and Two New Types of Viscosity. 19 



after they have been divided by the ordinary viscosity 

 7} , is expressed by means of the characteristic function 

 i(tc—t)/(t + 39')\^, which vanishes at the critical tempe- 

 rature and becomes infinite at —39°. The formula of 

 Graetz (Wied. Ann. xxxiv.) connecting viscosity and 

 temperature is 



v = A{t -t)/(t + Q, 



where t n is a temperature usually some tens of degrees below 

 the solidifying point. I have applied this formula to the 

 viscosity of water (" The Molecular Constitution of Water," 

 Phil. Mag. [5] 1.), taking account of the fact that water is a 

 mixture of (H 2 Q) 3 and (H 2 0) 2 , and have found that for 

 (H 2 0) 3 t n is about 33*1. For water as a whole tn is 

 about 39. Hence the right-hand side of (12) is a function 

 whose variation with temperature is closely connected with 

 that of rp and depends upon the ions, as is shown by the 

 difference between b for KC1 and for NaCl in (21). It is 

 very interesting to find the two temperatures t c and t n , which 

 mark the transition from liquid to gas and to solid, playing 

 so fundamental a part in the properties of the liquid as 

 a solvent. 



The data of Noyes and Coolidge enable us to follow up the 

 important theoretical principle involved in (10) and (13), 

 that (1 — X/\ )/(v,n)3 is proportional to 1/KI in dilute 

 solutions ; that is, that KI(1 — X/X^Ky^i)* is constant. But 

 K has not been measured above 80°, and I is unknown. So 

 for the value of K it is necessary to extrapolate by a suitable 

 formula. Drude (Wied. Ann. lix. p. 17) found for K 

 at 0°-2 the value 87*33, and at 76°'3 6282. As K fall 

 nearly to at the critical temperature, I have representee 

 these results by the formula 



K = 0-1315(365-0 + 0-000287 (365 — 2 , 

 with 365° C. for the critical temperature of water. Up to 

 218° this gives results in fair agreement with those of the 

 remarkable formula of Abegg, 



K = 372 e-V™, 

 which applies so well at low temperatures. But on account 

 of the provision for making K small at the critical tempe- 

 rature, I prefer the former formula for present applications. 

 The next Table contains the values of K calculated by that 



formula, the values of (1 — V^cO/Ov 1 )^ f° r NaOl and KC1 

 from Noyes and Coolidge, and those of v the volume of a 

 gram of water at the three higher temperatures from them, 

 with a value for 110° C. inserted by interpolation. The last 



02 



