PAPER BY PROF. BEZOLD. 263 



If now for a given value of Ei = K>, which may be called Rq, the point 

 of saturation is to be just attained by proper mixing, then the straight 

 line P Fi F2 must just touch the saturation curve Fi' F/. 



The point of taugency aS' gives therefore the temperature of the mix- 

 ture for which saturation will be just attained, and hence also the mixing 

 ratio. 



But the value R(,^ as the figure shows at the first glance, must be 

 exceeded by at least one of the components when condensation is to 

 become possible, and it therefore is precisely 

 that limiting value that is desired in question 

 No. (1). 



It is easily seen that the knowledge of these 

 boundary values is of high importance, it is 

 therefore carefully considered in tables to be 

 subsequently communicated. Equally simple J^ ■ 

 is the solution of the second question, which, 

 however, will here be considered only under 

 the special assumptions that Ri or i?2 is equal 

 to 100. 



If i^i = 100, that is to say, if the cooler of the two components is in the 

 state of complete saturation, then we obtain the minimum value of B2, 

 when we, as in Fig. 40, draw at Fi' a tangent to the saturation curve, 

 aud i)rolong this until it cuts the ordinate F-z' Ti at the point F2. The 



77" T 



desired value is ii^2=100 ^^ J , • As soon as J?2 exceeds this limit con- 

 densation occurs on mixing, provided that there is sufficient of the colder 

 component, that is to say, provided — i is large enough. 



If, however, we consider the other case as given and assume that 

 i?2=100, that is to say, that the warmer component is saturated, then 

 we find Ri when at F2' we draw a tangent to the saturation curve and 

 seek the intersection of it with the oidiuate Fi' Tj. 



Thus it becomes at once apparent to the eye that Ri is always smaller 

 than R2, so that for sufficiently great distance between Ti and T2 the 

 quantity Ri can even attain a negative value, if such were imaginable. 



The physical interpretation of this is that when warm saturated air 

 is mixed with colder the latter can have a high degree of dryness and 

 still condensation may occur for a proper mixing ratio; in many cases 

 even the cooler air may be absolutely dry; it might even have a nega- 

 tive Ri corresponding to its containing a certain mass of hygroscopic 

 substance, if only there is sufficient quantity of warmer air, that is to 



say, if only — is large enough. 



In such cases, therefore, in place of the minimum value Ri there 



occurs a limiting value of /i = —' which must be exceeded if conden- 

 sation is to occur. 



