152 



♦ KNOW^LEDGE ♦ 



[May 1, 1888. 



ferent material and size in diffe:-ent experiments, viz , H-inch 

 platinum, 2-inch ivory, 2. inch glass, 2-inch zinc, 2-inch lead, 

 2.Viuch lead, and 2.\-inch brass. In a small number of 

 experiments (fifty-six) the wooden rod was replaced by a 

 brass rod without balls. The torsion rod and its suspension 

 were enclosed in a case with a glass at one end. The devices 

 by which the effects of electricity, magnetism, radiation, and 

 other disturbing iniiuences were as far as possible eliminated 

 need not be described, u9r the multitudinous experiments 

 considered by which explanations of irregular discordances 

 were sought for or corrections introduced. Nor is it neces- 

 isary to describe or picture Baily's instrument either as a 

 whole or in detail — the general principle of liis method, 

 already sufficient!}' explained, being all that ij wanted and 

 all that the student really needs to understand. Let it 

 suffice to note that the experiments for the correction and 

 explanation of discordances were more numerous than those 

 actually employed for the determination of the earth's mean 

 density. 



The experiments thus used amounted in all to 753. Of 

 these, however, 5(i, above-mentioned, when only a brass rod 

 was used, were not seriously intended for the determination 

 of the earth's mean density. They are well described by 

 De Morgan as " a defiance to the apparatus to fail if it 

 could." Yet they indicated a mean density below (5 — a 

 result much nearer the truth than the Harton Colliery 

 experiments had given, costly and complicated though they 

 were. The remaining G97 experiments gave results ranging 

 from 5") to •5'8-t7. The mean value deduced by Baily (due 

 weight being given to each set of experiments) was 5'G6. 



Cornu, in 1872, applying the same method with improve- 

 ments suggested by recent scientific developments, obtained 

 the value 5'56. He did still better work in applying to the 

 more numerous experiments of Baily, as recorded, correc- 

 tions justified by recent physical discoveries. He found 

 that as thus corrected Baily's elaborate and beautiful 

 experiments indicated a mean earth-density of 5 '55. 



The following table presents the results of the application 

 of Michell's method : — 



Cavendish 5--I8 



„ (revised by Hattcn) . . . -. .5 32 



Reich . . . " .5-44 



Uaily .5Gli 



„ (revised by Cornu) 5 S.5 



Cornu . . " .■; 56 



Mean .5-51 



The trua mean value of the experiments made by this 

 method, due weight being given to each result, and Cornu's 

 revision of Baily's experiments being accepted, is so near 

 ■5-55, that this may fairly be taken to represent the most 

 probable mean density of the earth, the error being probably 

 not more than 05 — in other words, the density of the earth 

 probably lies between 5 5 and 5 6. 



Taking the eai'th's mean density at 5 '55 times the density 

 of water, the earth's mass=59b,(J54,000,000,OUU,000,000 

 tons. 



The earth's equatorial radius contains in round numbers 

 20,926,200 feet, the polar radius being . J^ less, and 35-943 

 cubic feet of water weigh one ton. Hence, the earth's mass, 

 expressed in tons, 



which when duly worked out (the use of logarithms will 

 greatly help the reader who cares — as every reader should — 

 to test the calculation) gives the above value. 



There is a method by which, I think, the mass of the 

 earth might be directly compared with that of a known mass 

 of lead or other heavy metal, without the difficulty arising 



from the varying torsion, under varying conditions, in the 

 Michell method. The plan suggested (but in an unwork- 

 able form) by Professors Richer and Mayer, of the Berlin 

 Universit}-, will be readily understood from figs. 2 and 3. 

 A B D is a globe of lead, which might be three or four feet 

 in diameter, whose centre is at C. At M, the highest point 

 of this globe, a small .steel block is set, on which rests the 

 knife-edge c of a balance a c h. The large globe A B D is 

 pierced along the vertical directions AD and BE, imme- 

 diately under the extremities n and h of the baUvnce-arms 

 c a and c b, in such sort that the balance can be u.sed to 

 weigh bodies either above A B or below D E, or one above 

 A B and the other below I) E, as in the case illustrated in 

 fig. 2, where a weight lu above A is weighed against a 



(t)- s>, 



Fifj. 2. Ilhistrating a plan suggosted for weighing the earth 

 directlj- against a globe of heavy metah 



weight w' below E. Fig. 3 .shows the balance on a larger 

 scale, and illustrates the arrangement suggested as best for 

 applying the weights. Immediately above the centre- 

 piece c (the knife-edge of which rests on the liorizontal 

 surface k I at e) is a thin ])late of polished steel which, when 

 the balance is level, has its plane at right angles to the then 

 horizontal direction a b. A horizontal beam of light from 

 a distant source, situate either on the left or on the right of 

 the apparatus as pictured, falls on this steel mirror, and 

 when the balance beam is level returns after reflexion upon 

 its horizontal track, but when the beam is inclined the 

 return ray is inclined to the horizon. Thus the reflected 

 ray ]iractically serves as a very long index by which to 

 measure the deflection of the balance. [In the actual 

 experiments the light could be sent out and received as in 

 the observations for determining the velocity of light by 

 Fizeau's and Wheatstone's methods.] Two weights exactly 

 equal and similar suffice for all the experiments, but pre- 

 ferably four sliould be provided, so that in any set of experi- 

 ments there need be no occasion to transfer a weight from 

 above the large globe to below or via versA. It would be 

 desirable also that sets of weights of different materials 

 should be employed, so that diversities depending on the 

 physical qualities or inter-relations of different substances 

 might be eliminated. The weight-holders are shown in 

 fig. 3 at ;), q, J) , and q . Their construction should be such 

 that with the least amount of disturbance a weight, such as 

 is shown at fi and 5', may be added, removed, or transferred, 

 as the experiments proceed. The scale-pans and weights 

 should depend from knife-edges at a and h, in tlie usual way 

 where delicate weighing is required. 



The method of the experiments is as follows in a case 

 where a full set of four weights is employed : — 



