4 REPOR'T — 18/3. 



Several of those classes need some little explanation. Thus D 9 and 10 are 

 intended to include the same class of constants, the only difference being that 

 in 9 accurate values are given, while in 10 they are only approximate ; thus, 

 for example, the accurate Bernoulli's numbers as vulgar fractions, and the 

 decimal values of the same to (say) ten places are placed in different classes, as 

 the former are of theoretical interest, while the latter are only of use in calcu- 

 lation. It is not necessary to enter into further detail with respect to the 

 classification, as in point of fact it is only very partially followed in the Report ; 

 the final index, however, will be constructed as much in accordance with it as 

 possible. 



The only perfect method by which all the tables on the above subjects could 

 be found with any certainty, is to examine all the volumes of the mathema- 

 tical and philosophical journals and transactions, given in the list prefixed to 

 the Eoyal Society's Catalogue of Scientific papers — a most laborious work, as 

 it requires every page in all these periodicals to be looked at, and any nu- 

 merical tables noted and subsequently examined, while if included in the 

 scojie of the Committee's work they must further be described. The mere 

 turning over the pages of several thousand volumes is a work of some labour, 

 and the completion of the lleport must occupy the Committee for several 

 years. The Avork is also of such a nature that it would not be possible to 

 obtain even an approach to completeness in any one class till very considerable 

 progress had been made with the preliminary examination. 



This, however, is not the case to any great extent with the groups A and 

 B, or with C 7 or the first part of F 12, as tables in these classes are gene- 

 rally to be found in separate books, and not in the memoirs of societies, or 

 journals. It was possible, therefore, to make progress in the above classes 

 immediately ; and the portion of the Report now presented to the Association, 

 practically contains a catalogue of tables which form separate books. The 

 three broad divisions into which mathematical tables divide themselves 

 practically are found to be : — 



I. Subsidiary tables, which are rather of value as a means of performing 

 calcidations than of interest in themselves : e. g. multiplication tables, 

 logarithms, &c. They generally form separate books. 



II. Tables of continuous functions, generally definite integrals. 



III. Tables in the theory of numbers. 



Divisions II. and III. contain conclusive (in opposition to siibsidiari/) 

 tables. 



A fuller description of the contents &c. of Division I. will be found in 

 § 2. ^ It is hoped next year to report on Division II., and the next year on 

 Division III. It will be necessary afterwards to add supplements to diflPerent 

 classes, and notably to the present portion of the Report, which has no claim 

 at all to be regarded as complete, but is published on the distinct understand- 

 ing that it is by no means exhaustive with regard to the subjects treated in 

 it : a supplementary Report on the same subject will be subsequently added; 

 and it is hoped that thus it will be rendered complete (see § 2). 



.§ 2. General Intro<lmtion to the present Bejiort, and Explanation of Its 



Arrangement and Use. 



Art. 1. The present Report is intended to include all general tables, viz. 

 tables that are of general application in all branches of mathematics, and 

 are therefore useful wherever calculations have to be performed. The most 

 simple instances arc multiplication tables, common logarithms of numbers, 



