274 MOREY 



AKT. G 



positive, the denominator remains negative, hence dp/dt is 

 negative. This continues until, in the case we are considering, 

 the phase K20-Si02 makes its appearance at the quintuple 

 point Qi. Consider the metastable continuation of the curve, 

 KaO-SiOs-^HaO + K2O -28102 + L + V (curve 6c). 



Beyond Qi, on further increase in temperature the triangle 

 Am approaches zero, the coefficients of (y' — v^) and (v" — v^ 

 in the denominator increase rapidly, reaching such a value that 

 the sum of the last two terms in the denominator becomes 

 numerically equal to the first, in spite of the large value of 

 (v' — «"). The denominator then approaches zero, and dp/dt 

 becomes infinite. At this point the p-t curve has a vertical 

 tangent. Beyond this point dp/dt again becomes positive. 

 An illustration of this case is found in the p-t curves of the 

 univariant systems, K2O -28102 + K2O - 48102 - H2O + L + V 

 (curve 46), and 8i02 + K2O - 48102 • H2O + L + V (curve 2), which 

 proceed from Qs to higher temperature and pressure. 



26. Coincidence Theorem. On further increase in tempera- 

 ture the hquid will He on the fine, K2O • 8102 - ^H20-K20 - 28102, 

 the area Ani becomes zero, and equation (16) becomes 



^ _ A21V iv' - 7?') - Ally iv" - ■>?0 

 dt ~ A21V W - uO - Aiiv iv" - v^) ' 



At this point the curve has the same slope as the common 

 melting-point curve of (K2O • 8102 • IH2O + K2O -28102), an 

 illustration of the general relation that when a linear relation 

 exists between the composition of n or fewer phases, the p-t 

 curves of all univariant systems containing these phases coin- 

 cide. When all the reacting phases have a constant composi- 

 tion, the curves will coincide throughout their course; when 

 the compositions of some or all of them are variable, and they 

 only casually have such a composition that the above linear 

 relation is possible, then the curves are tangent.* 



Let us prove this in detail for three phases lying on a straight 

 line in a three-component system. Consider the p-t curves 



* F. A. H. Schreinemakers (Proc. Acad. Sci. Amsterdam, 19, 514-27, 

 (1916) and subsequent papers in the same journal) mentions some special 

 cases of this general theorem. 



