20 PROCEEDINGS OF THE AMERICAN ACADEMY 



will proceed to a review of the results obtained by all others who 

 have worked in this field ; and shall show that for air and carbonic 

 acid no results are found giving a value of b (rate of change of j;^ : j;^ 

 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 in- 

 tervals employed ; that some results show a marked diminution, as 

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

 cussed, afford material for getting at a numerical measure of the 

 change in b which is iu substantial accordance with my own results. 

 These fa(5ts indicate, either that all measurements 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 

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

 experimental application or its mathematical theory. In the consid- 

 eration of this last proposition the statements which I have made at 

 page 25 should be reviewed. 



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

 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 some- 

 times 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 r]t=z rjJl -\^ ^), and for air ,;^ — ,,^, ^ 1 _|- — 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 r}t : j?,, from these equations, and sub- 

 tracting these from the experimental data for the same temperature 

 (or from ratios tj, : r]^ deduced by myself from the data), I have ob- 

 tained 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 ?;, : ?;„, 

 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 t, concavity upwards would show an increase of b, and no cur- 

 vature 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 verti- 

 cal row of points marked 1 f;^, 2 <j;^, — 1 %, etc., which indicate dif- 



* See Pickering, Physical Manipulation, i. 12; Jour. Franklin Inst., Ixi. 272. 



