254 



SCIENCE. 



[Vol. I., No. 9. 



Selective absorption of solar energy. — Pro- 

 fessor Laiigley publishes an extended, elaborate, and 

 exceedingly important paper on the selective absorp- 

 tion of solar energy, as determined by observations 

 with the spectro-bolometer at Allegheny observatory, 

 •and upon the summit of Mount Whitney. It consists 

 mainly of a statement of results, with comparatively 

 little detail, — perhaps in some cases not quite so much 

 as would be desirable in order to enable the reader to 

 judge how far the numerical conclusions are to be 

 trusted, since probable errors are seldom given. Fur- 

 ther papers are promised, however, in which these 

 matters are to be more fully treated. 



Prof. Langley's observations cover all the spectrum 



from about wave-length 0.''35 in the ultra-violet to 



o.^'OO in the infra-i'ed, — far below the limit reached 

 by any other investigator. 



The principal results are the following: 1. The 

 maximum of energy in the diffraction spectrum is 

 near the luminous maximum between the red and 

 yellow, though varying with the sun's altitude. 2. 

 Our atmosphere produces an enormous systematic 

 absorption, increasing continually from the infra-red 

 extremity of the spectrum, wliere it is comiaaratively 

 slight, to the ultra-violet, where it is very great. 

 This, however, is not to be taken as denying the ex- 

 istence of remarkble absorption-bands in the infra- 

 red. The observations, in fact, show four such bands 



at wave-lengths 0.''94, 1.''14, 1.''37, and Lf'SS, each 

 of them quite as remarkable as the great line A, near 

 the lower extremity of the visible spectrum. 3. The 

 character and color of the sunlight is markedly 

 changed by the atmospheric absorption; so that, to 

 the naked eye placed outside our air, the sun would 

 appear decidedly bluish. 4. Tlie solar constant indi- 

 cated by the observations is even higher than Forbes's 

 value : it rises to 2.84, and seems not unlikely to reach 

 3.00. (The units in which the solar constant is here 

 expressed are not calories per square metre per min- 

 ute, but ten-thousandtlis of a calory per square cen- 

 timetre per minute. ) 5. The apparatus used was so 

 delicate that all the princij)al Fraunhofer lines of the 

 visible spectrum showed themselves in the galva- 

 nometer readings. 0. The ratio of the luminous to 

 the dark heat is greatly changed by the atmospheric 

 absorption, being much greater outside our atmos- 

 phere than within it. The writer adds, " It is 

 probable, however, that the solar spectrum before 

 absorption, though probably weak below the red, yet 

 extended very much farther into the infra-red than 

 our charts indicate. We may even regard it as prob- 

 able that some agent of the atmosphere acts as an 

 almost complete barrier to the entrance or departure 

 of rays below the point charted." 



The salient features of the investigation are the 

 exquisitely sensitive apparatus devised for its prose- 

 cution, and the new method of deducing the solar 

 constant from pyrheliometer observations at the 

 earth's surface by means of separate co-efiicients of 

 transmission determined for radiations of different 

 wave-lengths. 



An intei'esting question arises, also, as to the way 

 in which our atmosphere acts to retain the sun's 

 heat on the earth, in view of the observed fact, that, 

 contrary to all previous suppositions, the air is more 

 transparent to the red and infra-red rays than to 

 those in the upper part of the spectrum. It would 

 seem, as the author suggests, that Ihe air must be 

 almost opaque to rays of wave-lengths below some 

 limit; that limit, however, being below the extreme 

 point reached by his measures. — (Amer. journ. tic, 

 March.) c. A. Y. [532 



MATHEMATICS. 



Algebraical curves. — M. Noether seeks to estab- 

 lish a thoroughly rigorous foundation for the general 

 theory of algebraical curves in space, and, to this end, 

 proposes to investigate all of the fundamental prop- 

 erties of such curves as can be derived from the 

 general theory of algebraical functions. References 

 are given to the most important papers which have 

 already appeared on this subject; and the author re- 

 marks that bvit two i^rocesses have been employed in 

 these earlier papers. The first, developed principally 

 by Cayley, depends upon the representation of these 

 curves by a cone and a ' monoid : ' the second seeks 

 to apply the theory of algebraical functions directly 

 to groups of points on the space-curve. The author 

 uses both of these processes; founding them, how- 

 ever, upon firmly established and constantly valid 

 theorems concerning algebraical functions, and shows 

 that the first method, although leading to very gen- 

 eral results, is not sufficient for a rigorous establish- 

 ment of the entire theory. The limits of applicabil- 

 ity of the second method are also indicated. The 

 curves treated are without multiple points; and, since 

 they are regarded as general intersections of surfaces, 

 these surfaces can have no multiple points, nor can 

 they have contact along a curve. The first part of 

 the memoir treats of special cases of intersections 

 of surfaces; and the second part, of the intersections 

 of surfaces in general, these surfaces being condi- 

 tioned only by the fact that they must contain the 

 space-curve under consideration, be destitute of mul- 

 tiple-lines, etc. This general theory has inversely 

 its most general application in the development of 

 the geometry of special surfaces. A brief section is 

 devoted to this latter subject, which the author pro- 

 poses more fully to develop in a forthcoming paper. 

 The present paper is undoubtedly a most important 

 addition to the existing literature of algebraical 

 space-curves. — (Journ. reine und angew. math., xciii.) 

 T. c. [533 



Orthogonal surfaces. — M. Bianchi announces a 

 theorem concerning certain triple systems of orthog- 

 onal surfaces ; viz., all surfaces of constant negative 



1 

 curvature, —"Si, give rise to a triple system of or- 

 thogonal surfaces, of which one system is formed of 

 surfaces having the same constant negative curva- 

 ture, and the other two of surfaces which have cir- 

 cles of radius, R, as one of the systems of their lines 

 of curvature. An application is given to the surface 

 formed by the revolution of the tractrix; the Carte- 

 sian co-ordinates, x, y, z, of a point in the corre- 

 sponding triply orthogonal surfaces, are given in terms 

 of three parameters, u, j>, w; and the method of gen- 

 eration of these surfaces is described. — (Atti delta r. 

 acad. dei lincei, vii.) T. c. [534 



On Fuchsians. — M. Poincar^, in a series of me- 

 moirs presented to the French academy, has treated 

 certain new functions, which he calls 'Fuchsians,' 

 'Kleinians,' ' theta-Puchsians,' and 'zeta-Fuchsians.' 

 These functions have a certain analogy to the elliptic 

 and Abelian functions; viz., while these latter func- 

 tions afford integrals of certain algebraic differentials, 

 the new functions afford means of integrating linear 

 differential equations with algebraic co-efBcients. In 

 the present paper the author merely introduces the 

 subject by studying certain projierties of Fuchsian 

 groups {r/roupes Fuchsiennes), and expresses the inten- 

 tion of returning later to the study of their conse- 

 quences from the point of view of the theory of func- 

 tions. A fuller account of M. Poincarg's paper will 

 be given later, the present brief notice being taken 



