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•6
ON
\V
AN  APPARENT  PERTURBATION
LAW  OF  DEFINITE  PROPORTIONS
OBSERVED  IN THE COMPOUNDS OF
ZINC   AND  ANTIMONY.
Bt JOSIAH P.  COOKE, Jr.,  Cambridge.
[Extracted from the American Journal of Science and Arts, 2nd Series, Vol. XX,
  Sept. 1855 ; from a Memoir of the American Academy, New Series, vol. v, p. 337. ]
      NEW  HAVEN,
PRINTED BY EZEKIEL HAYES-
           . 1855, 
c nVo
  1255
5" 
ON  AN  APPARENT  PERTURBATION, &c.
  In a former paper in this Journal* I described two new com-
pounds of zinc and antimony Sb Zns and Sb Ztia which I named
respectively, Stibiotrizincyle and Stibiobizincyle, because they re-
semble in their composition the metallic radicals of organic chem-
istry, and because the first decomposes water rapidly at 100° C.
I there stated  that crystals of Sb Zns could be obtained contain-
ing a much larger amount of zinc than  that required by the law
of definite proportions, and that this change was not accompanied
by any alteration of crystalline  form.  A similar variation of com-
position was afterwards observed in the crystals of Sb  Z112, and
it is the object of the present paper to describe the law of the va-
riation in both cases and  to explain its cause.
  In the course of my investigations on this subject, crystalliza-
tions  were made or attempted of alloys differing in composition
by one half to five per cent., according to circumstances, from the
alloy containing 95  per cent, of zinc to that containing 95 per
cent,  of antimony ; but only two crystalline forms were observed,
that of Sb Z113 and that of Sb  Zn2.   Well defined crystals, like
those described under Sb Zn2  in  the former paper,f  were ob-
tained from the alloys between  43 and 60 per cent, of zinc;  and
even  in alloys of a higher zinc per-centage, crystals of the same
form were still seen, although they were no longer well defined.
In the alloys between 20 and 33 per cent,  of zinc, well  defined
crystals,  like those described under  SbZti2 in the same paper,
were  formed ;  and finally there  separated from the alloys between
33 and 42 per cent, of zinc thin metallic plates, which  evidently
belonged  to  the  same crystalline  form.  In making the alloys
from  43  to 95 per cent, of zinc, the  zinc was  melted first,
* This Journal, voL xviii, p. 234.        f Ibid. 
4      J. P. Cooke on the Law of Definite Proportions
and  when in fusion  the antimony was  added.  As  the melt-
ing point of antimony is much above that of zinc, the fluid zinc
acted on  the  solid antimony as  a  solvent,  dissolving the  pure
metal, but not the impurities, which rose to  the surface forming
a scum.   This scum  seemed  to take with it  some of the anti-
mony and thus caused a loss, which, together with the impurity,
was  found by experiment to be about three per cent, of the an-
timony used.  This resulted  in raising the  per-centage of zinc  in
the alloy at  most  about eight-tenths of one per cent.  The alloys
below 43  per cent, of zinc were made by melting the  antimony
first, and then adding  zinc.  By this method the loss of antimony
was  very greatly diminished, and,  counting the impurity, was
found to be  only  about one per cent, and a half of the  antimony
used.  In preparing the alloys this loss was  always allowed for,
and the crystallizations were all made as nearly as possible under
the same  circumstances, so  that any unexpected cause of error
should affect all equally.   The crystals formed in the alloys were
all analyzed in my laboratory under my direction and immediate
supervision,  and the greater  part of them  by myself.   The rest
were  by my assistants,  Mr.  F. H. Storer,  Mr. C. W. Eliot, and
Mr. C. S.  Homer, to  whose  care and accuracy I take pleasure
in bearing witness.  Their work is  in  all  respects as reliable as
my own.  The results are collected in the following  table which
will explain itself.

     Analyses of the Crystals formed in the Alloys of Zinc and Antimony.
STIBtfl			TRIZIN mpo»it	CYLE.		STIB10B1Z1NCYLE.				
Composition		Co		on of		Composition Composition of				
•if the Alloys		the Crystals by			Name	of the Alloys the Crystals by				Name
by Synthesis. Perct Perct.		Analysis.			of th* Analyst.	by Synthesis.		Analysis.		of the Analyst.
		Perct. Perct., c ,				Perct.	Per ct. Per ct.	Per ct. 0___		
of Zn.	of Sb.	of Zn. 64 15	of Sb.! -3U""			of Zn.	,)f Sb. of Zn.	ot Sb.	9994	
70-40	29 60		35-77] 99-92		Cooke.	33-00	67 00 35-37	64-57		Cooke.
66 50 3350		61-00	3900	*ioo-oo	Cooke.	do.	do. 35-40	6460	+ 10000	Cooke.
64-503550		53 50	4144	9994	Cooke.	32 50	67-50 34-62	6492	99-54	Storer
. . . .		55-49	4442	9991	Homer.	do.	do. 34-61	6539	+ 100-1.0	Eliot.
60-6039-40		55-00	4509	10009	Homer.	31-50	6850 33-95	6609	100 04	Storer.
586041-4O		50-39	49 29	99-68	Eliot.	29 50	70-50 3362	66 38	+too-oo	Storer.
5660 43 40		49-92	50-05	99-97	Eliot.	do.	do. 33 62	6638	+ 100 00	Storer.
5470 45-30		4826	5142	99-68	Storer.	27-50	7250 33 85	65 81	99-66	Storer.
