( 241) ) 



Sivcn vjilnos of //., and ;.. The op|)ositc case, i. e. that the iniiiiirun]i 

 (lLsa])peai's after the case of (i,o-. G, will lake phace when r/-^ is 

 smaller than tliat valne. 



For, when the minim nni has alreadij (Usappcari'd, the vahie of 



/3' in tig. (6) will be smalkr than -~r-- We must accordinoly 



snbstitute a smaller value of /3' in (1), o,- whal comes lo the same 

 thing, give a higher value lo 7;, i. e. ijicrease the value of /. But 

 it is obvious from the above table that wheii 1 increases, a hhiher 

 value of ip^ will correspond to the same valne of ip.^. 



Let us take as tirst example T, = i ()()(), 1\ = 5(){), r/, = 4500 

 Gr. cal., q, = 250 Gr. cal. ;. is therefore = 7^, (p^ = 4,5 and (/., = 0,5. 

 ,Tlie value oi' (f^ ranges therefore within the interval 4 to 4,91, which 

 holds foi- ;. = V,, so that it is possible, that the minimum disappears 

 in the neh/hJjowhood of (or exactly in) the case of fig. 6. The condition 

 for its disapi^earance for the value of /i' coi-responding to that case, 

 would be that there corresponded to A = 7.^, r/^ = 4,5, according 

 to (4), a value of (p^, given by : 



% (1,2131 —e ' '' lo(, 1,0322 



''- = 0:5--=^: = ^v — = "•"'• 



' » / 18 



So to r/^ = 0,50 corresponds a greater value of (p^ than the one 

 given, viz. 4,5. This value is therefore too loir, and the minimum 

 will disai)pear after the case of fig. 6. 



Second example. Let 1\ be again 1000, T., be 500, but uonv 

 ry, = 3000, ry, = 1000. 



We shall not have to execute any calculation now, as this value tails 

 beyond the interval 4 to 4,91, (p^ being 3 with A = ^/^ ; <;,, is nmch 

 too low to be able to coi'respond with any value of r/., w hate\ei-, 

 and again the minimum will ha\e to disa|)pear when 'the case of 

 fig. 6 occurs. 



If on the other hand T, had been 1000, 7; = 500, ^/^ = 5000, 

 q.^ = 2000, then it Avould be clear without any calculation! that now 

 the minimum luis tdreadij disappeared when the case of fig. (j 

 occurs, 9^.^ = 5 now lying beijoud the interval on the ///v/z^ide. 

 A course as iji fig. 5 therefore becomes now possible, when the 

 value of ^' lies between that of fig. 8 and fig. (>. 



The case of fig. 5, observed among others by Hisslnk in mixtures 

 of AgNO, and NaNO,, belongs therefore to the posslbiUHes, and can 

 occur for given 7;, T, and q„ as soon as y, has a sufficiently 

 hujk value, oi- w hal comes to the same thing, as soon as for given 

 2\, 2\ ajid Y^ the (piaiitily y^ has a sufficiently loiv x'alue. The 



