of Bronzes from Machu Picchu, Peru. 547 



ties of the bronzes under present consideration. They may be 

 used to illustrate the generalizations formulated by Heyn and 

 by Tammann. Following the discussion of these curves from 

 such a standpoint, other significant facts will be pointed out. 



The curves, a, b, and c, of fig. 2, for example, represent the 

 number of grains counted at a magnification of 72 X along 

 a 3%" line superimposed upon the images of polished and 

 etched sections of cold worked, chill cast bronze containing 96 

 per cent copper, after different annealing periods at the respec- 

 tive temperatures, 700°, 775° and 850° C. 



Heyn, from an experimental standpoint, emphasizes the 

 principle of grain size equilibrium as opposed to ordinary equi- 

 librium in terms of the phase rule. According to this principle, 

 the grains, when brought to a given temperature, coalesce at 

 first rapidly and then more slowly until the mean grain size for 

 this temperature approaches a maximum equilibrium value. 

 This characteristic is distinctly seen in the curves mentioned 

 above. Here, the mean number of grains per linear unit, 

 instead of the mean grain size, is plotted against the time of 

 anneal. Obviously either of these graphical relationships may 

 be used equally well for the present purpose. 



Coalescence represents a natural tendency resulting in 

 decreased surface area and a higher order of stability in accord- 

 ance with the principles of energetics. Heyn remarks that a 

 certain mobility of the ultimate particles which constitute the 

 grains is necessary in order that coalescence may occur. This 

 mobility increases with the temperature. Hence the grains 

 can grow more effectively as the temperature is raised. At a 

 given temperature, the grains, after sufficiently long exposure, 

 will reach a size corresponding to the mobility for this 

 temperature. 



The earliest stages of rearrangement and growth in over- 

 strained metal, which are of great interest from a theoretical 

 standpoint, are not dealt with in these generalizations. As will 

 be seen later, the curves in this region are indeterminate as 

 far as ordinary counting methods are concerned. Phenomena 

 of this order are subject only to qualitative interpretation. The 

 later stages, i. e., those actually observed and recorded in 

 graphical form, are clearly defined and may be characterized 

 at any point. Thus, we see that, within certain limits, a given 

 grain size may be produced by anneal at different temperatures 

 when the time factor is properly adjusted. For example, a 

 count of about 12 grains is obtained in a 5-minute anneal of 