52-70 47-30		47-47	5253	fioo-oo	Cooke.	26 50	73-50 32 08	67 60	9968	Storer.
						26-00	74-00 30 74	69-06	99-80	Cooke.
50-70 49-30		4689	53-11	+ 10000	Cooke.	25 50	74 50 30 43	69-51	9994	Storer.
do. | do.		46 45	53 55	j-100-00	Cooke.	2500	75 00 29 88	/0-20	10008	Cooke.
48-70 51-30		48-66	5134	f 100-00	Eliot.	2450	75 50 28-76	71-24	100 00	Cooke.
46-70 53 30		46-77	53-23	+ 100 00	Eliot.	23-50	76 50 27-93	71-85	9978	Cooke.
44-80 55-20		44-265573		+ 100-00	Eliot.	2250	77-50 2662	7327	99 89	Storer.
43-80 5620		44 04j55-96		+ioo-oo	Cooke.	21-50	7850 24 83	74-74	9957	Cooke.
42-80 58-20		43-15 56-93		100 08	Cooke.	20-12	79-88 20-58	79-42	100 00	Cooke.
do. j do.		43-06 56 50		99-56	Cooke.					
do. | do.		42-83 57 24		100 07 Cooke.						
* In this analysis the antimony only was determined.
f In this analysis the zinc only was determined. 
in the Compounds of Zinc and Antimony.         5
  Curve of Variation in Composition.—In  order to compare to-
gether the composition of the crystals and that of the alloy in
which they form, I have resorted to the usual method  of Analyt-
ical  Geometry,  and  in  the  plate illustrating  this  paper,  the
lower horizontal line is the axis of abcissas,  and the vertical line
at the extreme  left the axis of ordinates.  The first has been
divided into equal parts, which denote  the  per cents, of zinc in
the  crystals  and the last  into  parts of  the same size,  which
stand  for  the  per cents,  of zinc in  the  alloys.   The  zinc
rather  than  the antimony determinations  have  been selected
for  comparison, as being generally more accurate, and as  hav-
ing been  all made in exactly the same  way.   The  points de-
termined by analysis are indicated with dots, and the  double line
drawn through these dots is a curve, which represents  the relation
of the composition of the crystals to that of the alloy in which
they form.   In order to make clear the connection between the
two, it will be  well to discuss this curve, commencing with what
may be termed the two  centres of crystallization,  the alloys of
42-8 and  315  per cents, of  zinc, and examining the  effect pro-
duced on the crystals by diminishing or  increasing the amount
of zinc in the alloy.
  It has already been stated  that the  crystals of Sb Zti3 are ob-
tained in their  greatest  perfection from  the alloy of 428 p. c.
of zinc.  They are then comparatively large, generally aggrega-
ted, and, as the three analyses cited  in the former paper prove,
have the same  composition as the alloy.   On increasing gradually
the  amount of zinc in the alloy up to 487,  the crystals continued
to  have the composition of the  alloy,  and the  only difference,
which could be observed in  their character, was, that they were
smaller  and more frequently isolated.  Between these  limits,
the  whole mass of the alloy exhibited a strong tendency to crys-
tallize, and, by pouring it, as it cooled, from one vessel to another,
it could be crystallized  to the last drop.   The portion  a, b, of the
curve is therefore a straight line equally inclined to the two axes.
On  increasing the amount of zinc in  the alloy to  50-7 p. c, the
amount of zinc found  in the crystals was  only 46 89 p. c, and
above this it was uniformly less than  it  was  in  the  alloy ;  but no
closer relation  between the  two could  be detected, owing un-
doubtedly to the unavoidable irregularity in the crystallizations
of  the alloys, which contained more  than 50 p. c. of zinc.   This
arose from a peculiar pasty condition, which  the fluid mass as-
sumed, at the  point of crystallization,  apparently caused by the
separation of the excess of zinc.   Definite crystals  however were
obtained even  from the alloy of 60 p. c. of zinc, which contained
55 p. c. ; above this, the crystals became less  and  less abundant,
and gradually faded  out, although the alloy even of 86 p. c. of 
 6      J. P. Cooke on the Law of Definite Proportions

 zinc exhibited a radiated crystalline texture ;  and a trace of this
 structure  could  still be discovered  even in  the alloy containing
 only 4 p.  c. of antimony.   It might  be supposed  that on return-
 ing to the alloy  of 428 p. c. of zinc, and increasing the amount
 of antimony we  should obtain crystals  containing an excess  of
 antimony ;  but so far is this from  being true that  the  slightest
 excess of antimony entirely changes the  character of the  crys-
 tallization.  On crystallizing an alloy containing 418 p. c. of zinc
 not a trace of any prismatic crystals  could  be seen, but in their
 place there was found a confused  mass of thin  metallic scales,
 which, as  will soon be shown, are imperfect crystals of Sb  Zii2.
 Thus it appears that although perfectly formed crystals of Sb Zns
 can be obtained containing 55 p. c.  of zinc they can not be  made
 to take up the slightest excess  of antimony.
