in the Velocity of Propagation of Light in Water. 349 



smr,= - sin r, sm r 9 = — sin r„ &c, 

 1 n l v x v > 



Vk • 



smrp ■ sinrn. 



If each of these equations be substituted in succession in 

 the following one, we find that 



smr k = ^sin«; 



that is, the refraction out of a warmed hollow prism into air of 

 T° is just the same as if the ray had passed out of the warmed 

 liquid into air of the temperature of the place of observation, and 

 had only suffered a lateral parallel displacement. 



The atmospheric pressure during the observation varied be- 

 tween 337'" and 330'" (Paris lines), for which we may put the 

 mean value reduced to millimetres*, 755 millims. By means 

 of the formula given on page 348 the relative indices of refrac- 

 tion may be reduced to absolute ones. The correction is 



+ 0-00038 for index of refraction 1*33570 

 4-000038 „ „ 1-32710 



+ 0-00038 „ „ 1-31850 



Consequently we have only to add 0*00038 to all the values con- 

 tained in Table IV. in order to obtain thence the absolute indices 

 of refraction of water for the lithium-, sodium-, and thallium-lines. 



From the numerical values found in Table IV. we get the fol- 

 lowing results. 



(1) The refractive index of water decreases continuously, and 

 therefore the velocity of propagation of light increases continu- 

 ously, from 0° to 80° R., without showing any variation from the 

 law of change at the maximum density. The change of the 

 index of refraction with the temperature may be satisfactorily 

 expressed by means of a formula, 



fiz= a — bt* + ct\ 



At higher temperatures, for the lithium-line at 77° E,., for the 

 sodium-line at 70° R., and for the thallium-line at 61° R,., there 

 are points of contrariflexure. These may be introduced by the 

 nature of the formula, and are not necessarily based upon the 

 actual nature of the phenomena. The diminution of the index 



* A difference of 10'" in atmospheric pressure introduces a difference of 

 not quite one unit in the fifth decimal place, in the calculation of the ab- 

 solute index of refraction ; so that the above introduction of a constant 

 pressure is allowable. 



