Intelligence and Miscellaneous Articles, 307 



From these numbers I draw the following conclusions : — 



1. The old theory of the freezing of lakes, which assumes a pro- 

 gressive cooling of the whole mass down to 4°, and then a further 

 lowering of the temperature of the superficial layers stratified from 

 0° to 4° according to the order of their densities, is perfectly correct. 



2. The penetration of the cold into the upper layers may descend 

 to a depth of 110 metres (Zurich). 



3. It was in consequence of its comparative shallowness that 

 Loch Lomond did not exhibit to Mr. Buchanan the temperature of 

 4° in its bottom layers. 



4. The penetration of cold into the upper layers takes place pro- 

 gressively and very gradually. The curve which can be drawn 

 from my numbers from the Lake of Zurich presents neither leaps 

 nor jerks ; it is altogther analogous to the curves of superficial 

 heating of a lake in summer. This, it seems to me, is quite suffi- 

 cient to put aside the supposition that the cooling, which penetrates 

 so deeply, takes place either by way of thermal convection or by 

 mechanical mixture under the action of waves and currents — with 

 the exception, perhaps, of the upper layer of from 5 to 10 metres 

 thickness. 



Must this penetration of cold be attributed to phenomena of 

 conductivity, or to phenomena of radiation, either of the water 

 itself or of the soil through the water ? The experiments have not 

 supplied me with any elements for answering this question. 



5. On comparing the two series of soundings made in the Lake 

 of Morat, separated by an interval of forty days, I find that the 

 mean temperature remained exactly the same. Therefore the layer 

 of ice absolutely stopped the cooling of the water, and the action 

 of the exterior cold was all expended in increasing the thickness of 

 the ice. 



6. During these forty days the water of the Lake of Morat be- 

 neath the ice underwent an equalization of temperature ; the colder 

 upper layers were warmed a little, while the warmer bottom layers 

 were cooled ; but we are still very far from finding complete unifor- 

 mity of temperature in the entire depth of the lake on the 1st of 

 February. — Comptes Rendus de VAcad. des Sciences, Eeb. 16, 1880. 



THE ELECTRIC CURRENT. BY PROF. LUDWIG BOLTZMANN. 

 In a memoir entitled " To the Theory of G-as-friction," the rela- 

 tive velocity and its longitude and latitude with respect to the ve- 

 locity of one of the molecules as axis, and to the plane of the velo- 

 cities of both molecules as first meridian, are introduced as integra- 

 tion-variables ; and thereby the equation for the distribution of 

 velocities in a moved gas is simplified. Here the velocities meant 

 are everywhere those before impact. The determination of the 

 coefficient of friction by the development of a series, exact account 

 being taken of the distribution of velocities, is then encountered by 

 no difficulty. 



