IMPERIAL STANDARD TROY POUND WEIGHT. 
481 
same, we might from that circumstance draw the highly probable conclusion, that 
the three single pounds of Mr. Harris, according to my hypothesis, were really made 
of the same identical metal ; and the specific gravity of the two remaining pounds 
might with safety be considered as that of the lost standard. If, on the contrary, 
the two remaining pounds prove to be of different specific gravities, the hypothesis 
that all three were made of the same metal is evidently erroneous ; and nothing can 
be inferred from the specific gravity of either of the two remaining. For in this case 
the metal of the lost standard may have been, 
1. Identical with that of Mr. Bingley’s pound, or 
2. Identical with that of Mr. Vandome’s pound, or 
3. A different metal from that of both these pounds. 
Now as there is no metal of which we know, except that of the two remaining 
pounds, that may be considered as identical with that of the lost standard, it is 
evident that if this also cannot be considered as being so, all hope is lost of arriving 
at the knowledge of the specific gravity of the late imperial standard troy pound. 
2 7- It may be worth while to express in numbers the uncertainty that remains 
about the true weight of the lost standard pound as the case now stands ; that is, 
without knowing if it was of brass or copper, and without having a precise know- 
ledge of its specific gravity. To do this it will be necessary to state the formulae and 
the numeric values used by me in the computation of its true difference of weight 
with all the pounds that have been compared with it ; or, what is the same, in the re- 
duction to a vacuum of all the weighings made. I have adopted both the formulae 
and the numeric values contained in M. Bessel’s excellent paper on the reduction 
of weighings in the Astron. Nachrichten, vol. vii. p. 373. 
The specific gravity of a body is the quotient of its density divided by the density 
of that substance, which is considered as unity : as such, pure water is here adopted. 
But since both these densities vary with the temperature, — because the same invariable 
quantity of matter which the body contains is always distributed over its volume, 
variable with the temperature, so that generally speaking (the exception which pure 
water affords will immediately be noticed) the body has at a higher temperature less 
density than at a lower, — we must fix a certain temperature at which the body as well 
as the water is to be considered. It is not necessary that this fixed temperature 
should be the same for the body and the water, its choice for both being quite arbi- 
trary. 
For bodies, the most natural seems to be that of one of the fixed points of the ther- 
mometer ; and the temperature of melting ice (Fahrenheit 32°, Reaumur and Centi- 
grade 0°) is here adopted. For pure water, it is known that there is a maximum of 
its density, which takes place at nearly 39° Fahr. ; and this maximum of density, or 
the density of pure water under the temperature of nearly 39° Fahr., is by preference 
adopted as unity. 
3 Q 
mdcccxxxvi. 
