163 



since, if the expression developed has not been reduced to the form 

 of a function of three rectangular coordinates, the development may 

 contain an infinite number of terms, which are introduced by the 

 operation without being essential to its final result. He takes for 

 the example of such a case the equation of a spheroid, prominent be- 

 tween the equator and the poles, somewhat resembling the figure which 

 was once attributed to Saturn ; and he shows that its development 

 in the form required will contain an infinite number of quantities 

 arising from the expansion of a radical, which are not to be found in 

 the original function. 



Mr. Ivory considers, in the second place, the differential equation 

 that takes place at the surface of a spheroid, and the demonstrations 

 which have been published by Laplace and by Poisson ; and he con- 

 cludes that this equation is wanted neither for proving the pos- 

 sibility of the development, nor for calculating its terms ; but in 

 this plainer way of considering the matter, it appears that the de- 

 velopment does not represent the given expression, when that ex- 

 pression is not an explicit function of three rectangular coordinates, 

 in the same sense that it does when it is such a function. There 

 is, therefore, a difficulty left unexplained ; and we may be permit- 

 ted to doubt whether so important a part of the celestial mechanics 

 as that regarding the figure of the planets, rests with sufficient evi- 

 dence on the doctrine laid down concerning the generality of the de- 

 velopment. 



On the late Extraordinary Depression of the Barometer. By Luke 

 Howard, Esq. F.R.S. Read January 24, 1822. [JPAtV. Trans. 

 1822, p. 113.] 



On the evening of the 24th of December last, Mr. Howard found 

 the barometer at his house at Tottenham Green at 28'20 inches. 

 The wind was moderate at S.E., the temperature 45, and water 

 boiled freely at 210. At 1 1 P.M. the barometer fell to 27'96 inches, 

 and at 5 A.M. on the 25th to 27'82, below which the author thinks 

 it did not descend. By 8 A.M. it again reached 28. In the twenty- 

 four hours preceding, 0'8 inch rain had fallen, but in the twenty- 

 four hours following there fell none, nor was the wind strong. By 

 midnight on the 25th the quicksilver reached 28'07 inches, and re- 

 mained there during the twelve hours following, a thing very rare 

 in our climate. The quicksilver then rose in an uninterrupted curve, 

 and on the 31st touched upon 30 inches, with fine weather. A di- 

 agram showing the state of the barometer during the last two months 

 of 1 821 , as well as the quarter of the wind and quantity of rain fallen, 

 accompanies this paper. During these two months the rain amounted 

 to 10- 10 inches, a quantity without precedent in the same space of 

 time at London. 



M 2 



