4 {Lactose, crystallized 0.38 {Glucose and galactose (.500 g each) 0.39 It is noticed that the agreement for each saccharose is as satisfactory as possible. Numbers obtained with the products of inversion are always a little low by reason of the destructive action of sulfuric acid, and in particular, upon levulose. This is, moreover, quite sensible when the product has to be heated for a long time with sulfuric acid in order to secure a complete inversion. It is evident from the data cited from the papers of Fischer, Maquenne, and others, that the determination of sugars by this method is not a very difficult analytical process and may, in the near future, become of great practical importance. =148. Molecular Weights of Carbohydrates.=—In the examination of carbohydrates the determination of the molecular weights is often of the highest analytical value. The uncertainty in respect of the true molecular weights of the carbohydrates is gradually disappearing by reason of the insight into the composition of these bodies, which recently discovered physical relations have permitted. Raoult, many years ago,[116] proposed a method of determining molecular weights which is particularly applicable to carbohydrates soluble in water. The principle of Raoult’s discovery may be stated as follows: The depression of the freezing point of a liquid, caused by the presence of a dissolved liquid or solid, is proportionate to the absolute amount of substance dissolved and inversely proportionate to its molecular weight. The following formulas may be used in computing results: _C_ = observed depression of freezing point: _P_ = weight of anhydrous substance in 100 grams: _C_ --- = _A_ = depression produced by one gram substance in 100 grams: _P_ _K_ = depression produced by dissolving in 100 cubic centimeters a number of grams of the substance corresponding to its molecular weight: _M_ = molecular weight: _C_ Then we have, _K_ = ---- × _M_. _P_ _K_ is a quantity varying with the nature of the solvent but with the same solvent remaining sensibly constant for numerous groups of compounds. The value of _C_ _A_ ---- _P_ can be determined by experiment. The molecular weight can therefore be calculated from the formula _K_ _M_ = ----. _A_ With organic compounds in water the value of _K_ is almost constant. Brown and Morris[117] report results of their work in extending Raoult’s investigations of the molecular weight of the carbohydrates. The process is carried on as follows: