well as on many others in connection with accurate weighing. (For fur ther information on the theory and use of the precision balance consult Stewart & Gee, (Les sons on Elementary Practical Physics' (Vol. I, London 1889) ; and Glazebrook & Shaw, 'Practical Physics' (New York 1893). Much advanced information may also be had in the (Travaux et Memoires) of the International Bureau of Weights and Measures). Consult also Braver, 'Die Construction der Waage' (3d ed., Leipzig 1906) ; Felgentraeger, (Theone, Konstruktion and Gebrauch der feineren Hebei wage' (Berlin 1907) ; Gerland and Traumiiller, der physikalischen Experimen tirkunst) ; Kohlrausch, 'Lehrbuch der prati scschen Physik' (Leipzig 1905) ;Sokeland, cient Desemers or Steelyards,)) in 'Smithsonian Annual Report for 1900' (Washington 1901). See also CHRONOMETER INDUCTION BALANCE; TORSION BALANCE.