403 Intelligence and Miscellaneous Articles. 



the number M exerts on the stability of the atmosphere ; but the 

 formula which gives the value of n shows that in the vicinity of the 

 soil the temperature decreases far more rapidly than aerostatic ascents 

 would seem to indicate. 



In a second note, M. Babinet gives a complete development of the 

 above formula ; and in a third note he gives a complete formula for 

 refraction. 



He supposed the heights h taken above the horizon of the observer, 

 and not from a point of the surface corresponding to dh. Taking, 

 as is necessary, the height A of a point of the trajectory of the ray 

 on the vertical passing by this point, it follows that for horizontal 

 refraction the atmospheric path is very limited, and that therefore 

 the expression for refraction could never be a formula which becomes 

 infinite for ^ = 90°. Supposing always a decrease of 1° C. for M 

 metres, the complete differential formula is 



\0-76D MJ 

 the integral being taken from *=0 to *= . It will pro- 

 bably be necessary to suppose that M varies with the height h, and 

 to replace M by M + tck, k being so determined that, for instance, 

 with a height of 7000 metres, 200 metres correspond to an increase 



220 -M 

 of 1°. Thus M+ 7000*= 220, and k= -^^- .—Comptes Rendus, 



September 2 and 9, and October 7, 1861. 



ON THE MAXIMUM DENSITY OP SEA-WATER. 

 BY M. V. NEUMANN. 



Von Neumann, in an inaugural dissertation (Munich, 1861), has 

 published a new determination of the maximum density of sea- 

 water. Like Kopp and other physicists, who have made this deter- 

 mination for pure water, he measured the volume at different tempe- 

 ratures in a glass vessel analogous in construction to a thermometer, 

 the coefficient of expansion of the glass being carefully determined. 

 This method is well adapted for liquids whose freezing-point is above 

 the point of greatest density. The sea-water used was obtained 

 from Trieste, Genoa, and Heligoland, and was previously well mixed. 

 Its freezing-point was found to be — 2 0, 6 C, and its specific gravity 

 at 0° C. 1-02S1 ; its point of greatest density was — 4°-7364 C. 



This number is more than that obtained by Despretz ( — 3 0, 67 C. 

 for sea-water of T0273 sp. gr.) and Erman ( — 3°'75 C), but would 

 probablyagreewiththatofAIarcet( — 5°-25C.)ano;Horner( — 5°-56C), 

 if a correction for the expansion of glass were introduced. — Poggen- 

 dorff's Annalen, August 1861. 



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