^'I^. Sketch of a Method of Introducing Discontinuous Constants into 

 the Arithmetical Expressions for Infinite Series, in cases where 

 they admit of several Values. In a Letter to the Rev. George 

 Peacock, &,c. &,c. By Augustus De Morgan, of Trinity College, 

 Fellow of the Society, and Secretary of the Royal Astronomical 

 Society. 



[Read May 1 6, IS 36.] 



Dear Sir, 



Two years ago, I presented to the Society through 

 yourself, the detail of some anomalies which I had observed to 

 exist in certain series which I then produced. They arose out of 

 investigations connected with Functions, and since published in my 

 Treatise on that subject in the Encyclopsdia Metropolitana. But on 

 further consideration, I find that I have not distinctly expressed the 

 method by which the anomalies of the series in question may be 

 reconciled, or rather by which the series may be so obtained that the 

 difficulties shall not appear. 



1 beg leave therefore, to request that you will lay the folloAving 

 view of the subject before the Society. 



The assumption of a given form for a development amounted to 

 an express exclusion of several considerations, which, so it happened, 

 did not affect the results of ordinary operations, in cases where the 

 form assumed was that of development in Avhole powers of a variable. 

 Among the exclusions, was that of the possibility of a discontinuou.\ 

 constant, which was never considered, I believe, until the errors which 

 the omission of it created in the inversion of periodic developments 

 Vol. VI. Part I. A a 



