132 PRINCIPLES OF CHEMISTRY 



less than at the atmospheric pressure. 26 However, hydrogen, like- 

 air and many other gases which are permanent at the ordinary tem- 



greater extent than is shown by this law, then under great pressures it would attain a 

 density greater than that of solid and liquid substances, which is in itself improbable and 

 even impossible by reason of the fact that solid and liquid substances are themselves but 

 little compressible. For instance, a cubic centimetre of oxygen at D and under the at- 

 mospheric pressure weighs about 0-0014 gram, and at a pressure of 3000 atmospheres 

 (this pressure is attained in guns) it would, if it followed Mariotte's law, weigh 4'2 grams 

 that is, would be about four times heavier than water and at a pressure of 10000 atmo- 

 spheres it would be heavier than mercury. Besides this, positive discrepancies are pro- 

 bable in the sense that the molecules of a gas themselves must occupy a certain volume. 

 Admitting that Mariotte's law only applies to the intermolecular space still we find the 

 necessity of positive discrepancies. If we designate the volume of the molecules of a gas 

 by 6 (like Van der Waals, see Chap. I. note 34), then it must be expected that^> (v b) = C. 

 Hence pv~C + bp, which expresses a positive discrepancy. Supposing that for hydrogen 

 j>y = 1000, at a pressure of one metre of mercury, according to the results of Regnault 's, 

 Amagat's, and Natterer's experiments, we obtain b as approximately 0'7 to 0*9. 



Thus the increase of pv with the increase of pressure must be considered as the 

 normal law of the compressibility of gases. Hydrogen presents such a positive compres- 

 sibility at all pressures, for it presents positive discrepancies from Mariotte's law, accord- 

 ing to Regnault, at all pressures above the atmospheric pressure. Hence hydrogen is, 

 so to say, a sample gas. No other gas behaves so simply with a change of pressure. All 

 other gases at pressures from 1 to 30 atmospheres present negative discrepancies that 

 is, they are then compressed to a greater degree than should follow from Mariotte's law, 

 as was shown by the determinations of Regnault, which were verified when repeated by^ 

 myself andBoguzsky. Thus, for example, on changing the pressure from 4 to 20 metres 

 of mercury that is, on increasing the pressure five times the volume only decreased 

 4'93 times when hydrogen was taken, and 5'06 when air was taken. 



The discrepancies from the law of Boyle and Mariotte for considerable pressures 

 (from 1 to 3000 atmospheres) are well expressed (for constant temperatures) by the 

 above-mentioned formula of Van der Waals (Chap. I. Note 34) ; Clausius' formula is more 

 closely approximate, but as it and Van der Waals' formula also do not in any way express 

 the existence of positive discrepancies from the law at low pressures, and as, accord- 

 ing to the above-mentioned determinations made by myself, Kirpicheff, and Hemilian and 

 verified (by two methods) by K. D. Kraevitch, they are proper to all gases (even to those 

 which are easily compressed into a liquid state, such as carbonic and sulphurous anhy- 

 drides) ; therefore these formulae, whilst accurately interpreting the phenomena of con- 

 densation and even of liquefaction, do not answer in the case of a high rarefaction of 

 gases that is, to that instance where a gas approaches to a condition of maximum dis- 

 persion of its molecules, and perhaps presents a passage towards the substance termed 

 ' luminiferous ether ' which fills up interplanetary and interstellar space. If we suppose 

 that gases are rarefiable to a definite limit only, having attained which they (like solids) 

 do not alter in volume with a decrease of pressure, then on the one hand the passage of 

 the atmosphere at its upper limits into a homogeneous ethereal medium becomes com- 

 prehensible, and on the other hand it would be expected that gases would, in a state of 

 high rarefaction (i.e., when small masses of gases occupy large volumes, or when furthest 

 removed from a liquid state) present positive discrepancies from Boyle and Mariotte's law. 

 Our present acquaintance with this province of highly rarefied gases is most limited, and 

 its further development promises to elucidate much in respect to natural phenomena. To- 

 the three states of matter (solid, liquid, and gaseous) it is evident a fourth must be yet 

 added, the ethereal or ultra-gaseous (as Crookes proposed), understanding by tins 

 matter in its highest possible state of rarefaction. 



26 The law of Gay-Lussac states that all gases in all conditions present one coefficient 

 of expansion 0'00367 ; that is, when heated from to 100 they expand like air; 

 namely, a thousand volumes of a gas measured at will occupy 1367 volumes at 100. 



