286 PRECISION 



the corresponding factor of certainty is 500 in the third 

 power, which is 125 oooooo. 



III. For the two elements, lo and Mo, the precision is 

 only 0.005, of which 200 make one unit. Hence, the cor- 

 responding factor of certainty is 200 in the second power, 

 or 40 ooo. 



IV. For the following nine elements Ca, Cl, Fe, Hg, 

 Mg, Na, Pb, Pt, S, the precision attained is o.oi of which 

 loo go to a unit. The corresponding factor of certainty is, 

 therefore, 100 raised to the ninth power, that is 



i oooooo oooooo oooooo, 

 or one followed by 18 ciphers. 



The certainty of the entire result is the product of these 

 factors, tabulated below. The single factors are resolved in 

 the numerical part and the number of ciphers following, so 

 that the final product can be most readily determined. 



We also once more enumerate the actual individual 

 elements of each group. 



Group. Precision. No. Elements. Factor. Ciphers. 

 I o.ooi ii Ag, As, Bo, Br, C, Cd, 



Cu, N, O, P, Tl, i 33 



II 0.002 3 Fl, H, Li, 125 6 



III 0.005 2 I> M> 4 4 



IV o.oi 9 Ca, Cl, Fe, Hg, Mg, Na, 



Pb, Pt, S, i 18 



Total : 25 Elements, 500 61 



or 5000 followed by 60 ciphers, 



or 5000 followed by 10 times the million group of 6 

 ciphers. 



This number is exactly five thousand times the greatest 

 number ever formulated by antiquity, namely, by Archi- 

 medes of Syracuse, in his Arenary or Sand-Calculus. He 

 obtained (in our notation) the number i followed by sixty 

 ciphers, by estimating the number of grains of sand that 

 could be contained in the entire universe as then known. 

 See the admirable French translation of his works, by F. 

 Peyraud, Tome II, p. 231-264; Paris, 1808. 