  In order to obtain crystals having  the composition of Sb  Zn2,
 that is, containing 33-5 p. c. of zinc, it is necessary to crystallize an
 alloy at least as low as 315 p. c. of zinc.  At this point  large  com-
 pound crystals are obtained corresponding to  the large  crystals of
 Sb Zii3.   0;i increasing the amount of zinc in the alloy up  to 33
 p. c, the proportion of zinc in  the crystals appeared to increase in
 the same  ratio,  so that the curve of Sb Zti2 is  at  this part a
 straight line parallel  to the curve of Sb Zti3.   It should however
 be noticed that the extent of this line k i is so limited  that a very
 small error in the analyses might change very considerably its di-
 rection.   The crystals of -Sb Zna containing an  excess of  zinc,
 are smaller and more frequently isolated  than those  containing
 exactly two equivalents.  A similar  fact, it will be remembered,
 is true of the crystals of Sb Zn3.   At the alloy  of 33  p.  c. of
 zinc, the definite crystals of Sb Zns  begin to disappear  and are
 succeeded by thin metallic scales, which, as the two following facts
 will prove, are imperfect crystals of the same crystalline  form.
 First, the  scales from  the alloy of  33 p. c. are frequently found
having a definite  crystal as a  nucleus, when it  is evident that
their surfaces are extensions of the basal plane O of fig. 2 of the
former memoir.  Secondly, the scales twin together like the  large
tabular crystals of  Sb Z112,  forming  a cellular structure, and the
angle  between two scales thus  united, measured with an applica-
 tion goniometer approximately  115° 30', and was  therefore  equal
 to the basal angle  of the definite crystals.  These scales continue
 up to the alloy of 418 p. c. of zinc, becoming however constantly
less abundant and  less  distinct.   Several specimens of them were
analyzed,  but no regularity in their composition could be  detected
except that they all contained a very much larger amount of zinc
than the alloys in  which they formed.   This irregularity and the
imperfection in  the crystallization  seem  to  be  caused by the
interference of Sb Z113, that is, by  a tendency to form  Sb Zri3
which exhibits itself in a proneness of the crystals of Sb Zns  to 
          in the Compounds of Zinc and Antimony.         7

an excess of zinc.  The line ki has been continued with dots in
order to show that the influence of  Sb Zti2 extends as far as the
alloy of 42-S p. c. of zinc.   On returning to the alloy of 31-5 p. c.
of zinc and adding an excess of antimony it was fonnd  that the
crystals formed continued to have the theoretical  composition of
Sb Zna until the amount of zinc in the alloy had fallen to 27 p. c,
so that the tendency towards the  theoretical composition was so
great, that in the alloys between 31*5 and 27  p. c. of zinc, crystals
were formed having very nearly this composition.  On still further
increasing the amount of antimony in the alloy, the composition of
the crystals  gradually approached that of the alloy, and  from the
alloy of 20 2 p. c. of zinc, very imperfect crystals were  obtained
having almost the same composition as the menstruum.   At the
same time, the crystals became less and less perfect  and  finally
disappeared altogether in the alloys below 20 p. c. of zinc.
   The portion of the curve k mnh, is the most important result
of this investigation and therefore  deserves especial notice.   It
has been shown that crystals of the form of Sb Zns, or at least
crystalline scales of the same character, are formed in the alloys
between 20 and 43 p. c. of zinc,  the first per cent, corresponding
to Sb Zn and  the second to Sb Zns.  Half way between these
two points,  that is the alloy of 315 p. c, is the point where crys-
tals having the  calculated composition of Sb Zns are  first ob-
tained.  Were the variations in the composition of the crystals of
Sb  Zns exactly proportioned to  the excess of zinc or of anti-
mony in the alloy, as is the case with  Sb Zn3, then the curve of
variation would be the straight line formed  by the continuation
of the line a b.  From this line b  h the course of the  curve is
deflected by the  force which determines the union of the ele-
ments in definite  proportions, and  which  for  the want  of a spe-
cial term, I will call the Chemical Force.   This is so strong that
the curve runs parallel to the  axis of ordinates through the dis-
tance k m.   Beyond this point, the influence of  the excess of an-
timony in the alloy becomes stronger than the chemical .force, and
the curve gradually bends towards  the line hb which  it finally
meets at h.   In the portion hn of the curve, the analyses are best
represented by the arc of a circle, of which the radius equals h e
 or one-half of h b, and to which the line km  is tangent.  In the
 portion  n m the points determined  by analysis may also be con-
 nected by the arc of a circle of which the radius o' n equals  the dif-
 ference between  the radius o n and twice g n, so that the two cen-
 tres 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  chemical force acting in the di- 
8       /. P.  Cooke on the Law of Definite Proportions

rection of the tangent k m.  It has already been stated that crys-
tals having  the calculated composition of SbZns are not first
formed in the alloy of the same composition 33 5 p. c. of zinc, but
in an alloy containing two per cent, less ; so that the line m k, in-
stead of extending to e, changes from this direction at k, and after-
wards runs parallel to the line b h.  Unless this fact can be explain-
ed by a tendency in Sb Zns to an excess of zinc caused  by the in-
fluence of Sb Zn3 as suggested above, the reason of this difference
between Sb Zns and Sb Zri3 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 remark-
able fact whose bearing cannot  be at present seen, but which like
the last  serves to corroborate  the general  accuracy of  the result
was pointed out by my colleague, Prof. Peirce, after the plate had
been engraved.  The distances of the three most important points
of the curve of Sb Zns from  the line a h,  viz. k d, mf, and n g,
are  simple multiples of the first; ng is twice and mf 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 very agreement of
so many different determinations by three  separate analysts is a
strong proof of the general correctness of the work.
