468 Frederick Guthrie on Eutexia. 



questioned. But that the whole should melt from first to 

 last at any fixed temperature, is so highly improbable as to 

 be practically impossible on account of the simplicity of the 

 proportion. 



According to Matthiessen and v. Bose zinc and bismuth form 

 two alloys, one containing 97*6 of zinc, and the other from 

 8*6 to 14*3 (instead of 7*15), which two alloys are immiscible. 

 The melting-points do not appear to have been given. In- 

 deed, as neither of these is eutectic, so neither has a proper 

 melting-point. 



The nearest approach to an eutectic alloy appears to have 

 been made by Budberg, who, on melting together 177 parts 

 by weight of tin, and 213 of bismuth (tin =45*38 per cent., 

 bismuth =54*62 per cent.), obtained an alloy which is said 

 to have a constant melting-temperature of 143°. Budberg 

 further states that all other ratios have higher melting-points, 

 and that, on cooling, the liquid portion reduces itself to this 

 ratio. The above ratio is intended for that between three 

 "atoms" of tin and two of bismuth. For if the atomic 

 weight of tin be 118 and that of bismuth 210 (Budberg takes 

 tin 56, bismuth 106*5), we should have in Sn 3 Bi 2 the per- 

 centage, tin =45*74 per cent., bismuth =54*26 per cent. It 

 has been shown above that the true eutectic alloy has a melting- 

 point 10° lower than Budberg's, and the composition, tin = 53*9, 

 bismuth =46*1 per cent. 



Again, it is stated that when lead and bismuth are fused 

 together, in the proportion of three atoms of lead to two of 

 bismuth, an alloy is obtained whose melting-point is con- 

 stant at 129°. This ratio requires lead 42*49, bismuth 57*51 

 per cent. The true eutectic alloy has a melting-point 6°*3 C. 

 lower, and, as we have seen, has the composition, lead 44*42, 

 bismuth 55*58. 



The preconceived notion that the alloy of minimum tempe- 

 rature of fusion must have its constituents in simple atomic 

 proportion, — that it must be a chemical compound, — seems 

 to have misled previous investigators. Such misconception 

 could scarcely have arisen if the existence and properties of 

 the cryohydrates had been known. 



§ 206 A. It was shown many years ago (about 35) by my 

 brother Francis, that if two counties are only then supposed 

 to be in contact when they have linear common boundary 

 to colour a map so that no two counties in contact shall be 

 coloured alike, four colours at most are needed. Taking the 

 special case in three dimensions it is clear that five, but no 

 more spheres, may touch one another (each touching all). If 

 there be such things as atoms, and if they be spherical or of 



