of Vapours to Mariotte and Gay-Lussac's Law. 293 



Furthermore we may also see from the above numbers an in- 

 crease of the product p l v l with an increasing temperature. Put 



— - =f(t) and Pi» x = (f>(t) ; then we shall have f{t) and </>(/) 



functions of the temperature t, and increasing with it. The 

 product of these functions, f{t) . <f>(t), or PV, must be a function 

 of the temperature such that PV = const, (a + t), if by (a + t) 

 the absolute temperature is denoted. This relation, as well 

 as the proportionate mode of increase of both the func- 

 tions /(/) and </>(/) when taken at all possible magnitudes, led 

 me to the conjecture that perhaps the assumption f(t) =c V a + t 

 and <f)(t)=c l \Za + t, where c and c x are constant, might fall in 

 with the numbers found. In order to prove this, in the first 

 place I selected some of the observed temperatures in which I 

 had seen with tolerable precision the point of cessation of maxi- 

 mum tension (i. e. I knew the value of i',), and calculated 

 therefrom, as the value of c, c = -059487, on the assumption 

 f(t) = c s/ a + t. With these values I then calculated the value 

 of v x for the other temperatures, where I had not so accurately 

 observed the limit of the maximum tension. The following 

 Table contains the values of v lt as well as the two members of 

 the calculation. 



Table I. a. 



Temperature t 



Mean of the observed I 

 PV } 



Mean PV corrected 

 for the mean vapour- 

 density 1-552 



^a + t 



05 95 V^T= (— ) 



p l v l calculated from ] 



this by the aid of PV. j 



p v mean of the obser- 1 



vations J 



v L calculated from this. 



23° 



30°-5 



36°-4 



41°-9 



47°-8 



57°-8 



62°-9 



69°-9 



10191 



10421 



10625 



10852 



11038 



11391 



11554 



11826 



10183 



10442 



10644 



10834 



11038 



11381 



11554 



11797 



17-205 



17421 



17-590 



17-745 



17-911 



18-188 



18328 



18-518 



102347 



1-03632 



1-04638 



1-05560 



1-06547 



1-08195 



1-09028 



1-10158 



9949 



10076 



10172 



10263 



10359 



10519 



10597 



10709 



50-23 



77-58 



10800 



144-70 



196-50 



315-80 



396-83 



537-63 



1981 



129-9 



94-2 



70-9 



52-7 



33-3 



26-7 



19-9 



Since the accurate determination of v x can hardly be made 

 in this way by experiment, because the tension recedes so slowly 

 from the maximum that the differences of the tension in the 

 neighbourhood of the real v x lie within the errors of obser- 

 vation, and since in the investigation of alcohol I had not so 

 carefully noticed the cessation of the maximum tension, I give 

 therefore, as follows, the extreme limits between which v Y must 

 always fall without directly contradicting the observations ; also 

 I have calculated for these limits the values of c in the formula 



f(t)=c\/a + t. 



