~Raoult's laws.~ Two laws have been discovered which give us just such information. They are known as Raoult's laws, and can be stated as follows: 1. _When weights of substances which are proportional to their molecular weights are dissolved in the same weight of solvent, the rise of the boiling point is the same in each case._ 2. _When weights of substances which are proportional to their molecular weights are dissolved in the same weight of solvent, the lowering of the freezing point is the same in each case._ By taking advantage of these laws it is possible to determine when two solutions contain the same number of molecules of two dissolved substances, and consequently the relative molecular weights of the two substances. ~Law of Dulong and Petit.~ In 1819 Dulong and Petit discovered a very interesting relation between the atomic weight of an element and its specific heat, which holds true for elements in the solid state. If equal weights of two solids, say, lead and silver, are heated through the same range of temperature, as from 10 deg. to 20 deg., it is found that very different amounts of heat are required. The amount of heat required to change the temperature of a solid or a liquid by a definite amount compared with the amount required to change the temperature of an equal weight of water by the same amount is called its specific heat. Dulong and Petit discovered the following law: _The specific heat of an element in the solid form multiplied by its atomic weight is approximately equal to the constant 6.25._ That is, at. wt. x sp. ht. = 6.25. Consequently, 6.25 at. wt. = -------- sp. ht. This law is not very accurate, but it is often possible by means of it to decide upon what multiple of the equivalent is the real atomic weight. Thus the specific heat of iron is found by experiment to be 0.112, and its equivalent is 27.95. 6.25 / 0.112 = 55.8. We see, therefore, that the atomic weight is twice the equivalent, or 55.9. ~How formulas are determined.~ It will be well in connection with molecular weights to consider how the formula of a compound is decided upon, for the two subjects are very closely associated. Some examples will make clear the method followed. The molecular weight of a substance containing hydrogen and chlorine was 36.4. By analysis 36.4 parts of the substance was found to contain 1 part of hydrogen and 35.4 parts of chlorine. As these are the simple atomic weights of the two elements, the formula of the compound must be HCl. A substance consisting of oxygen and hydrogen was found to have a molecular weight of 34. Analysis showed that in 34 parts of the substance there were 2 parts of hydrogen and 32 parts of oxygen. Dividing these figures by the atomic weights of the two elements, we get 2 / 1 = 2 for H; 32 / 16 = 2 for O. The formula is therefore H_{2}O_{2}.