THE VISCOSITY OF PURE LIQUIDS 587 



total (internal and external) pressure, but this is not found to 

 hold good with other liquids. On the whole, the logarithmic 

 formula 



log?? = log?/, + l(p—p + 7T— 7T.) 



agrees fairly well with the experimental data. 



Arrhenius points out that as the viscosity of liquids under 

 high pressures increases in accordance with an exponential 

 formula, it follows that in the interior of the earth where the 

 pressures are enormous, the viscosity of the magma, which is 

 very viscous even at low pressures, reaches such a high value 

 that it may be regarded as a solid substance when acted upon by 

 sudden changes of pressure — a conclusion rendered probable 

 by other considerations and in harmony with our experience of 

 the propagation of seismic disturbances. 



Dr. Phillips's observations of the viscosity of liquid carbon- 

 dioxide (Proc. Roy. Soc. 87 A, 56, 191 2) in the neighbourhood 

 of its critical point are specially interesting from the circum- 

 stance that we are here concerned with a change of physical 

 state, and a consequent alteration in the direction of change of 

 viscosity with temperature. Gases increase in viscosity with 

 an increase of temperature, whereas liquids decrease. In the 

 case of gaseous carbon dioxide the increase is about 0*35 per 

 cent, for i°C. At or near the critical point the viscosity is 

 nearly independent of the temperature and is dependent only 

 on the density. Arrhenius has discussed these observations 

 and finds that his formula expresses them satisfactorily, not 

 only for the liquid state but also for a short interval of the 

 gaseous condition. It seems very probable that the formula 

 with a change of numerical constant is valid so long as the 

 sum of the internal and external pressures does not exceed 

 220 atmospheres, which is consonant with the fact that vis- 

 cosity is nearly independent of pressure below one atmosphere. 



Attempts to express the change of viscosity with tempera- 

 ture by some simple and comprehensive formula have been 

 made by a number of investigators, but the results, as rational 

 expressions, are not wholly satisfactory. Bingham has sought 

 to connect fluidity, the reciprocal of viscosity, with vapour 

 pressure, and is of the opinion that at a sufficiently high tem- 

 perature the fluid ity of ethers and hydrocarbons is a linear func- 

 tion of the vapour pressure. This regularity is not generally 



39 



