in the Velocity of Propagation of Light in Water. 345 



and it was found that 



n,= l-3338-0-000003412* 2 + 0'00000001186* a , . (3) 



a formula which agreed with the observations quite as accurately 

 as the preceding one. An isolated previous observation, how- 

 ever, made it appear probable that for water below 0° the refrac- 

 tive index again diminishes. Bearing this in mind, I imagined 

 that the formula had a symmetrical form, and I finally tried 



fju^a + bfi + ct 4 , 

 and calculated 



n,= 1-3338 -0-000003110^+ 0-0000000001078 * 4 . . (4) 



This formula agrees so well with the observations and is so 

 simple that I determined to adopt it arbitrarily as the one ex- 

 pressing the alteration in the refractive index, and according to 

 which the arrangement was to be attempted. 



Since in n t = a + bft + ci 4 for low temperatures c has only a 

 trifling influence, the indices for 0° were determined from obser- 

 vations between 0° and 10° according to the formula n = a + bt°. 

 These values, moreover, are more correct than the other ones, 

 because, in the first place, the temperature of the liquid is only a 

 little different from that of the surrounding air, and therefore the 

 determinations of temperature are more correct, and, secondly, 

 because, in consequence of this, the refracted images of the lines 

 are much more sharp and distinct, whereby the error of adjust- 

 ment is less. 



In this way, by means of the method of least squares, 



For Li . . 710=1-33154, 

 „ Na . . w = 1-33374, 

 „ Th . . w = 1-33568. 



These values were controlled by the method of least squares 

 according to the formula 



or 



m=bt 2 +ct*. 



Since now both m and t are affected by error, we do not find 



m-bf~-ct 4 =0, 

 but 



m—bt*-ci 4 =8. 