  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-
moir.   Let the coordinates of any point of the curve be, x = per
cent, of zinc in the crystals, and z =  per cent, of zinc in the al-
loy.  In order to construct the curve of SbZn3, find  a  point
(a) of  which x — z = 43 p.  c. (the calculated per cent,  of Sb
Zn3) and draw  a straight line a b equally inclined  to the two
axes in  the direction from the origin.   To construct the curve of
Sb  Zns, produce the line a b in  the opposite direction to the point
x — z = 20, which will be the lowest point of the curve.  Find
next a point (k) of which x = 33-7 p. c. (the calculated per cent.
of  Sb Zns  is 335) and z = 315 p. c,  which  is  one-half of
43 + 20.  Through this point draw  a line  m k parallel to the
axis of  ordinates and intersecting the line a b h at c.  The line
m i is the tangent, and the  line b h the chord of  the required arc.
On the  line  mi take ci = ck, and i is the point at which the arc
should touch the tangent.  Erect a perpendicular on the tangent
at the point i, take oi = \ b h, and from 0 as a centre, with a ra- 
in the Compounds of Zinc and Antimony.         9
dius = oi, describe the arc hi.  Also  from the centre o let fall a
perpendicular og on the chord b h, and  produce  it to a point o'
making o' g = og.   It will intersect  the arc at (n).   From o' as
•a centre  with a radius o' n describe a second arc n m intersecting
the tangent at m.  Finally, draw from k, a straight line k I, paral-
lel  to b h, then the broken  line I k mnh will  be the required
curve.
  It will be noticed that the tangent  which has been  drawn
on the plate  through the points determined by analysis is  two-
tenths of a per cent, in advance of the line which would corres-
pond to Sb Zns.  This position is essential to the equality of k c
and  ci, if  we retain as the value of  the radius of the larger arc
R = \ b  h.   If the analyses  should  have  given  erroneously too
much zinc so that the true position of the  line should be at x =
33-5 per cent., then this equality would be destroyed, and the con-
ditions for finding the centre o would  be reduced to  the coordi-
nates of  the  point h, 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 Zris
have throughout a  proneness to an excess of zinc caused appa-       ✓
rently by the influence of Sb Zri3 ;  but it is  also true that the
tendency of  the error  in the  zinc determinations is in the same
direction.
  Before discussing  the conclusions to which  the facts already
stated  seem  directly to point,  it will be well to  see how far the
variation in composition corresponds to a variation in  the proper-
ties of the two compounds.   Three  classes of  properties  have
been examined in this connection, viz., Specific Gravity, Crystal-
line  Form, and Affinity for Oxygen, which will be treated of in
order.
  Specific  Gravity.—The specific gravities of all the  crystals
analyzed, as  well as  that of the zinc  and antimony used  in the
investigation, were  taken with the  greatest care.  The deter-
minations were made with a nicely constructed specific gravity
bottle, as this  method was found susceptible of greater accuracy
than any other, when the temperature was observed with precis-
ion.   In  calculating the specific gravity, the weight of the water
was  corrected for the temperature, so  that the unit is  in all -cases
distilled  water  at 4°C.  A similar correction could not be made
for the temperature of the substance,  as the coefficients of expan-
sion  of the crystals are not  known.   The results of the deter-
mination all made by myself are collected  in the following table
in the column headed " Sp. Gr. by Experiment."   In the column
headed ■' Mean Sp. Gr. of Zinc and Antimony" are given the cal-
                           2 
10
/. P. Cooke on the Law of Definite Proportions
Specific Gravities of Crystals, fc			rmed in tht	Alloys of Z	inc and Antimony.	
Composition of the Alloys.		Composition	of the Crystals	Sp.Gr. ofCrys" tals by Experi-	Mean Sp. Gr of Zinc and	Expansion in Crystal-
Per ct. of Zn. 1()0-00	Perct. of b.	Perct.ofZn	Per ct. of. b	ment.	Antimony.	lizing.
				7153	7-153	o-ooo
*96-00	4-00			7069	7-134	0-065
*86-20	13-80			6898	7-086	0188
*76-30	23-70			6769	7-039	0-270
7040	29-60	6420	35-80	6699	6-982	0-283
66-50	3350	c61-00	39-00	6628	6-967	0339
6450	35 50	58-56	4144	6596	6-956	0-360
62-50	3750	5553	4447	6506	6941	0435
60 60	3940	55 00	45-00	6440	6939	0499
58-60	4140	50 39	4961	6396	6-917	0521
5660	43-40	4995	5005	6388	6915	0527
48-70	51-30	48-66	5134	6-404	6-909	0-505
4670	5330	4677	53-23	6376	6-900	0-524
4480	5520	44-26	5574	6341	6-888	0547
4280	57-20	43-09	5691	6327	6882	0-555
*4000	60-00			6-386	6-867	0481
*3500	6500			6-404	6 844	0 440
33-00	6700	35-37	64-63	6401	6-845	0-444
29-50	70-50	3362	6638	6384	6837	0453
27-50	72-50	3385	66-15	6383	6 838	0 455
2660	7350	32-08	67-92	6400	6829	0429
2600	7400	3107	68-93	6418	6 824	0-406
25-50	74-50	30-43	69-57	6428	6-822	0394
24-50	7550	28-76	71-24	6449	6-813	0-364
22-50	7750	26-62	73-38	6453	6 803	0350
21-50	7850	24-83	7517	6467	6795	0328
*1500	8500			6 564	6-748	0184
* 10-00	9000			6603	6-725	0122
*500	95-00			6-655	6 701	0-046
	10000			6-677	6677	0000
ciliated specific gravities of the same crystals on the supposition
that  the two metals had  undergone no  expansion  on uniting.
