4i8 



NATURE 



[August 23, 1894 



treated provisionally as a rijiid system moving all as one piece, 

 which it certainly does not seem to be. For instance, the lead 

 balls, by their attraction of the gold balls, pull them out of the 

 perpendicular, so that their distance from the axis is greater than 

 that given by measurement by the optical compass. The error 

 amounts, in the case of the lower ball, when the lead is at its 

 nearest point, to i/io,C)00,cxx3 inch, and I have not taken any 

 notice of it. When the beam is oscillating through so great an 

 angle as 100,000 units the centrifugal force only makes the gold 

 ball move out four times as much, and I have taken no notice of 

 ihaL Again, when the mirror is under acceleration by the fibre, 

 the gold balls, hanging 5 and 11 inches below, do not follow 

 absolutely ; they must lag behind, and so affect the period. 

 Now in this case the gold balls arc suspended in a manner which 

 is dynamically equivalent to being at the end of a pendulum 54 

 miles long, the shortest equivalent pendulum that has ever been 

 employed in work of this kind ; but short as it is, I have not 

 thought it worth while to be perluibed by an uncertainty of a 

 few inches. There is one point which in some of the experiments 

 only has amounted to a quantity which I do not like to ignore. 

 It is due to the torsional mobility of the separate fibres, about 

 which each gold ball hangs, allowinj; them in their rotation to 

 slightly lag behind the mirror. As I did not see ho* to allow 

 for it, I applied to Prof. Greenhill, who immediately told me 

 what to do, and «ho, with Prof. Minchin, spent a day or two in 

 the country, covering many sheets of paper with logarithms, in 

 finding and solving for me the resulting cubic equation. The 

 correction on this account is 1/7850 on the stiffness of the 

 torsion fibre. 



There are four remaining corrections depending on the fact 

 that besides the gravitating spheres there are the ball-holders 

 and supporting wires and fiores, all of which produce small hut 

 definite disturbances in the gravitation. These are all calculated 

 and allowed for. They are : — 



Disturbances due to brass-holders of lead balls... 1/7320 

 ,, ,, copper ,, gold 1/265,006 



Attraction of lead balls for quartz fibres + 1/200,000 



,, gold ,, phosphor-bronze wires— 1/115,000 



Then in experiment 9 gold cylinders were employed. Mr. 

 Kdser, of the Royal College of .Science, calculated for me the 

 correction to be applied if they were treated as spheres ; this 

 amounted to 1/3300. 



I have already mentioned that experiment 8 was made under 

 more than usually quiet conditions. Such extreme quiet is desir- 

 able, that I manage to reserve Sunday nights, from midnight to 

 six or eight in the morning, for observations of deflection and 

 period. All the other operations can be carried on in the day- 

 time. Sunday is the only night that is suitable, as the railway 

 companies spend every other night shunting and making up 

 trains about a mile away, and this causes such a continuous 

 clatter and vibration, that hours of work may be lost. 

 A passing train does not seem so injurious ; but, 

 fortunately for me, most of the observations were made 

 during the coal strike, and fewer trains than usual were 

 running. However, though I may escape from the rattling 

 traffic of St. fJiles by working at night, and on Sunday nights 

 am not so badly affected by the trains, I am still not .sure of 

 quiet even when there is no wind. For instance, at a quarter 

 to four on Monday morning, Sept. 10, 1893, I was recording 

 chronographically the passage of every ten divisions. Every- 

 thing was quite quiet, and at ihc particular moment the marks 

 on the drum recurred at intervals of about three seconds. Sud- 

 denly there was a violent non-vibrating lurch of fifteen divisions, 

 or 150 units, which is enormously greater than anything that 

 either trains or traffic could produce ; of course, I could make 

 no further record. The time of the last mark was, allowing 

 for the known error of the clock, I5h. 44m. I4'3<. This was 

 er'--- ' •' •■ ime <lay in my note-book as an earthquake, and 

 1- Slanilatil I reail an account of a violent carth- 



'. < imania at about the same time. I have not yet 



l>ariicuiar!i from Vienna, for which .Mr. Horace Darwin has 

 wri'trn ; but though the shock reconled in the new>paper seem 

 " loo laic, preliminary shocks are by no means un- 

 I cannot help thinking that what I observed was the 

 ' ' 'ani effect of one of these. Of this, however, 



I Aas an earthquake that I observed, and not 



1 . :ui; to human origin. 



