394 



NATURE 



{Feb. 27, 1890 



It is a minor matter, but it seems a pity that the nomenclature 

 of the species in a standard work like "Darwinism " should not 

 be scrupulously exact. Thus (p. 17), " Phahena" graminis 

 should be Chancas graminis. ^^ Helisonia" (p. 44) should be 

 Helisoma, and it is only a section, or subgenus, of Planorbis. 

 On p. 235, "Jilipendula" and '^jacobecz" shoxAd read Jilipendu la; 

 a.nd jacobcea:. ^^ Sphinx' fucif or mis " of Smith and Abbott 

 (p. 203), is really Hemaris dijffinis, while on p. 204, *' Sphinx" 

 tersa is a Chccrocampa, and '■^Sphinx pampinatrix" is Ampelo- 

 phaga myron. T. D. A. Cockerell. 



West Cliif, Custer Co., Colorado, January 22. 



A Formula in the "Theory of Least Squares." 

 Some time ago, having had occasion to investigate the rela- 

 tion between 't{x'^) and tiv^) in the "Theory of Least Squares," 

 I found a simple formula which connects them, and which I 

 have never seen given in any of the text-books on the subject. 

 I inclose it, and hope it is worth publishing in your journal. 

 University of Toronto, February i. W. J. Loudon. 



Let a number of observations be made on a quantity whose 

 true value is T. If these observations be represented by M^, 

 Mj, M3, . . . M,i, then the most probable value is A, the arith- 



metic mean, and A 



2(M) 



If, moreover, the true errors be 



denoted by x-^, x,^, x<^, . . . .r„, and the residuals by z/j, v.^, v.^, 

 . . . Vn, then 'S,{v) = o by the definition of the arithmetic 

 mean. It is required to find a relation between Sf.t") and 2(z'-). 

 We have — 



Again- 



and adding 2(.r) - 2{v) + «(T - A) 

 and l,(zj) — o. 



2(x) = «(T - A) . , 



(I) 



2{.^r-) = ^(z'-) + 2!2(z')J{T - A} -(- «(T - Kf 



But 2(2/) = o; and from (i), T - A = H^"^^ ; 



n 



.: :^ix-) = 2(z/-) + « j^^ j' 



2(^:2) = 2(z'-) + 



■l2(.r)}-2 



This is the exact formula ; from which it may be seen that, 

 as positive and negative eiTors are equally likely, a close ap- 

 proximation will be obtained by taking {2(x)}- — 2(x-), neglect- 

 ing 2^{XX^). 



And we obtain Gauss's formula — 



2(.r2) = 2(2''^) + 



2(x'-') 



2(x^) _ 2(z'-) 



Galls. 



Admitting, with Prof. Romanes (Nature, February 20, p. 

 369), the plausibility of Mr. Cockerell's view that galls may be 

 attributed to natural selection acting on the plants directly, I 

 beg leave to point out a very obvious difficulty — viz. the much 

 greater facility afforded to the indirect action through insects, by 



the enormously more rapid succession of generations with the 



latter than with many of their vegetable hosts — oaks, above all. 



Freiburg, Badenia, February 22. D. Wetterhan. 



The Cape "Weasel." 



In Prof. Moseley's account of his visit to the Cape of Good 

 Hope (" Notes of a Naturalist on the Challenger" p. 153), the 

 following sentence occurs : — " Again, there are tracks of the 

 Ichneumon {Herpestes), called by some name sounding like 

 ' moose haunt.' " 



In Todd's "Johnson's Dictionary," 1827, we find : *' Mouse- 

 hunt, a kind of weasel;" two quotations being given: — (i) 

 "You have been a mouse-hunt in your time" (" Romeo and 

 Tu'iet," iv. 4). (2) " The ferrets and mouse-hunts of an index " 

 (Milton, " Of Ref. in Engl.," B. i). 



Halliwell's "Dictionary of Archaic and Provincial Words" 

 (1847) gives, on p. 564: ^^ Mouse hound. East. A weasel." 

 Halliwell denies the identity of this word with Shakespeare's 

 mouse-hunt ; and Nares (" Glossary ") inclines to a similar view. 

 But in any case it seems clear that Prof. Moseley's "moose- 

 haunt " is a dialectical English form — mouse-hunt or mouse- 

 hound ; a general word for " weasel." E. B. Titchener. 



3 Museum Terrace, Oxford, February 17. 



The Chaffinch. 



The chaffinch sings almost throughout the year in this locality. 

 The male bird never leaves us in winter like the female, and 

 can be seen in large flocks daily. A singular circumstance that 

 occurred here in December 1888 with regard to a chaffinch 

 may be of interest. At one o'clock in the morning, during a 

 gale, a chaffinch tapped at my study window. On this being 

 opened, it flew into the room and roosted on a bookshelf ; next 

 morning it was liberated. This was repeated on two subsequent 

 gales. Not only did it sing each time on being liberated, but 

 all through the winter and spring it followed me about the 

 garden, singing. E. J. Lowe. 



Shirenewton Hall, near Chepstow, February 11. 



ON THE NUMBER OF DUST PARTICLES IN 

 THE A TMOSPHERE OF CER TAIN PLA CES IN 

 GREAT BRITAIN AND ON THE CONTINENT, 

 W/TH REMARKS ON THE RELATION BE- 

 TWEEN THE AMOUNT OF DUST AND 

 METEOROLOGICAL PHENOMENA.^ 



THE portable dust-counting apparatus, with which the 

 observations given in the paper were taken, was 

 shown to the meeting. The apparatus, which was de- 

 scribed in a previous communication to the Society, is 

 small and light. It is carried in a small sling-case 

 measuring 8x5x3 inches. The stand on which it is 

 supported when in use packs up, and forms, when capped 

 with india-rubber ends, a handy walking stick, ij inch in 

 diameter and 3 feet long. No alterations have been made 

 in the original design, and the silver mirrors which at first 

 gave trouble and required frequent polishings, have been 

 used every day for two or three weeks without requiring 

 to be polished, when working in fairly pure country air. 



With the paper is given a table containing the results 

 of more than two hundred tests made with the appa- 

 ratus. In addition to the number of dust particles there is 

 entered in the table the temperature and humidity of the 

 air, the direction and force of the wind, and the trans- 

 parency of the air at the time. 



The first series of observations were made at Hyeres, a 

 small town in the south of France, situated about 2 miles 

 from the Mediterranean. The observations were made on 

 the top of Finouillet, a hill about 1000 feet high. The 

 number of particles on dififerent days varied here from 

 3550 per c.c. to 25,000 per c.c, the latter number being 

 observed when the wind was blowing direct from Toulon, 

 which is distant about 9 miles. 



Cannes was the next station, the observations being 



^ Abstract of Paper read before th^ Royal Society of Edinburgh on 

 February 3. Communicated by permission of the Council of the Society. 



