The following Papers were read :—

I. "On a method of using the Balance with great delicacy, and on its employment to determine the Mean Density of the Earth." By J. H. POYNTING, B.A., Fellow of Trinity College, Cambridge, Demonstrator in the Physical Laboratory, Owens College, Manchester. Communicated by Professor B. STEWART, F.R.S. Received June 21, 1878.

[PLATE 1.]

In the ease and certainty with which we can determine by the balance a relatively small difference between two large quantities, it probably excels all other scientific instruments.

By the use of agate knife edges and planes, even ordinary chemical balances have been brought to such perfection that they will indicate one-millionth part of the weight in either pan, while the best bullion balances are still more accurate. The greatest degree of accuracy which has yet been attained was probably in Professor Miller's weighings for the construction of the standard pound, and its comparison with the kilogramme, in which he found that the probable error of a single comparison of two kilogrammes, by Gauss's method, was 14000000th part of a kilogramme.* ("Phil. Trans.," 1856.)

But, though the balance is peculiarly well fitted to detect the relatively small differences between large quantities, it has not hitherto been considered so well able to measure absolutely small quantities as the torsion balance. The latter, for instance, was used in the Cavendish experiment, when the force measured by Cavendish was the attraction of a large lead sphere upon a smaller sphere, weighing about 1 lbs., the force only amounting to 50000000th part of this weight, or about 5th part of a grain.

The two great sources of error, which render the balance inferior to the torsion balance in the measurement of small forces, are:

1. Greater disturbing effects produced by change of temperature, such as convection currents and an unequal expansion of the two arms of the balance.

2. The errors arising from the raising of the beam on the supporting frame between each weighing, consisting of varying flexure of the beam and inconstancy of the points of contact of the knife edges and planes.

The disturbances due to convection currents interfere with the torsion balance as well as with the ordinary balance, though they are

* Even so far back as 1787, Count Rumford used a balance which would indicate one in a million and measure one in seven hundred thousand. ("Phil. Trans.,"

more easily guarded against with the former, by reason of the nature of the experiments usually performed with it. They might, perhaps, as has been suggested by Mr. Crookes, be removed from both by using the instruments in a partial vacuum, in which the pressure is lowered to the "neutral point," where the convection currents cease, but the radiometer effects have not yet begun. But a vacuum balance requires such complicated apparatus to work it, that it is perhaps better to follow the course which Baily adopted in the Cavendish. experiment. He sought to remove the disturbing forces as much as possible, and to render those remaining as nearly uniform as possible in their action during a series of experiments, so that they might be detected and eliminated. For this purpose the instrument was placed in a darkened draughtless room, and was protected by a thick wooden casing gilded on its outer surface. Most of the heat radiated from the surrounding bodies was reflected from the surface of the case by the gilding. The heat absorbed only slowly penetrated to the interior, and was so gradual in its action, that, for a considerable time, the effect might be supposed nearly uniform. Under this supposition it was then eliminated by the following method of taking the observations. The resting point (that is the central position of equilibrium, about which the oscillations were taking place) of the torsion rod, at the ends of which were the small attracted weights, was first observed when the two large masses pulled it in one direction. The masses were then moved round to the opposite side, when they pulled the rod in the opposite direction and the resting point was again observed. The masses were then replaced in their original position and the resting point was observed a third time. These three observations were made at equal intervals of time; if, then, the disturbing effect was uniform during the time, the mean of the first and third observations gave what the resting point would have been, had the rod been pulled in that one direction at the same time that it was actually observed when pulled in the opposite direction. The difference between the second resting point and the means of the first and third might, therefore, be considered as due to the attractions of the masses alone.

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In the experiments of which this paper contains an account, I have endeavoured to apply this method of introducing time as an element to the ordinary balance. But, before it could be properly applied, it was necessary to remove the errors due to the raising of the beam between successive weighings, as they could not be considered to vary any uniform way with the time. I think I have effected this satisfactorily, by doing away altogether with the raising of the beam by the supporting frame, between the weighings. For this purpose I have introduced a clamp underneath one of the pans, which the observer can bring into action at any time, to fix that pan in whatever position it may be. The weight can then be removed from the pan,

and another, which is to be compared with it, can be inserted in its place without altering the relative positions of the planes and knife edges. The counterpoise in the other pan, meanwhile, keeps the beam in the same state of flexure. The pan is then unclamped and the new position about which it oscillates is observed. The only changes are due to the change in the weight and the effect of the external disturbing forces; the latter we may consider as proportional to the time, if sufficient precautions have been taken, and by again changing the weights and again observing the position of the balance, we may eliminate their effects.

Though the method when applied to the balance does not yet give such good results as Baily obtained from the torsion balance-partly, I believe, because I have not yet been able to apply all his precautions to remove external disturbing forces-it still gives better results than would have been obtained without it. This may be seen by the numbers recorded in the tables, where a progressive motion of the resting point may be noticed in most cases, in the same direction, during a series of experiments. Even when this is not the case, the method at once shows when the disturbing forces are irregular, and when we are justified in rejecting an observation on that account.

