April 29, 1880] 



NATURE 



Chapters V. and VI. deal with the " Distances, Azi- 

 muths, and Triangles on a Spheroid," and with the 

 difficult subject of " Geodetic Lines." By a spheroid is 

 here meant an ellipsoid of revolution of small ellipticity 

 As, in the sequel, a figure will be sought for which shall, 

 in some respects and for certain limited purposes, serve 

 as a Figure of Reference more closely than any ellip- 

 soid, it may be objected that the term "spheroid," which 

 includes all such ?«<w/-spherical forms, should be here 

 qualified by the descriptive adjective "elliptic " And— 

 though it has little to do with these chapters-we may 

 here too remark that the necessity of casting calculations 

 of triangulation into practical forms is the real reason 

 why such non-elliptic spheroids are, and probably must 

 ever remain, unavailable as Figures of Reference on 

 which Trigonometrical Survey calculations can be based 

 Perhaps all that can be done in that direction is to vary 

 the elliptic spheroid so as to suit the local curvature of 

 special areas of triangulation. But this is anticipating 



The next two chapters are on the "Measurement of 

 base Lines" and on "Instruments and Observing" 

 Something ,s said in the earlier about standards We 

 would gladly have seen a great deal more. Col. Clarke 

 seems often to avoid purposely telling us anything of the 

 origin and meamng of things, and doubtless he would 

 reply to such a stricture that it formed no part of his 

 design. But while bowing to that, one cannot but wish 

 that he had devoted a few pages to giving a concise 

 review of the antecedents of the national standards now 

 in recognised existence. It cannot be that he does not 

 know ,t all, more thoroughly, perhaps, than any other 

 living person except Sir George Airy. It must be that he 

 is unconscious of the sense of impotent ignorance which 

 so many feel and lament. We know that the Toise 

 wh!ch is now the national standard of Germany, has its 

 prototype in the Toise which Godin copied afthe Chatelet 

 and that the prototype of the Metre bears a definite 

 relation to Godin' s-or la Condamine's, as it is often 

 called, because la Condamine procured its recognition as 

 a standard; but what do we know of the Austrian 

 Klafter? and alas, what do we common English folk 

 know o our own yard ? Is there not in existence an Act 

 of Parliament defining it in terms of the seconds 

 pendulum? May we affirm that the defining clause was 

 only provisional, and that the whole Act has been 

 repealed ? Is it true that our yard is a real entity lying at 

 Westminster; and that there is no other so real and 

 actual a standard having a tangible existence ? All this 

 we believe-but of what value is such a belief on the part 

 of an unknown reviewer? It is true that Col Clarke 

 does not leave us wholly in the dark. "The standard 

 yard of this country and its copies," he says, "are bars 

 an inch square in section, of iron, steel, brass, or copper " 

 There are, we believe, one Standard, five Parliamentary- 

 Copies, and some sixty to eighty Secondary Copies-a 

 large number of which are of bronze. 



In this, as in so many other parts of his subject, CoL 

 Clarke has entirely failed to appreciate the relative worth 

 of information. He is full to overflowing of the know- 

 ledge that we want, but there is a part of it which he 

 gives us— not grudgingly we may be sure— but hastily 

 sparingly, and almost apologetically, as who should say -' 

 this we all know ; excuse my alluding to it. But in fact 



all these common things-things of which the want is 



hem, we find the greatest difficulty in learning about 

 hem ; and our common knowledge is lamentably defective 



through the want of them. We hope earnestly that Col. 



Clarke w,U recognise this and meet the want in future 



:o. t k°as S 7h f0rthat ^^ Wi " be futUre editions ofsX 

 «o.k as this is as certain as that the vast areas beingyear 

 by year colonised and brought under civilised manage- 

 ment will hkewise be brought under theodolite and chf.n 



e Ln"V°7 e - " - iS Wkh a View t0 this '""Stable 

 extension of surveying operations that we desire so 

 anxiously to see the broader principles of geodesy esta- 

 blished on a basis of economy and utility very different 

 lands SC Wh ' Ch haVC regulated the surve y s ° f older 

 The chapter on Instruments and Observing is em- 

 bellished with several excellent representations of theodo- 

 lites, zenith telescopes, and transit instruments. Thoueh 

 necessanly scarcely more than glancing at the numberless 

 details more or less familiar to the practical surveyor and 

 astronomical observer, it runs through the subject skil- 

 fuUy. We could wish that more were said about the 

 American methods, and we miss at least a notice of the 

 superb alt-azimuth designed by the late Col. Strange— 

 which has never seen service-and his far more successful 

 zenith-sectors, which have both established a reputation 

 second to none. But we are quite aware that nothing less 

 than a series of volumes could do justice to this branch 

 of the subject. 



Astronomical observations for the determination of 

 latitude constitute the most important part of the work of 

 a geodetical survey next to those for the determination 

 of distance. These observations consist practically— 

 where a sector is used— in determining the zenith dis- 

 tances of numerous stars. And since these concurto 

 give at any one station but one co-latitude, it follows that 

 they afford a test of the correctness of the N.P. Distances 

 of the stars employed, to each of which is assignable an 

 apparent error, as one of the results of the combination. 

 Where a single station of observation alone is under con- 

 sideration these apparent errors are rightly enough 

 attributable rather to observation and graduation than to 

 place. But where the same star is thus tested again and 

 again under different latitudes the accordance or approxi- 

 mate constancy of such apparent error can have no 

 rational explanation in any other source than in erroneous 

 N.P.D. This is a practical result which is far from being 

 hypothetical ; and we have often thought that neglect to 

 utilise latitude observations in this way with a view to 

 perfect the astronomical place is a waste of material 

 which is well worth attention. The examination here 

 suggested may be readily put to the test of trial by any 

 one who has access to a considerable body of published 

 results of such observations ; and if due attention is paid 

 to the identity of the star's place employed at different 

 stations, we can afford to prophesy with confidence that 

 in many cases there will be found sufficient evidence to 

 condemn— and therefore to rectify— the places used. 



So much remains to be said in connection with the 

 final chapters that we must abstain from commenting on 

 the next in order— Chapter IX., on the " Calculation 

 of Triangulation," and Chapter X., on "Heights of 



