74 Scientific Intelligence. [Jan. 



Theorem, originally proposed by the celebrated John Bernouilli, 

 and which I have exracted from Bossut's Calcul. Integral, torn. i. 

 p. 484. 



The learned author, from whose invaluable work I have taken it, 

 has not 2;iven the investigation ; and I therefore solicit the favour 

 of your inserting it, in hopes that some of your correspondents may 

 be able to lurnisii a solution to it. 



I am. Sir, your humble Servant, 



GjiORGE Harvey. 



Theorem. 



" Let A 4 B be the semi-circumference of a circle, of which 

 AB, the diameter, is equal to the two semi-axes, 

 A, C, B C, of a given elipse. Divide the serni- 

 circumference, A 4 B, into a number, 2, 4, 8, 16, 

 &c., of equal parts j draw straight lines from the 

 point C to all the points of division : take the 

 arithmetical mean of all the straight lines drawn to 

 the points of division denoted by odd numbers, 

 and aho the arithmetical mean of the sum of all the 

 lines drawn to the points of the even numbers, and 

 the half of AB; these two arithmetic means shall 

 be tlie radii of two circles, the circumference of one of which 

 shall be less than that of the elipse, and the circumference of the 

 other greater." 



Required the demonstration ? 



V. Burning Gas in the Appenines. 



Sir Humphry Davy lately discovered, in the Appenines, a jet of 

 gas burning with great brilliancy, and forming a column of flame 

 six feet high. The gas was pure carbureted hydrogen. This is a 

 fact of considerable interest in a geological point of view. The 

 Appenines consist chiefly of limestone, and belong, unless I am 

 misinformed, to tiie floetz formation. It would be of importance 

 to know, whether any coal exists in the neighbourhood of this 

 flaming jet of gas, or whether it proceeds from a great depth under 

 the surface. This gas is formed in great abundance at the bottom 

 of dirty stagnant water during the summer time. But that fact 

 throws no apparent light on the formation of the gas iu the moun- 

 . tains of the Appenines, 



VI. JVeather in Iceland during the IVinter ISIS — 14. 



Some of my meteorological friends are anxious to know through 

 the medium of the Annals of Philosophy, whether there was any 

 thing peculiarly severe in the last winter in Iceland. If any of my 

 readers happen to be acquainted witli the matter of fact, it would 

 be considered as an obligation if they would communicate what 

 " they know. 



