128 



NATURE 



{Dec. 8, 1887 



the measurements were numerous. The proper course is to 

 determine it by the method of least squares. 



Writing/ for /{«/) and omitting i + - , (3) may by the aid of 



(7) be written in the form— 



f 2m 



Po'')- 



This is exactly analogous to the equations used by Maxwell in 

 the determination of the quantity Aj, which in bis notation and 

 method of development corresponds to Pq ("Electricity and 

 Magnetism," second edition, vol. ii. p. 100). It is unnecessary 

 to occupy the pages of Nature with a reproduction mutatis 

 mutandis of his formulae. We can get, as he does, a general 

 expression for P,, when we have n equations at our disposal, 

 and when « = 2 this reduces (in the notation of Prof. Harkness) 

 to— 



(«) 



Po = (A - Ai)/(A/r^ - Ai/ri^). 



If then in a magnetic survey observations are made at two dis- 

 tances at a number of stations, we should take as the final value 

 of P„ the mean of the most probable values found at each 

 station. As this would be unduly laborious, we approximate. By 

 an obvious transformation (a) becomes — 



log (^ I - ?5 j - log ('i - ^^)=\og A - log Ai 



Po(''- 



2 



*) + &c. = 



log A - log Ai 



M 



Thus to a first approximation — 



()3) 



And if we substitute this value in the small term- 



p _ rh-^ log A - log A 



(7) 



Pn = 



;-"-;-,^ log A - log Aj 



+ ;-'= 



{ri' - r^f 



M 



f log A - log A^- N 



I M J 



This is the expression I gave. The effect of the small term in 

 (7) is, as I pointed out, less than the error of experiment, but it 

 diminishes the difference between the rigorous and approximate 

 values of Pg given in (o^ and (;8), and it is useful in indicating 

 the magnitude of the difference between them. 



Fortunately all methods lead to (j8) as a first approximation 

 which we are agreed is close enough for practical purposes. If, 

 however, we regard the observations as fallible, (o) gives a better 

 value of P,) than (14), and equation (7) gives a closer approxi- 

 mation to it than (3) does. Arthur W. Rucker. 



Science Schools, South Kensington, November 24. 



P.S. — It may be well to add that, although the formula for 

 Ag is correctly given by Maxwell in line 17, p. loi, the value of 

 Aj deduced below is incorrect, being really that of 2MA.2/H. 

 There is another misprint immediately below, 5D being sub- 

 stituted for SQ in the second edition. 



Instability of Freshly Magnetized Needles. 



I SHOULD like to be permitted to support Prof. Riicker in his 

 reply to Prof. Nipher (Nature, vol. xxxvii. p. 77), with a few 

 remarks on the subject of observations of magnetic dip. 



The question of the degree of accuracy of dip observations 

 is one that has been repeatedly raised and discussed. In 1864 

 in his report to the Board of Visitors, the Astronomer-Royal, 

 Sir G. B. Airy, referred to the matter, and a correspondance 

 between him and the Chairman of the Kew Committee (Mr. 

 L. P. Gassiot) ensued, which is printed in cxtcnso in the Report 

 of the British Association for 1864, pp. xxxiv.-xlvii. 



In reply to an inquiry by Mr. Gassiot as to whether the 

 paragraph in the Report was intended to apply to dip observa- 

 tions made at the Kew Observatory, Sir G, B. Airy quoted the 

 following statement by Sir E. Sabine :■ — " The probable error of 

 a single observation of the dip with reliable instruments of easy 

 procurement is known to be ± i'*5. It has been shown to be 



so by a series of 282 observations made at Kew, employing 

 twelve circles and twenty-four needles, all of the pattern which 

 has been in use at Kew for several years past. The observa- 

 tions were made by seven different observers ; the results are 

 published in the Proceedings of the Royal Society, March 1861, 

 vol. xi. p. 156, from entries in the Kew Observatory books, not 

 a single observation having been omitted. The probable error 

 -j- i'5 may be regarded as including constant errors, considering 

 the number of different circles and needles which were employed, 

 as well as the peculiarities of different observers, of whom there 

 were seven " (the italics are General Sabine's). The Astronomer- 

 Royal then concluded by stating "these are the probable errors 

 which I cannot accept as accurate." 



As a result of the correspondence, a series of observations 

 was made at both the Greenwich and Kew Observatories by the 

 observers of both institutions, with the same Kew pattern instru- 

 ments, and then Sir G. Airy wrote, in a letter dated November 15, 

 as follows : "As regards the results of observations, those made 

 with the Kew instruments are consistent to a degree which I 

 never saw before ; and the results for. dip obtainable with the 

 Kew dip instruments are undoubtedly more consistent and more 

 certain than I had supposed them to be." 



A similar inquiry was set on foot by Dr. II. Wild, of St. 

 Petersburg, and in 1886 we made a large number of observations 

 \\ ith different needles for him, the resulting error of an observa- 

 tion being in this case ± i''3. The most severe test, so far as 

 we are aware, wliich has been applied to dip observation, is that 

 recently de-cribed by M. E. Eeyst, of St. Petersburg, in a quarto 

 volume of 133 pages, published in the Repertoritan fiir Meteoro- 

 logic, entitled " Untersuchung iiber Nadel Inclinatorien. " 



The author discusses s^me 6576 observations of dip made 

 with different instruments and needles, and determines their 

 ]jrobable errors, which he always find small, so much so that he 

 deduces the corrections to hundredths of a minute of arc. To 

 quote particular ca'^es, he determines from thirty series of com- 

 parisons between observations and the simultaneous readings of 

 the magnelographs and the induction inclinometer, that the 

 diffeience amounts to only i''o6 ; and again, by comparing at 

 Pawlowsk the fifteen needles of the three dip instruments of the 

 Pawlowsk, Irkutsk, and Ekaterinburg Observatories (all of 

 English make, obtained through this Observatory), he finds their 

 mean correction to be nil. 



Judging from the experience gained at Kew by the examina- 

 tion of probably 150 circles and 500 needles by various makers 

 and different observers, I can thoroughly indorse Prof. Riicker's 

 opinion that Prof Nipher's instruments are scarcely capable of 

 satisfying modern requirements as to accuracy, and are such that 

 were they submitted to us for examination they would be 

 promptly returned to their makers for adjustment. 



G. M. Whipple. 



Kew Observa'or}', November 26. 



Gore's Railway. 



As I have had several letters concerning my use of Dr. Gore's 

 arrangement, depicted on p. 107 of your last week's issue, 

 perhaps I may as well say that I am aware it is commonly re- 

 garded as a Trevelyan rocker, and that I doubt not its function 

 in that connection. This point of view is so familiar to every 

 one, through Tyndall's " Heat," that I thought it unnecessary 

 to mention it. But I have occasionally heard the motion of the 

 ball attributed to the electro-magnetic action of the current on 

 itself — which is impossible — and I thought it useful to point out 

 that it could nevertheless be used as an illustration of electro- 

 magnetic force, provided a vertical magnetic field is applied as 

 well as a current. I should imagine the earth not too weak to 

 have an effect under favourable conditions ; but of course such 

 an effect would be strictly definite in direction, and reversible. 



Oliver J. Lodge. 



The Highclere Bagshots. 



The notice in Nature for December i (p. 104), by my 

 friend Mr. R. S. Herries, of casts of shells in the Bagshot Beds 

 at Highclere tends strongly to confirm the results of my own 

 work in that district. On the strength of physical and strati- 

 graphical evidence, I have shown the development in that 

 neisjhbourhood of all the three stages of the Bagshot formation 



