88 



KNOWLEDGE. 



[April 2, 1894. 



Tliat the comet is identical with tlie one recorded 

 in the Chinese annals five centuries before is exceedingly 

 doubtful ; a glance at the elements of the orbit of the 

 latter as computed by Peirce will at once show how un- 

 certain they are, as is remarked by Jlr. Hind in his 

 '• Comets." Oppolzer's determination of the orbit of the 

 comet of 1866 is probably as accurate as could be made 

 from observations which extended over an interval of less 

 than a month. To compute its perturbations with much 

 accuracy would not be a very hopeful task at present ; 

 after the return in 1899 (which will probably take place 

 in March) this will be more practicable. — W. T. Lynn.] 



WEIGHING THE EARTH. 



By J. J. Stewakt, B.A., B.Sc. 

 (Co)ttiniu-d from page 32.) 



THE method adopted by Prof. Poynting in his 

 earth-weighing experiments, concluded a year or 

 two ago, is a modification of that of Cavendish, in 

 which the balance is directly made use of, and the 

 force of attraction due to a sphere is found by 

 placing it beneath a scale pan, and then balancing the 

 disturbance of the beam produced by the sphere in this 

 position, by adding weights to the other pan. 



" In using the common balance to find the attraction 

 between two masses, perhaps the most direct mode of 

 proceeding would consist in suspending a mass from one 

 arm of a balance by a long wire, and counterpoismg it in 

 the other pan. Then bringing under it a known mass, 

 its weight would be slightly increased by the attraction of 

 this mass. The increase would be the quantity sought if 

 the attracting mass had no appreciable influence before its 

 introduction beneath the hanging mass, and if, when 

 beneath it, the eSect on the balance could be neglected. 

 This is very nearly the principle of the method used by 

 Von Jolly." 



Prof. Poynting used a differential method. A spherical 

 mass was placed first under one of two masses suspended 

 from the beam of a balance, and then placed under the 

 other, the tilt produced in the beam being observed. 

 Then the suspended masses were raised to a higher 

 position, and the attracting mass placed under each 

 alternately as before ; in this last case the attraction 

 on the beam is the same as in the first experiment, and 

 this attraction can thus be eliminated, for the difference 

 between the two observations of the increase of weight on 

 one side is caused solely by the alteration of the positions 

 of the suspended masses with reference to the attracting 

 sphere below them ; the attraction on the beam remains 

 the same in each case. From the observed effect of a 

 known alteration of distance, the attraction at any distance 

 can be arrived at. 



The attracting mass used in the experiments consisted 

 of a metallic sphere. This was placed on a turntable, and 

 could thus be gently moved into its position below the 

 balance or away from it. The experiments were com- 

 menced at the Cavendish Laboratory, Cambridge, in a 

 room in the basement. The apparatus was afterwards 

 moved to Birmingham, and the experiments continued at 

 the Mason College there. The balance room was in the 

 basement of the building, and observations were taken by 

 a telescope placed m the room above through an opening 

 in the floor. The balance used was of the large bullion 

 balance type, and was made specially for the experiment 

 with extra rigidity of beam. The movement of the pointer 

 of the balance was shown by reflection from a suspended 



mirror. Both the attracting and attracted masses were 

 made of an alloy of lead and antimony for the sake of 



I hardness, and their surface was gilded. 



I Errors were detected due to alteration of the slope of 

 the floor on monng the weight. There was also a slow 

 gradual change. Another mass, half as great as the 



I attracting mass, was placed on the opposite side of the 

 turntable and twice as far from the axis. This arrange- 

 ment caused the resultant pressure to be always through 

 the axis. A second set of experiments was made with the 

 masses turned over, to get rid of any error which might 

 arise owing to want of symmetry, the mean of the two 

 sets of experiments being taken. 



Errors due to air currents were the most difficult to get 

 rid of. In warm, quiet weather the air was steadiest. 

 Prof. Poynting says the opening or shutting of a door 

 anywhere in the building had a visible, though transient, 

 effect on his apparatus, doubtless through the production 

 of an air wave. In a high wind the balance was always 

 unsteady, partly owing to rushes of air into and out of the 

 case with sudden changes of pressure, and partly through 

 changes of groimd level with variations of wind pressure 

 against the building. 



The law of universal gravitation states that when two 



masses m m"^ attract each other the attraction is 



K 



d- 



K being the gravitation constant, which is the same for all 



masses, and il the distance between the masses. 



When the gravitation constant K is known, the mean 



density A of the earth can be found immediately ; for if 



V = volume of the earth considered to be a sphere of 



radius R, the weight of any mass. M' being the attraction 



K y A Ml 

 of the earth upon it, is rp ; but if g denotes the 



acceleration produced by gravity the mass is also = M^ r/. 



1/ R2 

 Therefore A = 'f^^- 



Prof. Poynting finds as the mean value of A from his 

 experiments 5-493. In one set of his experiments the 

 value found was less than that got by Cavendish, in 

 another set it was greater, the mean being as above. 



It has been suggested that a good way of finding the 

 earth's mass would be to observe the change of deflection 

 produced in the plumb line by the filling and emptying of 

 an estuary by the periodic movements of the tides. The 

 quantity of matter occupying the space of the estuary or 

 arm of the sea would undergo regular periodic changes, 

 and by observations of the changes of latitude every six 

 hours a good determination of the constant required might 

 be obtained. 



A method very similar to this, and of a very in- 

 teresting character, has quite recently been employed by 

 M. Alphonse Berget. who described his experiments in the 

 Comptef: rendus of the Paris Academy of Sciences last 

 year. 



The experiments consisted in artificially causing a change 

 of level in the waters of a lake. The level was raised 

 or lowered through a distance of a little over three feet, 

 and the eft'ect of this alteration on a hydrogen gravimeter, 

 such as that which was employed to measure the diurnal 

 variation in gravity, was observed. The lake on which 

 these trials were made is in Luxembiu'g, and has an area 

 of seventy-nine acres. Its level could be raised or lowered 

 by the above-mentioned amount in a few hours, and the 

 variation in the column of mercury of the observing 

 instrument was determined by a very delicate method, 

 which consisted in noting the appearances and changes in 

 Fizeau's interference fiinges, formed in vacuo between the 



