[ 40I ] 



it by 8 will be compofite ; for, fince neither the given num- 

 ber, nor the number which exceeds it by 2, is meafured by 3, 

 according to the firft fuppofition, the number which exceeds 

 the given one by unity, will be mealured by 3 (for 3 muft 

 neceffarily meafure one of three fucceffive numbers) and there- 

 fore the number exceeding the given one by 4 will be mea- 

 fured by 3. Since, in the fecond place, either the number 

 which exceeds the given one by 2, or that which exceeds it 

 by 4 is meafured by 3 ; if the number which exceeds it by 4 

 be prime, that which exceeds it by 2, and therefore, that alfo 

 which exceeds it by 8, will be meafured by 3. 



It were eafy to fhew, that, in the application of the above 



produdls of three dimenfions, differing by 4, to the conftruc- 



tion of logarithms, the numerator of the fradion — reduced to 



s 



itsloweft terms is always unity. In this cafe — = 



^^ r -1. . ' x+iY^x~2 + 2. 



Now, Imce either x+ i^Sor ^- 2, is even, 2 will meafure their 



produd increafed by 2. 



Make '-- -+ i ^j-; the general feries will then be 



reduced to this form, ^ + ^ + ±t + lP_ 4., &c. Half the 



^ 3;'' 5/5 7 J 7 

 Vol- VI. 3 E fun, 



