April 2, 188S.] 



♦ KNOWLEDGE ♦ 



123 



WEIGHING THE EARTH. 



^HE great ditEculty in determining the earth's 

 mass arises from the circumstance that it 

 surpasses so enormously that of any known 

 body -with whicli we can compare it. A 

 mountain may exert an attraction measur- 

 ably comparable with that of the earth ; but 

 a mountain is not a known mass, for we are 

 not able to examine the mountain's whole structure, and 

 short of such examination the mountain's mass must remain 

 doubtful. We may descend into mines and recognise a 

 change in the force of gravity suggestive of the law or laws 

 according to which the density of the earth's interior varies 

 as the centre is approached ; but we must always remain in 

 doubt how far the change may be due to peculiarities in the 

 structure of the strata through which the mine penetrates. 

 The only trustworthy determinations of the earth's mass are 

 those in which the attraction of some known mass of matter, 

 as a globe of lead or platinum, Ls directly compared with 

 that of the earth ; and the largest masses of the kind which 

 have yet been used in this way have been so infinitesimally 

 small compared with the mass of the earth, that it is only 



of being thoroughlj- surveyed by geologists, and must 

 present such features as suggest probable uniformity of 

 interior stratification. Suppose now that B and B' are two 

 stations on a meridian — that is, on the same north-.and-south 

 line — whose positions have been determined by trigono- 

 metrical survey. Observations made at B and B with 

 the zenith sector would indicate the true difference of 

 latitude between B and B', were the plumb-lines at B and 

 B' in the true vertical directions A B and A B . But if the 

 attraction of the mountain's mass draws these plumb-lines 

 into the positions A b and A' b', then the latitudes of 

 B and B' as determined by the zenith sector would be 

 incorrect. Evidently, B being the northern station, and 

 B P' the direction of the polar axis, the plumb-line A b 

 makes a smaller angle than A B, the true vertical, with the 

 direction of the pole, or seems to indicate for B too high a, 

 latitude; while A'6' makes a larger angle than A'B' with 

 the polar axis, and seems to indicate for B' too low a 

 latitude. Both displacements increase tbe apparent differ- 

 ence of latitude; and comparing the diffeience of lati- 

 tude determined by trigonometrical survey with the 

 difference indicated by the plumb-lines at B and B', the 

 disturbing effect of the attraction of the mountain-mass is 



Fig. 1. — The Schehallien Experiment for determining the Earth's Mass. 



by apparatus of extreme delicacy that any measurable 

 alteration of terrestrial attraction has been produced ; so 

 that all experiments of the sort are affected by a certain 

 degree of uncertainty, depending on the delicacy of the 

 methods employed, and what may be called the tenuity of 

 the results deduced. 



It is a serious mistake to describe the measurements of 

 the earth's mass made by ilaskelyne on Mount Schehallien, 

 and by Mr. Dunkin in the Hartley coal-mine, in terms 

 implying that the precision of the processes employed 

 involved a corresponding degree of accuracy in the results 

 obtained. Nothing but the most precise and careful obser- 

 vation and experiment could have led to any observable, 

 still less to any measurable results. But we must not sup- 

 pose, because exceedingly delicate and precise observation 

 can alone lead to any results at all in such experiments, that 

 therefore results obtained by such observation are themselves 

 of corresponding precision ; on the contrary, the reverse 

 must be a.ssumed, unless the results obtained by different 

 researches of thLs class shall be found to agree so closely as 

 to indicate more trustworthiness in such methods than had 

 been anticipated. But this has not happened. On the 

 contrary, the reverse has thus far proved to be the case. 



The Schehallien experiment, and experiments of the 

 same type, may, with amply adequate precision, be thus 

 described : — 



Let M »', M' m', fig. 1, be the slopes of a mountain such 

 as Schehallien, suitably situate so that whatever attraction 

 its mass may be capable of exerting can be estimated with 

 fair chance of freedom from serious error ; in other words, 

 the mountain must stand in some degree apart, must admit 



determined. Hence, after reductions and computations 

 which, though seemingly complex, depend on established and 

 even simple principles, the astronomer is able to compare 

 the attraction of the earth with the attraction of the 

 mountain, and if the mass of the mountain can be ascer- 

 tained, the mass of tbe earth can be deduced. 



Bouguer and La Condamine, during experiments on 

 Chimborazo, recognised the effect of the mountain's attrac- 

 tion in deflecting the plumb-line (by .about 11"), but no 

 estimate of the earth's mass was obtained, the conditions 

 being too complex and uncertain. It was not till 1774 

 that a definite attempt was made to measure the earth's 

 mass by this method. In that year Maskelyne made obser- 

 vations on the northern and southern slopes of Schehallien, 

 a mountain only 3,000 feet in altitude, but well suited for 

 the experiment. The sum of the deflections observed 

 amounted to ll'-G ; and from this result Messrs. Hutton &. 

 Playfair, after as thorough an examination of the moun- 

 tain's structure as could be made, deduced for the earth's mass 

 a value corresponding to a mean density exceeding that of 

 water 4-713 times. Ob.servations made in 1885 on Arthur's 

 Seat by Colonel James, Superintendent of the Ordnance 

 Survey, indicated a mean density of 5-31G. 



Another method depends on the diminution of attraction 

 as we ascend above the earth's surfoce. The rate of oscilla- 

 tion of a pendulum will be calculably reduced at a height of 

 two or three miles above the sea-level. If set at such a 

 Leifht on a mountain summit, the attraction of the moun- 

 tain's mass will diminish the reduction of the rate of oscilla- 

 tion. Hence, if we know the ma.ss of the mountain and 

 measure the effect of its attraction, we can deduce the mass 



