62 



J. F. Tennant — On Standard Weif/7its. 



[No. 1, 



labour and witbout its being necessary to refer back to a primary weight. 

 Tlius, checking becomes much more manageable, and, by such a plan 

 as I have adopted in dealing with the P set, one of the duplicates is far 

 more accurately determined than the other, and can be laid aside for re- 

 ference ; the accuracy of the second being ordinarily sufficient. 



The English Bullion system, as we have seen, contains the means of 

 determining the values of all the weights without duplicates, and it is 

 possible to have one weight practically unused, if we consent to make either 

 8 or 9 by three weights ; this reference weight, however, is not so convenient 

 for use as in the other cases. 



The English Grain system has this advantage over all the others, that 

 any weight from 1 to 10 requires at most two weights to make it. It has 

 the disadvantage that 6 is not the half of ten, but, on the other hand, 3 is 

 the half of 6 ; and I do not see the great gain of this relation, unless it be 

 admitted that the system of division should be binary. In France, it was 

 proposed that each multiple of a unit by ten, and each division by ten, 

 should be a new unit. Some slight gain might have come if this had 

 become a thoroughly practical procedure ; but, in fact, one rarely hears of 

 any but the kilogramme, gramme, and milligramme, and so of the other 

 numbers of the series. I think, then, that the advantage of being able to 

 have a single weight for half a hectogramme, &c. is dearly purchased, if 

 there be a disadvantage in the determinations ; and, in deciding on a system 

 of weight, it is necessary to consider the probable errors of these deter- 

 minations. 



In each of these proposed systems, 5 comparisons, giving 5 equations, 

 are enough to connect all the weights in a decad. If this number be 

 alone used, then the probable errors of W^q derived from will be 



English Grain System e \/ 2i 



I if the best equa- 

 " ' \ tion be taken. 



„ Metric e v^38~ 



Original Metric e \/ 2G 



In this respect the English Grain system seems best, and the Modified Metric 

 System the worst. The Original Jletric system is nearly as good as the 

 English Grain system, and it is possibly better if a good deal more labour 

 be given to each ; but I think — when it is considered that weighing by the 

 English Grain system requires only two weights iu each decad, and that 

 the standard system should coincide if possible with that in use — the palm 

 will be assigned to the Grain system. 



I think, too, that those who have gone with me so far, will feel as 

 strongly as myself the great gain of a "large primary unit." It has 



