I02 



NATURE 



{Dec. 7, 1 87 1 



ever, that even this little may do some good, for it does seem 

 hard, when the labours of men like Fritz Miiller, Weismann, 

 and Lubbock, are throwing light on this intricate subject, 

 that darkness should return in the form of manifest miscon- 

 ceptions of well-known phenomena. B. T. LOWNE 

 99, Guilford Street, W.C. 



Aspect 



Mr. Laughton's aspect is not only a felicitous word in rela- 

 tion to a plane, but it it susceptible of a wider application than 

 that which he proposes for it, since it expresses a fundamental 

 idea in the theory of surfaces. Every surface has at every point 

 an aspect, which is the direction of a normal at that point. This 

 may be regarded as the first property of surfaces, for if we define 

 a surface as that form of extension which has at every part two 

 and only two dimensions, we virtually say that, among all the 

 directions in space that radiate from any point of the surface, 

 there is one and only one perpendicular to all those (infinite in 

 number) that lie within the surface at that point ; in other words, 

 that the surface has a normal at every point. A plane is then a 

 continuous surface which has the same aspect thnnighotit, the 

 angle of two planes is the measure of their difference in respect of 

 aspect; parallel planei (as Mr. Wilson points out) are those 

 which have the same aspect, a plane tangent to a surface is one 

 wh'ch contains a point of the surface, and has the aspect of the 

 surface at that point, and a line tangent to a surface is one that 

 contains a point of tlie surface, and has a direction -sjhich lies 

 within the surface (or is perpendicular to the normal) at that 

 point. Then a straight line tangent to a plane lies wholly in the 

 plane, and if such a line, pissing through any assumed point of 

 a plane— rotate about that point— always remaining tangent to 

 the plane, it must sweep n'cry point of the plane, for it will 

 generate a continuous and infinite surface coincident throughout 

 its extent with the plane, and the plane, being continuous, can 

 have no points without this surface. Therefore, a straight line 

 which joins tioo points of a plane lies wholly in the plane, whence 

 the propusitions that a plane is determined by three points, and that 

 the intersection of tiuo planes is a straight line, together with the 

 other elementary theorems of the geometry of space, are readily 

 derived. 



The use of aspect in the sense now proposed is not absolutely 

 new, as Mr. Proctor (Nature for October 26) seems to argue. 

 It has the high authority of Sir W. R. Hamilton in his " Lectures 

 on Quaternions" (1853). Thus we read on page 92 (the italics 

 and capitals of the original are preserved) : — "A biradial has 

 also a I'LANE and an asi'ECT, depending on the star or region of 

 infinite space, towards which its plane may be conceived to 

 FACE. . . . When two bi-radials have, in the sense just now 

 explained, the same aspect, their planes both facing at the same 

 moment \.\\t same star, ihej mdcy besaid to be condirectional 

 BiRADlALS. When, on the other hand, they face in exactly 

 contrary ways, and, therefore, have orrosiTE aspects, they 

 maybe called contradirectional. . . . Boththesetwo 

 latter classes may be included under the common name of 

 parallel biradials, so that the planes of any two parallel 

 biradials are either coincident or parallel." 



Vaguely, indeed, aspect of a plane may be used in the sense 

 Mr. Proctor would assign it, as well as in several other senses. 

 But if we could give it an exact and technical signification, that 

 which is proposed by Mr. Laughton seems to issue directly from 

 the proper meaning of the word ; and it is a signification which 

 no other word yet suggested will so easily bear. At present, 

 therefore, it ought to be accepted as the very word that is 

 needed in the re.construciion of geometry. 



As for position, it is pertinent to ask whether anyone would 

 say that parallel planes have the same position. The attri- 

 bute of plane.s, for which a word is demanded, is precisely that 

 element of position in which parallel planes agree ; and the 

 position of a plane requires for its determination not that element 

 only, but also some other element whereby the plane shall be 

 distinguished from its parallels. 



Permit me, by way of appendix to my too long note, to call the 

 attention of those who are interested in the early teaching of 

 Geometry, which has lately been discussed in your columns, to 

 Dr. Thomas Hill's " First Lessons in Geometry. Facts before 

 Reasoning." (Boston, 1856.) 



