253 



Northampton, the Swedish and Carlisle tables, and the supposed ex- 

 perience of the Equitable Assurance Office. The results of these 

 comparisons are stated in a tabular form, and are very favourable to 

 the law supposed. 



In the second chapter, the author, after briefly explaining by al- 

 gebraical reasoning, the mode of applying these principles to calcu- 

 lations of annuities, proposes general* tables for facilitating this ap- 

 plication in practice. These tables (which occupy 28 folio pages, and 

 represent the logarithm of the present values of annuities for every 

 value of a certain argument,) are actually calculated, and annexed to 

 the communication, forming the principal part of the second chapter. 



Observations of the apparent distances and positions 0/458 Double and 

 Triple Stars, made in the years 1823, 1824, and 1825 ; together with 

 a re-examination of 36 Stars of the same description, the distances 

 and positions of which were communicated in a former Memoir. By 

 James South, Esq. F.R.S. Read November 17, 1825. [Phil. 

 Trans. 1826, Partly. 1.] 



The author prefaces these observations with a brief account of the 

 instruments with which, and the circumstances under which, the ob- 

 servations previously communicated to this Society were made, and 

 being fully described in the former paper alluded to in the title of 

 this, require no further particular description ; he contents himself 

 therefore with noticing that by a different adaptation of their parts, 

 higher magnifying powers than those formerly employed were ob- 

 tained, and a series of powers from 92 to 787 used in a part of the 

 observations. 



A large portion of these observations were made at Passy near 

 Paris, and the author takes occasion to make honourable mention of 

 the facilities afforded him on the part of the French Government for 

 the ingress and egress of his instruments into and out of France, and 

 of the attention and assistance uniformly afforded him while resident 

 there by many distinguished individuals. 



Of the stars whose measures are here presented, he states that 

 about 160 are hitherto undescribed and probably new. The places 

 of these are given merely with sufficient exactness to enable ai\y one 

 to find them in future. The remainder are in great measure stars 

 comprised in Mr. Struve's catalogue of 796 double and triple stars, 

 and among them about 1 60 belong to those examined for the first 

 time by Sir William Herschel. 



The observations themselves are stated in a manner somewhat dif- 

 ferent from that adhered to in the former communication already 

 alluded to. Instead of giving all the individual micrometrical mea- 

 surements on which they depend (about 14,000 in number,) which 

 would have swelled the paper to an enormous bulk, only the mean 

 results of each set of measures are given : but to afford every opportu- 

 nity of forming an impartial judgement of their validity, not only the 

 number of measures on which it depends is annexed to each mean 



