Decembkr 21, 18S3. 



SCIENCE. 



797 



cecded in finding any thing approaching full 

 light on the snbjcct " (p. ;^32). Then follows 

 an enumeration of the i)ossible forms of c<iui- 

 libriinn. including the single and miilti|)le rings 

 into which an ellipsoid would be changed when 

 rapidly rotated, and the detached portions, 

 nearly spherical, into which an elongated ellip- 

 soid must separate when rapidl}- rotated about 

 its shorter diameter. 



Now, on the supi)Osition that the figure of 

 the earth is approximately an ol)late spheroid, 

 the next matter of importance is to show how 

 to compute the alterations in figure due to 

 local inequalities in its density, and irregulari- 

 ties in the distribution of the material com- 

 posing it. This at once raises the question 

 as to what we are to consider as the surface of 

 the earth at any point which forms part of its 

 figure. The true figure of the earth may be 

 taken to be the water-surface when undisturbed 

 b\- tides. AVhenever it is desired to find such 

 surface on land, a canal could be sui)i)0sed to 

 be cut from the ocean to the place under con- 

 sideration. Of course, a plumb-line is every- 

 where perpendicular to such a surface, whose 

 outline is evidently affected by all existing in- 

 equalities of density and distribution of the 

 substance of the earth. For example : it is 

 computed that a set of several broad parallel 

 mountain chains and valleys, which are twenty 

 miles from crest to crest, and seventy-two hun- 

 dred feet above the bottom of the valleys, would 

 cause a corresponding undulation of the water- 

 surface whose crests would be five feet above 

 the bottoms of the hollows. This statement is 

 equivalent to s.iyiug, that the plumb-line is de- 

 viated from its mean direction by the attraction 

 of the mountain chains. Deviations of nearl}- 

 •'50" have been actually observed near the Alps 

 and near the Caucasus INIountaius. The com- 

 paratively small deflections observed near the 

 vast mass of the IIimala_vas in India — -which, 

 according to Pratt's calculations in his treatise 

 on attractions, etc., should be vastl}' greater 

 than an3- thing actually observed — indicate 

 that extensive portions of the globe under those 

 mountains are less than the average density. 

 Localities have been found in fiat countries 

 also, notably in England and Russia, where 

 the deflection of the phunb-line exceeds l.j", 

 which is, of course, due to underlying material 

 of great density. From this it appears, that 

 the true figure of the earth is nearlj- as diver- 

 sified as the contours of its hills and valleys, 

 and docs not correspond to any known geo- 

 metrical figure; although, to be sure, these 

 undulations are of small amount. Now, as 

 a first rude approximation, the figure of the 



earth can be taken as a sphere, having the 

 same volume as the actual earth. The earth 

 at the equatorial regions will then project be- 

 yond the figiue, and at the poles lie within it. 



A second and better approximation can be 

 made b}- taking the figure to be that' of an 

 oblate s|iheroid : and this is the basis upon 

 which our present geodetic and astronomical 

 measurements are based. Of course, it is pos- 

 sible to find an ellipsoid having three unequal 

 axes which will coincide still more nearly with 

 the results of observations upon the true figure 

 of the earth ; and this will furnish a third still 

 closer approximation. This is what has been 

 done by Capt. Clarke in his various publica- 

 tions. A summary of his results is given upon 

 pp. 1367 and 368. 



It is evident, when the astronomical latitude 

 is determined at any point of the earth's sur- 

 face by measuring the elevation of the north 

 pole above the horizon, as given by the spirit- 

 level, that that determination will be in error bj- 

 the entire amount of the local deviation of the 

 plumb-line, which error ma}- be as much as 

 30", or more than half a mile, although the 

 observations are made with all possible precis- 

 ion ; and the outcome of geodetic triangula- 

 tion may show that any such station whose 

 position was supposed to have been determined 

 astronomicall}- to single feet really occupies a 

 position, when referred to the spheroid, which 

 at present furnishes the basis of all our astro- 

 nomical and geodetic work, which is a consid- 

 erable fraction of a mile from its position as 

 so determined. « 



The last grand subject treated in the work 

 is that of the tides on the corrected equilibrium 

 theorj-, and matters closel}' connected with it. 

 To explain what is meant bj' this, we shall 

 briefly sketch the rise and progress of the 

 theory of the tides. 



Sir Isaac Newton, whose Principia appeared 

 in 1G87, showed that universal gravitation 

 would not only account for the motions of the 

 heavenh' bodies in their orbits, but would also 

 account for the tides, — phenomena whose cause 

 had not, before his day, been traced to an^- 

 simple law of nature. lie showed that there 

 would be a tide due to the attrac'tion of the 

 sun, and another to that of the moon, the latter 

 being in general the larger : and that the 

 actual tide would depend upon the relative 

 position of those bodies, so that the highest or 

 spring tides would be due to their combined 

 eff"ect, and the lowest or neap tides would occur 

 when the tide due to the sun partially neutral- 

 ized that of the moon. He showed how other 

 known variations iu the tide could be account- 



