balloon at the temperature t' is, if k be the coefficient of cubic expansion of the glass (free from lead= 00255)— v' = v(1 + k t'). Therefore the weight of an equal volume of air under like cirb' cumstances 1 =·0012932 . v [1 + k t'] · 1 +·00367ť' ' 760 the vapour density D of the body being (without correction for any residual air in the balloon) P' (P-p) D= ·0012932. v. (1 + k t') . 1 b' 760 29. Two important methods based upon the second principle are now in use-viz. the methods of Hoffmann and Victor Meyer, which are based upon the method of Gay-Lussac, now seldom used. Hoffmann's method is applicable to bodies whose boiling point is considerably below 100° C., and whose vapours already follow the laws of Marriotte and Gay-Lussac at the boiling point of water. This excellent method may also be used for the vapour density determination of less volatile bodies, as by the employment of a torricellian vacuum accurate measurements of the volumes may be made at a much lower temperature than the body's actual boiling point under atmospheric pressure. A graduated barometer tube about 1 metre long a (fig. 14) is completely filled with dry mercury and inverted in a vessel full of mercury. The tube is then surrounded by a wider tube b, fitted tightly to it by the cork c. At the upper end of this surrounding tube a tube d is fitted for the entrance of vapour, whilst an exit tube, united to a condenser, is attached to its lower end. A small bottle of 1 cc., or less, content, provided with a glass stopper, is completely filled with the substance under investigation, and the weight P of the contents determined by weighing. The bottle is then sent up the barometer tube, when the stopper is generally expelled by the excess of interior pressure. A good stream of the vapour of some substance of known boiling point is then passed through the annular space between the cylinder and measuring tube, by which the latter and its contents are soon raised to a like tempe rature. The substances generally used in the vapour bath are water for the more volatile and aniline for the less volatile bodies. The liquid contained in the bottle is converted into vapour, depressing the mercurial column. As soon as this has reached a constant position in the measuring tube the volume of vapour v is read off, together with the atmospheric barometric pressure B, the height H of the mercurial column inside the measuring tube and the boiling point of the liquid used for the vapour bath being also noted. When aniline or other high-boiling liquids have been employed, the pressure on the vapour at the temperature t is not simply interior mercurial column being considerably heated and its sp. gr. = B H, the thereby diminished. The height must therefore be calculated to the temperature t' of the exterior air; this may be accomplished approximately by the formula H' = H [1·00018 (t - t')] A correction must also be made for the tension of the mercurial vapour T. This has been determined by Regnault, and can be read off directly from his tables. The pressure which the vapour exerts is therefore BHT. The weight of an equal volume of air under the same condition is 30. A more recent method, that of Victor Meyer, allows of the density of bodies being very accurately determined within very wide ranges of temperature. The principle of the process is similar to that of Hoffmann's, and consists in comparing the weight of an equal volume of air with that of the substance in the gaseous state. The apparatus employed is shown in fig. 15. The bulb a of the vapourisation tube A is immersed in a cylindrical vessel containing a liquid to serve as bath; this latter is heated until a constant temperature is attained, when the substance-about 1 grm.-previously weighed in the small tube e, 10 to 20 mm. long and 2 to 4 wide, and lightly held on the bent wire g passing through the cork of the a vapourisation tube (shown on an enlarged scale at B, fig. 15), is allowed to fall to the bottom of the 6 FIG. 15. A B f h 2 wide portion by slightly rotating the wire. As soon as the substance arrives at the heated portion of the tube, it passes into the vaporous state, and expels an equal volume of air by the side tube d, which is received in a measuring tube over water, and its amount read off, temperature and pressure being noted. The temperature in the vapourisation tube need not be accurately known, only that it be sufficiently high for the whole of the substance to be in a gaseous state. For very high temperatures the wide portion of the vapourisation tube must be of platinum or porcelain, and the bath, instead of water, aniline, &c., may be melted lead, or for the highest temperatures a small reverberatory gas furnace. The abbreviated formulæ where D = density sought, 8= weight of substance used, (B-w)= barometer minus tension of water vapour at to, the temperature of observation reduced to 0° C., v = volume air in c. centim., ·0012932= weight of 1 cc. air at 760 mm. B and 0° C., t°= temperature of room or air in measuring tube, will give the required density with sufficient accuracy. RATIONAL FORMULE AND ORGANIC RADICALS. 