306 A. W. Witkowski on the 



of a. By means of graphical interpolation isothermal s were 

 then drawn, differing but little from the final ones given on 

 PL I. With the aid of these isothermals I constructed 

 another large diagram on which the values of a were col- 

 lected on lines of equal pressure; i. e. temperatures were 

 drawn on the axis of abscissae, the values of a belonging to 

 like pressures formed the ordinates. 



The inclination of these lines to the axis of abscissae could 

 now be used to find the correction which was to be added to 

 the coefficient 0^,-33 say, in order to obtain the value of 

 a p# _35, belonging to another isothermal, but to the same 

 pressure p ( — 35° in this example being the mean value of 

 temperatures in the chloride-of- calcium series). This I did 

 by drawing through the point a Pt9 (experimental value) a 

 short piece of the corresponding isopiestic line, to its inter- 

 section with the ordinate —35°, or any other desired tempe- 

 rature. In most cases these lines were nearly straight ; 

 instead of drawing them I found it convenient to use a glass 

 plate on which a straight line had been drawn with a diamond 

 point. In some cases, however, the corrections were con- 

 siderably larger, so that it was no longer possible to disregard 

 the curvature of these lines ; they were then drawn with 

 reference to the inclination and curvature of the neighbouring 

 isopiestic lines. 



§ 15. Results. — The whole of the results obtained are repre- 

 sented in a graphical form on PL I. The isothermal lines 

 for the nine temperatures experimented on have been drawn 

 by hand along the dots, representing experimental results*. 

 Although some of these dots fall off rather considerably from 

 their respective mean curves, yet, considering the whole of 

 the diagram, I suppose the final results may be considered 

 accurate, at least to four decimals. It is scarcely possible 

 at present to aim at a greater accuracy : this will be admitted 

 on considering the discrepant values of the coefficient of ex- 

 pansion of air given by different experimenters in the relatively 

 simple case of atmospheric pressure and temperature of 

 boiling water. 



From the diagram PL I., drawn on a large scale, I took 

 the mean values of the coefficient a p ^, reproduced in the 

 following table : — 



* In the original memoir extensive tables are reproduced giving full 

 information on the particular data belonging to every experiment. 



