272 



NATURE 



[yan. 19, I 



by a good section on analysis of silicates and some 

 technical products. The book does not attempt to cover 

 all the field of analysis, but what is done will be found 

 really useful bv a beginner or a junior student. 



W. R. H. 



LETTERS TO THE EDITOR. 



[TAe Editor does not hold himself responsible for opinions 

 expressed by his correspondents. Neither can he under- 

 take to return, or to correspond with the writers oj, 

 rejected manuscripts. No notice is taken of anonymous 

 communications. 



\_The Editor urgently requests correspondents to keep their 

 letters as short as possible. The pressure on his space 

 is so great that it is impossible otherwise to insure the 

 appearance even of communications containing interesting 

 and novel facts. 



"A Conspiracy of Silence." 



The Duke of Argyll can scarcely be congratulated upon his 

 latest discovery of a new ground of attack upon geologists. In 

 the year 1862 a very eminent physicist, whose loss we all so 

 deeply deplore, made the somewhat rash suggestion that flint 

 implements are found deep down in the drift, owing to their 

 high density as compared with that of the matrix in which they 

 are inclosed. Seeing that the material in which the implements 

 are found is usually ay?^;^^gravel, everyone acquainted with the 

 subject saw that the suggestion was, to say the least, a somewhat 

 unfortunate one, and Prof. P. G. Tait, in seeking for an oppor- 

 tunity to sneer at "advanced geologists," was scarcely kind_ to 

 the memory of a deceased friend in rescuing such a suggestion 

 from oblivion. But to the Duke of Argyll, the finding of a new 

 basis from which to attack geologists seems to have been a 

 chance which he could not afford to let slip. 



The Duke of Argyll now asks when we are going to begin to 

 discuss his magazine- article upon coral reefs. I reply that in 

 the article in question there is not a single new fact or fresh 

 argument — nothing which has not been already brought forward 

 by Mr. Murray himself, or by Dr. Archibald Geikie, and met 

 by Prof Dana in a singularly exhaustive memoir well known to 

 all geologists. The subject has, moreover, been treated at 

 considerable length by Profs. Prestwich, Green, James Geikie, 

 De Lapparent, and others. Surely no exception can be taken 

 either to the eminence of the authorities who have written on the 

 subject, to the length to which their notices have extended, or 

 to the prominence of the journals or treatises in which these dis- 

 cussions have appeared. If it be said that the general scientific 

 public have not had the matter fully laid before them, it is only 

 necessary in reply to call attention to the pages of Nature, in 

 which a succession of articles dealing with the subject will be 

 found. 



The Duke of Argyll says that he has "nothing to retract." 

 Here I regret to have distinctly to join issue with him. He has 

 asserted that scientific men have refrained from discussing a 

 particular theory, and that in taking this course they have been 

 actuated by the worst of motives — a fear of the truth ; he has 

 charged the Geological Society with refusing in the spring of 

 1885, through its then President, to accept a certain paper from 

 the same cause ; and now he adopts and gives fresh currency to 

 an equally offensive charge of a similar kind. 



These charges have, each and all of them, been shown to be 

 absolutely destitute of foundation. The Duke of Argyll must judge 

 for himself if the principle of noblesse oblige should not lead him, 

 not only to retract the charges, but also to apologize for having 

 made them. But his Grace may rest assured that, until he does 

 so, the grounds for the deep indignation at his conduct, which is 

 so strongly felt both at home and abroad, will still remain. 



John W. Judd. 



On the Constant P in Observations of Terrestrial 

 Magnetism. 



I REGRET that Prof Riicker should have largely misunderstood 

 my last letter. I have not raised the question of fallible obser- 

 vations at ad. Referring to the correspondence on pages 127-8 

 of the present volume of Nature, my principal contention was 

 and is that the ordinarily accepted formula for P differs by terms 



of the second and higher orders from Gauss's theory, and that that 

 difference necessarily persists in any rigorous expansion of the 

 formula. By the ordinarily accepted formula for P I mean Prof. 

 Riicker's formula (a) ; and by Gauss's theory I mean my formulae 

 (i), (2), and (3). From two observations oi f[u), made respec- 

 tively at the distances r andr^, the L of Gauss's theory might be 

 found by a direct solution of equations (i) and (2) ; but instead 

 of that, it is customary to find L from equations (7) and (8) by 

 substituting in them the value of Pq computed through equation 

 (a). To render the latter procedure rigorous, P should be used 

 in (7), and P^ in (8). Equation (11) shows that P and P^ differ 

 by ; quantities of the second and higher orders, and as the 

 ordinarily accepted value of Vq lies between P and Pj, it neces- 

 sarily differs from one orVboth of these quantities, and there- 

 fore from Gauss's theory, by terms of the second and ;_higher 

 orders. 



While freely admitting the justice of Prof Riicker's criticism 

 upon my arbitrary assumption that Pq — ^ (P + P^), I cannot 

 assent to the process by which he has deduced equation (7). 

 Equations (7) and (8) show that we may have either one L and 

 two P's, or two L's and one P. In the latter case these 

 equations become — 



y^\J = k(i - V,r--) (15) 



>^L" = Aid - Porr-) (16) 



and Pfl must be determined so as to make L' and L" as nearly 

 as possible identical with L. To that end we must have 

 2h = U + L" ; and then, from the difference between (7) + (8) 

 and (15) + (16) 



Po=B(A- Ai)- 



Ar■^^ + A^r- 

 Expanding to terms of the second order 



,(A - Ai) r - , r"' /A 



B' 



I + 



Ai 



Whence, by equation (13) 



Pn = 



log A - log AA 



'^ M J 



/l og A - log A^ -" 



(17) 



(18) 



(19) 



This result agrees better with equation (14) than with equation 

 (7). Wm. Harkness. 



Washington, D.C., December 30, 1887. 



I AM afraid that the new method of calculating Pq adopted 

 by Prof Harkness is not less arbitrary than that which he 

 previously employed. He says that " Pq must be determined 

 so as to make L' and L" as nearly as possible identical with L." 

 If the object is only to deduce a correct value of L by combining 

 equations (15) and (16), this condition is certainly not necessary. 

 For if we substitute from (17) in (15) and (16), and take the 

 mean of the values of 1/ and L", we get by a very roundabout 

 process the same value of L as we should have obtained without 

 using Pq at all. But we should have reached the same final 

 result if we had started with the assumption that 



{n + m) L, — Ji L,' + m L'', 



where n and m are any numbers whatever. By properly choosing 

 n and f/i we could deduce the correct value of L with any assigned 

 value of Pq. It appears to me that the equation 2L — L' 4- L" 

 is based upon the tacit assumption that L'and L" are to be com- 

 bined in accordance with the rules applied to fallible measures, 

 and cannot otherwise be justified if the only object is the correct 

 deduction of L from (15) and (16). 



If, however, Po is introduced to enable us to calculate 

 another approximate value of L by observing (say) A, at some 

 other distance, r^, the best value to select will depend on circum- 

 stances. If ra is nearly - r we shall get the best result by 

 writing Pq = P and so on, so that the equation 2L = L' -|- L" is 

 again arbitrary. 



I am quite in agreement with Prof. Harkness as to the fact 

 that if we start from the basis of equations (i) and (2) a small 

 theoretical error is introduced by substituting P,, for P and Pj. 

 Indeed I think this step can only be justified by our knowledge 

 that the inaccuracy thus caused is less than the error of experi- 



