June 4, 1896] 



NA TURE 



I area-; on m\ps by means of the planimeter. In 1891 Dr. Heide- 

 rich, a stiulent of I'rof. I'enck's, pubHshed a series of calculations 

 of areas and volumes of land and sea, based on an entirely 

 different process. His method was to draw profiles of the 

 earth's crust from contoured maps along parallels 5° apart, 

 from the highest northern to the highest southern latitude 

 for which data could be found. The areas of land or water for 

 each zone of 10° of latitude wide were calculated from the length 

 of the land or water on the three parallels 5" apart, by Simpson's 

 formula 



F = ///6 (,/ +- 4"'i + 4) 



where F = the area of the zone 10' wide, /; the value of the 

 10' interval in units of length, d, d^ the length of the land (or 

 of water) on the parallels bounding the zone, and r/, the length 

 on the parallel midway between them. Then using the areas 

 of the profile above or below sea-level on each parallel, the 

 volume of land (or of sea) in a zone of 10° is calculated by the 

 same formula; in this case F st>anding for volume, and d for 

 measured areas. 



Metres 

 SSco 



much importance. Were it not for the balancing of innumer- 

 able errors of measurement, we could not hope to gain any in- 

 formation at all from planimeter work on small scale maps, and 

 no two independent measurements could possibly agree. Visible 

 errors must of course be excluded by the e.vercise of all possible 

 vigilance ; but even in Prof. Wagner's critical pages there are 

 one or two examples which show that the best intentions, the 

 utmost vigilance, and a life-long experience of the desperate 

 deceitfulness of proofs cannot guarantee perfect accuracy. On 

 page 688 " II." occurs instead of " IV. " in a reference to a 

 volume, but the date being given correctly neutralises the error. 

 On page 738 "g" should be " g, " in referring to the mathe- 

 matical formula there given, and on page 745 the expression 

 " 9,620,000 qkm. (9,000,000 -f 6,200,000)" contains just such 

 an oversight as might very seriously vitiate a calculation, the 

 last number being obviously intended for 620,000. 



The results obtained by Murray in 1888 are criticised in 

 detail, and various sources of error pointed out. The corrections 

 we do not hesitate to accept, but we cannot look on the original 

 work as claiming the degree of accuracy which Wagner's criticism 



WAGNER'S HYPSOGRAPHIC CURVE. 



Prof. Wagner's main effort is to show the errors of Heiderich's 

 work, first by comparison with his own new planimeter measure- 

 ments, and then on theoretical grounds from the consideration 

 of the natural difficulties introduced in Simpson's formula. In 

 the former task Wagner was able to confirm his own estimates 

 of the area of the land in a very neat and satisfactory way by 

 comparison with Karsten's measurement of the oceans in zones 

 of 10', and he had the satisfaction of finding that the two sets 

 of figures when added together gave a near ajiproximation to 

 the calculated area of the zones. The nett result of the inquiry 

 is to show that Simpson's formula to be satisfactory must be 

 applied to narrower zones than 10", and that means must be 

 taken to ensure that the intermediate values, which have four 

 times the weight of either extreme in the final result, are really 

 typical of the whole intermediate region. Hut I'rof Wagner 

 enters into the minutest criticism of Heiderich's work, detecting 

 errors of calculation and of typography, and showing ho-.v the use 

 of round numbers gives rise to fresh errors in the totals. The 

 balancing of errors which produces a fair consistency in the 

 final result is interesting, but we believe that it receives too 



implies. Had Murray's measurements been made on maps of a 

 much larger scale, contoured at the same intervals, the results 

 would probably have been nearer Wagner's ; but we must 

 also remember that it is the stimulus to this particular study, 

 given by Murray's work, which has, in the ordinary course of the 

 advancement of science, furnished his critic with data superior to 

 those possessed in 1S88. 



While in several places Prof Wagner acknowledges that his 

 figures are only approximations, with noclaimsto absolute exact- 

 ness on account of the uncertainty of the data, it does not appear 

 that he realises the magnitude of this uncertainty. In the first 

 instance measurements, even on large scale maps, are so difficult 

 that increased precautionsalmost alwaysshow different results. The 

 best example is in the case of France, where the re measurement 

 on the plates of the i : 80,000 map in 1894 showed that the area of 

 that country was I '48 percent, greater than had previously been 

 supposed. Again, it must be borne in mind that outside Europe, 

 India, and some parts of the United States, there is not a single 

 continental coast-line the position of which can be taken as 

 correct. Some coast-line has to be assumed, but, except on 



NO. 1388, VOL. 54] 