The last column was obtained by subtracting the numbers of the
former from those of the latter, and therefore shows the  relative
amount of expansion.  On examining the table, it will be found
1st.  Than the union of antimony and zinc is accompanied by ex-
pansion.  2nd. That the  specific gravity of the crystals varies
slightly with the composition.   3d. That the two minimum spe-
cific gravities correspond precisely to the composition of Sb Zns
and Sb Zn3, so that the specific gravity increases and the expan-
sion  diminishes as you depart on either side from these two  cen-
tres.  4th.  That the specific gravijy of Sb Zns  is smaller than
that  of Sb  Zri2.   We find then that  the specific gravity deter-
minations confirm in general the results of the analysis pointing
out the same two centres of crystallization.
   Crystalline Form.—It  has already been stated  that only two
crystalline forms can be obtained from the alloys of zinc and an-
timony, that of Sb Zti3 and that of Sb Zns.   A large number of
* Alloys not crystallized, 
          in the Compounds of Zinc and Antimony.        11

crystals of SbZns from different alloys, and therefore containing
different proportions of zinc, were carefully measured for the pur-
pose of ascertaining whether the angle was at all affected by the va-
riation of composition.  Fortunately four different crystallizations
afforded excellent crystals, the angles of which could be measured
to a minute.   The crystals contained respectively 43-15, 44-14,
4690 and 5500  per cents, of  zinc, and on all these by  repeated
measurements the angles were found to be identical with  those
given under figs. 1 and 2.  Crystals from many of the other alloys
were also measured, but on account of the imperfections of their
surfaces the angles could  not be determined  within  five or ten
minutes.  In  all these cases  however the values of the angles
given above were included within the limits of uncertainty.
   The faces of the crystals of  Sb Zns are not  generally so per-
fect as those of Sb Z113, nor is their tabular form so well adapted
for measurement; moreover variations in some of the angles
have  been  noticed  in crystals from  the same crystallization
amounting even to ten minutes.  The angle  0 on 1 however ap-
peared to be very constant for in all cases where it could  be  accu-
rately measured the same value was  obtained.   As none of the
crystals of Sb Zns, containing an excess  of  antimony, could be
measured wilh precision, no constant variation of angle could be
detected and on the other hand it could not be proved to be inva-
riable.
   Affinity for Oxygen.—The affinity of the crystals of Sb  Zn3,
of different compositions,  for oxygen, may be estimated  by com-
paring the amounts of hydrogen gas evolved in  a given time on
boiling alloys of the same composition with water.   The results
of such experiments were given in the former memoir in a  table,
a  mere glance at which  will discover the two  following facts—
   1st,  That up to 40 per cent  no great increase in the amount of
hydiogen evolved is obtained by increasing the amount of zinc in
the alloy.
   2nd,  That at the alloy containing 42 per cent, of zinc there is
an immense maximum confined at most between two per cent on
either side.
   General Conclusions.—Before stating the conclusions to which
as I think the facts now established directly point, it will be well
to consider the only  two  admitted principles  of chemical science
which could  possibly be brought forward to explain similar  varia-
tions.  They  are, first,  that of impurities in crystals; second, that
of isomorphous mixtures.   It will  not  be difficult  to show that
the variations in  composition of Sb Zns and SbZii3 cannot be
caused by either of these  principles.
   It is a well known fact that  crystals frequently take up impuri-
ties which are either dissolved  or mechanically suspended in the 
12     /. P. Cooke on the Law of Definite Proportions

me/istruum in which they form, and it might be supposed at first
sight that the excess of zinc or antimony in Sb Zti3 or  Sb Zt)2,
bore the  same relation to their crystals that  the sand does to the
rhombohedron  of calcite from  Fontainebleau,  or  oxyd of iron
and  chlorite  to-crystals of quartz;  but, in the first place, in all
cases where a  considerable amount of impurity is present the
crystals are either imperfect  or  else the angle  is  considerably
changed  at times even as  much  as two or three degrees;  and
secondly, as such impurities are merely mechanical, the amount in
the crystals would in all probability be proportional to the amount
present in the menstruum at the time of their formation.  Now in
the crystals of Sb Zn 3, from the alloy of 60 p. c. of zinc, there is
present at) excess of zinc amounting to 15 p. c. and  nevertheless
the crystals are as perfect as, and their angles identical with, those
obtained  from the alloy of 43 per cent.  In the crystals of Sb Zn 3
the excess of zinc is to a certain limit directly proportional to the
excess in  the alloy, but  in those of SbZns the excess of anti-
mony is far from obeying this rule ; and were the excess in both
cases a mechanical mixture the variation in both eases would un-
doubtedly follow the same  law: again,  the crystals of SbZns,
take up an excess of zinc  but do not take up an excess  of anti-
mony, while those of Sb Zns crystallize with an excess of either,
—facts which are as inconsistent  with the idea of mechanical
impurity  as the last: finally the form of the curve of Sb Z112 of
itself alone proves that the  excess of antimony in the crystals is
not in the condition of mechanical impurity; for in that case the
variation  of composition would not  be influenced,  as the curve
shows that it is, by  the chemical force.
