§ 9 OF ARTS AND SCIENCES. 39I 



liquid, and phosphorous chloride, which has a coefficient 

 C some thousand times greater than the average (no 

 other liquid exceeding it by more than seven times), thus 

 clearly implying that this substance is an exception, like 

 water, to the general law of expansion.* 



We shall see that the existence of such exceptions does 

 not militate, in any way, against the truth of our theory. 



In the construction of Table VI. the calculated values 

 of ^, B and C were taken by interpolation from Table IV. 

 so as to represent, as correctly as possible, both the vol- 

 ume and coefficient of expansion of the liquid, between o° 

 and the boiling point, using of course the table calcu- 

 lated for the given range of temperature. 



The observed values are taken directly from Sharpies' 

 Tables, omitting however several figures which we have 

 proved to be insignificant; when two values, not differing 

 greatly, were given for different ranges of temperature, the 

 mean was taken. The influence upon the result would in 

 no case be perceptible. 



The diflerences are given for the three coefficients A^ 

 B and C, calculated and observed; and it will be found 

 that the mean difference for A being only .000,003,3, that 

 for ^ is .000,001 -f-? ^incl that for C, throwing out number 

 74, is .000,000,012 -|-, which we see in all cases is less 

 than the mean difference between the two observers al- 

 ready found in the case of the eleven liquids which they 

 determined in common. 



It is proposed to subject these eleven liquids to a still 

 more searching examination. At intervals of 10°, by aid 

 of the empirical formula, 



F= I + ^/ + ^/^ + Ct' 



* The probability of an error, by chance, exceeding the probable error, as in this case, by 

 more than a hundred times was too small to be included in the tables of Chauvenet or in those 

 of Haskell which are appended. 



