Density of Water with the Temperature. Ill 



heat (Thomson, Van der Waals, Tait, and others) we know of 

 the existence of a sort of relation between the pressure and 

 melting-points of ice and the maximum density of water; also 

 that with respect to this last property Amagat demonstrated 

 a lowering of the temperature of the maximum density as the 

 pressure rises * ; but the fact of a change of density being 

 dependent upon an alteration of pressure at different temper- 

 atures, although theoretically admissible, still requires experi- 

 mental investigations, confirming those general laws which 

 govern the volumes of gases and liquids in relation to changes 

 of temperature and pressure. 



The Influence of the Expansion of Solids. — For water as yet 

 we have no determinations of expansion made independently of 

 a change of volume in other bodies (for instance, the containing 

 vessel or solids in general) , because the process of determining 

 the height of columns of water at different temperatures pre- 

 sents practical difficulties which I consider it out of place to take 

 into account here, but which I desire to overcome if it be at 

 all possible. The true volume of water, V*, is determined from 

 the apparent (observed) volume W* by multiplying it f by 

 the changed volume v t of the solid envelope; hence it is evident 

 that however accurate the measuring of the apparent volume 

 be, the resulting V* will include the entire error contained 

 in the expansion of the envelope. As regards the expansion 

 of envelopes, in spite of numerous investigations, there is a 

 great deal of confusion and doubt and more or less improper 

 application. 



1. Very frequently! , in order to obtain the true volume V*, 



* By using formula No. 7, it is easily seen that, as the pressure rises, 

 the temperature of the maximum density falls, and that, at a pressure of 

 1000 atni., it will be far below +4°. Hence it is necessary to consider 

 the pressure when treating- of questions relating to the temperature of 

 the maximum density of water. I may here remark that the solution in 

 water of alcohol, sulphuric acid, salt, &c, also lowers the temperature of 

 the maximum density (and also that of the formation of ice) ; that is, it 

 acts the same as compression. 



t Reg-nault {Relation des exper. i. p. 225) remarked long- ago that the 

 addition of the apparent volume to the increase of volume of the vessels 

 involves an incidental error, because the true expansion is equal to the 

 apparent multiplied by the volume of the vessel. 



X As an example I may cite the determinations of Weidner (Pogg. 

 Ann. I860, lxxix. p. 300). He was, however, f idly justified in having 

 recourse to a simplified method for determining the true volume of water, 

 because his determinations were made at temperatures not differing from 

 0° by more than 10°, and were not distinguished for any great degree o( 

 accuracy. When the temperatures, on the other hand, lie distant 

 from 0° and the precision of the investigation is considerable, then the 

 usual method of finding the true volume from the apparent volume must 

 be abandoned, as it is erroneous in principle and introduces errors 

 which may easily be avoided. 



