arch which fits on to the beam, as shown in the end view (fig. II, 2). In each of these sides are cut two V-shaped notches directly opposite to each other, one of the opposite pairs being 6-654 millims. (about 4 inch) distant from the other pair. Two equal riders of the shape shown in fig. II, 3, are placed across the bridge, and are of such a size that they will just fit into the bottom of the notches. When one of these rests across the bridge the other is raised up from it. The lowering of one rider and the raising of the other corresponds herefore to a transference of a single rider from one pair of notches to the other. The length of the half beam being 202-716 millims. and the distance between the notches 6.654 millims., this transference will be equivalent to the addition to one pair of 3·03284 of the weight of the rider used. As I have generally used a centigramme rider this means 0.3284 mgms.

Two levers l' (fig. II, 4), with hooks hh' are used to raise one rider while the other is lowered. These levers are worked by two cams cc' on a rod R, which is prolonged out of the balance case to the observer. By turning this rod round, the one lever is raised while the other is depressed. The hook at the end of the raised lever picks up its rider while the other hook deposits its rider on the bridge, and then sinks down between the raised sides (as shown in fig. II, 4), leaving the rider resting freely on the bridge.

The levers are so adjusted that the beam even in its greatest oscillations never comes in contact with the hooks.

This arrangement might probably be still further perfected by introducing two small frames for the riders to rest upon, the frames resting on the bean by knife edges. It would then be certain that the movement of the riders was equivalent to a transference from one knife edge to the other, whereas the rider at present may not rest exactly over the centre of the notch. But I find that I get fairly consistent results by lowering the rider somewhat suddenly so as to give it sufficient impetus to go to the bottom of the notch, and have not therefore thought it necessary as yet to introduce more complicated apparatus.

In place of the right hand pan of the usual shape, another of the shape shown in fig. III, 1, is employed. To the centre of the pan underneath is attached a vertical brass rod which passes downwards through the bottom of the inner case of the balance. To the under side of this case is attached the clamping arrangement before referred to. This consists of two sliding pieces (fig. IV, 1, ss) working horizontally in a slot cut in a thick brass plate which is fastened to the case. Through a circular aperture in this plate (the slot is not cut through the whole thickness of the plate, but only as shown in fig. IV, 2) and about the middle of the slot hangs the rod r attached to the scale pan.

By means of right and left handed screw on a rod R, which is pro

longed out of the case to the observer, these two sliding pieces can be made to approach, and clamp the rod, or to recede and free it. By having the opposite surfaces of the sliding pieces and the rod polished and clean, it is possible to clamp and unclamp without producing any disturbance. The clamp is of great use also to lessen the vibrations when they are too large, as it may be brought into action at any moment, and on releasing carefully the beam will start again from rest without any impetus. It may be used too to increase the vibrations by releasing suddenly when the beam will have a slight impetus in one direction. or the other.

The weights which I have compared are two brass pounds avoirdupois, made for me by Mr. Oertling, and marked A and B respectively. They are of the usual cylindrical shape with a knob at the top (fig. III, 2). Two small brass pans (fig. III, 3) with a wire arch by which they can be suspended, are used to carry them; these are called respectively X and Y. I found on beginning to use them that there was too great a difference between A and B. I therefore adjusted them by putting a very small piece of wax upon A, the lighter. But the difference between them increased by 0-0782 mgm. in two days, which I thought was probably due to the wax. After the fourth series I therefore removed it and scraped B till it was more nearly equal to A. The weighings I-IV have, however, been retained, for though the differences on different days vary they are fairly constant on the same day.

The weights are changed by the following apparatus which has been designed to effect the change as simply and quickly as possible.

A horizontal "side rod" or link (ss, fig. V) is worked by two cranks (cc, fig. V, 2), which are attached to the axles of two equal toothed wheels (tt) with a pinion (p) connecting them. A second pinion (9), on a rod prolonged out of the case to the observer, gears with one of the toothed wheels. By turning this rod the toothed wheels are set in motion, both in the same direction, moving the horizontal "side rod from the right say upwards and over to the left. A pin (pn) stops its motion downwards further than is shown in fig. V, 1. Near each end of the rod is cut a notch, and across these are hung the pans carrying the weights. The apparatus is fastened to the floor of the case between the central upright supporting the beam and the scale pan, the side rod being perpendicular to the direction of the beam, and exactly over the centre of the pan. In fig. V, 1, one of the weights B is supposed to be resting on the scale pan (the wires suspending the pan from the beam not being shown), the side rod having moved down so far below the wire of the smaller pan carrying the weight that it leaves it quite free. If, now, it is desired to change the weights the rod R is turned, setting the wheels in motion, the side rod moves up, picks up B-the notch catching the wire-then travels

over round to the extreme right, when A will be just over and nearly touching the scale pan. By continuing the motion slightly A will be gently deposited on the pan, and the side rod will move slightly down leaving the weight quite free. On the scale pan are four pins, turned slightly outwards, acting as guides for the small pan, and ensuring that it shall always come into the same position. The wheels and pinions are of such a size that two revolutions of the rod just suffice to change one weight for the other.

It will be seen that all the manipulation required from the observer during a series of weighings is the simple turning of three rods, which are prolonged out of the balance case to where he is stationed at the telescope. By turning one of these he can change the position of the rider on the beam by a known amount, and so find the value of his scale. By turning a second he clamps the scale pan, and so steadies the balance while the weights are changed by turning a third rod. I have made this arrangement not only because it seems as simple as possible to secure the end required, but also because it seemed more applicable to a vacuum balance (with which I hope ultimately to test it).

