Dec. 25, 1884] 



NA TURE 



167 



GEODESY AND MEASURES OF PRECIS TON 

 A Treatise on the Adjustment of Observations, with 

 Applications to Geodetic Work and other Measures of 

 Precision. By T. W. Wright, B.A., C.E., late Assistant 

 Engineer United States Lake Survey. (New York : 

 D. Van Nostrand, 1S84.) 



THIS treatise will be found a valuable addition to the 

 literature of geodetic operations ; the title is, how- 

 ever, misleading, — it implies a discussion of the various 

 corrections required to allow for the effects of tempera- 

 ture, refraction, &c. : such corrections, however, are 

 either omitted or only superficially dealt with, and the 

 principal subject-matter is the adjustment of unavoidable 

 errors by the method of least squares. 



The work commences by a discussion of the various 

 causes of error, and several practical hints are given as to 

 how to diminish them. A remark in connection with 

 personal error is worth quoting : — " A good observer, 

 having taken all possible precautions with the adjustments 

 of his instruments and knowing no reason for not doing 

 good work, will feel a certain amount of indifference 

 towards the results obtained. The man with a theory to 

 substantiate is rarely a good observer, unless, indeed, he- 

 regards his theory as an enemy and not as a thing to be 

 fondled and petted." 



In the second chapter the usual law of error is stated, 

 and the method of least squares is deduced therefrom, 

 together with formula for calculating the mean square 

 error, the probable error, and the average error. The 

 author points out that the name "probable error" is 

 unfortunate, and so we think ; he is also of opinion that 

 the average error might with advantage be more used 

 than it is at present as a measure of the precision of a set 

 of observations. This chapter is concluded by a most 

 instructive discussion on the laws of error, based on 

 various assumptions as regards the number of sources of 

 unavoidable error. It is first supposed that there is only 

 one source of error, and that all errors between certain 

 limits are equally probable ; the curve of error then 

 becomes a finite straight line. The next case considers 

 two independent sources of error, the curve then becomes 

 two straight lines intersecting on the axis of y at an angle 

 of 45 . In the third case three sources of error are 

 assumed, and the curve of error is shown to consist of 

 three parts, which together form a close approximation to 

 the usual curve of error. The method of least squares is 

 further developed in the succeeding three chapters, and 

 applied to the adjustment of the direct observations of 

 one unknown, to indirect and to condition observations. 

 Various methods of solving the numerous resulting equa- 

 tions are given, both rigorous and approximate ; amongst 

 the latter the method of solution by successive approxi- 

 mations as used in reducing the primary triangulation of 

 the Ordnance Survey of Great Britain is strongly recom- 

 mended. The author also recommends the use of a 

 calculating machine, or of Crelle's Tables, in order to 

 diminish the arithmetical labour. 



The remainder of the work is devoted to applying the 

 foregoing to triangulation, to base-line measurements, to 

 spirit levelling, to trigonometrical levelling, to the gradua- 

 tion of line measures, to the calibration of thermometers, 

 and to the discovery of empirical formula?. The applica- 



tion to triangulation is treated very fully, and several 

 methods of solving the necessary equations are given and 

 exemplified by means of examples. One of these examples 

 is the adjustment of the angles of a quadrilateral taken 

 from the Survey of the Great Lakes of North America, 

 executed by the United States engineers ; three methods 

 of solution are given, one of them being that adopted by 

 the LTnited States engineers. 



The author remarks very truly that it is a waste of time 

 applying the rigid methods of adjustment to tertiary or 

 even to secondary triangulation, and he proposes a 

 method of successive approximations by first adjusting 

 the angles at each station for the local conditions, and 

 then using these adjusted values for the further adjust- 

 ment in connection with the side and angle equations of 

 the net. It may be mentioned that the reduction of the 

 secondary triangulation of Great Britain, now being 

 carried out, is effected by a graphic method applied after 

 the angles have been locally adjusted : this method is 

 found to give excellent results with far less labour than 

 even an approximate method of calculation. The criti- 

 cism on the title of the work is well exemplified in the 

 chapters on base-line measurements and on the gradua- 

 tion of line measurements. For instance, there is no 

 mention of the corrections required to be made to a base- 

 line measurement to allow for errors in alignment or of 

 level, for the effects of temperature and for reduction to 

 sea-level. We think that at any rate a sketch of these 

 and other sources of error and their methods of adjust- 

 ment would not have been amiss. 



The adjustment of the errors of trigonometrical levelling 

 is very fully considered, and one of the examples proposed 

 for solution is the adjustment of the levels taken trigono- 

 metrically during the triangulation executed to determine 

 the axis of the St. Gothard tunnel. 



The following remark is, we think, worth quoting : — 

 " Closely allied to the preceding (elimination of accidental 

 errors) is the common idea that if we have a poor set of 

 observations good results can be derived from them 

 according to the method of least squares, or that if work 

 has been coarsely done such an adjustment will bring out 

 results of a higher grade. A seeming accuracy is ob- 

 tained in this way, but it is a very misleading one. The 

 method of least squares is no philosopher's stone ; it has 

 no power to evolve reliable results from inferior work." 



An excellent feature in the work is the illustration of 

 the text by means of examples, embracing almost every 

 possible case that occurs in practice. Some of these 

 examples are fully worked out, others are proposed as 

 exercises. Most of them are t'erived from geodetic work 

 carried out in the L'nited States. In conclusion we can 

 stronglv recommend this book. 



OUR BOOK SHELF 



On the Higher Teaching of Agriculture. Bv the Rev. 

 J. B. McClellan, M.A. (Edinburgh : T. and A. 

 Constable, 1884.) 



Not the least among the benefits of the International 

 Health Exhibition was the series of Conferences held in 

 connection therewith ; and of these, one of the most 

 valuable was the Conference on Education held in August 

 last. Dr. Armstrong's paper on science-teaching in 