  A theory that the variation in composition resulted from  the
mixture of two or more isomorphous compounds would be even
less tenable than the one just discussed.  For in  the first place it
would be necessary to assume the existence of two other com-
pounds of zinc and  antimony isomorphous with  SbZri2 and of
one  other, if not more, isomorphous with  SbZns.  Not only
would such an assumption be contrary to all the analogies of chem-
istry and  therefore  require strong evidence  to  sustain it; but in
the second place it can almost be demonstrated that  no such com-
pounds exist.   The crystals having the calculated composition of
either SbZn3 or Sb Zns  are marked as has been shown by stri-
king peculiarities, and with one possible exception  similar pecu-
liarities were not observed throughout the whole series of crystals
which have been examined. The crystals containing 50 per ct. of
zinc and  of  the composition of Sb Zii4 were  found to have a
slightly smaller sp. gr., than those just above or just below them,
but the difference is so small that it may he  accidental, and as the
crystals exhibited none of the  other peculiarities, which charac-
terize crystals having the calculated composition of SbZn3 or 
         in the Compounds of Zinc and Antimony.        13

Sb Zns, I could not attach sufficient weight to the one circum-
stance to feel authorized  in admitting a third  compound of zinc
and  antimony.  Admitting  however  the existence of Sb Zih
yet, as exactly the same angle has been observed in crystals con-
taining 55 percent,  as on those containing 43 per cent of zinc,
it would be necessary in order to explain the variation in compo-
sition by the  principle of isomorphous  mixtures, to assume the
existence of still a  third compound isomorphous with  Sb Z113,
and  containing more zinc  than Sb Ziu,  which  would  increase
greatly the improbability of the theory in question.  Again, the
only probable  compound of zinc and antimony containing less
zinc than Sb Zns would be Sb Zn ; and  it will be remembered
that the crystals of Sb Zns which contained the largest excess of
antimony corresponded very nearly to  this  compound.  In like
manner the crystals of Sb Zns which  contained the largest ex-
cess of zinc corresponded very nearly to SbZti3.  If then the
excess of antimony  or zinc in the crystals of Sb Zns, arises from
a mixture of isomorphous compounds,  it  must be that  SbZii3,
Sb Zns and Sb Zn are isomorphous.  That the first two are not
isomorphous may be seen by turning back  to  the description of
their crystalline form ;  and  that there is no crystalline compound
SbZn is sufficiently proved by the fact that the crystals of SbZns,
which correspond most closely to it, are  so very imperfect that
they would hardly be recognized as crystals did they not  form the
lower limit of a series.  Several other facts pointing in the same
direction might be added, but sufficient it is thought has been said
to show that the variations of composition described in this paper
can not be explained either by mechanical impurities in the crys-
tals or by the mixture  of isomorphous compounds.
  In the absence of any known principle of chemical science by
which the remarkable variations of composition, that have been
demonstrated in this memoir, can be explained, the conclusion is
almost forced upon  us that zinc and antimony are capable of uni-
ting and producing definite  crystalline  forms in other proportions
than those of their chemical equivalents : in other words, that the
law of definite proportions is not so absolute as has been hitherto
supposed.   The explanation then of the variation of composition
which I would offer is : that it is due to an actual perturbation of
the law of definite proportions  produced by the influence of mass.
I suppose for example that in the crystals  of Sb Zns, containing
55 per cent, of zinc, the zinc and antimony are united in exactly
the same way as in those  containing  43 per cent., or in other
words, just as if the equivalent of zinc were increased to  5257,
that of antimony remaining the same.  In  supportof this position
I would offer two considerations.   The first is that if the  varia-
tion is not caused by mechanical impurities or by the mixture of
isomorphous compounds, we can conceive of no other  explana- 
14      /. P. Cooke on the Law of Definite Proportions

tion for the phenomenon than the one offered.  This of course is
merely negative evidence ;  for although science as yet presents us
with no principle for explaining variations of composition  other
than those which have been discussed, and although  we can con-
ceive of none others,  it does not follow that others may not exist
or may not hereafter be discovered ;  but, nevertheless, this consid-
eration is important inasmuch as it meets an obvious  objection,
which  would be urged against any new doctrine, which conflicts
with a generally received  canon  of chemical  philosophy.   The
second consideration  has the  character of demonstration.   It is
that the curve of variation is evidently  generated by a second
force counteracting directly the  chemical force.  This second
force, as has  been shown,  is exerted by the excess of one or the
other element present  in the menstruum, and  it may  therefore be
appropriately  termed  the  force of  mass.   While  the chemical
force tends to make the curve a straight line  parallel  to the axis
of ordinates,  the force of  mass would reduce it to a straight line
making an  angle of 45° with  the axis;  under the  influence of
both these forces  it follows  the arc  of a circle between the two.
Now I urge that the character of this curve proves that the chem-
ical force has been directly influenced  by what we have called,
the force of mass, in the same way that the irregularities of the or-
bits of the planets prove that the  force  of gravitation exerted by
the sun  has been  disturbed in  its action  by the influence of the
other members of the system.   As the details in the  form of the
curve have been  fully discussed in  the previous part of the me-
moir, it does  not seem to be necessary to dwell upon this argu-
ment, and I would therefore without further comment offer the
curve as it has  been laid down on the plate as the  proof of the
validity of the explanation  of the variation in composition  here
advanced.
