Miscellanies. 395 



cal changes do not precisely coincide with the thermometer. If the 

 effect of heat and cold were alone the cause of the greater or less 

 density of the air, the effect should be strikingly obvious and uniform 

 near the Pole, where the mercury of the barometer should be much 

 higher than at any other place. But that is not the case. The 

 maximum at 66° and 74° N. lat. has never been seen, many lines 

 higher than thirty inches, which is the barometrical indication esti- 

 mated by Kirwan as the natural state of the atmosphere at the level 

 of the sea, over the whole globe. 



Mr. Hudson intends to pursue his researches into collateral branch- 

 es of the subject, and a much more full development may be expect- 

 ed from his additional investigations. He professes to be guided by 

 the results alone, without reference to any previous theory or opinion. 

 Among other points, he will endeavor to ascertain whether any con- 

 nexion exists between the variations of the barometer and those of 

 the magnetic needle, which will of course lead to an examination of 

 electrical influences ; and he will also make a further and complete 

 estimate of the effect of temperature on the barometrical changes. 



In aid of his views, Mr. Henderson, Astronomer Royal at the Cape 

 of Good Hope, Mr. Dunlop, Astronomer Royal at Paramatta, and 

 Mr. Forbes, now on a scientific tour through Italy and Greece, have 

 promised to undertake a series of observations, to be made simulta- 

 neously with those of Mr. Hudson in London. 



8. Propositions, stated by Isaac Orr. 



TO THE EDITOR. 



Dear Sir — Will you do me the favor to publish, in your JournaJ, 

 the three following propositions, addressed to the mathematicians of 

 this country, and also, through your work, *to the leading ones in 

 Europe. 



To the mathematicians of the United States and of Europe. 



All mathematicians are respectfully invited to answer or demon- 

 strate the following propositions. 



1. Supposing the attractive power of the particles belonging to 

 the material universe, to be, inversely as the square of the distance 

 from their centres ; and their repulsive power, or rather the excess 

 of the ratio of the repulsive power, over the attractive, to be, as 

 Newton has made it, inversely as the distance from their centres ; 

 and supposing both powers to be limited by and to the actual sur- 



