March 21, 1901] 



NA TURE 



489 



it should have been stated on p. 91 that the original 

 idea of the spectroheliograph was due to Dr. Janssen, 

 who first suggested it at the Exeter meeting of the 

 British Association in 1869. Again, with reference to 

 the first observation of the spectrum of a nebula, it is 

 stated (p. 242) that " it was seen at a glance that the 

 spectrum consisted of a few bright lines," though the 

 observer at first attributed what he saw to some possible 

 derangement of his instrument. 



Looking forward, Prof. Turner believes that, among 

 other changes, the transit circle will be gradually super- 

 seded by the almucantar for star observations, and by the 

 heliometer for observations of the positions of planets, 

 and in celestial photography he predicts a great future 

 for the portrait lens. 



The illustrations, some thirty in number, are of in.- 

 different quality, and that of Eros, on p. 109, is almost 

 unintelligible. 



Chemistry an Exact Mechanical Philosophy. By Fred. 

 G. Edwards, Inventor of Atomic Models. Pp. xii + 100. 

 (London : J. and A. Churchill, 1900.) 



"The object of this work is to determine the exact shape 

 of the atoms, to find their relative position in space, and 

 to show that chemical force is purely a function of mattet 

 and motion." Further, " the shapes obtained for the 

 different atoms is the subject-matter of a British patent 

 (atomic models) dated 1897." Again, " the conclusions 

 herein deduced (when accepted as true) will form a 

 fitting climax to the discoveries of a century which has 

 produced the atomic theory of Dalton, the theory of 

 heat as a mode of motion, and the discoveries of the 

 correlation of physical forces, and that force, like matter, 

 is indestructible." 



For the scientific reader there is little need to add any 

 comments to these quotations. There is, however, always 

 the possibility that an author may have a good idea but 

 an unfortunate way of presenting it, and one does not 

 forget that "the law of octaves" was received with some- 

 thing like ridicule. It is necessary to add, therefore, 

 that a careful examination of the present work, made 

 with every desire to find precious metal in it, has failed 

 to reveal anything that seems likely to aid the advance- 

 ment of science. 



In dealing with the exact shape of atoms, the author 

 starts with the assumption that the lightest known ele- 

 ment, hydrogen, consists of two tetrahedra placed base 

 to base, and that the atoms of the whole of the remain- 

 ing elements may be similarly formed by tetrahedra 

 built up symmetrically, every two tetrahedra represent- 

 ing one unit of atomic weight. It is practically im- 

 possible, without the models before one, to judge whether 

 there is any outcome from this view of things that com- 

 pensates in any degree for its arbitrariness and com- 

 plexity. There can be little question, however, that as a 

 whole the book and its doctrines will not command the 

 serious attention of men of science whose leisure and 

 patience are limited. A. S. 



The Chemists' Pocket Manual. By R. K. Meade, B.S. 

 Pp. vii -t- 204. (Easton, Pennsylvania : The Chemical 

 Publishing Co., 1900.) 



A LARGE amount of information of use to professional 

 chemists is brought together in this pocket book. The 

 tables include almost everything to which occasional 

 reference has to be made in chemical laboratories ; and 

 with the formuUe, calculations, physical and analytical 

 methods, should be of service not only to chemists, but 

 also to assayers, metallurgists, manufacturers and stu- 

 dents. Among the points worthy of special mention 

 are the applications of graphic methods to conversion 

 tables ; and the descriptions of select methods of technical 

 analysis. 



NO. 1638, VOL 63] 



LETTERS TO THE EDITOR. 



[The Editor does not hold himself responsible for opinions ex- 

 pressed by his correspondents. Neither can he undertake 

 to return, or to correspond with the writers of rejected 

 manuscripts intended for this or any other part of Nature. 

 No notice is taken of anonymous communications.^ 



The Use of the Method of Least Squares in Physics. 



The application of the method of least squares to physical 

 measurements is described in several standard text-books — to ' 

 wit, Kohlrausch's "Introduction to Physical Measurements" 

 (third edition, 1894), Stewart and Gee's "Elementary Practical 

 Physics" (1885), and others. In none of these is it pointed out 

 that the method as set forth offers in certain cases a choice of 

 results, and that the solution is practically unique only if a 

 sufficient number of observations be taken. Nor is any indica- 

 tion given how the method is to be applied when none but a 

 small number of observations is available. Since the method is 

 intended for use only when a high degree of refinement is aimed 

 at, these points are of practical importance. 



As illustrating the necessity for examining the matter, we 

 may take the example given by Kohlrausch on p. 13 of the book 

 referred to above. The object is to determine the law con- 

 necting the length L and temperature of a standard metre bar 

 from the following four observations : — • 



9 = 20°, 40°, 50°, 60" 



/(the excess over I metre) = 'aamm., •65mm., 'gomm., I'oSmm. 



The law deduced is 



L = 999 '804 + o "02 1 29. 



It is not, however, pointed out that the law would be different if 

 the equation connecting x and y, in this case 9 and /, were 

 written to begin with in a slightly different form. On the 

 contrary, the above solution is presented as if it were altogether 

 beyond doubt. 



In the working of the example as given by Kohlrausch, the 

 equation is written 



y-ax -b — O', 



but if it be written 



cy - x-d=o, 



and exactly the same procedure as that adopted in evaluating 

 a and b be followed in determining c and d, the law thence 

 deduced from the observations becomes 



L = 999 '800 + '02 136. 



It will be seen that the constants in these two laws differ by 

 one in two hundred, or 0*5 per cent., as regards the significant 

 figures ; and that from the precisely similar way in which they 

 are obtained, they are each equally entitled to recognition. 



In fact, corresponding to the values for a and b usually given, 

 viz. : — 



_ ' Zx'Zy - M-Zxy , , _ 'S.x'S. xy - tx'-'S.y 

 [txf - nlx^ ' {-ix,^ - «2jr« ' 



there are always another pair of values, giving the second form 

 of the law, viz. : — 



,^ CSy)'-«2y . ^,^ _ ly-lxy - l.y'^ lx 

 Ix'Zy - n'Zxy ' txty - nXxy 



The first pair of values corresponds to the supposition that the 

 X measurements are guaranteed correct, and the experimental 

 errors are all confined to the y measurements ; and the second 

 pair corresponds to the supposition that the y measurements are 

 correct and the errors are all in the x measurements. The 

 two lines 



y = ax + b 



y — a'x + b' 



intersect at the centre of mass of the system of points obtained 

 by plotting the observations. 



The question naturally arises : How shall a relatively small 

 number of observations, or a series of observations which are 

 relatively discordant, be made to furnish the best mean result 

 obtainable when no other observations are available ? 



In order to answer this question, we may recur to the remark 

 above that differences in the result are obtained by writing the 

 equation in different forms. The various forms of the equation 

 correspond to the several directions in which the divergencies of 



