1880.] 



J. F. Toniiant — On Standard Weiglits. 



61 



To find the probable error of this we must substitute in the above equation 

 the symbolic values of Ok, + 0^ and thus we have — 

 Prinsep's Pounds 12 Oi + P-q^ + i P.^, + 4 P.^,, — SP.^ + 4 23606 P, 03 

 from which the probable error will (when the errors generated in deter- 

 mining O2 and Oio, and also in the single comparison of this weight are 

 allowed for) 



= ^gv/8878998 = 0-002890 

 and we may consider Prinsep's Pound = 5760'148 ± 003 grains. 

 Section X. — Considerations as to tJie Weights luhich sJiould be made use of 



in a series. 



The only generally used decimal system of weights, is the metric, 

 which is so largely diffused. In it the weights between and Wj^g are 

 Wj, in duplicate, and W^. When the system was adopted in England 

 permissively, the intermediate weights chosen were W3 and W^. The 

 other series in use, are those I have described before as the Bullion, and the 

 English Grain Series. In making a series of weights of tolahs for the use 

 of the Indian mints, I have therefore a choice ; and it is worth considering 

 which series is the best. 



Commercially, the fewer weights required to make any weighment, the 

 better. I think, too, that' commercially it is undesirable to have duplicate 

 weights, and of course none should be superfluous. In the strict French 

 Metric system there are 8 weights required to weigh 9 and 8, while two are 

 wanted for 7, 6, and 3, and the 2 is in duplicate ; and in the English modifi- 

 cation there are 3 weights wanted for 9 only, while 8, 7, 6, and 4 require 

 two each, and there is no duplicate : I think then that the English modi- 

 fication is preferable to the original system. 



In our English Bullion systeui there are never 3 weights wanted for 

 any purpose ; and 9, 8, 7, and 6 require two weights. But there are more 

 weights than are wanted, there being 5 weights in each decad instead of 4. 



In the English Grain system there are never 3 weights wanted ; 9, 8, 7, 5. 

 and 4 require two each, there are no duplicates, and none superfluous. I think 

 then that the English Grain system is the best for commercial purposes. 



Scientificalh/, the best system is that of which the values can be most 

 accurately deduced from the standard Prototype. It is worthy of note, 

 that neither of the Metric systems, nor the English Grain system, admit 

 of the weights of a decad being completely determined without a second 

 unit in each decad. 



This is not an unmixed disadvantage. Tlic 1, 10, &c., being necessary 

 for this purpose only, and not used in common, may be kept separately, and 

 referred to for vcriUcations whenever desired, and by such use the errors 

 of the weights of any decad, can be determined with comparatively little 



