^36 



NA TURE 



[July 5, 1906 



some have two, one for the subject-matter and one for 

 names of authors. The loss of time which arises from 

 one's ignorance as to where to look for the index cannot 

 be estimated simply by what is spent on the search, but 

 nrust include the time necessary to regain the placidity of 

 thought which is essential to scientific work. 



It is time we turned to the more serious aspect of 

 those international associations which directly aim at an 

 advance of knowledge. Mathematicians have drawn 

 interesting conclusions from the contemplation of ideal 

 beings who are confined to live on a surface and have no 

 knowledge of anything that goes on outside that surface. 

 Our Euclidean geometry would be unknown to them, and 

 spiritualistic tricks could be performed by anyone possess- 

 ing, even to a minute extent, the power of controlling a 

 third dimension. It is, I think, worth while investigating 

 the extent of the direct knowledge of a third dimension, 

 which makes us so infinitely superior to the two-dimensional 

 beings. We are able, no doubt, through our eyes, to 

 penetrate the depths of space, but we should be unable to 

 interpret the impressions of our sight if we had not some 

 tangible knowledge of three dimensions, and had not 

 learned to bring the sense of sight and the sense of touch 

 into harmony. But our sense of touch is confined to a 

 very small distance from the ground on which we stand, 

 and independently of artificial means of raising ourselves 

 above the surface of the earth, a layer 6 feet or 7 feet 

 thick represents the extent of our three-dimensional know- 

 ledge. Compared with the radius of the earth, the thick- 

 ness of such a layer is small enough, for it would represent 

 only the thickness of a sheet of paper on a sphere having 

 a radius of 250 metres ; compared with the solar system, 

 and even more so with stellar distance, a thickness of 

 layer of 8 feet seems infinitesimal. Yet the infinitesimal 

 is essentially different from the zero, and even were our 

 bodies much smaller than they are we should continue to 

 have the power to interpret three dimensions. These con- 

 siderations show how iinportant it is for us to increase 

 our knowledge of the earth itself, and to extend it so far 

 as possible to the depth below our feet and the height 

 above our heads. 



In passing from the arbitrary units to which we refer 

 our terrestrial measurements of length, to the scale on 

 which we measure the dimensions of the solar system, and 

 from them to stellar distances, the magnitude of the earth's 

 radius or circumference forms an all-important intermediate 

 quantity. One of the first acts of the French Academy of 

 Sciences, founded in i666, consisted in organising the work 

 of accurately measuring the dimensions of the earth, and 

 this at once enabled Newton to confirm his celebrated theory 

 of universal gravitation. As improvements in the methods 

 of measuring kept pace with the work actually accom- 

 plished our knowledge steadily increased, but we are still 

 improving on it. New problems have arisen requiring 

 more minute study, and the measurements of the shape 

 and size of the earth still remain a question of the first 

 importance. The actual surveys and triangulation required 

 for the purpose are of necessity left to the initiative of in- 

 dividual States or to the combination of the States primarily 

 concerned, but the general discussion of results, so far as 

 they apply to the earth as a whole, is entrusted to an 

 International Geodetic .'\ssociation, which at present con- 

 sists of twenty-one States. These, together with their 

 annual contributions to the general fund, are entered in 

 the following table : — 



i. £ 



Belgium 80 Austria 300 



Denmark 40 Portugal So 



Germany 300 Roumania 80 



France 300 Russia 300 



Greece 40 Sweden 40 



Great Britain 300 Switzerland 40 



Italy 300 Servia 40 



Japan 300 Spain 150 



Mexico 150 ! Hungary 150 



The Colonies of the United States of Ame- 



Netherlands 40 rica 300 



Norway 40 1 



The Central Bureau of this association is attached to the 

 Royal Geodetic Institute of Potsdam, which is under the 



NO. 1914, VOL. 74] 



distinguished direction of Prof. Helmert, who acts as 

 secretary to the association. 



The question of measuring the size of the earth depends 

 to a great extent on the measurement of arcs of meridian. 

 So long as we were confined to Europe for the measure- 

 ments of these arcs they remained necessarily short, but 

 larger and larger portions of our globe have become 

 accessible to the theodolite, and there is especially one 

 arc which is distinguished by the fact that it is the longest 

 possible which can be traced along the land covering the 

 earth's surface. It runs about 30° east of Greenwich, and 

 a large portion of it passes through Africa. Owing to the 

 great energy and enterprise of Sir David Gill, the work of 

 measuring this arc is well in hand, though at the present 

 moment want of funds threatens to endanger its completion. 

 The Egyptian Survey entrusted to Captain Lyons will no 

 doubt receive continued support, and by an arrangement 

 entered into between representatives of the German Govern- 

 ment and Sir David Gill at a conference held in Berlin 

 in 1S96, Germany undertook to carry out the triangulation 

 through her territory in South-West Africa. I under- 

 stand this work has been done, and the triangulation of 

 the Transvaal and the Orange River Colony is also com- 

 plete. There is still a gap in the southern part of 

 Rhodesia, but there is every hope that this will soon be 

 bridged over. The British South African Company has 

 spent 36,000/. on the work and thus has very materially 

 assisted an important enterprise. When the African arc 

 is complete it will be connected with the Russian and 

 Roumanian arcs so as to form a continuous chain of 

 105° extending from 70° north to 35° south latitude 

 I have to point out, however, that, in the opinion ot 

 those best able to judge, the completion of the South 

 African arc is not the only undertaking to which this 

 country is called upon to pay attention. The triangu- 

 lation of our own island, excellent as it was when first 

 made, has fallen below the accuracy required in modern 

 geodetic work. Until our fundamental triangulation has 

 been repeated, the sums which at present are being spent 

 on the detailed survey might find a belter use. 



The main result of the recent work has been that, so 

 far as present measurements allow us to judge, the 

 surface of the ocean can be well represented by a surface 

 of revolution, and it is not necessary to assume a more 

 complicated shape. The mean radius of the earth is de- 

 termined to about 100 metres, which means a possibility 

 of doubt amounting to about i part in 60,000. 



Geodetic work is, however, not confined to measurements 

 of length, for important information may be derived from 

 an exact knowledge of the acceleration of gravity over its 

 surface. The introduction of the pendulum of short length 

 intended for relative and not for absolute measurement 

 has greatly facilitated this work, and it is hoped that these 

 pendulum observations may be carried out over still more 

 extended regions. India is setting a good example. It has 

 measured two arcs of meridian, and the gravitational work 

 carried out by Captain Burrard, and recently published by 

 the Royal .Society, is of primary iinportancn. But other- 

 wise English colonies require encouragement to do inore. 

 I am assured that measurements of the gravitational con- 

 stant in Canada would be of the greatest importance. 



The bearing of such work on our knowledge of the 

 earth may perhaps be illustrated by one example. It has 

 often been a matter of wonder how mountain chains such 

 as the Himalayas could rest on the lower strata of the 

 earth without crushing them and forcing them in by the 

 pure power of their weight, and the most plausible theory 

 to account for this was found in the idea first suggested 

 by Pratt, that the mountain chains must not be com- 

 pared with a large weight resting on an under-structure, 

 but rather with a lighter body partially immersed in a 

 heavier one. Mountains, according to this theory, float in 

 the body of the earth very much like icebergs float in 

 water. The truth of this theory can only be tested by 

 accurate measurement of the gravitational force, from which 

 information may be derived on the distribution of density 

 in the earth's strata near the surface. On the whole, the 

 measurements so far available have confirmed Pratt's 

 hypothesis. 



More recently another probleirt has occupied the atten- 



