result is confirmed by vapour-density observations. The effect of adding a substance to a solvent is to diminish the vapour pressure of the liquid. Hence, since the boiling-point of a liquid is that temperature at which the vapour pressure is equal to the atmospheric pressure, the effect of adding the soluble substance is to raise the boiling-point, since a higher temperature is required in order that the pressure of the vapour shall equal that of the atmosphere. It has been proved that equal volumes of solutions in the same solvent which have the same boiling-point contain an equal number of molecules of the dissolved substance. The equation for the molecular increment of the boiling-point for a solvent is _d_ = 0.02T²/_w_, in which _d_ is the increment of the boiling-point caused by the solution of one gram-molecule of a substance in 100 grams of the solvent, T the _absolute_ boiling-point of the solvent, and _w_ the heat of vaporisation of the solvent for one gram. The molecular rise of the boiling-point is therefore independent of the nature of the dissolved substance. The molecular weight of the substance _m_ is obtained from the formula _m_ = _pd_/Δ, in which _p_ = the percentage weight of the dissolved substance, _d_ = the molecular increment in boiling-point (0.02T²/_w_), Δ = the observed rise in boiling-point. If the latent heat of vaporisation of the liquid is unknown, the value of _d_ may be obtained by preliminary experiments with a substance of known molecular weight; in this case _d_ = _m_Δ/_p_. The calculation of the molecular weight _m_ may also be made by the formula _m_ = K(_s_/ΔL) × 100, in which Δ is the rise in boiling-point, _s_ the weight of dissolved substance, L the weight of solvent, and K the molecular boiling-point increment. Convenient forms of apparatus for using these methods have been devised by Beckmann, and are now in general use. * * * * * From the time of Berzelius, each successive generation of chemists has striven to better the example of that master of determinative chemistry in the effort to obtain accurate values for the atomic weights of the elements. Among the immediate successors of Berzelius in this work should be mentioned Turner, Penny, Dumas, and Marignac. Dumas in 1859 published the results of an extensive revision of the atomic weights of the elements. On this he based the far-reaching generalisation that, in the language of Prout, “the combining or atomic weights of bodies bear certain simple relations to one another, frequently by multiple, and consequently that many of them must necessarily be multiples of some one unit.” Dumas further agreed with Prout that “there seems to be no reason why bodies still lower in the scale than hydrogen (similarly, however, related to one another, as well as to those above hydrogen) may not exist, of which other bodies may be multiples, without being actually multiples of the intermediate hydrogen.”