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NATURE 



[April 29, 1880 



Stations," interesting and suggestive as they both are. 

 Few will care to master the former who have not either 

 the misfortune to have a mass of triangulation on hand 

 awaiting reduction, or the luck to have nearly done with 

 one and the curiosity to see whether it is yet open to them 

 to modify their plans. To such as are in the former 

 predicament we may say with the most entire confidence 

 that they will find no safer guide. 



In this chapter we remark a short notice of the recent 

 completion of the connection between the Spanish and 

 Algerian triangulations, by a quadrilateral figure whose 

 longer sides, spanning the great inland sea, are 170 miles in 

 . length, the longest, we believe, on which luminous signals 

 have been observed. " Thus," remarks Col. Clarke, " a 

 continuous triangulation now extends from Shetland into 

 Africa." 



The subject of terrestrial refraction receives ample 

 attention in the chapter on Heights of Stations. We 

 remark as noteworthy that a distinction is found to be 

 necessary between the factor for rays crossing land and 

 those crossing sea. We must here also notice one of the 

 very few errors in [the book. On p. 281 "the average 

 amount of refraction " is said to vary from yVth. to ^th 

 of the arc between the stations. What is meant is no 

 doubt the average amount of minimum refraction. 



Our task would now be completed by an impartial 

 review of the remaining two chapters on the " Connec- 

 tion of Geodetic and Astronomical Operations " and on 

 the " Figure of the Earth." Unhappily our attitude in 

 presence of these chapters is a prejudiced, though cer- 

 tainly not a hostile, one. We have regarded the earth, 

 mentally, for so many years as an irregular spheroid, and 

 all ellipsoids or other mathematically simple figures as 

 mere conveniences that we cannot bring to bear upon the 

 exact determination of any particular one of these that 

 intense curiosity which is necessary to sustain one in the 

 search for "the most probable." Under these circum- 

 stances it seems both wiser and more courteous not to 

 contend against views whose only demerit is that we do 

 not sympathise with them, but rather to confess dissent 

 and to offer some considerations from a different point of 

 view. 



That the sea-level surface of the earth — by many called, 

 for-reasons not very clear, the mathematical surface — is 

 an irregular spheroid, no one nowadays will dispute. 

 Neither is it any longer open to question that an elliptic 

 spheroid of revolution, whose compression at the poles is 

 (say) TrJrijth* is very like that irregular spheroid. Let us 

 regard these two things as distinct. We may speak of 

 them as the Earth, and the Form. And we may recognise 

 that the latter is provisional, in the sense of being liable 

 to modification if expedient. If, so prepared, the question 

 be propounded, What is the object of geodesy ? the 

 answer must surely be on all hands, to determine the 

 Figure of the Earth, by reference to the Form. By 

 reference to, not by confusion with, or by means of, still 

 less by moulding the Form until it has ceased to be an 

 elliptic spheroid, and has become, if possible, identical in 

 contour with the actual Earth. The Earth remains the 

 Earth, and the Form remains the Form ; and Geodesy 

 aims at determining the want of exact conformity between 

 the two. This is the first consideration. 



The next is, How can this be done ? The answer 



clearly is, In the first place it cannot be done at all for the 

 whole Earth, by any means at present known ; but it can 

 be done partially in two ways, viz., by the pendulum, 

 wherever there is terra firma; and by surveying instru- 

 ments where this terra firma has ample extension ; and, 

 in the next place, it can be done by such and such 

 employment of these implements. 



Now it seems to us that it is for the proper compre- 

 hension of the scope and bearing of this last instruction 

 that light is needed to be thrown by those who are com- 

 petent. The interest aroused by pendulum operations, 

 for instance, is almost painfully unintelligent, if we compare 

 the simplicity of the fundamental ideas necessary for its 

 comprehension with the obscurity which has throughout 

 characterised the practical development of those ideas. 

 And though there has been no analogous obscurity in the 

 practical development of the other method, it is not 

 the less true that a shadow of another kind has been 

 cast by something like a misdirection. We cannot study 

 the history of this branch of geodesy without recognising 

 that attention has been constantly directed, not upon the 

 Earth, but upon the Form. The whole power of analysis 

 and of calculation has been devoted to perfecting and to 

 designing a "more probable " form, and to showing that 

 on certain conditions (which the earth, if it were only 

 moderately amenable to reason, would recognise the 

 justice of) the form so designed; comes very near indeed 

 to what the earth should be. What is the inevitable 

 verdict which results from a charge of this description ? 

 We find that the mean figure of the earth is a 

 spheroid whose axes are in the proportion of 

 about 292 : 293. The finding is brief enough, truly ; 

 but is it in accordance with the evidence? Surely, yes ! 

 for that word " mean " will cover whatever we like to put 

 under it. But it is none the less an unsatisfactory verdict. 

 Let it be remembered that the accuracy insisted on in 

 trigonometrical surveying operations and reductions is 

 far greater than is required for fiscal, commercial, or what 

 are commonly called practical purposes. The object of this 

 exceeding accuracy is geodetical. Thus,for instance,no one 

 would dream of surveying a small isolated island with such 

 accuracy. A great part of the cost of v a continental sur- 

 vey, therefore, has to be reckoned as sunk for the sake of 

 ultimately learning more about the exact shape of the 

 earth than we could at present see any direct utility in. 

 But as yet we have got very little further than a positive 

 certainty that that shape is irregular. As surveys extend 

 and get connected with each other, some better return 

 for the labour expended is demanded. The geodesist 

 begins to think of phrenology, and to speculate whether 

 he can yet venture to map out the earth's bumps as he 

 has already mapped out land and sea. He learns to 

 regard what were looked on as local disturbances of the 

 plumb-line as the means to that end. He sees in them 

 no longer mere errors, to be herded by the theory of 

 probabilities, but distinct indications of that which he 

 has to work out. 



And if, meanwhile, despairing of obtaining, by the slow 

 and grievously costly processes of land measurement, 

 data enough for such a purpose, his eyes should be 

 opened to the practical facility of obtaining such, ad 

 libitum, by means of the pendulum ; he may well be 

 pardoned if he turns somewhat impatiently away from the 



