378 Proceedings of Philosophical Societies. [May, — 
new methods of investigating the sums of several classes of infi- 
nite series, by C. Babbage, Esq. From the nature of the subject, 
this paper did not admit of being read in detail. But the object 
of the author appears to have been to explain two methods of 
finding the sums of a variety of infinite series. One of these 
was discovered several years ago; but finding that some of the 
results to which it led were erroneous, he did not then publish 
it. On inquirmg into the cause of these errors, he detected 
the second method. The cause of the fallacy was afterwards 
discovered, and arule was proposed for judging of the truth of 
the results, and a mode of correcting them when found to be 
erroneous. The author stated that nearly similar results were 
found by MM. Poisson and Lagrange, but that neither of these 
mathematicians had explaimed the cause of the error, or given a 
method of correcting them. 
The Society adjourned till after Easter. 
GEOLOGICAL SOCIETY. 
Jan. 15.—A paper was read, from 8. Babington, Esq. “ On 
the Geology of the Country between Tellichery and Madras.” 
The face of the country in general below the ghauts is marked 
by low rounded hills, composed cf a porous substance called, by 
Buchanan,, laterite. The mountains denominated ghauts, and 
the other mountains traversed in the course of his journey, the 
author describes as consisting of granite, gneiss, mica slate, Kc. 
varieties of horneblende rock sometimes containing garnet, and 
in one place cyanite. The Carnatic, or country east of the 
eastern ghauts, is flat, as though it had been once covered by 
the sea; and in digging a well about two miles from the coast, 
a stratum of brown clay was first cut through to the depth of 
about five feet, then a stratum of bluish black clay nearly 30 
feet, containing beds of oyster, cockle, and other shells ; and at 
about 37 feet from the surface water is obtained. 
Feb. 19.—A paper was read from the Hon. W. 1. H.F.Strang- 
ways, on the Rapids of Imatra on the Voxa river, in Carelia, 
N.W. of St. Petersburgh, with an outline of the probable history 
of their formation, and a notice of the bursting of the lake 
Loubando into the Ladoga in 1818. 
The greater part of the course of the Voxa may be considered 
rather as a chain of lakes than a river; near Imatra it is con- 
tracted into a narrow channel within rocky banks, about 60 feet 
in breadth, which continues about 500 yards ; the eastern bank 
is a section of a table land of inconsiderable extent, deeply 
channelled and covered with pebbles and bolders of great size, 
some of which are hollowed into the most fanciful shapes. The 
river rushes with great fury and a tremendous noise through 
this channel; the rock through which it passes is the common 
red granite of Finland, which is easily disintegrated by mere 
exposure to the weather, and hence may have presented no 
. 
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