6o6 



NATURE 



{April 29, 1880 



course described as Kater's, and the ball and wire as 

 Borda's, the opportunity being once more lost of assigning 

 both to their proper epoch, viz., 1735. The method of 

 coincidences is described, but without correcting the 

 common misapprehension of it as a modern improve- 

 ment, while the introduction of the lens, by means of 

 which Bessel separated the experimental from the clock 

 pendulum by several feet, without impairing but rather 

 facilitating the exact observance of coincidence, is not 

 noticed. In selecting the data with which the recent 

 Russian and Indian observations are to be combined for 

 a new evaluation of the ellipticity, the materials are 

 taken direct from Baily's table, which is open, to say 

 the least, to considerable objection on several grounds. 

 The absolute determinations, both those anterior to 

 Baily's time and those of more recent data, are all 

 tacitly excluded. Granting that this exclusion is not 

 unreasonable, it is impossible not to feel surprise that the 

 existence even of the enormous body of work which is 

 thus passed sab silcntio is not even mentioned. The 

 recently recognised fact that most, if not all, the modern 

 absolute determinations with the reversion-pendulum are 

 vitiated to a sensible but unknown extent, which can at 

 best be approximately estimated, is noticed, and might 

 have been given as a reason for deferring their use as 

 available data. As it is, we must reckon the estimation 

 in which they are held from their non-appearance here. 

 The same may be said, mutatis mutandis, about the older 

 ones, which are without exception impaired, and as yet 

 unavailable on account of the want of the reduction for 

 air-resistance. 



We have scarcely approached as yet the subject of this 

 most valuable volume, and already a considerable portion 

 of our available space has been swallowed up. It is in 

 fact as impossible to give a full account of what the 

 author has compressed into its 350 closely-printed octavo 

 pages as it probably seemed to him to give a full and fair 

 account of the enormous amount of work which has been 

 done in all the many countries where surveys have been 

 and are being carried on. Indeed, as of the history so of 

 the present aspect of geodesy, we may say that it is 

 scarcely more than touched on. Whatever is said of the 

 various survey operations in different parts of the world 

 is introduced in the course of description of methods of 

 observing and of reducing, and by way of acknowledg- 

 ment of sources and of data, or for the sake of illustration. 

 The book does not pretend to give a digest of geodetical 

 operations so much as to declare broadly, and of course 

 in certain respects particularly, what does and what 

 should constitute geodetical practice and theory. 



In reviewing, it is above all things necessary to remem- 

 ber that an author has an indefeasible right to frame, 

 arrange, and treat his subject and material as he pleases. 

 Cut on the other hand the reader has an equal right to 

 be pleased or displeased with the result, and to say in 

 what respects. When, as in the present case, it happens 

 that a very extensive field and a very difficult subject has 

 remained unappropriated by any competent writer for 

 half a century, and is then claimed by a writer who has 

 been before the world as an authority in that connection, 

 his work almost inevitably takes a place which may be 

 said to await it, irrespective of its actual merit. In such 

 a case an undeniable responsibility attaches to the author, 



and a no less clear onus lies on the reviewer — on the one 

 hand to fall into no errors through carelessness ; and on 

 the other to judge fearlessly, rather than add unneces- 

 sarily to authority, which already has so much in its 

 favour. If the one is] a difficult task, the other is an 

 ungracious one at best. 



Passing on now to what is the real body of this work, 

 we find Chapter II. devoted to " Spherical Trigonometry " 

 and Chapter III. to " Least Squares." With regard to 

 these we appeal to what has been said above about the 

 rights of an author and the duty of a reviewer. They are 

 pure mathematics, and we admire them honestly, as deft 

 and elegant condensations of the principal requirements 

 of a geodesist; but not without a sigh, as the truth dawns 

 upon us that this is but the threshold to mathematical 

 labyrinths, of which no plan is furnished, and in which, 

 therefore, we run a fair chance of failing to find the broad 

 paths to which all must keep who would be in accord and 

 who would work together. And in effect in the next 

 chapter we take the desperate plunge into the theory of 

 the figure of the earth, with the method of potentials as 

 our only guide. It is in vain to resist, but, like Christian 

 in the Slough of Despond, we struggle through, with the 

 burden of numberless volumes of National Surveys and 

 Geodetical Operations on our back ; and if haply there- 

 after we meet with a Mr. Worldly Wiseman, surely we 

 will listen to his counsel, and endeavour to find rest 

 without undergoing further like perils. 



Towards the close of this chapter we come upon notices 

 of the discussion of twenty years ago as to the possibility 

 of explaining anomalous surface attractions, or the 

 absence of them, by different suppositions as to submon- 

 tane density. It would be idle to add here a single word 

 to that discussion — not because it has been in any sense 

 closed, so much as because there is room for almost any 

 quantity or kind of fresh assumptions, and because we 

 are unable to see how any decisive result can be reached 

 where all the assumptions are contestable — as for instance 

 that the solid crust is lighter than the plastic nucleus upon 

 which it is supposed to float. 



Perhaps the most remarkable result reached in the 

 course of this chapter is the following : — As an example 

 the disturbance of the sea-level is calculated which would 

 be caused by a sphere of matter of surface density one 

 mile in diameter, situated at or near the surface. The 

 calculated amount is found to be only 2 inches ; but small 

 as this is, it is further shown that the maximum deflection 

 of the normal to the protuberance thus caused .would be 

 5" at a distance rather less than 2,000 feet from the 

 summit, or a relative deflection of 10" between the two 

 points 4,000 feet apart. There can be no manner of doubt 

 that the sea-level surface is not of the same form as 

 would be the case if the mountains were cast into the 

 sea ; and if we call the difference " disturbance " of form, 

 then the extent to which the irregularities of form, of 

 whose existence we have abundant proof, is explicable or 

 not explicable by such disturbance is a legitimate part of 

 geodetical study. At the same time, to some it may be a 

 question whether the term geodesy ought not to be under- 

 stood to consist of the means and methods by which the 

 earth's form and size are discoverable, whatever these 

 may actually be, rather than a general name for all and 

 any studies of the causes or explanations of that form. 



