256 Mr. M. Ponton's further Researches regarding 



the circumstance that if Powell's index of H be rejected, and if 

 his other indices be treated like Gladstone's, they exhibit the 

 same close agreement with the exponential law, and in like 

 manner conform to the regular type, as respects the laws of 

 extrusion. 



Thus treated, PowelFs observations at temp. 22°*5.C. give, with 

 the exponent w = 3*l, the following values: log e n =(H955608, 

 and a n = 0008324, whence arise these indices : — 



B C D E F G II 



1-589507 1-592902 1-602713 1617366 1-631422 1662470 1-692841 



Excluding H, the differences between these and the observed 



indices are 



B-f- C- D+ E- F+ G- 



0-000007 0000098 0000113 0-000034 0-000042 0000030, 



a result still more favourable than with Gladstone's observations. 

 Powell's observations at temp. 14° C, yield with exponent 

 n=3-4, log e n =0'1979154, and « n =0'006895; but a better 

 equalization of errors is obtained by making #„= 0*006886. 

 Hence arise the following indices : — 



B C D E F G H 



1-594624 1-597724 1-606959 1621213 1*635279 1-667343 1699744. 



Excluding H, the differences between these and the observed 



indices arc 



B+ C- D- E+ F- G+ 



0-000124 0000176 0000341 0-000513 0000521 0000243. 



Those at temp. 10° C, yield with exponent n=3, log e n = 

 0*1971516, and « = 0*008815 ; but a better equalization of errors 

 is obtained by making a =0*008840. Hence arise the follow- 

 ing indices : — 



BCD E F G h 



1-596758 1-600245 1-610314 1625189 1-639332 1670242 1700156. 



Excluding H, the differences between these and the observed 



indices are 



B+ C- D- E-f' F+ G+ 



0-000458 0-000455 0-000086 0000289 0-000432 0000442. 



The differences in these two latter cases exceed those in the 

 two former. Still, they are within the probable limits of error 

 for single observations, and are but slightly in excess of those 

 incident to mean observations. 



In judging of these results, allowance must be made for pro- 

 bable variations of temperature or mechanical agitations occur- 

 ring in the course of the experiments. A change of 1° C. will 

 alter an index in this medium by about 0*001 on an average ; 

 so that a variation of a fraction of a degree, occurring while the 



