867 



whereas K and T^ approach a final value of 0, M goes tlirough a 

 minimum and then rises once more to a limiting value. Similarly 

 there is a maximum- value for A\ above which with a given T it 

 cannot rise ; for higher values of ff K would become negative and 

 T„ imaginarj" ; the limit lies at a higher value, as T itself is larger, 



but compared to T it becomes smaller and smaller, so that — 



becomes itself zero for 7^^oo. 



On the other hand to ever>' finite system of values of K and M 

 corresponds a finite set of values for tf and T. In order to make 

 this clearer a graphical representation of the Tables may be given 

 in a K, ilf-diagram. Here the drawn-out curves are those along 

 which T is constant, the dotted curves those for (^ =: constant. A 



fK ^, A 

 few T^ curves are also given I— =6('».v/. I to which the corre- 

 sponding T curves approach asymptotically. 



8. The Tables and corresponding diagram can also be utilised 



in a more general case ; K must then be replaced by the charac- 



K 

 teristic constant 6', ^ — — and M by the characteristic constant 

 u K' 



(J* = . The values given in the Tables for T, /i, V, « and 



iiT , ^^ uRV '/. 



A = e'~''' are then in general those ot , o/t, , — and e—^''^^, 



fxR^ ?j R 



corresponding to a set of values of C, and C^; from tliose values 



it is thus possible to calculate T,h,V,X and L under other more 



general circumstances. The value of rf as well as that of - nalu- 



^'„ 

 rally remain unaltered. 



The above results can also be used to derive what happens when 

 one of the quantities is gradually altered, the others remaining the 

 same. As an example, without making any eliange in the adjustment 

 of the apparatus, liquids can be taken of increasing viscosity ; in 

 that case 6', does not change, whereas C^ diminishes continually ; 

 Ó and T are then found to increase gradually, V diminishes, A 

 increases and L approaches the value 1. 