I take this opportunity of expressing my thanks to Mr. Thomas Foster, mechanician of Owens College, for his aid in the construction of the apparatus, and in the planning of many of its details.

Method of conducting a Series of Weighings.

After the counterpoise has been adjusted so that the beam swings nearly about its horizontal position, the frame is lowered so that the balance is ready for use. The pan is then clamped and the balance is left to come to a nearly permanent state of flexure if possible, sometimes for the night or even longer. The lamp is lighted usually halfan-hour or more before beginning to observe, so that its effect on the balance may attain a more or less steady state. It is necessary also to wait some time after coming into the room, for the opening of the door will always cause a considerable and immediate deflection of the beam. When a sufficient time has elapsed, the observations are commenced with a determination of the value of one scale division by means of the riders. The three extremities of two successive oscillations are observed with one of the riders resting on the beam. These are then combined as follows:-The mean of the first and third is taken, and the mean again of this and the second, this constituting the "resting point," that is, the position of equilibrium of the beam at the middle of the time. For instance, in weighing No. I (see tables at the end) the three extremities of successive oscillations were 280-5, 312·0, and 286-0 (column 2). The resting point was taken as—

the rider on the beam being the right hand one denoted by R, column 1. The balance is the clamped, and the other rider is brought on to the beam while the first is taken up. The resting point is again observed. In No. I it was 270-05. The balance is again clamped, and the first rider again brought on the beam, and in unclamping the resting point again observed. In the same weighing it was 296-75. These three are sufficient to give one determination of the deflection due to the transference of a rider. This will be the difference between the second resting point and the mean of the first and third. For 297 62+296.75 instance, -297·18=27·13 divisions. This number is

2

found in the fifth column.

This process is continued, the resting points being combined in threes till several values of the deflection due to the rider have been obtained, and the mean of these is taken as the true value. This plan of combining the resting points requires that the observations should be taken at nearly equal intervals. After a little practice it will always take the observer about the same time to go through the same operations of clamping, changing the riders, unclamping, clamping again to lessen the vibrations about the new resting point, and then beginning to observe, and I have considered that this was a sufficiently correct method of timing the observations.

When a series has been taken it will at once be seen whether they were begun too soon after entering the room, or whether any irregular disturbing force has acted. For instance, in weighing No. II, determination of one scale division, the first resting point is so much lower than the succeeding with the same rider that evidently the balance was still affected by my entrance into the room. It was, therefore, rejected. Again, in weighing No. III determination of the difference between the weights, the fourth resting point was much lower than the others with the same weight in the pan. The resting points, when the other weight was in the pan, showed no similar sudden drop of such magnitude. This observation was, therefore, rejected as being affected by some irregular disturbance.

When the value of the deflection is determined, the value of one scale division is at once found by dividing 3282 mgm. by the number of divisions of the deflection, since the charge of the sides is equivalent to the addition of 3282 mgm. to one pan.

The determination of the difference between the weights is then begun. This is carried on in a precisely similar manner, the only difference being, that the rod changing the weights is now turned round in place of the rod changing the riders. I have usually taken a greater number of observations of the difference between the weights than of the deflection due to the riders, as the former is somewhat more irregular than the latter. This irregularity I believe to arise

from slight differences of temperature of the two weights, and perhaps from air currents caused by their motion inside the case. They do not seem to be due to any fault in the clamping arrangement, since that is employed equally in both, and the changing of the weights, if effected gently, does not move the beam at all.

When the deflection has been determined, it is multiplied by the number of milligrammes corresponding to one scale division, and this, of course, gives the difference between the weights. I have interchanged the weights in the two pans X and Y, between the series of weighings, in order to make the experiments like those conducted in the weighings for the standard pound. But my object has not been to show at all that the method gives consistent results day after day, and, in fact, the difference between the weights has varied. For instance, according to weighings I and II, A-B 0446, while, according to weighings III and IV, A-B = '0232. There is a greater difference between these than can be accounted for by errors of experiment, and it probably arose from the small piece of wax with which I made A nearly equal to B. The difference between the weights when measured to such a degree of accuracy as that which I have attempted, will, no doubt, vary from time to time, partly with deposits of dust, partly with changes in the moisture in the atmosphere, and so on.

But I think the numbers which are given in the tables are sufficient to show that the difference between two weights in any one series of weighings can be measured with a greater degree of accuracy than has hitherto been supposed possible. I give in the tables a full account of the weighings, each series containing a determination of the value of one scale division and a determination of the difference between the weights. The greatest deviation of any one of a series from the mean of that series of differences is always given. This I consider a better test of accuracy of weighing than the probable error. What is wanted in weighing is rather a method which will give at once a good determination of the difference between two weights. But I may state, that if the error of any one of a series be taken as its difference from the mean of that series, the probable error of a single determination of the difference between the weights in the first four series is 4344 of a division, or 0054 mgm., that is, 500000th of the total weight, while the greatest error is 1.8 divisions, or 0224 mgm., that is 0000000th of the total weight. It may be remarked that these weighings were all made during peculiarly unfavourable weather when there were frequent heavy showers, causing sudden changes of temperature, and thus seriously affecting the working of the balance. In the series V-VIII the greatest error is only 30000000 of the total weight, the weather having improved considerably.