548 



SCIENCE. 



[Vol. I., No. 19. 



WEEKLY SUMMARY OF THE PROaBESS OF SCIENCE. 



ASTRONOMY. 



Siemens on solar physics. — In a recent lecture 

 at the Royal institution, Sir. W. Siemens discusses the 

 subject of solar radiation. He gives reasons for fix- 

 ing the temperature of the photosphere at about 

 2800° C, based, first, upon the behavior of a rod of 

 carbon and a gas-flame in the focus of a reflector 

 exposed to the sun; second, upon a comparison be- 

 tween spectra of different luminous intensities ; and, 

 third, upon experiments for determining the relation 

 between temperature and radiation made by means 

 of an iridio-platinum wire a metre long, heated by an 

 electric current. He finds the radiation to be expres- 

 sible by the formula, Radiation = Jft^ -|- ipi^ jf being 

 a coefficient due to the radiating substance. He dis- 

 cusses also the effect of diminished pressure in lower- 

 ing the dissociation temperature of compound gases, 

 and restates and advocates anew his last year's theory 

 of the maintenance of the solar heat. — (Nature, May 

 3.) c. A. Y. [1061 



Scintillation of stars as affected by the aurora 

 borealis. — M. Ch. Montigny, observing for many 

 years at Brussels, has noticed, as previous observers 

 have done, that the scintillation of stars is much in- 

 creased during the occurrence of an aurora. He has 

 noticed, further, that every aurora ' produces imme- 

 diately its effects upon the scintillation,' that stars 

 in the north are most affected, and that the influence 

 of the phenomenon is most marked for the stars 

 which are observed across the upper regions of the 

 air. Magnetic disturbances also, even when accom- 

 panied by no aurora visible at Brussels, increase the 

 scintillation to a marked extent. On two occasions 

 during July, 1881, the effect of magnetic disturbances 

 was observed with no aurora visible in Brussels, or 

 even, so far as can be learned, in any part of Den- 

 mark. — (Comptes rendus, Feb. 26.) E. H. H. [1062 



Deviation of axis of meridian-circle. — M. 

 Loewy of the Paris observatory gives two new 

 methods of determining the azimuth constant of a 

 meridian-circle. The first method depends on the 

 following principle : if we take two points in the path 

 of a star so that the chord joining them is approxi- 

 mately at right angles to the instrumental plane, and 

 not greatly different in length from the polar distance, 

 the inclination of the instrumental axis to the equa- 

 tor can be determined by readings of the instrumen- 

 tal declination and distances from the instrumental 

 plane. Owing to the limited field, only those stars 

 whose polar distances are about 1° 40' or less can be 

 used. About one hour and forty-six minutes before 

 meridian-transit, simultaneous readings of the right 

 ascension and declination micrometers are made, 

 and also a reading of the circle. It is not necessary 

 to record the time. After an interval of about three 

 hours and a half, the series is repeated. The chord 

 of the path described by the star during this interval 

 will equal its polar distance. From these observa- 

 tions, we can deduce the inclination of the instru- 

 mental axis to the equator, and by means of this the 

 azimuth constant, without using the right ascension 

 of the star. The method gives thus an independent 

 determination of the azimuth. The old method, 

 that of upper and lower culminations of the same 

 star, requires an interval of twelve hours, thus great- 

 ly increasing the uncertainty of the determination 

 on account of instrumental changes ; besides, for a 

 large part of the year it can be applied to only one 

 star, a Ursae Minoris. 



M. Loewy's second method, which he does not 



consider as good as the first, depends on observations 

 of the distance of the star from the instrumental 

 plane, time of observation being accurately noted. 

 When both right ascension and inclination of axis 

 are sought, it is best to observe these polars at an 

 hour angle of about three hours. When the interval 

 between observations is twelve hours, the inclination 

 of the axis can be determined Independent of the 

 right ascension. 



M. Loewy gives some results of determinations 

 of inclination by his first method which show a vei7 

 close agreement with the results given by that ordi- 

 narily employed. He believes that the probable error 

 of his method will not exceed 0".02. — {Complex ren- 

 dus, April 16 and 23. ) M. mc n. [1063 



MATHEMATICS. 

 Spherical representation of surfaces. — In a 



series of previous communications, M. Darboux 

 treated the particular case of spherical representa- 

 tion when the spherical images of the lines of cur- 

 vature form an orthogonal and isothermal system. 

 In the present communication, he sho%vs how the 

 method previously employed conducts to the com- 

 plete solution of the problem of spherical representa- 

 tion whenever this solution can be obtained in finite 

 terms. Employing certain propositions due to M. 

 Montard, the author arrives at the conclusion that 

 we can obtain all the cases in which the problem of 

 spherical representation is susceptible of a solution 

 in finite terms, and that, whenever the problem of 

 spherical representation has been solved in any man- 

 ner for a system of orthogonal curves, we can de- 

 rive from the obtained solution an entire unlimited 

 series of orthogonal spherical systems. — [Complex 

 rendus, Feb. 5.) t. c. [1064 



Motion of a material point. — In concluding a 

 piaper on a certain peculiar case of the motion of 

 a material point, M. Gascheau considers the problem 

 of finding the equations of. motion of a material 

 point acted upon by a central attractive force, vary- 

 ing inversely as the cube of the distance from the 

 point to the centre of action. The trajectory is 

 shown to be an hyperbolic spiral. The curve itself 

 is discussed, and a formula is obtained for its rectifi- 

 cation. Special phases of the motion of the point 

 are also investigated. — {Bull. soc. math., x. no. 7.) 

 T. c. [1065 



Partial differential equations. — It is impossible 

 to do more than call attention to this memoir by M. 

 Lemonnier, which treats of the integration of partial 

 differential equations of the first order in n independ- 

 ent variables. The process followed is new, and 

 decidedly simple and interesting; but an abstract can 

 scarcely be given here without introducing a good 

 deal of algebraical work. — (Bull. soc. math., x. no. 

 7.) T. c. [1066 



A differential equation. — Capt. MacMahon 

 considers the differential equation, 



X~hlx + T~"Hy + Z~'dz = 0, 

 where X and Y are cubic functions of x and y re- 

 spectively. The equation obtained from the above 

 by dropping out the term in z has been investigated 

 by Allegret {Comptes rendus, Ixvi. p. 1144), who has 

 obtained the integral in an irrational form. If a 

 denote the constant of integration, Allegret's result 

 is symmetrical in x, y, and a. Capt. MacMahon puts 

 a equal to z, and obtains a solution of the above 

 equation in the form of a rational algebraical integral. 



