5o8 



NATURE 



{Sept. 29, 1887 



Permit me to remark that far from "ignoring" Messrs. Hall 

 and Knight's use of the terms "Elementary" and "Higher" 

 for the two parts of their Algebra, I have called special attention 

 to it. It seems to me that the term " Higher Algebra" {algebre 

 superieure) having been employed by Serret as embracing "the 

 algebraic resolution of equations " in general, and that of " Modern 

 Higher Algebra" by Salmon for what "with greater precision 

 might be called the Algebra of Linear Transformations," it is 

 hardly open to the writers of what is really a text-book of 

 elementary algebra in two parts to apply the same term to 

 the second part of their work, and to oi)ject to a gentle protest 

 from a reviewer. I am at a loss to see where in my subsequent 

 remarks I have practically ignored their own use of the terms. 



I observed that " the fundamental laws of algebra are for the 

 first time gathered together and discussed in the thirty-fourth 

 chapter." This implies that they have appeared dispersedly in 

 the book before, but the references in this chapter hardly justify 

 the contention that they have appeared as '^ the fundamental 

 laws." In fact, the distinctive law of ordinary algebra that 

 ab = ba, instead of being emphasized, is introduced as a fact 

 "with which the student is familiar in arithmetic" ("Ele- 

 mentary Algebra," Art. 13), and nothing more said, as perhaps 

 at this early stage might be expected. So again the "remainder 

 theorem " does in fact appear in an article, marked with an 

 asterisk, at the end of a chapter of " Miscellaneous Theorems" 

 in the " Elementary Algebra," but only as an isolated pro- 

 position with a few exemplifications of its use. The point of my 

 remark was that I should have expected such a fundamental 

 theorem to be put in the forefront and largely made use of in 

 the chapter on ' ' Harder Factors. " I would suggest this for the 

 consideration of the authors in a future edition. 



In like manner, as to my remark on the roots of equations 

 involving radicals, the caution, which I regret that I overlooked 

 in p. 99, appears only as a remark on one particular example, 

 while nothing is said about it in the next, to which it is equally 

 applicable, and in the answers at the end I find roots given 

 which do not satisfy the equations as they stand. It is the 

 practice of not requiring the pupil to select the signs suitable to 

 each root, which I regretted to find that our authors in this way 

 sanction. 



Regard for your space prevents my adding more than the 

 single remark that I regret that the practical commercial con- 

 sideration of the cost of the first part of the book should have 

 necessitated what I have regarded, and what, by urging this 

 plea, the authors seem almost to admit, as, in itself, a "defect of 

 plan." On reconsidering the matter for a future edition, 

 the authors will, I cannot help thinking, find it possible, as it 

 is desirable, to transfer so much from the second to the first 

 part as will make the latter sufficient by itself, as at present it 

 hardly is, for many pupils who need only a small portion of their 

 higher part. R. B. H. 



On the Constant P in Observations of Terrestrial 

 Magnetism. 



Having been absent from town, I have to-day for the first 

 time seen the letters of Prof. Harkness and Mr. Ellis on the 

 calculation of P. 



Though unaware that it was used at Greenwich, or elsewhere, 

 Dr. Thorpe and I have, for a year at least, employed the 

 formula given by Mr. Ellis in the reduction of observations 

 made for the magnetic survey. We have, in fact, made it still 

 more accurate by the addition of another term. Thus, if we 

 write / and /j for log A and log A^, and p. for the modulus, it 

 may easily be shown that — 



P = 



^-A _ .,V^(.,^-Hr^) //^Y nearly. 



Using the metric system of units and taking as is usual r = o'3, 

 r^ = o"4, this becomes — 



P = 0-4737 (/ - /,) - i-947(/-/i)^. 



The value of P for our first year's work calculated by the 

 ordinary method is •000817. Deduced from the formula given 

 by Mr. Ellis it is "000824, which, the second term given above 

 reduces to '000818. 



