Ill 



liquity, gives the diminution for au interval of nearly sixty years, 

 with almost sufficient accuracy to state with some confidence the 

 mass of Venus ; but to obtain this point with certainty, the present 

 obliquity, deduced from a mean of the observations of different as- 

 tronomers, should be used. Upon this subject the author alludes to 

 the opinion of astronomers, that observations of the winter solstice 

 have given a less obliquity than those of the summer solstice, an 

 opinion sustained by the observations of Maskelyne, Arago, and Pond, 

 but questioned by Bessel and Bradley. Dr. Brinkley refers this dif- 

 ference to some unknown modification of refraction ; he has observed 

 that at the winter solstice the irregularity of refraction for the sun is 

 greater than for the stars at the same zenith-distance. He points 

 out the necessity of paying attention to the observations at the winter 

 solstice, and gives a table, exhibiting the mean obliquity reduced to 

 January 1813. 



Dr. Brinkley next alludes to the maximum of the aberration of 

 light, which appears from his observations of last year to be 20"' 80. 



On some New Methods of investigating the Sums of several Classes of 

 Infinite Series. By Charles Babbage, Esq. A.M. F.R.S. Read 

 April 1, 1819. [Phil Trans. 1819, ;>. 249.] 



The object of this paper is to explain two methods of finding the 

 sums of a variety of infinite series. One of these the author disco- 

 vered several years ago ; but finding that some of the results to which 

 it led were erroneous, he then declined publishing it. In inquiring 

 into the causes of these errors, he was led to the second method, 

 which employs the process of integration relative to finite differences. 

 The cause of the fallacies in the former method was afterwards dis- 

 covered, and in this paper a criterion is proposed for judging of the 

 truth of the results, and a mode of correcting them where found to 

 be erroneous. The sums of a variety of series are found by these 

 methods ; and the author concludes by observing, that he has since 

 been informed by M. Poisson, that that gentleman had arrived at 

 some nearly similar results in investigating a problem in physical as- 

 tronomy, and also that some investigations of a similar nature were 

 found amongst the papers of Lagrange, but that neither of these ma- 

 thematicians had explained the cause of the errors, or given a method 

 of correcting them. 



On the Optical and Physical Properties of Tabasheer. By David 

 Brewster, LL.D. F.R.S. Lond. and Edin. In a Letter to the Right 

 Hon. Sir Joseph Banks, Bart. G.C.B. P.R.S. #c. Read May 6. 

 1819. [Phil. Trans. 1819, p. 283.] 



Tabasheer is a substance found in the cavities of the bamboo, ex- 

 isting originally in the state of a transparent fluid, but gradually in- 

 durating into a solid of different degrees of hardness : it consists of 

 70 silica, + 30 potash and lime. One variety has a milky trans- 



i 2 