J. M. Peirce 



Cambridge, Massachusetts, Nov. 15 



Cause of Low Barometric Pressure 



In the number of Nature for July 20, 1S71, I find a paper 

 by Ferrel, "On the Cause of Low Barometer in the Polar 

 Regions," &c. The author says that the law which deflects a 

 body to the riglit in the northern hemisphere and to the left 

 in the southern is not understood by meteorologists, and that it 

 is admitted only when the movement is north and south. 



I believe this law is now admitted by almost all meteorologists. 

 The proof of it is the general acceptance of Buys Ballot's law 

 of winds, which states that the wind wiU always blow towards 

 a barometrical depression, and be deflected to the right in the 

 northern hemisphere. 



The most important meteorological works of the last years are 

 based on this principle, as, for example, Buchan's " Mean 

 Pressure and Prevailing Winds," and Mohn's "Storm Atlas." 

 Mr. Mohn states the error which was committed in former times, 

 and gives the expression of the deflecting force (page 17). — 

 15°. sin L. (latitude) per hour. As to Mr. Ferret's explanation 

 of the low barometer at the poles, I must first state that it is not 

 lowest near the poles. In the northern hemisphere, the lowest 

 ])ressures are near Iceland and near the Aleutian islands, but 

 northwards they are higher, as the observations of Greenland 

 have shown, as is seen also in the prevalence of N.E. winds in 

 winter at Stykkissholm (Northern Iceland) ; this would indicate 

 that the pressure to the north and north-west of the last place is 

 higher. 



The great barometric depressions which so often visit Iceland 

 cannot exist at temperatures of some degrees below freezing 

 point. This explains why the barometer cannot be lower at the 

 Arctic Pole than near Iceland in winter ; the temperature there 

 must be certainly much lower, even if the pole be surrounded 

 by open water. 



It is the low temperature also that explains the course of the 

 Atlaulic storms across European Russia (from N. W. to S.E.), as 

 the winter temperature of Siberia is too low to admit the storms. 

 This was already stated by Mr. Mohn, and I can but confirm his 

 opinion.' In southern latitudes the barometrical depression 

 seems to increa-e towards the pole, but do we know enough of 

 these regions to say that the lowest barometer will be at the 

 pole? In the highest southern latitudes attained by Sir James 

 Ross the barometer was a little higher than northward. All that 

 we know about the origin and propagation of barometrical 

 depressions gives us the right to say that pressure cannot be 

 lowest at the south pole, but that, as in the northern latitude, the 

 greatest depression will be found at some distance from the pole, 

 perhaps as far as the Antarctic Circle. 



St. Petersburg, November 28 A. Wc.lElKOFER 



Symbols of Acceleration 



I WISH to direct the attention of the reviewer of the " New 

 Works on Mechanics," in No. 107 of Nature, to the following 

 statements which he makes while speaking of Wernicke's book : — 

 "The symbol / is here and throughout the work used to denote 

 an acceleration ; for exampley" .r {sic) is the acceleration parallel 

 to the axis of x. This notation (unfamiliar to English readers) 

 has obvious advantages when the more appropriate language of 

 the differentid calculus cannot be employed." 



Now I cannot see how the notation is " infamiliar to English 

 readers," when we have in common use a to denote an ac- 

 celeration, and a^ an acceleration parallel to the axis of .r. 

 Again, though I agree with the reviewer thaty^ (or the English 

 a -) " has obvious advantages when the more appropriate language 

 of the Differential Calculus cannot be employed," yet itshould be 

 remembered that there is a more appropriate notation still, viz., 

 that of Newton's Fluxions, recalled to its proper position in 

 mixed mathematics by Sir W. Thomson (see Thomson's and 



rf2 X 



df 



Tate's "Nat. Phil.") and beginning to spread, in which 



or an acceleration parallel to the axis of ,1 is denoted by x. This 

 notation can be employed at all stages of the student's progress, for 

 it is as easy for him to learn that acceleration parallel to the axis 

 of:, actual acceleration in the path, &'c.,are denoted by z, s, &c., 

 as to make himself acquainted with Wernicke's symbols After- 

 wards, when studying the Differential Calculus, he may be told 

 the name of the notation, and have his knowledge of it enlarged, 

 but he will never need to unlearn it ; on the contrary, he will 



* See also my paper "On Barometrical Amplitudes," in the jfotinuit 

 0/ the Austrian Meteorological Society, 1871, No. 10. 