   It  is worthy of remark  that while the curve of variation  may
be said almost to demonstrate that the law of definite proportions
may be disturbed  in its action,  it also most clearly sustains the in-
tegrity of the law itself; for, as may be seen  on  inspection, the
chemical force is sufficiently strong to retain the curve of  Sb Zns
parallel to the axis of ordinates through a variation in the  men-
struum of nearly  five  per cent., and  it is only when the excess of
antimony  present in the alloy exceeds six  per cent, that the force-
which  it exerts becomes  strong enough  to disturb the action of
the law.   What the nature of the disturbing  force is must be for
the present a matter of theory.   1 am inclined to think that it is
a phase of the  chemical force  itself, in the same way that the per-
turbations in  the  motions of the planets are a secondary result of
the force of gravitation.
   Accepting  the  view of the subject, which  has been offered, it
will  be  obvious that the very large extent of the variation in the 
          in the Compounds of Zinc and Antimony.        15

compounds of zinc and antimony  is due to the very weak affinity
between these elements.  Were  the chemical force stronger in
proportion to the disturbing force the variation would be lessened ;
were it weaker,  the variation would be increased.  This is illus-
trated in the difference between the curve of Sb Zns and that of
Sb Zns.  It is  evident from  the action of chemical agents on
the two compounds, that one equivalent of antimony and two of
zinc are united  by a stronger  force than one  equivalent of anti-
mony and three of zinc, and we find that the crystals of Sb Zns
retain the calculated composition under a considerable  variation
iti the composition of  the  menstruum,  while  the composition of
those of Sb  Zn3 varies with the slightest increase of the amount
of zinc in the alloy.
   To what extent this  perturbation of the law of definite pro-
portions prevails among chemical compounds  it must remain  for
future investigation to  determine.   There are  however a number
of facts which  tend  to prove that it is very general whenever
chemical affinity is weak.   Four of these I  will cite as  being re-
markably analogous to the facts under discussion.
   1. Rieffel, to  whose investigation of  the compounds of tin and
copper  we have already referred,  says, after  the paragraph quoted
in the introduction to this  memoir, " Les  aiguilles de CuSns4
sont plus grosses que celles de CuSii4 8".   "  On croit,  sans oser
Vafijirmer, qu'elles sont, par compensation, en nombre moindre, et
que des differences analogues ont lieu dans les autres  CuSnqo  a
mesure que<p augmente jusqiC  a 9=00 , ou jusqu'  a detain pur."
It will  be noticed that the difference between  these needles is
precisely the same as the difference between  the  crystals of Sb
Zna containing a small and a large  amount of zinc, and I think
that no one after reading Rieffel's paper can doubt that  the com-
pounds of copper and tin vary  in composition  like those of zinc
and antimony.
   2. The mineral Discrasite, a compound of silver and antimony,
crystallizes  in trimetnc prisms, of which Ion I— 119° 59'.* The
analyses given below are copied from Dana's System of Mineral-
ogy, changing slightly the order.
   Sb Ag3 = Antimony 28-5 Silver, 71-5=100. Sb Ag4 = Anti-
mony 23, Silver 77= 100.
1. Andreasberg (foliated granular), Antimony 24-25 Silver 75-25=99.5, Abich.
2. Wolfach (coarse granular),       "     24     "   76=100, Klaproth.
3. Andreasberg (foliated granular),  "     23     "   77=100,
4.    "         "     "      "     22     "   78=100, Vauquelin.
5. Wolfach (fine granular),         "     16     "    84=100, Klaproth.
   It needs  no comment on these results to show  that   Discrasite
is homaeomorphous with SbZns, and varies like it in compo-
sition.
* Dana's System of Mineralogy, 4th ed., vol. ii, p. 35. 
 16     J. P. Cooke on the Law of Definite Proportions

   3.  In a paper recently published,* W. Sartorius von Walters-
 hausen gives descriptions and then analyses of a new mineral oc-
 curring with Dufrenoysite in the Binnen Valley, Switzerland, in
 Dolomite.  As the analyses do not agree with each other and do not
 correspond to a simple formula, von Waltershausen regards the com-
 pound as consisting of  two hypothetical isomorphous compounds
 Pb S  + As S3 and 2Pb S + As S3 and calculates the proportions
 in which these compounds are mixed  in the specimens analyzed.
 He infers  that they are isomorphous from their analogy in com-
 position to Zinkenite  and  Heteromorphite,  PbS + SbSs and
 2Pb S 4-Sb S 3 which he regards as isomorphous. Prof. J. D. Dana
 questions the isomorphism of the last and thinks that the hypoth-
 esis that  the new compounds are isomorphous requires further
 evidence.f
   4.  It is stated  by StaedelerJ that  crystals of the compound of
 grape sugar and common  salt  can be  obtained containing for
 every equivalent of grape sugar one or two equivalents of chlorid
 of sodium and also of intermediate composition. He states more-
 over that "Calloud,  who first observed  that the grape sugar of
 honey combined with chlorid of sodium, found that the amount
 of the latter varied between 8-3 and 25 per cent."  Staedeler re-
 fers the variation in  composition to a  mixture of the compound
 of one with the  compound of two equivalents of chorid of sodi-
 um which  he assumes to be  isomorphous.  He adds that it  may
 be  caused by  "enclosed crystals of chlorid of sodium  although
 the eye could not distinguish any heterogeneous constituents."
  All  the above compounds are examples of weak chemical affin-
 ity accompanied  by large variations in composition without any
 change in  the general crystalline form.  It is not meant to assert
 that the variations are identical in character with those of Sb Zns
 and Sb Z112, but only that there is a strong probability that this
 is the case, which in the first two instances amounts almost to a
 certainty.
