721 



EARTH, MEAN DENSITY OF THE. 



EARTH, MEAN DENSITY OF THE. 



722 



it never is reduced to absolute rest. The instrument is so delicate 

 that it is in continual oscillation to a small extent, and its position of 

 rest, say mm' is found by taking the mean of the extreme positions on 



one side and the other. Even this mean position is continually shifting 

 its direction, BO that it cannot be permitted to take a series of obser- 

 vations and make use of them all in determining one mean place. The 

 mode of finding the point of rest, that is of deducing it from observing 

 the extremes of the vibration, is described in the work cited. As soon 

 as the line of rest of the undisturbed pendulum is ascertained, and 

 the large balls are brought into the attracting positions at A and B, on 

 continuing the observation an immediate alteration of the line of rest 

 is seen towards the large balls ; say that it becomes nn'. Then the 

 position of equilibrium of the pendulum is altered by the angle ?iom, 

 in consequence of the approach of the balls.* The precautions taken 

 are abundantly sufficient to assure us that the alteration is no con- 

 sequence of heat, electricity, magnetism, or any of the variable 

 accidents of matter ; there is nothing to which it can be referred except 

 that attraction which, when the earth is the agent, we know under the 

 name of weight, and the assumption of which, as a universal property 

 of matter, led Newton to his explanation of the planetary motions. 

 Many of those who were content to receive Newton's hypothesis to this 

 extent, that the planets attract each other, were staggered by the idea 

 that every particle in the universe attracts every other. Such objectors 

 might have here received conviction from the evidence of their own 

 senses, which would have rendered obvious not only the attraction of 

 the balls upon each other, but its transmission through the wood, 

 flannel, and gilding, which it was found necessary ultimately to inter- 

 pose between the attracting substances and the torsion-rod in order to 

 destroy the effects of radiant heat. 



Two observations are necessary, that of the time of oscillation of 

 the pendulum, and that of the displacement of the line of rest which 

 the approach of the larger balls produces. The first observation, the 

 tune, enables the observer to deduce the force of torsion, or the quantity 

 of pressure required to produce any given displacement. And in this 

 particular it was found that the pendulum altered its character from 

 one quarter of an hour to another ; showing that the instrument was 

 so delicate, that circumstances of which no explanation can be given 

 were continually altering its character. The consequence was, that at 

 every new trial, both the time and displacement had to be scrupulously 

 observed together, in order that to each displacement produced the 

 proper producing attraction might be applied. The complete formula 

 for calculating the mean density of the earth, implies, 1. The calcu- 

 lation of the character of the pendulum, or the amount of attraction 

 necessary to alter its line of rest by a given quantity ; 2. The deter- 

 mination of the attraction actually employed, namely, that of the 

 larger balls, by means of the displacement actually observed ; 3. The 

 determination of the attraction which the larger ball would exert, if it 

 had been at the centre of the earth, instead of at the distance t 

 employed ; 4. The number of tunes the whole earth would contain 

 such a leaden ball, and its easy consequence, namely, the number of 

 times the whole earth would contain a similar bulk of water ; 6. All 

 the necessary corrections for the attraction of the other parts of the 

 apparatus upon the torsion pendulum. 



The larger masses were leaden balls, but the smaller balls attached 

 to the torsion pendulum were changed from time to time, and dif- 

 ferent substances were used. The following table of results will be 

 more interesting than any description we could give in the same space. 

 It shows the result of the experiments made after the effects of 

 radiation were removed + by additional precautions. The first column 



* In nuking the experiment the effect was usually doubled by placing the 

 Urge balls first on one side of the smaller ones, and then on the other, and 

 noting the -whole of the double displacement. 



t This distance of course was accurately measured. 



X An enormous mass of experiment* was made and rejected in the course of 

 the attempts to remove singular discordances, of which no explanation could be 

 giren. The mean resnlt of these would not have differed much from those of 

 tbe more correct sets, but would, of course, hare been less satisfactory. The 

 removal of the discordances was due to the suggestion of Professor Forbes, of 

 Edinburgh, who continued to believe they might arise from radiation long after 

 others thought the precautions then already taken must hare been sufficient to 

 remove that source of disturbance. 



ABTS AND SCI. DIV. VOL. HI. 



is the number of experiments made, with the small balls and mode of 

 suspension described in the third ; the second contains the mean 

 density of the earth as deduced from that set of experiments ; the 

 third describes the small balls and mode of suspension employed ; the 

 numerals, which are fractions of an inch, representing the diameter of 

 the suspension wire, when single, and the distance of the wires when 

 double or bifilar : 



The results of individual experiments vary considerably, but it is 

 important to observe that there is nothing which indicates that dif- 

 ferent kinds of matter attract each other according * to different laws. 

 If the large ball of lead exerted different attractions upon particles of 

 brass and ivory of the same weight, the effect would be to give the 

 whole earth one mean density or another, according as the smaller ball 

 is of brass or ivory. Now it is true that the experiments give all manner 

 of resulta from 6'500 to 6'154, but on examining the results, there 

 appears no evidence whatever of the larger balls attracting the different 

 smaller ones differently. If such were the case, undoubtedly the mean 

 densities obtained from different substances would be different ; but 

 though such is the case in the preceding list, and even though it would 

 seem that the lighter balls give the larger densities, yet there is every 

 reason to suppose that the effect is to be attributed to the alteration 

 of the pendulum. Thus it will be seen that there is not so much 

 difference between the results of 2-inch ivory and lead balls sus- 

 pended in the same way by a single copper wire, as there is 

 between the results of 2-inch lead balls suspended by bifilar iron 

 wires, and the same suspended by bifilar brass wires, and also 

 that ivory balls differently suspended give results which have differ- 

 ences as great as any. The mode of suspension and the effect of 

 merely increasing the weight of the smaller balls, appear much to 

 exceed that of applying different substances ; but not according to any 

 law. In fact, the differences are altogether of that character to which 

 the term discordance is applied ; following no settled rule, and exhi- 

 biting every appearance of as often affecting the truth by a positive 

 as by a negative error. The first three sets, in which a brass rod 

 alone is used, were rather a defiance to the apparatus to fail if it could, 

 than seriously intended to help the result. Almost all the experi- 

 ments were made with a light wooden torsion-rod, and comparatively 

 heavy balls appended. The trying a brass rod by itself, that is, 

 the attempt at obtaining a mean density by noting the attraction 

 of the larger balls upon the torsion-rod only, was the introduction 

 of an extreme case, to increase confidence in the more ordinary 

 experiments. 



The mean of the whole is 5'6747, and, rejecting the experiments ol 

 which the character would be d priori most doubtful (though it is not 

 certain thef ought to be rejected) it is reduced to 5-6604. From the 



That it is not the cae, is also established without a doubt by pendulum 



experiments. 



o A 



