The determination in the case of solids lighter than water is effected by the introduction of a sinker, i.e.
Nitzsch, Dillmann, Ritschl and Sinker are convinced that the book was not a translation but was written originally in Greek.
If W be the weight of the experimental solid in air, w the weight of the sinker in water, and W, the weight of the solid plus sinker in water, then the relative density is given by W/(W+w - Wi).
A number 10 line weighs the same whether its a fast sinker or a floater.
All that talk about purity - and I swallowed it hook, line and sinker.