Sept. 26, 1878] 



NATURE 



579 



At this period, when it was resolved to overhaul the accumu- 

 lated material, subjecting to further mathematical treatment what 

 was valuable, and leaving unregarded what was faulty, then it 

 was resolved to work out the problem theoretically in so clear 

 and accurate a manner as to be worthy of the high standpoint 

 of mathematical and natural science. Thus it appeared, above 

 all, necessary to get rid of the inequalities of the earth's surface, 

 to reduce all measurements to an ideal form of surface, the most 

 suitable being that (according to Gauss's definition) which the 

 still water of the ocean would assume if it covered the whole 

 surface of the earth. It is also defined as a surface which is 

 at every point at right angles to the direction of a free- 

 falling body. But in order that this ideal surface might 

 be observed in reality, researches on a large scale would have 

 to be undertaken on the tides, in order to obtain a mean 

 water-level. At that time, also, theory fell upon a new and 

 suitable method of ascertaining the amount of the earth's obla< 

 tion, in the theoretical perfection of the long-known phenomena 

 of precession and nutation. And while both the theory and 

 the practical methods of measurement were being carried to a 

 high degree of perfection, in spite of the political storms in 

 nearly all European nations, new preparations were made to 

 find a worthy solution of this problem by means of the newest 

 and best acquisitions of science. Especially now was there a 

 people who not only emulated the noble efforts of other nations, 

 but whose savants, the first of their time, were able soon to place 

 themselves, through their thoughtful and ingenious researches, 

 supported by a liberal people, at the head of the efforts made by 

 nearly all civilised nations to obtain a knowledge of the truth — 

 this was the German. 



In what follows we shall explain these acquisitions as to a 

 knowledge of our earth which have been made in our century, 

 and in great part by our people. 



The operations which have been undertaken during the present 

 century for the purpose of obtaining an accurate idea of the figure 

 of the earth and its dimensions, have by no means been confined, 

 as nearly all the early operations were, to the carrying out of 

 degree measurements ; but even in the earlier periods a method 

 already mentioned was brought prominently forward, which 

 would not only show the form of the surface, but from which it 

 was also expected that conclusions could be drawn as to the 

 internal physical condition of the crust of the earth, and the 

 manner in which the mass under the surface is distributed — we 

 refer to pendulum measurements. We have already seen how 

 Richer found a difference of lengths of the pendulum in Paris 

 and Cayenne, and after Bouguer in Peru and Lacaille at the Cape 

 had made similar observations, an idea was obtained of the 

 law of variation of the lengths of the pendulum at different 

 la itudes. It was soon seen from this that the differences in 

 length of the pendulum at the extreme points, the pole and the 

 equator, would only be very small, and that the very nicest 

 observations would be necessary to allow conclusions to be 

 drawn as to the form of the earth. The Spaniards were the 

 next who, in two ships of war, carried out measurements in very 

 different parts of ihe earth, but which unfortunately proved not to 

 be of the requisite accuracy. Shortly afterwards, a new triangula- 

 tion was vmdertaken in France, and while Laplace sought by it 

 as far as possible to obtain data as to the oblateness of the earth, 

 several other savants, especially Biot and Arago, carried on 

 pendulum measurements dong the meridian of the great degree- 

 measurement (Dunkirk). In connection with this new triangu- 

 lation, extended and exceedingly accurate measurements of 

 longitude were carried out. In England efforts were now made 

 to utilise triangulation for both methods of measuring degrees, 

 and now, especially in the southern hemisphere, pendulum 

 observations were accomplished on a scale and with an accuracy 

 such as had not previously been known. These observations 

 established the fact that the southern hemisphere had no essen- 

 tially different condition from the northern hemisphere. There 

 was used for this purpose a very delicate pendulum apparatus, 

 the " Reversible Pendulum," the inventor of which was Bohnen- 

 berger, a German. From 1822 to 1824 such observations were 

 carried out at many coast stations as far north as the Arctic 

 Ocean, embracing an extent of 93'' of latitude. 



Accurate methods of observation of this kind, as also very 

 exact and ingeniously-constructed pendulum apparatus, were now 

 invented and brought into use mainly by German astronomers ; 

 Bessell especially has done lasting service in this respect, his 

 method, perfected with the greatest ingenuity, being still fruitful 

 in results. 



The principle of this method, viz., from various pendulum 



measurements to obtain the figure of the earth — caimot be here 

 explained, on accovmt of the mathematical principles involved, 

 and we can only give some of the results obtained from the 

 above-mentioned measurements. The first Spanish measure- 

 ments gave the oblateness of the earth as -r^ ; the French, ^^3^ ; 

 the English results varied between -^ and ■^\^. The vsdue 

 obtained from the earliest mentioned astronomical observations 

 (precesssion and nutation) was ^7. The difference of the 

 results obtained by means of pendulum measurements could 

 not be ascribed to erroneous observations, but rather to the 

 unequal density of the earth, as was shown quite clearly 

 by later measurements. It was sought, especially in Ger- 

 many, to discover the amount of this disturbing influence, and 

 to obtain observations free from these disturbances. Already, 

 in the year 1806, a German published the thus improved results 

 of the measurements, and obtained from the various methods of 

 observation the following nearly accordant results : — Newton's 

 theory gave ^^ ; precession and nutation, -^-^ ; the theory 

 of the moon's motion, ■^\f^ ; pendulum measurements, ^^ ; and 



A 



Q 



^; 



Tv 



D 



% 



Fig. 



degree-measurements, sl^, Laplace and Sabine deduced, ac- 

 cording to the newer mathematical methods, the most probable 

 value of the oblateness of the earth, from all these results, and 

 found, the former ^^j^, the latter -^tj. German savants also 

 repeated this calcidation, and obtained, certainly not exactly the 

 same, though very similar results ; but more accurate results 

 could only be based on more delicate measurements. 



These more accurate measurements were soon carried out, 

 mainly in Germany and Russia. Gauss, in 1821-24, measured 

 the distance between Gottingen and Altona, and obtained for 

 latitude, 52° 2' 17", 57126 toises as the length of the degree. 

 For this purpose he had adopted greatly improved methods of 

 observation. Schumacher made a new measurement in Denmark, 

 and found for 54° 8' I3"*5 the degree-length to be 57092 toises. 



It may, perhaps, be interesting to show here what the 

 improvement was which had been introduced at that time into 

 these operations in Germany ; it was the method of enlarge- 

 ment of the base-line, whereby the very difficult labour of base- 

 line measurement was considerably reduced and more accurate 

 measurements thereby became possible. For example, let the length 

 A B be the distance to be measured, but with only a small plain 

 surface on which a base-line can be measured (Fig. 2). The small 



