260 Mr. M. Ponton's further Researches regarding 



Observed. Differences. 



Oil of cassia . . . 1589241 +0-000054 

 Bisulphide of carbon. 1-6114 -0-000145 



Hydrate of plicnyle . 15377 -0-000195 



Water 1*328 L +0000241 



Alcohol 1-36 -0-000148 



Anhydrous ether . .13529 +0-000748 



These discrepancies, excepting the last, are quite moderate, 

 lying within the limits of probable error for mean observations ; 

 while even the large discrepance in the case of ether is within 

 the probable limits of error for single observations. The indices 

 for oil of cassia and bisulphide of carbon are those from which 

 the best judgment maybe formed; because any alteration of the 

 normal tells more on these indices than on any of the others. 

 The close agreement with observation in these two cases shows 

 that the above value of the normal wave-length corresponding 

 to the line A must be very nearly exact. 



It may be interesting to show the effect of introducing A into 

 the account in the process for correcting the indices. Take, for 

 example, the bisulphide of carbon. Assuming the same ex- 

 ponent as before, ti=2*6, we obtain log €„= 0*2022496, and 

 « n = 0-009543. The indices thence arising differ very slightly 

 from those obtained without taking A into account. The distri- 

 bution of errors is somewhat different. The following are the 

 differences between the calculated and observed values : — 



0-000074 0000017 0-000132 0000000 0-000026 0-00008G 



/-i I IT 



0000302 0000351. 



Seeing that the greater the number of observations on which the 

 calculation is based the more likely are the individual indices to 

 be rendered accurate, the above are probably more correct than 

 those previously obtained without taking A into account. 



It may accordingly be well, in all future observations, to take 

 the deviation of A, as well as those of the other seven principal 

 lines, and base the calculation on the whole eight. This, how- 

 ever, is rather practically expedient than theoretically needful. 

 Had we given only two extreme indices and one central, such 

 as ^A, KD, **H, and could we rely implicitly on their perfect 

 accuracy, it would be easy from these to determine all the other 

 five. It is only because of the imperfection of the present modes 

 of observation, and the consequent impossibility of obtaining 

 absolutely accurate indices for these three lines, that it becomes 

 expedient to take observations on all the eight indices into 

 account, the better to secure a mutual compensation of experi- 