I give in this paper two applications of the method, one to the comparison of two weights, the other to the determination of the mean density of the earth. The latter is given only as an example of the method, but I hope shortly to continue the experiments with a large bullion balance, for the construction of which I have had the honour to obtain a grant from the Society. The balance is now in course of construction, by Mr. Oertling, of London.

Description of the Apparatus.

The balance which I have employed is one of Oertling's chemical balances, with a beam of nearly 16 inches, and fitted with agate planes and knife edges. It will weigh up to a little more than 1 lb. To protect it from sudden changes of temperature, the glass panes of the case are covered with flannel, on both sides of which is pasted gilt paper, with the metallic surface outwards. This case is enclosed in another outer case, a large box of inch deal, lined inside and out with gilt paper. The experiments have been conducted in a darkened cellar under the chemical laboratory at Owens College, which was kindly placed at my disposal by Professor Roscoe. As the ceilings and floors of the building are of concrete, any movement near the room causes a considerable vibration of the floor and walls. It was necessary, therefore, to support the balance independently of the floor. For this purpose, six wooden posts (A, B, C, D, E, F, fig. 1) were erected resting on the ground underneath and passing freely through the floor to a height of 6 feet 6 inches above it. They are connected at

the top by a frame like that of the table, and stayed against each other to give firmness. The wider part of the frame, near the posts E and F, is boarded over to form a table for the telescope (t, fig. 1) and scale (s), by which the oscillations of the balance are observed. The box containing the balance rests on two cross pieces, on the narrower part, ABCD, of the frame, with the beam parallel to AD, and its right end towards the telescope.

In order to observe the position of the beam, a mirror, 14 inches by inch, is fixed in the centre of the beam, and the reflection of a vertical scale (s, fig. 1) in this is viewed with a telescope (t) placed close to the scale. The light from the scale passes through two small windows cut in each of the cases of the balance and glazed with plate glass. The position of the beam is given by the division of the scale upon the cross line on the eyepiece of the telescope. The scale, which was photographed on glass, and reduced from a large scale, drawn very carefully, has 50 divisions to the inch. These are ruled diagonally with ten vertical cross lines. It is possible to read, with almost certainty, to a tenth of a division, orth of an inch. Since the mirror is about 6 feet from the scale, a tenth of a division means an angular deflection of the beam of about 3".*

The scale is illuminated from behind by a mirror (m), several inches in diameter, which reflects through it a parallel beam from a paraffin lamp (1). A plate of ground glass between the scale and mirror diffuses the light evenly over the scale and, by altering the position of the mirror, any desired degree of brilliancy may be given to the illumination of the scale. A screen (not shown in fig. 1) prevents stray light from striking the balance-case.

This method of reading-which, of course, doubles the deflection— has been so far sufficiently accurate for my purpose; that is to say, the errors arising from other sources are far greater than those arising from imperfections of reading. But in a long series of preliminary experiments I used the following plan to multiply the deflection still further. A rather smaller fixed mirror, ab, is placed opposite to and facing the beam-mirror, AB, fixed on the beam, and a few inches from it. Suppose the beam-mirror to be deflected from the position BL, parallel to ab, through an angle, 0, to the position AB. If a ray, PQ, perpendicular to ab strikes AB at Q, it will make an angle, 0, with QM, the normal at Q, and will be reflected along QR, making an angle, 20, with its original direction, and therefore with the normal RO, at R, when it strikes it. If it be reflected again to AB at S, it will make an angle, 30, with the normal SN, and the reflected ray, ST, will make an angle, 40, with the original direction, PQ, of the ray. It may be still further reflected between the two mirrors, if

The numbers on the scale run from below upwards, so that an increase in the weight in the right hand pan is indicated by a lower number on the scale.

desirable, each reflection at the mirror, AB, adding 20 to the deflection of the ray. I have, for instance, employed three reflections from the

beam-mirror, so multiplying the deflection six times. In this case, one division of my scale, at the distance at which it was placed from the beam, corresponded to a deflection of 7" in the beam, and this could be subdivided to tenths by the eye. The only limit to the multiplication arises from the imperfection of the mirrors and the decrease in the illumination of the successive reflections.*

The chair of the observer is placed on a raised platform, and a small table rising from the platform and free from the frame on which the instruments rest, is between the observer and the telescope. On this he can rest his note-book during an experiment. As the differences of weight observed are sometimes exceedingly minute, the balance is made very sensitive-usually vibrating in periods between 30" and 50". The value of a division of the scale cannot be determined by adding known small weights to one pan, as the deflection would usually be too great. Any approach of the observer to the case causes great disturbances, so that the ordinary method of moving a rider an observed distance along the beam is inapplicable. In some experiments made last year I calculated the force equivalent to the small differences in weight, in absolute measure, by observing the actual angular deflection and the time of vibration. With a knowledge of the moment of inertia of the beam and treating it as a case of small oscillations, it was possible to calculate the value of the scale. But the observations and subsequent calculations were so complicated that the following method of employing riders was ultimately adopted.

A small bridge about an inch long (fig. II, 1) is fitted on to the beam. The sides of the bridge are prolonged about half an inch above the

*This method was used in the seventh and eighth series here recorded. Two reflections from the beam mirror were employed, giving four times the actual deflection.