218 Prof. Silas W. Holman on the Effect of 



carbonic acid no results are found giving a value of b (rate of 

 change of r) t : t) with rise of temperature) increasing with the 

 temperature ; that some results can give only a constant 

 value to b, owing either to the want of sufficient precision, 

 or to the insufficient number of temperature intervals em- 

 ployed ; that some results show a marked diminution, as do 

 my own, of b ; and that many of these last, when carefully 

 discussed, afford material for getting at a numerical measure 

 of the change in b which is in substantial accordance with my 

 own results. These facts indicate, either that all measure- 

 ments show conclusively that b does diminish with rise of 

 temperature, or that the method of transpiration through 

 capillary tubes upon which these demonstrations rest (for the 

 measurements with oscillating plates are of insufficient pre- 

 cision for determination of this change) is faulty in either its 

 experimental application or its mathematical theory. In the 

 consideration of this last proposition the statements which I 

 have made at page 205 should be reviewed. 



In the discussion of the results of former observers, I have 

 adopted the graphical method as best adapted to the purpose ; 

 but as the point to be considered is one in which changes in 

 the fourth and sometimes the fifth place of significant figures 

 must be exhibited, a special device must be resorted to. 

 I have therefore assumed for carbonic acid an equation 



^=^1 -f — j, and for air Vt = Vo[ 1 +j^J, as convenient 



equations to which to refer the results on these gases re- 

 spectively. I have computed for two or many temperatures 

 (usually those of observation) values of rj t : r) from these 

 equations, and subtracting these from the experimental data 

 for the same temperature (or from ratios rj t : 7) deduced by 

 myself from the data), I have obtained differences or residuals, 

 which I have used as ordinates in the lines shown in the plots 

 on Plates I. and II. These lines or " residual curves "* 

 easily show the fourth place of decimals in the ratio rjt : t) , 

 and develop as a curvature the change of the rate b. As the 

 residual curves are plotted, convexity upwards shows a 

 diminution of b with rise of /, concavity upwards would show 

 an increase of &„, and no curvature of course indicates a 

 constant value of b. Above and below the 50°, 100°, and 

 200° points of my own results will be seen a vertical 

 row of points marked l°/ , 2 u / , — 1%, etc., which indicate 

 differences in rj t : rj of 1, 2, &c, per cent, from my results, 

 and afford a convenient means of comparing the relative con- 



* See Pickering, Physical Manipulation, i. p. 12 ; Journ. Franklin Inst. 

 lxi. p. 272. 



