Z?^^. 8v 188;]! 



JSPATORE 



1-27 



index itself, with a list of abbreviations, consisting of 

 twenty pages closely filled in with places in three columns. 

 The colouring of the maps is excellent, and it is obvious 

 that no attempt has been spared to make the book 

 as complete as possible in every way. A. L. 



The Young Collector's Haftd-book of Ants, Bees, Dragon- 

 Flies, Earwigs, Crickets, and Flies. By VV. Harcourt 

 Bath. (London ; Swan Sonnenschein, 1888.) 



Any boy who may wish to form a collection of insects 

 will find in this little hand-book all the information he 

 will be likely to need at first for his guidance. The author 

 does not pretend to go deeply into the subject, but he has 

 brought together a sufficient number of facts to show 

 beginners that the study of entomology will well reward 

 any labour that may be devoted to it. His explanations are 

 simple and clear, and the value of the manual is much 

 increased by a large number of good illustrations. 



LETTERS TO THE EDITOR. 



{The 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 of, 

 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. 



An Earthquake in England. 



As no account has been given in Nature of a recent earth- 

 quake, perhaps room may be found for the following. I was 

 standing near my garden door at 8.20 a.m. on Sunday, Novem- 

 ber 20, when the quiet was suddenly broken by a heavy smothered 

 crash, followed by reverberations as in a clap of tl. under of rather 

 short duration. I felt no shaking of the ground, but many 

 persons here felt it, and the shaking is stated to have been very 

 marke I near Dagnall, between here and Hemel Hempstead. 

 The sound was like the falling in of an immense mass of rock — 

 followed by echoes — in a cavern. 



Some persons say they heard a second, but much less loud, 

 crash later in the morning, but this was not heard by me. 



At Ampthill, near Bedford, persons left the town to meet the 

 first train from London to inquire of the passengers as to a 

 possible explosion having occurred in London. 



The crash was heard in Bucks, Beds, Herts, Suffolk, Essex, 

 Cambridge, and possibly in other counties. I have seen reports 

 from Newmarket, Hitchin, Cambridge, Wimpole, Heydon, 

 Royston, and ■ Saffron Walden, in addition to accounts from 

 many positions close to this place. 



It is curious that Stow records, under A.D. 1250, the thirty- 

 fourth year of the reign of Henry 111. : — " Upon St. Lucie's 

 Day, there was a great earthquake in this town (St. Albans) and 

 the parts thereabouts, with a noise underground as tho' it 

 thundered, which was the more strange for that the ground is 

 chalky and sound, nor hollow or loose as those are where earth- 

 quakes often happen ; and this noise did so fright the daws, 

 rooks, and other birds which sat upon houses or trees, that 

 they flew to and fro, as if they had been frighted by a 

 gosshawk." WoRTHiNGTON G. Smith. 



Dunstable. 



On the Constant P in Observations of Terrestrial 

 Magnetism. 



The formula for P given by Mr. Riicker (Nature, vol. 

 xxxvi. p. 508) has evidently been obtained by expanding the 

 usual expression rigorously to terms of the second order ; but as 

 the usual expression differs from Gauss's theory by terms of the 

 second order, Mr. Rucker's expansion is necessarily inexact to 

 the same extent, and in fact his second order term has no 

 existence in Gauss's theory. 



Going on^y to terms involving r-', Gauss's equations may be , 

 written — 



/(«) = Lr-» + LV-« (I) 



/(«i) = Lri-3-H LVi-» (2) 



S =>^L(' + |) '3' 



where f(u) signifies either sin u or tan « according to the form 

 of instrument employed. 

 By putting 



A = >^ry(«) (4) 



Ai= yirm^^i) (5) 



B = -^^^ (6) 



r^^ - H 



we find from (i) and (2) respectively 



;4L = A j I - b(^^Ai^;-2 j = a (I - Pr-2) . (7) 



;^L = Ai j I - B^^^^-^y,-^} = Ai(i - Vr^) (8) 



Whence, by inspection, 



p = b(^A). (9) 



Pj=b(^^i^A (lo) 



To find >^L we may use either (4) and (9), or (5) and (10) ; 

 and in either case the result will be as accurate as our funda- 

 mental expressions. 



Expanding (10) to terms of the second order. 



Pi = b(^^^) + b(^^^J ... (") 



and therefore the mean of (9) and (10) is 



whence, by putting 



C = log A - log Ai 



and remembering that 



AjiA, = £-C!, -^-Ci,&c. . . . (13) 

 A M [2M^ ^M^' 



in which M is the mcdulusof the common system of logarithms, 

 we have to terms of the second order — 



Equation (9) is what I gave in my letter on p. 366 of the last 

 volume of Nature, where I was careful to say that it was 

 derived from Gauss's original equations. When properly used it 

 is as accurate as equations (i) and (2). Equation (14) was given 

 by Mr. Ellis in his letter on p. 436. It is slightly easier to 

 compute than (9), and differs from that expression by a term of 

 the second order which is less than the accidental e rror of obser- 

 vation. The second order term added by Mr. Riicker renders 

 his expression less accurate than either (9) or (14), if Gauss's 

 theory is accepted as correct. Wm. Harkness. 



Washington, D.C., November 4. 



I THINK that on reconsideration Prof. Harkness will admit 

 that it is not I who have fallen into error. If only two obser- 

 vations are made, equations (7) and (8) are identical, and there is 

 no need for the introduction of Po- - In like manner if numerous 

 measurements were available in which the error of obser\'ation 

 was nil, any pair would give the same value of L, and Pf, would 

 again be unnecessary. If, however, the equations are affected 

 by errors of observation, and it be agreed that in combining them 

 we may replace the P's by a single quantity, Po, it must not be 

 arbitrarily defined. Prof. Harkness assumes that in the case of 

 two observations it must be the mean of P and Pj, but he gives 

 no reasons, and he does not state what value he would adopt if 