In this case the effect of the correction on the value of H is 

 considerably below the error of experiment, but as attention has 

 been drawn to the matter, it may be as well to point out that by 



means of the second term the accuracy of the approximation 

 can be readily tested without the trouble cf calculating P 

 directly. Arthur W. Rijcker. 



September 21. 



A Meteor's Flash and Explosion. 



At 8.52 p.m. (Dublin time) of yesterday, Tuesday, Sep- 

 tember 13, my wife and I while walking home were startled by 

 a sudden bright flash like lightning, ^^ but slower and more 

 regular in its movement. Simultaneously an intensely brilliant 

 meteor shot majestically across the sky from north-north-west 

 towards south-south-east, passing near, but to the eastward of, the 

 zenith in its route. It seemed to take its origin from between 

 the Pointers and the constellation Perseus, and died out at a height 

 of 25° or 30° above the horizon. 



Precisely three minutes and a halflater aduU report was heard, 

 which resembled that of a very distant field-gun, or of a peal 

 of thunder far away, but it did not reverberate as thunder would 

 have done. 



It was impossible not to connect the phenomena of the flash 

 and the report with each other. I accordingly made a rough 

 calculation, which gave 43 "4 miles as the distance — not necessarily 

 vertical, but absolute — at which the meteor had become in- 

 candescent, and exploded, as a result of its collision with the 

 earth's atmosphere. John William Moore. 



40 Fitzwilliam Square West, Dublin, September 14. 



A Monstrous Foxglove. 



Mr. Tennant in Nature of September 22 (p. 482), after 

 describing a curiously abnormal specimen of Digitalis purpurea, 

 writes to ask if" such monstrous forms are at all usual." Think- 

 ing your correspondent may be unacquainted with Mr. Herbert 

 Spencer's " Principles of Biology," I write to draw his attention 

 to p. 226, vol. i. of that work, where, in speaking of some fox- 

 gloves growing in Derbyshire, Mr. Spencer says of one : — 



" The following are the notes I took of its structure : — First 

 or lowest flower on the stem, very large ; calyx containing eight 

 divisions, one partly transformed into a corolla, and another 

 transformed into a small bud with bract (this bud consisted of a 

 five-cleft calyx, four sessile anthers, a pistil, and a rudimentary 

 corolla) ; the corolla of the main flower, which was complete, 

 contained six stamens, three of them bearing anthers, two others 

 being flattened and coloured, and one rudimentary ; there was no 

 pistil, but, in place of it, a large bud, consisting of a three-cleft 

 calyx, of which two divisions were tinted at the ends, an imper- 

 fect corolla, marked internally with the usual purple spots and 

 hairs, three anthers sessile on this mal-formed corolla, a pistil, 

 a seed-vessel with ovules, and, growing to it, another bud of 

 which the structure was indistinct. Second flower, large ; calyx of 

 seven divisions, one being transformed into a bud with bract, 

 but much smaller than the other ; corolla large, but cleft along 

 the top ; six stamens with anthers, pistil, and seed-vessel. 

 Third flower, large ; six-cleft calyx, cleft corolla, with six 

 stamens, pistil, and seed-vessel, with a second pistil half un- 

 folded at its apex. Fourth flower, large ; divided along the top, 

 six stamens. Fifth flower, large ; corolla divided into three parts, 

 six stamens. Sixth flower, large ; corolla cleft, calyx six-cleft, 

 the rest of the flower normal. Seventh and all succeeding flowers 

 normal." F. Howard Collins. 



Churchfield, Edgbaston. 



THE " UMBRIAS " IVA VE. 



I HAVE been instructed by the Meteorological Couni 

 to send you the following report of the Umbria'sv/a: ^ 

 from Capt. Watson, F.R.Met.Soc, who is General Supep^ 

 intendent of the Cunard Line of steamers. 



Henry Toynbee, 

 Marine Superintendent 



Meteorological Office, September 18. 



I 



My dear Capt. Toynbee,— I send you all tb^ 

 particulars I can get regarding the so-called " big wave 

 that struck the Umbria. No doubt there were some big 

 waves knocking about the Atlantic on the morning ol 



A 



