228 J.P. Cooke on the Law of Definite Proportions 
By making hypotheses in regard to the nature of the two forces, 
which have generated 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 giving its geometrical 
construction on a chart ruled like the plate illustrating the me- 
Let the coérdinates of any point of the curve be, x = per 
cent. of zinc in the crystals, and z = per cent. os zine in the al- 
loy. In order to construct the curve of Sb Zns, find a point 
(a) of which e = z = 43 p.c. (the calculated i cent. of Sb 
Zo) and draw a straight line a 6 equally inclined to the two 
axes in the direction from the origin. T'o construct the curve of 
Sb Znz, produce the line ad in the opposite direction to the point 
xz = z = 20, which will be the lowest point of the curve. Find 
next a point (k).of which ¢ = 33:7 p. c. (the calculated per cent. 
of Sb Zna is 33:5) and aie p. ¢., which is one-half of 
43 +20. ‘Through this point draw a line mk parallel to the 
axis of ordinates and intersecting the line abhat c. The line 
m tis the tangent, ee me line 6 A the chord of the required are. 
On the line mi take ci = = ck, and 7 is the point at which the are 
should touch the Sant Erect a perpendicular on the tangent 
at the point ¢, take o¢ = 3 bh, and from o as a centre, with a ra- 
dius = 01, describe the arc hi. Also from the centre o let falla 
perpendicular o g on the chord } A, and pense it to a point o’ 
making o It will intersect the arc at (m). From o/ as 
a centre with a radius o’ m describe a second arc n m intersecting 
the tangent at m. Finally, draw from &, a straight line & é, paral 
lel to 6h, then the broken line 1k mmnh will be the required 
curve 
It will be noticed that the tangent ehh has been drawn 
on the plate through the points determined by analysis is two- 
tenths of a per a3 in advance of the line which would corres- 
pond to Sb Znz. This position is essential to the equality of k ¢ 
i ci, if we retain as the value of the radius of the larger are 
R=3bh. If the analyses should have given erroneously too 
much zine so that the true position of the line should be at r= 
33°5 per cent., then this equality would be destroyed, and the con- 
ditions for finding the centre o would be reduced to the coérdi- 
nates of the point A, the length of the radius and the position of 
the tangent, from which by a very simple construction the curve 
might be drawn. It should however be remarked that the posi- 
tion of the tangent in advance of the line x = 33:5 is in accord- 
ance with the fact, already noticed, that the crystals of Sb Zuz 
have throughout a proneness to an excess of zinc caused appa- 
rently by the infuence of Sb Zn : but it is also true that the 
Fonte of the error in the zinc determinations is in the same 
