390 PROCEEDINGS OF THE AMERICAN ACADEMY § 9 



that wc cannot reh' on these coefficients for the expansion 

 at any temperature, however accurate the volumes may be. 

 Before proceeding to a comparison of the results of our 

 theory with those of observation, let us examine a little 

 more closely into the probable error of the latter. The ex- 

 ample quoted is an extreme case, and we will give Pierre 

 the advantage of choosing the nearest of his two coeffi- 

 cients A, for comparison, thus considerably reducing the 

 difference between the two observers; let us, moreover, 

 take the mean of the coefficients in the case of fusel- 

 oil and butyric acid, by which the agreement will be 

 still further increased; we shall find nevertheless between 

 Kopp and Pierre (by the method of squaring the errors), 

 in the eleven liquids which they have determined in com- 

 mon, a mean difference for the coefficient A of .0000489 

 -)- (between four and five per cent.), for the coefficient 

 J^ a mean difference of .000001318 -|- (nearly fifty per 

 cent.) and for the^ coefficient C a mean difference of 

 .00000001345 -|- (between sixty and seventy per cent, of 

 the average value of the coefficient). 



The details of the calculation are embodied in Table V., 

 in which the figures of Kopp and Pierre are quoted in full 

 from Sharpies. It is thought that the figures will not need 

 explanation. 



§ 9. We are now prepared to make a direct com- 

 parison of theor}' and observation. Table VI. contains the 

 values of A, B and C calculated and observed for 75 

 liquids, which may be identified by means of the numbers 

 Ibllowing their name and symbol in Table XVIII. It was 

 not thought necessary to include in Table VI. the eleven 

 liquids alluded to in the last section, as they are to be sub- 

 jected to a much severer test. Besides these, the only two 

 omitted from thc> table were sulphurous dioxide, which 

 w^as out of the reach of the volume table, and is hardly a 



