602 



NATURE 



{Oct. 3, 1878 



Parrakeet {Pyrrhulopsis tabuan), a Masked Parrakeet {Pyrrhu- 

 lops is per sonata) from the Fiji Islands, purchased; a Chestnut- 

 backed Weaver-bird {Hyphantornis castaneo-fusca), four Rufous- 

 necked Weaver-birds {Hyphantornis textor), two Grenadier 

 Weaver-birds {Eupledes oryx), a Barbary Turtledove (Ttirlur 

 risortus), a Vinaceous Turtledove ( Turtur vinacms) from West 

 Africa, a Turquosine Parrakeet {Euphema pulchella) from New 

 South Wales, two Undulated Grass Parrakeets {Melopsittacus 

 undulata), seven Crested Ground Parrakeets (Calapsiita tiovcB- 

 hollanduz) from Australia, deposited; eight Mocassin Snakes 

 ( Tropidonotus fasciatus), born in the Gardens. 



THE FIGURE AND SIZE OF THE EARTH ^ 



D' 



III. 



|URING the years 1816-52 a Russo-Scandinavian degree- 

 measurement was carried out by Struve and Gen. Tenner, 

 of unusual length and wonderful accuracy. It extended from 

 Hammerfest in the north (70° 40') to Ismail in the south (45* 20'), 

 a length of 25° 20'. From this it followed that for latitude 

 56° 3' 56'', the degree length is 57,137 toises, and in this was 

 included a Swedish degree-measurement which gave 57i^09 

 toises as the length of a degree in lat. 66° 20' 12". At this time 

 extensions of earlier operations were undertaken in other 

 countries ; as in England with the result of ^^-^ for the earth's 

 oblateness. Everest extended Lambton's East Indian degree- 

 measurement, which at present has a length of over twenty- 

 one degrees. Also a longitude measurement begun at an earlier 

 period in Central Europe was recommenced and reaches now 

 from Brest, Paris, Strassburg, Munich, to Vienna. With the 

 assistance of the new data the amount of the earth's oblateness 

 was again investigated, and now that there was no doubt of 

 the accuracy of the measurements, it was shown distinctly that 

 the earth was not an entirely regular elliptical spheroid, that 

 the flattening did not pass regularly over the earth's surface. 

 The theory was next propounded that the earth was an ellipsoid 

 of three axes, but the proposition was not fully supported by the 

 measurements." A newly elaborated mathematical method, by 

 which from the existing measurements, the figure of the earth 

 could be obtained, and by which the remaining errors could be 

 reduced to a minimum, was now applied by the great Bessel to 

 the data before him, and according to these principles and on the 

 basis of the best measurements, he obtained dimensions of the earth 

 which still form the ground of all astronomical and geodetical 

 calculations, and which are as follows : — He found for the equa- 

 torial radius of the earth 327207714 toises = 6377400 metres; 

 for the polar radius 3261 13933 toises = 6356080 metres; and 

 for the length of the earth's quadrant 10000855765 metres ; 



while he gave the earth's oblateness as . He also de- 



^ - 298-153 



duced formulae giving the length of a degree or of a parallel 

 of latitude for any part of the earth ; these formulae will 

 be found in most geodetic handbooks. New values for the 

 dimensions of the earth were, ten years ago, deduced by 

 Leverrier with the assistance of other measurements, but 

 they differ very little from those of Bessel, and in almost 

 all scientific works Bessel's constants are adopted. Thus, 

 about the middle of the present century the solution of the 

 original problem has been attained. And yet since that time there 

 has unmistakably been an altogether unusual progress in all 

 departments concerned in the solution of the problem. First 

 of all, mechanical precision has in the last decades attained such 

 perfection, that now astronomical observations, and especially the 

 geographical determination of places, can be made with consider- 

 ably greater accuracy than was possible a few decades ago. More- 

 over, these improvements have been accompanied with extra- 

 ordinarily suitable new methods. The telegraphic determination 

 of longitude, a method for the determination of the lengths of 

 parallels, has above all, especially in the last ten years, attained 

 such perfection, theoretically and practically, that the measure- 

 ments carried out on this method are most accurate, and we may 

 justly expect in the future most brilliant results from it. Alto- 

 gether the problem is near a more substantial solution now than 

 it ever was before, as there are so many well-equipped observa- 



Continued from p. 580. 

