ME. W. CROOKES OK THE ATOMIC WEIGHT OF THALLIUM. 
287 
ments, it will be necessary to substitute the weight of a litre of air in the locality of the 
laboratory for the coefficient of V. The formula, as it now stands, is calculated for 
the volume in litres; if a cubic centimetre be taken, the coefficient of V becomes 
0-001293651 ; if a cubic decimetre, 0-01293651. For laboratory purposes, the ratio of 
the pressures might be tabulated ; this is scarcely necessary, however, if the ratio 759:760 
be taken = 0-9987 as sufficiently accurate, for a tabular difference of 0-0013 will enable 
the operator to speedily determine the ratio he requires. 
In particularly describing the vacuum-balance, I have one peculiarity to note in rela- 
tion to the effect of heat in diminishing the weight of bodies. That a hot body should 
appear to be lighter than a cold one has been considered as arising from the film of air 
or aqueous vapour condensed upon or adhering to the surface of the colder body, or 
from the upward currents of air caused by the expansion of the atmosphere in the 
vicinity of the heated body. ' But neither hypothesis can be held when the variation of 
the force of gravitation occurs in a vacuum as perfect as the mercurial gauge will 
register, and under other conditions which I am now supplying, and which I purpose 
embodying in a paper to be submitted to the Eoyal Society during a subsequent session. 
The Weights. 
A set of weights as ordinarily supplied by even the best instrument-makers is never 
absolutely exact; however carefully they may be adjusted, the pieces of metal which 
respectively represent 1000 grs., 100 grs., 10 grs., &c. are only more or less approxima- 
tions to the true weights. In most chemical analyses, the error arising from such inac- 
curacies in the weights used is so small, in comparison to errors of manipulation or to 
imperfections inherent in the chemical processes adopted, that it may generally be dis- 
regarded; but when the chemist has for his object the determination of an atomic 
weight, or is engaged in other researches demanding the highest refinement of accuracy 
which chemistry and physics can supply, then he is bound to neglect no correction which 
will increase the precision of the results. That chemists, whose well-trained reasoning 
powers allow them to take for granted nothing which is not capable of experimental 
verification, and who insist upon the utmost attainable precision in their balances, 
should, as a rule, neglect the probable errors which the inaccuracies of their weights 
may introduce, is somewhat inconsistent. But in considering these eliminations in my 
memoir, I must disclaim any originality in the process, the description of the method 
I employed being intended solely to place others on the same footing as myself in 
their judgment of the possible inaccuracies of my investigations and their effect on the 
result. 
Professor W. IT. Miller, of Cambridge, in his valuable researches on the determina- 
tion of the standard pound (Philosophical Transactions for 1856, pp. 811, 827, 937), 
has given full directions for attaining a similar object. These, however, will not 
exactly apply to the systems of weights used by chemists ; for, of the three cases 
described by him, the former two concern a peculiar system of weights, and in the 
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