Owing 10 the viscosity of the air, which limits the time 



during which an observation for period can be made to about 



NO. 1295, VOL. 50] 



40 minutes, on .account of the resistance that the slowly moving 

 mirror and gold balls experience in their passage through it, I 

 made one experiment, with the view of reducing this difficulty, 

 by the use of an atmosphere of pure dry hydrogen gas, which 

 possesses a viscosity only half that of .lir. I did find that on 

 this account a great advantage could be g.iined ; but this was 

 more than counterbalanced by the difficulty of gelling up a 

 sufficient swing in the gas, and of efliciently controlling the 

 mirror. At the same time, I think that il I had had time to 

 provide means for feeding the gas into the tube without entering 

 the corner, and at the same time were to prevent diffusion at 

 the lower screw, that a little trouble in this direction would be 

 well rewarded. Meantime I found within the limits of error, 

 which were greater than without the hydrogen, that the deflec- 

 tion and the period corrected for the diminished damping were 

 the same. The chief interest of this experiment lies in the f.ict 

 that it revealed an action unknown to me, and I believe to 

 others, that a thin plane glass mirror, silvered and lacquered on 

 one side, definitely bends to a small extent, becoming slightly 

 convex on the gl.iss side when in hydrogen, and instantly 

 recovers its form when surrounded by air again. This happened 

 many times, producing a change of focus in the telescope of 

 about five-eighths of an inch. I do not offer any explanation 

 of the fact. 



There is an observation which should be of interest to elas- 

 ticians. In experiments 4 to S the torsion fibre carried the beam 

 mirror and the "25 inch gold balls, weighing, with their hooks 

 and fibres, 5'3I2 grammes. In experiment 9. gold cylinders were 

 substituted, weighing, with their hooks and fibres, 7976 

 grammes. The weight of the mirror was '844 gramme. In 

 consequence of the small increase of load the torsional rigidily 

 of the fibre fell more than 4 per cent., an amount far too gre.at 

 to be accounted for by the change of dimensions, even if 

 Poisson's ratio were as great as J. There is no doubt about the 

 great reduction in stiffness, for this figure is one of the factors 

 in the final expression for G, which does not show a change of 

 more than I part in 1570. 



It will not be possible at this late hour to explain how the 

 observations are treated so as to obtain the value of G. It is 

 sufficient to state that in one of these clips all the observed 

 deflections and corrected periods are collected. In the second 

 all the geometrical observations are collected and reduced, so as 

 to obtain what I call the geometrical factor, i.e. a number 

 which, when multiplied by the unknown G, gives the torsion on 

 the fibre. In the third, the moments of inertia and periods are 

 made use of to find the actual stiffeness of the fibre in the 

 several experiments, and in the fourth these are combined so as 

 to find G. From G the density of the earth A immediately 

 follows. 



The annexed table contains the important particulars of 

 each experiment. From this it will be seen that the lead balls 

 were twisted and interchanged in every way, so as to show any 

 want of gravitational symmetry if it should exist. For instance, 

 after experiment 7 the ball that was high was made low, the 

 .side that was outwards was turned inwards, and their dis- 

 tance apart was reduced by 1/50 inch, but the change in 

 the result w.as only I pari in 2764. The experiments 7, 8, 9, 

 10 were made under widely dififerent circumslances. Afler 

 experiment 8 the gold balls were changed for heavier gold 

 cylinders, which, as has already been stated, reduced ihe 

 torsion of the fibre by 4 per cent., but Ihe result is practically 

 the same as that of experiment 7. I then broke the end of ihe 

 torsion fibre. After keeping it in London three monlhs, I 

 broke the other end. I then rcsoldered each end and put the 

 fibre back in its place, and after making every observation afresh, 

 found with the new shorter and stiffer fibre a result diflering 

 from that of experiment 8 by only i part in 27,635, These four 

 experiments were all made under favourable circumslances, and 

 on ibis account I feel more able to rely upon them than on the 

 earlier ones, which were subject to greater uncertainty. The 

 last experiment was made under most unfavourable conditions. 

 The periods and deflections were taken in the first four hours 

 alter midnight, then, afler a few hours' sleep, and far too sooii 

 for Ihe temperature to have quieted down, I took the period 

 with Ihe counlerwcighl, but w.as only able to give ten minutes, 

 as 1 had to catch a train in order to be able to give my mid- 

 day lecture at South Kensington. It is not surprising that 

 under such conditions a difference of I part in 600 should arise. 

 There is a difference of about Ihe same order of magnitude 

 between the earlier experiments and the favourable four. There 



