Mr. G. K. Akin on the Compressibility of Gases* 295 



Regnault's investigation, and obviating any such intermediate 

 deductions as are described above. 



Before entering, however, on the Appendix, it is necessary to 

 speak yet of a series of apparently casual errors which have crept 

 into M. Regnault's calculations, — those mentioned above being, 

 if we err not, of the class generally designated as systematic. 

 The occurrence of such casual errors was first noticed by Prof. 

 Neumann of Konigsberg (who kindly directed my attention to 

 the matter) in the case of two of the values m belonging to atmo- 

 spheric air obtained in the manner stated in the previous article, 

 by observing that they varied more from the actually tabulated 

 similar values of nearly coincident argument than the difference 

 of arguments might seem to warrant. On reference to the curves 

 on which the m's were professedly measured, the discrepancy, and 

 consequent presumption of mistake, was found confirmed ; and 

 on further extending the examination to the several m's belonging 

 to other gases, and their respective curves, a number of addi- 

 tional disagreements, similar to those first remarked in the in- 

 stance of atmospheric air, were detected. The greatest of these 

 amounts numerically to 0*001 exactly, belonging to CO 2 gas ; 

 but whilst here the divergence is easy to explain, as owing J;o a 

 simple oversight in counting the divisions on the scale of ordi- 

 nates (each of which is =0*001), as regards the minor errors 

 no account can apparently be given. 



A last series of errors (seemingly in writing) is met with in 

 pp. 411, 418, 419, and 424 of M. Regnault's memoir, to which, 

 however, this is not the place to furnish corrections. Similarly 

 it will be sufficient merely to advert to a singular statement in 

 p. 416, referring to the value of /3 or (m — 1) in the case of in- 

 finitesimal values of the argument p Qi which clearly originates in 

 some misapprehension. 



Appendix. 



4. The formula, serving to express the accurate relation be- 

 tween finite volumes and ordinary pressures of gases, in the case 

 specified in art. 1, is due to Prof. Neumann, by whom it was 

 deduced after the following manner, as communicated to the 

 writer. The mass M of a column of gas of the height a and 

 base =1°, is given by the integral 



M 



= \ pdx, . (i) 



where p denotes the density of the layer whose distance from the 

 top of the column, supposed to be a cylinder or prism, is x ; and. 



