OF ZINC AND ANTIMONY. 355 



tween the radius o n and twice g u, so that the two centres are at the same distance 

 from the line a h. The whole curve is evidently the result of two forces ; one acting 

 along the chord in the direction b h, a. force tending to increase the amount of anti- 

 mony in the crystals proportional to the amount in the alloy, the same force in fact 

 which acts undisturbed in forming the portion of the curve b a ; the other, the chemi- 

 cal force acting in the direction of the tangent k m. It has already been stated, that 

 crystals having the calculated composition of SbZuj are not first formed in the alloy of 

 the same composition, 33.5 per cent of zinc, but in an alloy containing two per cent 

 less ; so that the line m k, instead of extending to e, diverges from this direction at k, 

 and afterwards runs parallel to the line b h. Unless this fact can be explained by a 

 tendency in SbZn^ to an excess of zinc caused by the influence of SbZuj, as suggested 

 above, the reason of the difi"erence between SbZuo and SbZnj in this respect is not 

 clear ; but as some evidence that it is not accidental, it may be stated that the distance 

 k c equals c i, the last point being the one at which the tangent line m k extended 

 meets the curve. Another remarkable fact, whose bearing cannot at present be seen, 

 but which, like the last, serves to corroborate the general accuracy of the result, was 

 pointed out by my friend and colleague. Professor Peirce, after the plate had been en- 

 graved. The distances of the three most important points of the curve of SbZu^ from 

 the line a h, namely, k d, mf, and u g, are simple multiples of the first ; n g is twice 

 and ??iy three times k d. The curve has been fixed, as will be noticed from the dots, by 

 a large number of points determined throughout the greater part of its length at every 

 per cent, and in the portion m n at every half per cent. They certainly coincide with 

 the curve as closely as could possibly be expected, and the veiy agreement of so many 

 different determinations by three separate analysts is a strong proof of the general cor- 

 rectness of the work. 



By making hypotheses in regard to the nature of the two forces which have gener- 

 ated the curve just described, it would not be difficult to obtain for it a mathematical 

 expression ; but as such hypotheses in our ignorance of the nature of these forces would 

 be premature, I must content myself with ginng its geometrical construction on a 

 chart, ruled like the plate at the end of the memoir. Let the co-ordinates of any 

 point of the curve be x = per cent of zinc in the crystals, and y == per cent of zinc in 

 the alloy. In order to construct the curve of SbZua, find a point {a) of which x = y 

 =: 43 per cent (the calculated per cent of SbZn3), and draw a straight line a b equally 

 inclined to the two axes in the direction from the origin. To construct the curve of 

 SbZn.j, produce the line a bm the opposite direction to the point x =^ y =^ 20, which 

 will be the lowest point of the curve. Find next a point {k) of Avhich x =^ 33.7 per 



