294 M. Avogadro on the relation of the Density of Bodies 



crease of temperature and positive, the other subtractive and 

 proportional to the square root of this same increase of tem- 

 perature reckoned from a determinate point of temperature 

 for each liquid, or expressed by the ordinate of a parabola, 

 whose abscissa?, reckoned on a diameter of this parabola, are 

 proportional to the increments of temperature. He calls that 

 the minimum of temperature for each liquid, which corresponds 

 to the origin of the diameter of the above parabola, where the 

 ordinate of the parabola becomes nothing, and below which, 

 consequently, this ordinate, and the term of the law of dila- 

 tation which it represents become imaginary, because he sup- 

 poses, that at this point a new subtraction of caloric would 

 augment the temperature anew, in place of farther diminishing 

 it, and would give rise to a new branch of the curve represent- 

 ing the law of dilatation, for which we ought to take the ordi- 

 nate of the parabola with the positive in place of the negative 

 sign. 



Let T be the number of centigrade degrees, which the mini- 

 mum of temperature for each liquid is below the tempera- 

 ture of ebullition of this liquid under the pressure 0™.76 ; d 

 the density of this liquid at this minimum of temperature, 

 taking the density of water at zero as unity ; and g, the co- 

 efficient of the term of the law of dilatation of this liquid, pro- 

 portional to the increase of temperature, or the increase of vo- 

 lume which that liquid takes in virtue of this term for each 

 centesimal degree of the increase of temperature, taking for 

 unity the volume at the minimum of temperature : The densi- 

 ty of this liquid, at its boiling point, such as it would be if its 

 law of dilatation from the minimum of temperature had been 

 expressed by the single term of which we have spoken, will 



obviously be ^ ™. Since the densities are in the inverse 



ratio of the volumes, let m be the mass of the gaseous molecule 



of the liquid, or the density of its gas, taking that of oxygen 



d d 



for unity, the fraction 1 X^T , or jj- — =?— .„ , 



Ji — - — (l-fg-I)m, will express the 



ratio between the density of the liquid in the state supposed, 

 and the density of its gas under a given pi'essure and tempera- 

 ture. 



