2 Sketch of the Improvements in Science [Jan. 



and the state of Italy has for some years nearly interrupted all 

 scientific communication between that country and Britain. 



I have made the preceding statement to enable the reader to 

 appreciate in some measure the defects of the following sketch. It 

 may be considered rather as a detail of the progress of science in 

 Britain and France, than of its progress throughout Europe. 



I. Mathematics. 



This science has now advanced so far that we are not entitled to 

 look for important additions to it every year ; yet the last year has 

 been fortunate in this respect, having produced two works, each of 

 them of great importance to the progress of the science. 



1 . The first is Mr. Ivory's paper on the Attraction of an extensive 

 Class of Spheroids, published in the Philosophical Transactions for 

 1S12. This subject, which is of great importance in physical 

 astronomy, has occupied the attention of mathematicians for these 

 seventy years. Maclaurin resolved it in a particular case in 1740. 

 Lagrange and d'Alembert extended his demonstration. Legendre 

 and Biot endeavoured to generalize it; but without success. At 

 last Mr. Ivory has reduced the subject to a wonderful degree of 

 simplicity, by demonstrating that the attraction of a homogeneous 

 ellipsoid upon any external point whatever may be reduced to that 

 of a second ellipsoid upon a point within it. 



2. The second work to which we allude is the Analytical Theory 

 of Probabilities, by Laplace, published at Paris during the year 1812, 

 but not received in this country until the summer of 1813. This 

 book, as might be expected from the profound knowledge of the 

 author, contains much new matter of a very valuable kind ; but as 

 I have not had an opportunity of perusing it, I can only refer to the 

 account of it given by Delambre, and to be found in the Annals of 

 PhUosophy, vol. i. p. 3 11. 



Three other mathematical papers have made their appearance ia 

 the Philosophical Transactions, all of them of considerable value. 

 The first, on the Attraction of such Solids as are terminated by 

 Planes, by Thomas Knight, Esq. This investigation has been 

 carried much farther by Mr. Knight than by preceding mathemati- 

 cians. It claims the attention of chemists ; for if ever chemical 

 aflinity be brought under the reach of mathematical investigation, 

 it will be necessary to investigate the effect of figure in determining 

 the strength of attraction of difTerent atoms for each other. To 

 Mr. Knight we also owe the solution of a very curious and beautiful 

 problem respecting the penetration of a hemisphere by an indefinite 

 number of equal and similar cylinders. The only other mathema- 

 tical paper in the Transactions is an application of Cote's theorem 

 by Mr. Herschell, sufficiently curious, but not capable of being 

 explained without enterini^ into details inconsistent with the object 

 of this sketch. 



II. Astronomy. 

 This science has made so much progress, and astronomical 



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