1878.] 



Mr Glaisher, On circulating decimals. 



193 



Thus 11 = '973684 and the other digits of the period, viz. 

 2105263157894, are at once completed by the aid of the period at 

 the head of the column : similarly || = '921052 and the rest of 

 the period is completed as before. If the numerator is in the 

 right-hand column, the complementary digits are to be taken : thus 

 3V = '026315 and the rest of the period, viz. 789473684210o, is 

 completed as before. When there are several periods, these are all 

 given at the head of the column. The 'tabular series' is similar 

 to the ' tabular series' of 1823 except that it only contains fractions 

 whose numerators and denominators are both not greater than 100 

 arranged in order of magnitude up to ^. As regards therefore the 

 conversion of vulgar fractions into decimals, the arrangement in 

 the 'first centenary' is, as Mr Goodwyn remarks, much more conve- 

 nient for entry. 



Two years previously (in 1816) Mr Goodwyn had printed for 

 private circulation the 'First centenary.' There is a copy of this 

 earlier edition in the library of the Royal Society : it exactly 

 resembles the ' First centenary' of 1818, but the ' Tabular series' is 

 not added\ The introduction to the 'Tabular series' of 1818 



1 There is no title-page in the copy, but the following address appears on the 

 first page. 



"The Calculator of about a Chiliad of Tables, from the application of which, in 

 varioiis ways, he has himself derived considerable benefit, has been induced to print 

 the annexed Centenary as a Specimen. Encouraged likewise by Friends — not, 

 perhaps, quite impartial — to give them some publicity, yet still doubtful in himself 



