60 J. F. Tennant—Zxperiments [No. 1, 
The value of # shows that sufficient copper burns away to raise the 
fineness by 0°109 milliémes for each 100 tolahs of free copper and this 
quantity should be added as extra alloy: and the value of y shows that, 
during the processes of converting ingots into coin, sufficient alloy is 
removed to make the coins 0°583 of a milliéme finer on the average than 
the ingots from which they are made. 
Thus in order to have accurate Rupees it would seem necessary that 
the Calculated or Theoretical fineness of the pots should be 
916-667 + 0:085 — 0:583 — 0:109 C 
or 916169 — 0109 C. 
Now if S be the amount of pure silver in a mass and W be its weight, 
the fineness f = = and dW = — = df. 
If in this equation we put W = 12,500, f = 0:916667 and df = 
0'000109 C, we shall have d W or the additional alloy = 1:48 C. 
Practically then to get Rupees of standard fineness we should alligate 
to 916:169 and then add 1 per cent. of the free copper. 
For smaller coins the increase of fineness will be greater and the alli- 
gation will be lower. | 
When the alloy in the silver is at all volatile or very oxidable 
the above rule would not serve of course. So far as possible it is sought 
to guard against this by melting all low-touch or suspicious silver before 
receipt and heating it strongly ; or even, in some cases, partially refining it. 
The probable error of the fineness of the pots for any one day is 
deduced from 10 reports of as many pots assumed to be alike. Its mean 
value is 0:0276 of a milliéme. Hence the probable error of the report of 
a pot is 0-087* of a milliéme. As each report is the mean of two single 
assays, the probable error of a single assay will be 0'123 milliémes. 
Again, the probable error of coins used above is derived from 20 single 
assays of coins; its mean is 0:0806 milliémes, thus the probable error of a 
single coin assay on the mean of all will be 0°360 milliémes. This probable 
error is the probable error of a single assay combined with the probable 
error of a single coin as compared with the mass from which it is taken. 
The former has been found 0:123 milliémes, hence the latter will be 0°1389 
milliémes, 
Again, it is customary here to check the single assays of coins daily 
by a double assay of the melted mass resulting from 20 coins spoilt in 
the stamping presses. The probable error of each such report is combined 
of the probable error of tle mean of 20 coins together with that of a double 
* T have assumed that 0°1 of a milliéme is a sufficient approximation in valuing 
the Theoretical fineness, 
