Isometrics relative to Viscosity. 93 



8. Viscosity and Temperature. — It is next in place to find 

 a suitable expression for the relation of viscosity to tempera- 

 ture. Contrary to my expectations this was comparatively 

 easy ; and the reason seems to be that so long as pressure is 

 constant, the error due to slipping is less liable to change. 

 An example of the results worked out from triads as above, 

 and obtained with screw tubes is given in the following tables. 

 Ap = 505 atm. 



Observed. 



Computed 





Observed. 



Computed. 



Temperature 77/IO 9 



7?/l0 9 





Temperature 



7//10 9 



??/10 9 



12° 7-70 



7-78 



A— H'895 



15° 



8-15 



8-13 A = 12-385 



14° 3-75 



3-G1 



B= -167 



17° 



3-82 



380 B— -165 



16° 1-61 



1-67 



770 = 7-8 x 10" 



19" 



1-72 



1-78 r/ =:2-4 x 10 12 









21° 



•81 



•83 









23° 



•42 



•39 



It is seen at once that within the range of observation (12°- 

 16° C, 15° to 23° C.) temperatures increase in arithmetical 

 progression while viscosities decrease in geometrical progres- 

 sion. Hence (2) log q g = ^°gy n — ' an( ^ ^ e ^ ac ^ or & 

 has the large value, - 165. Of the two sets of data given, the 

 initial viscosity, -q Pt0 is fully three times larger in one case 

 than in the other. Nevertheless the quantity B is practically 

 the same in both. For this reason I shirked the great labor 

 attending experiments at higher pressures and concluded con- 

 formably with the suggestions of the preceding paragraph, 

 that as a first approximation the rate at which viscosity in- 

 creases with temperature at the temperature 6°, is proportional 

 to the viscosity at 6°, and is independent of pressure. 



9. Summary and chart. — With the principle thus laid down 

 I am able to give a graphic exhibit of the isothermals and the 

 isopiestics. This is done in the chart, figure 3, where the 

 ordinates are absolute viscosities, and the abscissas, pressures 

 and temperatures respectively. The isopiestic for p = 250 

 atm. is directly observed between 15° and 23°. The other 

 curves are computed from this by aid of the coefficients deduced 

 in §§ 7, 8. The range as a whole may be taken as that of the 

 present experiments. The (computed) initial viscosity ^ 00 (for 

 p = and 6 = 0) is very nearly 10 12 . As usual p = Ap/2. 



10. Isometrics. — From these data the isometrics may be 

 constructed graphically and in this way the curves marked q 

 were obtained. I am now able to answer some important 

 questions as to how temperature and pressure must vary, in 

 order that viscosity may remain constant. Equations (1) and 

 (2) lead easily to 



(dp/dd) = (In 10) B (I +bp)/b (3) 



Hence the isometrics are all identical as to contour and ob- 



