Dec. 19, 1889] 



NATURE 



^7 



position for the attracting masses, because, in showing 

 the experiment to an audience, the largest effect should 

 be obtained that the instrument is capable of producing ; 

 while in exact measures of the constant of gravitation this 

 position has the further advantage that the only measure- 

 ment which there is any difficulty in making, viz. the 

 angle between the line joining the large masses and the 

 line joining the small, which may be called the azimuth of 

 the instrument, becomes of little consequence under these 

 circumstances. In the ordinary arrangement the slightest 

 uncertainty in this angle will produce a relatively large 

 uncertainty in the result. I have already stated that if 

 an angle of 45° is chosen, the distance between the centres 

 of the large balls should be 2 sj'2 times the length of the 

 beam, and the converse of course is true. As it would 

 not be possible at this distance to employ attracting balls 

 with a diameter much more than one and a half times 

 the length of the beam, and as balls much larger than this 

 are just as easily made and used, I have found by calcula- 

 tion what are the best positions when the centres of the 

 attracting balls are any distance apart. 



If the effect on the nearer ball only is considered, then 

 it is easy to find the best position for any distance of the 

 attracting mass from the axis of motion. Let P (Fig. 2) 

 be the^ centre of the attracting ball, N that of the nearer 



Fig. 2. 



attracted ball, o the axis of motion, c and a the distances 

 of P and N from o, and x the distance from N of the 

 foot of the perpendicular from p on ON produced. Then 

 the moment of N about O will be greatest when 



x^ + ^ JI X = 2{c^ — d^), 



or what comes to the same thing when 



cos^ 6 + ^' +^' cos 6 = z- 

 ca 



Now, as the size of the attracting masses M M is in- 

 creased, or, as is then necessarily the case, as the distance 

 of their centres from the axis increases, their relative 

 action on the small masses m m at the opposite ends of 

 the beam increases, and so but a small fraction of the 

 advantage is obtained, which the large balls would give 

 if they acted only upon the small balls on their own side. 

 For instance, if the distance between the centres of M M 

 is five times the length of the beam, the moment due to 

 the attraction on the opposite small balls is nearly half 

 as great as that on the near balls, so that the actual 

 sensibility is only a little more than half that which would 

 be obtained if the cross action could be prevented. 



I have practically overcome this difficulty by arranging 



the two sides of the apparatus at different levels. Each 

 large mass is at or nqar the same level as the neighbour- 

 ing small one, but one pair is removed from the level of 

 the other by about the diameter of the large masses 

 which in the apparatus figured below is nearly five times 

 as great as the distance in plan between the two small 

 masses. 



In order to realize more fully the effect of a variety of 

 arrangements, I have, for my own satisfaction, calculated 

 the values of the deflecting forces in an instrument in 

 which the distance between the centres of the attracting 

 balls is five times the length of the beam, for every azi- 

 muth and for differences of levels of o, i, 2, 3, 4, and 5 

 times the length of the beam. 



The result of the calculation is illustrated by a series 

 of curves in the original paper. The main result, how- 

 ever, is this. 



In the particular case which I have chosen for the in- 

 strument, i e. where the distance between the centres of 

 M M and the axis, and the difference of level between the 

 two sides are both five times the length of the beam, as 

 seen in plan, and where the diameter of the large masses 

 is 6"4 times the length of the beam, the angle of deflection 

 becomes 187 times as great as the corresponding angle 

 in the apparatus of Cavendish, provided that the large 

 masses are made of material of the same density in the 

 two cases and the periods of oscillation are the same. 



Having now found that with apparatus no bigger than 

 an ordinary galvanometer it should be possible to make 

 an instrument far more sensitive than the large apparatus 

 in use heretofore, it is necessary to show that such a piece 

 of apparatus will practically work, and that it is not liable 

 to be disturbed by the causes which in large apparatus 

 have been found to give so much trouble. 



I have made two instruments, of which I shall only de- 

 scribe the second, as that is better than the first, both in 

 design and in its behaviour. 



The construction of this is made clear by Fig. 3. To 

 a brass base provided with levelling screws is fixed the 

 vertical brass tube /, which forms the chamber in which 

 the small masses a b are suspended by a quartz fibre 

 from a pin at the upper end. These little masses ^are 

 cylinders 1 of pure lead 11 "3 millimetres long and 3 m'illi- 

 inetres in diameter, and the vertical distance between 

 their centres is 5o"8 millimetres. They are held by light 

 brass arms to a very light taper tube of glass, so that their 

 axes are 6"5 millimetres from the axis of motion. The 

 mirror m, which is 127 millimetres in diameter, plane, and 

 of unusual accuracy, is fastened to the upper end pf the 

 glass tube by the smallest quantity of shellac varnish. 

 Both the mirror and the plate-glass window which 

 covers an opening in the tube were examined, and after- 

 wards fixed with the refracting edge of each horizontal, 

 so that the slight but very evident want of parallelism 

 between their faces should not interfere with the defini- 

 tion of the divisions of the scale. The large masses M M 

 are two cylinders ^ of lead 50"8 millimetres in diameter, 

 and of the same length. They are fastened by screws to 

 the inside of a brass tube, the outline of which is dotted 

 in the figure, which rests on the turned shoulder of the 

 base, so that it may be twisted without shake through any 

 angle. Stops (not shown in the figure) are screwed to 

 the base, so that the actual angle turned through shall be 

 that which produces the maximum deflection, A brass 

 hd made in two halves covers in the outer tube, and 

 serves to maintain a very perfect uniformity of tempera- 

 ture in the inner tube. Neither the masses M M, nor 

 the hd, touch the inner tube. The period of oscillation 

 is 160 seconds. 



With this apparatus placed in an ordinary room with 



• Cylinders were employed instead of spheres, because they are more 

 easily made and held, and because spheres have no advantage except when 

 absolute calculations have to be made. Also the vertical distance a b was 

 for convenience made only about four times the length abia plan. 



