NATURE 



THURSDAY, SEPTEMBER 14, 1905- 



.l.sTfiO.YOMY FOR TRAVELLERS. 

 Ilandhiich dcr geographischen Ortbestimmiing fiir 

 Geographcn unci Forschungsreisende. By Dr. 

 Adolf Marcuse. Pp. x + 342 + 2 charts; illustrated. 

 (Brunswick : Friedrich Vieweg und Solin, 1905.) 



A SHORT preface by the author tells us that this 

 book is designed, in the first place, to give 

 assistance to geographers and explorers, to aid 

 students of the mathematical sciences and pupils in 

 the higher schools, and to serve as an introduction 

 to those parts of astronomy which, since they are 

 concerned with the determination of time and of 

 position on the earth's surface, have an important 

 influence on everyday life. One does not expect, there- 

 fore, a description or an explanation of the nicest 

 details that lead to the greatest accuracy, but rather 

 the exhibition of the general principles on which the 

 determination of coordinates depends ; and on the 

 whole this ground is fairly well covered, both from 

 a theoretical and practical point of view. But when 

 an author poses as a teacher, we are apt to examine 

 his book a little closely, to see if he has shown any 

 sign of clearly apprehending the difficulties that 

 learners and pupils encounter when attacking a new 

 subject, and made any adequate effort to remove these 

 difficulties. There is no evidence of any particular 

 care in this direction, though, of course, it is no easy 

 matter to detect beforehand where the pitfalls and 

 misconceptions on the part of the pupil will arise, and 

 points that seem to one teacher to demand a 

 lengthened explanation or further illustration do not 

 present themselves in the same way to the judgment 

 of another expert. 



But there is another test which may be more safely 

 applied. Are any matters introduced which give 

 needless complexity, or delay the continuous progress 

 of the work? In this respect we think the author 

 is not altogether blameless. For instance, the section 

 on " probable error " and the solution of equations 

 by the method of least squares seems on this ground 

 out of place. The subject in the space given to it is 

 not, and cannot be, treated exhaustively ; it must leave 

 but a very hazy notion in the student's mind, and 

 the application of the theory is not wanted in the 

 discussion of the rough results which are derived 

 from the instruments that are employed. Similarly, 

 what has a traveller dealing with approximate values 

 of latitude and longitude to do with 'the small vari- 

 ations arising from the motion of the Pole? It seems 

 a little inconsistent to suggest a degree of accuracv 

 in the final results which cannot be realised with the 

 particular means adopted. 



If these are details into which it would have been 

 better not to have entered, there are, on the other 

 hand, omissions, or at least what appear to be 

 omissions, to which some reference should have been 

 made. Thus, by way of illustration, we may men- 

 tion the absence of all reference to the sextant and 

 artificial horizon in the portion of the book devoted 

 to the description of instruments. The author is 

 NO. 1872, VOL. 72] 



perhaps desirous that his book should not be con- 

 founded with the many treatises on nautical astro- 

 nomy and the methods of reduction therein employed ; 

 but the sextant has as distinct a value in exploring 

 new country as the chronometer, to which the author 

 devotes a very satisfactory section. In the determin- 

 ation of longitude, the sextant applied to the measure- 

 ment of lunar distances affords more trustworthy 

 results than does the observation of Jupiter's satellites, 

 on which the author would apparently rely. Occult- 

 ations of stars by the moon, which is merely a par- 

 ticular case of the method of lunar distances, are 

 referred to at considerable length. . A numerical 

 example of the application of the method is worked 

 out in full, and in all the various methods of deriving 

 the latitude and longitude detailed examples are 

 furnished. This is a very satisfactory feature of the 

 book, and we could have wished that the selection 

 of examples had been more varied and had included 

 the method of lunar distances. 



If these omissions seem to us to be slight blemishes 

 on an otherwise excellent book, it is with the greater 

 pleasure that one can turn to the consideration of the 

 sections which treat of matters of more novelty and 

 originality. In the chapter devoted to instruments 

 we meet with a " level-quadrant " (Libellenquadrant) 

 with which we are unfamiliar, and though it appears 

 to be distinctly inferior to the sextant, it may be of 

 advantage in some situations. The peculiar feature 

 of the instrument consists in the fact that the bubble 

 of a level carried on a rotating arm is reflected into 

 the field of view and made to do the same service 

 as the reflection of the sun to the horizon by means 

 of the ordinary arrangements found in the sextant. 

 In the case of determining the position of a balloon 

 when the earth may be invisible owing to clouds 

 passing beneath the observer, such an arrangement 

 can be used with effect. In the chapter on the deter- 

 mination of a balloon's course, the method is applied 

 with very considerable success. The path of a balloon 

 from Berlin to a point beyond Breslau, a complete 

 run of about 400 kilometres, is worked out, and the 

 average error appears to be about 16 kilometres. 

 This would be a large error on board ship, but the 

 conditions are not the same, nor is there the same 

 necessity for accuracy. The aeronaut has simply to 

 take care that he does not run out to sea ; the 

 navigating officer has to make a land fall. The 

 calculations in this section have been materially 

 shortened by the use of the so-called Mercator func- 

 tion, which, in the examples given, does away with 

 the necessity of logarithmic tables, and suggests a 

 method of working that seems to be well worth the 

 little study that is necessary to master the application 

 of it. 



Lastlv, we may mention an ingenious method of de- 

 termining approximately geographical positions with- 

 out the use of graduated instruments. Threads sup- 

 porting a weight at the apex of a triangle so as to 

 ensure verticality and to give steadiness can be hung 

 on tent poles, and over these threads the transit of 

 stars can be observed with the naked eye. Then, 

 knowing the time, the latitude, longitude, and 

 azimuth can be approximately derived; and when 



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