31. The molecular formula of an organic compound shows which elements and what number of atoms of each are contained in the molecule, without expressing the order and method of their union. The study of chemical changes shows that in the greater number of organic molecules, atoms of any ingredient elements can be replaced singly or in groups-with differing ease, by other elementary atoms, or eliminated without replacement, and that they must be united with varying degrees of firmness. In order to express this fact in the formula, the symbols of the respective elements are not written once only, but repeated as frequently as may be required to indicate the varying degrees of firmness of union. The number of atoms in each particular form of union are expressed in the usual manner. Formulæ modified in this way are termed rational formula. In such rational formulæ there must evidently exist some groups of atoms which suffer no change during a given reaction; such an unattacked residue or constituent common to both the original and derived body is termed a radical, and when it contains carbon it is termed an organic radical or residue. An example will easily demonstrate these statements. Ordinary (ethylic) alcohol whose formula is C2H6O gives up one of its six hydrogen atoms when treated with sodium, being thereby converted into the body C,H,NaO. In this reaction the group C2HO remains unchanged, and is therefore the radical of ethylic alcohol, and the rational formula would be C2H2O.H. This body is, however, capable of further changes; by treatment with ozone or with easily reducible bodies, it loses two hydrogen atoms, without replacement, being converted into aldehyde, C2H,O, which can further take up an additional atom of oxygen, yielding acetic acid. From this the rational formula of alcohol is C2H2O.H2, in which the group C2H2O appears as the radical. By numerous decompositions groups of different elementary atoms are simultaneously removed from the original compound. By the action of hydrochloric acid, alcohol is changed into the body C2H,Cl and water, having its oxygen atom, together with one of the hydrogen atoms, removed, and only a single chlorine atom entering in their place. This reaction leads to the formula C2H5.OH, 5 in which the organic radical C,H, (ethyl) is united to the inorganic radical OH (hydroxyl). An organic compound can have in this way different rational formule, corresponding to the different methods in which it suffers decomposition. Rational formulæ of such a kind are only reaction or decomposition formula. Both the reaction formulæ for ethylic alcohol, C2H ̧.OH and C2H2O.H, can be united into the single formula C2H.O.H, from the fact that the atom of hydrogen replaced by solium, is no other than the one which is expelled simultaneously with oxygen by action of hydrochloric acid. = C2H5.O.H+Na C2H5.O.Na + H C2H.O.H+ HCl = C2H5.Cl + HOH. By this the united rational reaction-formulæ obtain a further significance. The actual connection of this hydrogen atom to the oxygen atom can only be that both are united together, that the monad H is united to the organic residue C2H, by means of the dyad O. The rational formula C,H,.O.H expresses the order of combination of at least two atoms in the alcohol molecule, as well as certain decomposition possibilities, and becomes therefore a constitutional formula. Similarly to the oxygen and one hydrogen atom of the ethylic alcohol, the method of union of the elements composing the radical CH, may be settled by the study of reactions of greater extent, not alone by decomposition processes, but also by the reverse-synthesis, the building up of the organic compound from simpler bodies, or even from its constituent elements. Alcohol, as already mentioned, is converted by oxidation into acetic acid, C2H,O,. In this, by treatment with phosphoric chloride, one hydrogen and one oxygen atom are replaced by one chlorine atom, the body C,H,OC1 being formed. Acetic acid has, therefore, the hydrate formula C2H2O.OH. If its sodic salt C2H3O.ONa be submitted to dry distillation with sodic hydrate, NaOH, a residue of sodic carbonate, is left, and marsh gas, CH4, is evolved. According to the equation: C2H3O.ONa+ NaOH= CO,Na2 + CH, the sodic carbonate obtaining CO,Na, the marsh gas CH3, from the sodic acetate. The reaction is expressed completely in accordance with the facts by the rational formulæ : CH3-CO.ONa+ HONa = CH2H + CO.ONa.Na. From this it is highly probable that in acetic acid three hydrogen atoms are united to one carbon atom, the two oxygen atoms, and by means of one of them the fourth hydrogen atom, to the other carbon atom. Numerous other reactions lead to the same conclusion. The detailed constitutional formula obtained for acetic acid in this way, leads to the further conclusion that in ethyl alcohol also the same group, CH,, must occur, and makes it probable that the constitutional formula is CH3.CH2.OH. Complete confirmation of this view is obtained in the synthesis of ethyl alcohol from marsh gas. On exposing a mixture of this gas and chlorine to diffused daylight, |