MAKES DECIMALS. 283 



" obtain a fifth place. The calculated values of the weights 

 " were carried to the sixth decimal, in order to avoid inac- 

 l< curacy in the fourth and fifth places when several values 

 " were summed.'* 



If Mr. William Crookes had strictly carried out this 

 intention, and in the published results dropped the last two 

 places, he would have only subjected himself to needless 

 drudgery. 



But on page 691 he gives a table of the individual weights 

 of his fine set to the sixth place, that is to the millionth of a 

 grain; and there can remain no doubt but by this table he 

 summed up his actual weighings, and obtained the millionth 

 of the grain in his published results, requiring " expurga- 

 tion " at our hands, see p. 128, supra. 



The/a^ that " Crookes continued calculating till he got 

 tired, and did not get tired till he had passed the limit of 

 precision by three places beyond the ken of his balance," as 

 we surmised (pp. 129-130, supra) remains. 



According to his own footnote he passed it by t-wo places. 



Instead of using the oscillation method, he simply used 

 his actual weights to the hundredth of a grain (% rngr.) and 

 a rider of this weight. 



All the decimals beyond this and there are four of them 

 are the result of his weighing of his weights, the compari- 

 son of his actual set of platinum weights, by means of his 

 balance "that would not indicate beyond the fourth place." 



He has also adjusted a rider of o.oi grains, which would 

 give him the fourth decimal, which his balance will "indi- 

 cate," but not determine. 



How very readily Mr. William Crookes takes decimals is 

 shown in a striking manner in the extract from his paper 

 in question, reprinted in his "Select Methods" of 1886, 

 before me. 



The loco grain weight he balances by the 600-1-300-]- 100 

 and o.oi grain; that is solid work, to the hundredth of a 

 grain (=%mgr.). 



His 600 grain weight is determined to five places, as are 

 all other weights; that is, the balance responds only to the 

 fourth, but 10 trials give him a mean to the fifth. 