 J This is scarcely correct : the figure of three unequal axes agrees better 

 ■with the observations than does the spheroid of revolution. But there is a 

 necessity for this, and the ellipsoidal figure cinnot be regarded as estab- 

 uhed. 



tories at work, bound together by a network of the most accu- 

 rate determination of longitude and latitude, extended over the 

 surface of the earth, and the completion of which is yet going 

 on. Of the greatest importance also in this connection is the more 

 recent theory of measurement, according to which the points to be 

 connected need not lie in one and the same meridian or parallel, 

 but, on the contrary, are connected by an arc of a great circle 

 lying in any direction — the geodetic line. 



Thus have we seen how from the remotest times, among all the 

 nations of the earth not only has the wish to obtain a know- 

 ledge of the form and size of our dwelling-place prevailed, but 

 also the most earnest activity in attaining this knowledge of nature ; 

 how this has in an increasing degree gone hand in hand with the 

 progress of the mathematical and physical sciences, having at 

 last reached a worthy solution in our time ; and we have the 

 best reasons for believing that, closely following the progress 

 of the sciences, our knowledge in this connection will soon reach 

 the highest degree of certainty. 



Remarks on Karl Maiia FriedericHs Paper, by CoL Clarke, R.E. 



One feature of modem geodesy that has been left imnoticed by 

 the writer of the foregoing paper is the application of the theory 

 of probabilities, under the form of the " method of least squares," 

 to the reduction of the observations. In any network of triangu- 

 lalion if it were required to obtain the distance apart of two of 

 the extreme points, we should obtain varying results according to 

 the set of triangles used in the calculation, and the question arises. 

 What is the degree of credibility to be given to each result, or 

 what the " probable error " of each ? This implies, of course, 

 that there is a superfluity of observations, that is, more than are 

 absolutely necessary to fix all the points. If there were no 

 superflaous observations there could be but one result obtained — 

 an advantage in one respect (in saving calculation)— but then we 

 should be wholly at sea as to the degree of trust to be placed in 

 this one result. The theory of probabilities teaches us how to 

 treat superfluous observations, and practically it leads to the 

 calculation of a system of corrections to all the observations in 

 order to bring them into harmony. Now there could be found 

 an infinite variety of systems of corrections that would harmonise 

 the observations, but the particular system we are led to by the 

 method of least squares has this feature, that the sum of the 

 squares of the corrections is an absolute minimum. In plain 

 words, the triangulation is harmonised with the least possible 

 alteration of the original observations as a whole. 



These calculations, however, involve an enormous aniount 

 of labour, and one is compelled sometimes to relax the rigour 

 of the theory, and accept some slight modifications. For 

 example, in the triangulation of Great Britain and Ireland this 

 method required the solution of an equation of 920 unknown 

 quantities ; this hopeless task was evaded by breaking up the 

 triangulation into some fifteen or more parts. 



The principal triangulation of India — unlike that which vmi- 

 formly covers the face of this country— consists of chains of 

 triangles running in a meridian direction crossed by several other 

 chains perpendicular to them ; as the longitudinal series from 

 Kurrachee to Calcutta, and that from Bombay to Vizagapatam, the 

 north-east longitudinal series, and others. The reduction of 

 these chains of triangles by the method of least squares is a vast 

 labour not yet completed. 



The enormous mass of the Himalayan Mountains causes, or 

 rather might theoretically be supposed to cause, an immense 

 disturbance of the direction of gravity at the stations of the 

 Indian arc amounting at the northern stations to 30", with 

 smaller amounts as the distances of stations southwards in- 

 creases. Now it is very singular that, except at the very 

 foot of the mountains, these discrepancies do not actually 

 appear (to anything like that amount) in the arc itself or 

 when it is used in the problem of the figure of the earth. 

 This very remarkable circumstance has led to the hypothesis 

 that the attraction of the superincumbent visible mass must be 

 compensated for by a diminution of density in the strata under- 

 lying the mountains. Pendulum observations made for the 

 purpose of elucidating this point have shown conclusively that 

 the density of these underlying strata is actually less there than 

 elsewhere. A compensation therefore takes place— but 10 a 

 general way only ; it cannot be shown that it is a mathemati- 

 cally exact compensation, consequently there is some residual 

 doubt as to what really are the deflections of the vertical at 

 the astronomical stations of the Indian arc 



We may supplement Karl Maria Friederici's account of how 

 to calculate a meridian arc by a description of the method foU 



