Aprils, 1879] 



NATURE 



505 



and arguments we have referred to marshalled in an im- 

 posing array, and finally summed up in the following 

 condensed formula : — 



" Insects produce flowers. Flowers produce the colour- 

 , sense in insects. The colour-sense produces a taste for 

 ■ colour. The taste for colour produces butterflies and 

 brilliant beetles. Birds and mammals produce fruits. 

 Fruits produce a taste for colour in birds and mammals. 

 The taste for colour produces the external hues of hum- 

 ming-birds, parrots, and monkeys. Man's frugivorous 

 ancestry produces in him a similar taste ; and that taste 

 produces the final result of human chromatic arts/' 



Although I totally differ from Mr. Allen's conclusions 

 as to the production of the varied colours of the animal 

 world, I must express the extreme pleasure with which I 

 have read his book, which I most cordially recommend to 

 all who lo\'e colour, and can enjoy a thoroughly well- 

 ^^Titten volume on a most interesting but difficult subject. 



Alfred R. Wallace 



GEODESY 



Die geoddtischen Hmtptpunkte unci ihre Coordinaten. 



Von G. Zachariae. (Berlin : Oppenheim, 1878.) 



THE science of geodesy, though far from a popular 

 one, exercises something like a fascination over its 

 own devotees. It is not a standstill science ; how to 

 devise instruments — theodolites, altazimuths — which shall 

 excel their predecessors ; how to use these instruments 

 so as to eliminate the sources of possible error they indi- 

 vidually present ; how, having got the observations, to 

 eliminate in the use of them, their own errors as far as 

 possible ; and finally, how, after obtaining final results, 

 to express the degree of reliance"to be placed on them : 

 these are all ever-fresh questions, capable, many of them^ 

 of engaging — as one may, for instance, see in the works 

 of the late Prof. Hansen — considerable mathematical 

 ability. The work before us is of Danish origin, and it 

 is clear that the Danish meridian arc and the geodetic 

 operations connected therewith have been executed in a 

 thoroughly scientific manner. To thor;e who are employed 

 in geodetic operations, this treatise will be most welcome. 

 In an introductory chapter we have the definitions of the 

 mathematical surface of the earth, expressions for the 

 radius of cur\^ature and various lines connected with the 

 spheroid, and remarks on the deviation of the actual 

 surface from that of a true spheroid. The first section 

 treats of the method of laying out a triangulation, of the 

 measurement of angles, and of the measurement of base 

 lines, together with the calculation of the probable errors 

 of results. The second section deals with the calculation 

 of triangles : after giving Legendre' s theorem, the writer 

 shows how spheroidal triangles may be computed as 

 spherical, and gives the expressions for the differences 

 between the angles of a spherical triangle and a spher- 

 oidal triangle having sides of the same length, with any 

 position in azimuth. Then the method of calculating a 

 triangulation by least squares is entered into. The third 

 section deals with the subsequent expression of the 

 results in the form of co-ordinates — of the method of 

 calculating differences of latitude and longitude. Through- 

 out the work, in all formulae which are approximative, 

 the nature or order of the terms omitted is expressed by a 

 neat notation which is very usefiiL The fourth section 



I 



is devoted to the measurement of heights, and levelling 

 operations and calculations ; the subject is gone into 

 thoroughly, including the investigation of the coefficient 

 of terrestrial refraction and the errors which may accumu- 

 late from various sources. The last part of the section is 

 devoted to the consideration of the " Schlussfehler," or 

 " error of close " in levelling. This error may arise from 

 mountain attraction, or may exist even without it. We 

 know that at the surface of the spheroidal earth the equi- 

 potential surfaces — take any two of them a few hundreds 

 or thousands of feet apart — are not parallel, but the dis- 

 tance between them at any point is inversely proportional 

 to gravity there. If P, Q be two points on the higher of 

 two equipotential surfaces, p, q, their projections on the 

 lower, then levelling from / to Q, if we in imagination take 

 the path, p P,P Q, we have p P^s the height of Q above/y 

 then continuing the levelling from Q by the path Qq, q p, 

 to p, it is clear there will be an error in the close of the 

 levelling of the amount Qq — Pp. Practically, of course, 

 this is very smalL An error of close of levelling may 

 occur in working over a mountain ; the attraction of the 

 mountain deflects the vertical, and too small a height is 

 the result ; of course if the hiU is sj-mmetrically shaped, 

 the same amount of error is involved on both sides, and 

 there would be no discrepancy in results obtained by 

 levelling over and round or through the hill. But gene- 

 rally the error on the two sides is not the same. In the 

 work before us the case is supposed of levelling being 

 carried over a mountain-chain of uniform triangular sec- 

 tion. In the triangular section A £ C, C being the ridge 

 and A B the base, suppose levelling to be started from A 

 the foot of one slope, along a level surface through the 

 mountain, or, which is the same, along a level surface 

 round it, to B, a point on the same level-surface as A ; 

 then up the slope from B toC, then down the other slope 

 from C to the starting-point A. Then the error of close, 

 or the " Schlussfehler," is a certain multiple of the integral 

 of the difference between the horizontal component of the 

 attraction of the hill at any point as P on the slope and 

 the horizontal component of the attraction at p, which is 

 the projection of P on the level surface A B, multiplied 

 by the element of horizontal distance, and taken from A 

 to B. So that if we do not misunderstand the writer, the 

 numerical examples of " Schlussfehler," given at p. 290, 

 are very much too large. In fact the before-mentioned 

 multiple of the difference of potential at A and B, when 

 added to the right-hand member of the equation (3) on 

 the page referred to, very nearly cancels that term. 



The fifth and last section of the work treats of the in- 

 fluence of small alterations of the spheroid of reference 

 on the reduced triangulation, and of the determination of 

 the elements of that particular spheroid which is most in 

 accord with the results of the triangulation under consi- 

 deration. The formulae throughout the work are very 

 neatly developed and the typography is admirable. 



A. R. C. 



OUR BOOK SHELF 



A History of the Birds of Ceylon. By Capt. W. Vincent 

 Legge, R.A. Part I. Imp. 4to. Pp. 1-345- (London : 

 Published by the Author, 1878.) 

 The many interesting papers on Ceylonese birds pub- 

 lished during the last few years by Capt. Legge in the 



