Notices respecti)ig New Books. 229 



requisite information, as to the circulating or repetend part of 

 the quotients, in the whole suit of arithmetical works pubhshed 

 or further contemplated by the author : but besides the uses 

 of these tabular circles, in connection with the others of 

 Mr. Goodwyn's Tables ; by itself, this volume may sometimes 

 prove of important use, in abridging the labour of very long 

 divisions, by any divisor under 1025: thus, after having care- 

 fully found the quotient to 8 or 1 places of figures (but some- 

 times a less number may suffice) ; then, by comparing the same 

 with the several circles here set down under the given divisor, 

 the peculiar succession of several of the last digits, in the quo- 

 tient, and of others in the table, being found the same, will 

 mostly detect the particular circle, applicable to the case, and. 

 also the digit of the quotient, found by actual division, as above, 

 whereat tlie circulating or repetend part of the quotient be- 

 gins ; and then, by help of such tabular circle, any fiirther 

 required number of places in the quotient can be supplied, 

 however numerous, and may, if requisite, be easily proved^ by 

 a converse multiplication, by the divisor. 



The second of the volumes before us, is an importantly use- 

 ful one ; it is the first of five parts, wherein, in case of a favour- 

 able reception by the public, the author intends to give 152,096 

 decimals to 8 places, arranged in an increasing series, and 

 having opposite to each, the vulgar fraction equivalent thereto ; 

 so that by the aid of the arithmetical complements, taken out 

 almost by inspection, all the 304,192 proper fractions of diffe- 

 rent values, expressible by numbers under 1001 in numerator 

 and in denominator, may be found, and the complete decimal 

 value of each ascertained, by mspection and reference to the 

 volume of circles above mentioned. 



In the volume, or part rather, which is before us, the first 

 30,414' decimals of this series are comprised, extending from- 

 •001 to -09989909 ; and wherefrom, a like number of the last 

 of the same series are deducible, as complements, almost by 

 inspection, extending from '90010090 to '999; besides which, 

 (although the author has not pointed it out) by merely remov- 

 ing the decimal point, and abating or adding a cipher, equiva- 

 lent to a general multiplication by \0, throughout the table,, 

 this volume will exhibit also 30,414 decimals, distributed 

 through the whole series (with the exception of its extreme 

 parts which the table itself supplies) from '01 to "9989909, 

 with their equivalent vulgar fractions, from -j-iy to %'^^ ; and 

 in like manner, a general multiplication by 100, of all the first 

 3025 decimals and fractions in the table, will give as many 

 such, distributed in the same way through the whole series, 

 except its extremes below •! and above '998690: which table, 



especially 



