456 Mr. Owen Glynne Jones on 



Any such equation, fjb = Ae~ kt , means that the percentage 

 variation per degree is constant, since its differential equa- 

 tion is 



-~ = constant. 



fJbdt 



For olive-oil this constant is '0123 and the percentage 

 variation is 1*23 for any temperature within the given limits — 

 about one ninth of the change in the viscosity of glycerine 

 per degree. In this case the thermometer should read to ^ 

 of a degree. It is useless to calculate the viscosity of gly- 

 cerine beyond the fourth significant figure unless there be 

 means for the accurate determination of temperature correct 

 to at any rate *001° C. 



The liquids experimented upon are all bad conductors of 

 heat, and though this is advantageous in that the change of 

 temperature during the course of an observation is not likely 

 to be great, it is a disadvantage in that it takes a long time for 

 the temperature to become uniform throughout the length of 

 the column of liquid. It is quite possible for a difference of 

 temperature of '1 C. to exist at points in the liquid 1 dcm. 

 apart even though the water has been circulating in the jacket 

 for some minutes. 



The temperature can only be expected to be uniform when 

 the circulation has been of constant temperature for about 

 20 minutes. 



But it is of importance to note that small variations in the 

 temperature of the liquid at different points along the path of 

 the falling sphere need not trouble us much if the mean 

 temperature be known. And, similarly, small changes in 

 the mean temperature of the whole during the course of an 

 experiment may be harmless if the mean temperature during 

 the interval be known. 



For it can be proved that the speed of flow of a body is 

 the speed corresponding to the mean temperature, however 

 the temperature may vary along the length, if the speed be 

 small and if the temperature-variation be small. Both these 

 conditions are satisfied in the actual experiments undertaken. 

 The inertia of the body is so small that it almost instantly 

 assumes the limiting speed corresponding to the temperature 

 of that part of the liquid through which it is moving. 



Let the temperature vary from 6 X at one end to 2 at the 

 other end of the column of length I. Let the corresponding- 

 viscosities be juli and ^ 2 > an( ^ ^ and jju be the temperature 

 and viscosity at a point at distance x from the top of the 

 column. 



