444 



SCIENCE. 



[Vol. II., No. 34. 



there need have been no more than two direc- 

 tions of movement, south-westerly- and south- 

 easterly ; for the pebbles carried a part of their 

 course in one direction maj' have been carried 

 the rest of the way in the other, and so pro- 

 duced any resultant direction between the two ; 

 or materials carried b}- floating ice may have 

 come in a far more crooked course (and the 

 places of origin are all on the shores of the 

 Baltic, or on streams flowing into it). The 

 lower sedimentary bed, with only a couple of 

 exceptions, contains, so far as now known, 

 every kind of pebble found in the upper ones, 

 so that no inferences can j-et be drawn as to 

 changes with time in the direction of trans- 

 port. The main result would seem then to be, 

 that the Kiel sediments have all come from 

 more northern parts of the Baltic basin, and 



might have been carried chieflj- by floating 

 ice, without a climate so ver3- different from 

 the present one. 



The author is highly to be commended for 

 his liberalit3' in printing his pamphlet of sixty- 

 six large octavo pages at his own expense, and 

 that, too, in a countrj- where good European 

 printing is particularlj' troublesome. The two 

 maps might, perhaps, have been advantageously' 

 combined in one, if one of the two sets of lines- 

 had been of a different character (say, dotted 

 or broken) or of another color ; for the verj' 

 object of cartographic representation is to show 

 at one view as much as can possibly be dis- 

 tinguished clearl}* of anj- given subject, — to as- 

 semble for convenient comparison on one sheet 

 as many as may be of the scattered facts of 

 nature bearing upon any given point. 



WEEKLY SUMMARY OF THE PROaRESS OF SCIENCE. 



ASTRONOMY. 

 Spectra of comets observed in 1881. — P. 



Tacchini discusses the varying appearances presented 

 by the spectra of the comets h and c 1S81, and ac- 

 companies his remarks with an extensive series of 

 nearly forty lithographed drawings illustrating the 

 changes which occurred. These changes, for the 

 most part, consist merely in variations of the bright- 

 ness and diffusion of the observed bands, and not in 

 any alterations of position. He gives also a single 

 figure of the spectrimi of Encke's comet, observed 

 the same year, and a set of twenty drawings of the 

 comets (6 and c) themselves. The paper, with its 

 accompanying plates, constitutes an important col- 

 lection of observed data; and some slight discre- 

 pancies between these representations and those of 

 other observers raise interesting questions. — {Mem. 

 soc. spettr. ital.) c. A. T. [263 



Uranus. — Within the last few months, considera- 

 ble attention has been paid to this planet, and a 

 number of series of observations upon it have been 

 published. Safarik {Astr. nadir., 2505), Meyer 

 (Astr. nadir., 2.524), and Schiaparelli (Astr. nadir., 

 2526), all present the results of their measures made 

 for the purpose of determining its diameter and 

 ellipticity. The observations of Schiaparelli are the 

 most numerous and complete. He finds for the 

 equatorial diameter of the planet 3".911, and, for 

 the polar, 3".555 (both reduced to the mean distance 

 19.1826). This gives the ellipticity of the planet 

 A, nearly the same as that of Saturn. He also re- 

 ports the existence, upon the planet's disk, of spots 

 and changes of color, too faint, however, to admit of 

 delineation by means of a telescope of only eight 

 inches aperture. In fact,, to have seen them at all 

 with such an instrument is a most remarkable evi- 

 dence of the wonderful clearness of the Italian sky. 



The writer of this notice also made a series of 

 observations upon the same object, in May and June, 

 with the twenty-three inch equatorial of the Prince- 

 ton observatory. Markings upon the i:)lanet's disk 

 were unmistakably visible as belts resembling those 

 of Jupiter and Saturn. The equatorial diameter 

 determined by the writer's measures is 4".280, and 

 the polar, 3".974, giving an ellipticity of ,^-4. Miidler, 

 in 1843, obtained 4"..304 and 3".S69 for the two 

 diameters, and an ellipticity of it,. There can no 

 longer be any doubt that the planet lias a rapid 

 rotation nearly in the plane of the satellite-orbits. — 



C. A. Y. [264: 



MATHEMATICS. 

 Perimeter of the ellipse. — Mr. Thomas Muir, 

 referring to a recent article by M. Mansion, infers that 

 the following formula, which he has known for some 

 time, for calculating approximately the perimeter of 

 an ellipse, has not j'et been published. Denoting as 

 usual by a and h the semi-axes of the ellipse, the 

 expression for the perimeter is 



7i 



;fff I g^ + ft^ 



or, the perimeter of an ellipse is approximately equal 

 to the perimeter of a circle whose radius is the semi- 

 cubic mean between the semi-axes of the ellipse. — 

 {3Iess. math., xu. no. iO.) t. c. [265 



Calculus of variations. — The general problem 

 of the calculus of variations is to find the variation 

 of an 7i-tuple integral of a function of n independ- 

 ent variables, and of depending also upon a number 

 of arbitrary functions of these variables, together 

 with the differential coeflficients of the functions. 

 M. Picart in his paper, which he entitles Theorie nou- 

 velle du calcul des variations, confines his attention 

 to a triple integral containing only one arbitrary 



