166 IntelUf/ence and Mkcellaneom Articles. 



If / be the length of the string, and a and b the apsidal distances 

 of the orbit described by the bay, then the apsidal angle 



-\{ 



3_ ff6 27 oft(«2 4.^«) 



8' l^ 256 /« J 



and consequently the progression of the apse in one revolution 



=,3a=x^*(i + |.-±*:> 



i have been informed that a result, not differing much from this, 

 was given by the Astronomer Royal in a communication read a short 

 time since before the Astronomical Society. His paper, I believe, 

 has not yet been printed*. 



I am. Gentlemen, 



Your obedient Servant, 

 Trinity College, Cambridge, . A. Thackeb. 



Julys, 1851. 



ON ATMOSPHERIC SHADOVTS. BY PROFESSOR E. WARTMANN. 



In a former Number of this Journal (June 1849), I described an 

 obsen'ation made at Nyon, by M. Thury, relative to a blue ray which 

 was seen before sunrise. In my opinion it was only an effect of 

 shadow. Analogous appearances are frequently observed at sunset, 

 when the atmosphere is charged with vapours or dust. But it is 

 easier to study them on heights, from the greater transparency of 

 the atmosphere and the less absorption which it exercises on the 

 light : the vicinity of large surfaces of water and of glaciers is par- 

 ticularly favourable to the development and the study of these optical 

 illusions. Every one has been able, in the morning, to follow at 

 considerable distances, in the humid and diaphanous air of the still 

 dark valleys, the course of the solar rays which border the surround- 

 ing crests. 



A similar phsenomenon was manifested on the 3 1 st of last July, 

 toward three o'clock in the afternoon. I was on the signal-station of 

 the Dole, 1680 metres above the sea. The temperature was high. 

 A thin band of mist extended horizontally on the mass of Mont 

 Blanc and on the heights of that chain, at a mean height of 2400 

 metres. Only one cloud was perceptible in the sky, displaced slowly 

 by the south-east wind, and the image of which was distinctly pro- 

 jected on the slopes of the mountains of Faucigny. The whole space, 

 deprived of light by the interposition of this cloud, was depicted in 

 .transparent grayish- black with great clearness. Thus, the floating 

 vesicles of vapour, which, reflecting the rays of the sun, whitened 

 the blue of the sky, existed abundantly at 1!)00 metres above the 

 lake. 



The same day, and at the same hour, I remarked much more cu- 

 rious shadows. On examining the strata of the air comprised 

 between my eye and the bottom of the lake, towards the east, I saw 

 four nearly pai*allel and equidistant bands, which, inclined toward 

 the sun, appeared to rise from the surface of the water to a height 

 of about 30 degrees. These sombre but indistinct bands had the 

 * An abstract of the paper will be found at p. 14/.— Ed. 



