in the Velocity of Propagation of Light in Water. 343 



and a, (2) in the determination of the distances, (3) in the deter- 

 mination of the temperature. 



The measurement of the least deviation may be considered 

 correct to 5" between the temperatures 0° and 10°, where there 

 is no difficulty attending the maintenance of the temperature con- 

 stant. With higher temperatures the errors may easily increase 

 to 30"; and for the highest temperatures, with the thallium and 

 lithium-lines, which were then rather dull, the errors, judged 

 from the results, rise to 1'. Hence, for the lower temperatures, 

 we may rely upon accuracy as far as three units in the fifth de- 

 cimal place. From 10° to the higher temperatures the fourth 

 decimal place may be subject to an error of one unit. Between 

 70° and 80° the error may rise as far as two units of the fourth 

 decimal place, since an error in $ of 1' exactly corresponds to two 

 units of the fourth decimal place in the index. 



The determination of the lengths may also give rise to errors, 

 since the magnitude of the correction yjr depends upon them. 

 An alteration in the greater distance of 10 millims. corresponds 

 to an alteration of 5' in yjr. This error, however, cannot exceed 

 4 millims. The separate measurements of this value agree with 

 one another much more perfectly (see p. 342). An alteration of 

 10 millims. in the shorter distance corresponds to an alteration 

 of 1' 45" in i/r ; but I believe, in my method of determination, 

 the error in this length scarcely reaches 2 millims. Errors in 

 the measurement of length may therefore produce alterations in 

 <f> to the extent of 26" in addition to other errors. The probable 

 error in the angular determination of the prism does not exceed 

 10", as was shown by the agreement of the angles measured for 

 a known temperature. These measurements were the more exact 

 because usually these angular measurements were conjoined for 

 the determination of one of the values given. A deviation of 10" 

 in a causes a possible error of two units in the fifth decimal 

 place of the index of refraction. The errors in the reading or in 

 the correction of the temperature may reach 0°*3, which has an 

 almost imperceptible effect for low temperatures, while for higher 

 temperatures it may cause an error of one or two units in the 

 fourth decimal place. 



V. Correlation of the Results. 



After the observations in Tables I., II., III. had been obtained 

 in the manner described, they were first represented graphically 

 in order to see if any of them were so far removed from regular 

 law as to point to some gross error of calculation or observation. 

 As this nowhere appeared, and as the application of tests showed 

 the correctness of the calculation, I endeavoured to express the 



2 A2 