  If variations in composition  of such  magnitude  are  possible
 when the force of chemical affinity is weak, it is highly probable
 that some variation  may occur when the  force is strong,  and,
 whatever view may be taken of  the cause of the variation it will
 now become a matter of importance to ascertain whether many
 discrepancies in  analyses  hitherto referred to  imperfections  in
 the process, may not be owing to the same  cause which influ-
ences  the composition of the crystals of zinc and antimony.  For
 this purpose, it will be best to make several analyses of the same
compound, prepared  under circumstances differing as widely as
possible, and then to apply to the results "Peirce's Criterion for

          * Poggendorff's Annalen, vol. xciv, p. 115.
          f American Journ. of Science, vol. xix, p. 355.
          % Chemical Gazette, vol. xiii, p. 44. 
          in the Compounds of Zinc and Antimony.         17

the rejection  of  doubtful observations."   Such investigations
will be greatly simplified by tables prepared by Dr. B. A. Gould*
for facilitating the application of this criterion to which I would
refer all chemists who are inclined  to take up this line of inves-
tigation.
   I am well aware that in announcing the existence of perturba-
tions of the law of definite proportions I am  calling in question
one of the  most  fundamental dogmas of chemical philosophy,
and that  the  new doctrine will  have to encounter  prejudice on
this very  ground.   This law is so intimately  associated in many
minds with the atomic theory, that, to such, absolute definiteness
seems to  be its essential characteristic ;  nevertheless, I can not
but believe that, laying aside the  prejudices which the theory be-
gets,  it will be seen by all,  that  the analogies of nature support
the doctrine of variation as  maintained  in this memoir.   The
phenomena of some of  the  phenomenalf laws of  nature  have
that definiteness of character which  is claimed for  those of the
chemical  law.  The planetary orbits are not perfect ellipses.  The
ratios of the harmony scale are but approximately realized.  The
arrangement of leaves  on the  stem  is  not perfectly regular.
Isomorphism is seldom  absolute.  In all we  observe only a ten-
dency towards a maximum effect which is the perfect expression.
of  the law, but which is rarely fully  reached.   The limits of va-
riation are broader in some instances  than in  others, but we find
no  case in which there is absolutely none.  This same character
which pervades the other phenomenal laws of nature, I claim for
the great  law of chemistry.   The definite proportion I regard as
a maximum toward which the chemical force strives,  a maximum,
from which the deviations in most cases are  small, although in
others it maybe very large ;  and  I maintain that this view of the
subject, which the memoir has aimed  to establish, is supported by
the analogies of nature.
   When  the dynamical  law has been  discovered, of  which the
phenomenal law was merely the  outward manifestation, as  Kep-
ler's laws were  merely the  phenomena of the  law of universal
gravitation, the very variations have  been seen to  be necessary
consequences of the law itself, and if even the dynamical  law,
which governs chemical phenomena, shall be discovered, it is most
probable that the variations from the law of definite proportions
will become as much a matter of calculation as the perturbations
of Astronomy.  In both cases the perturbation is apparently due
to the influence of an extraneous mass of matter.

  *  Astronomical Journal, vol. iv, p. 81.
  f  I have used the term phenomenal laws to designate a class of laws of  nature
which are empirical in their character inasmuch  as they are obviously not ultimate,
although their deviation has not been discovered, but which are more universal than
those to which the term empirical is commonly applied.
3 
18    J. P.  Cooke on the Law of Definite Proportions, <$rc.

  The argument from analogy becomes stronger, when we con-
sider the equivalent  numbers.  I have shown in a former memoir*
that these numbers  may be connected by a very simple numeri-
cal law, but  here, as in other cases, we find merely a tendency to-
wards the law, not an absolute agreement with it, the differences
between the theoretical  and  the  experimental equivalents  being
in many cases too great to be covered by errors of observation.
The present memoir may throw light  upon these discrepancies;
for, to say the least,  it is possible that the differences may origin-
ate in variations of the equivalent itself, and  that the theoretical
equivalent may be the  maximum towards which the chemical
force tends.   On comparing carefully the different determinations
of the chemical equivalents, many facts may be noticed support-
ing this view ;  those equivalents for  example, which  coincide
with or very nearly approach whole numbers such  as  those  of
oxygen, carbon and  sulphur, will  be found as  a general rule to
have been determined by the analysis or synthesis of compounds
whose elements are united  by a strong force ;  also when the
equivalents  have  been determined  by essentially different pro-
cesses it will be noticed that they seldom perfectly agree ; so that
whatever view may be  taken of  the subject it  will now become
a matter of the highest importance to ascertain how far, if  at all,
the determinations of the chemical equivalents  have been  influ-
enced by similar causes to those which have produced the  varia-
tions described in this memoir.  This  influence  can  only be de-
tected  by multiplying the determinations, by as many different
processes  as possible,  and submitting the results to a rigorous
mathematical scrutiny.
  If the doctrine of this memoir is correct and the chemical
equivalents are really liable to variation it will have an important
influence  on chemical  philosophy.    The atomic theory  as  at
present  interpreted  by chemists is  irreconcilable with it, and
our present  ideas  in regard to isomorphism  must be materially
changed.  But  it must  be remembered that  the conclusions of
the memoir  are drawn  from the examination of only two com-
pounds, and  therefore that it  would be premature to dwell on
these obvious consequences of the principle until it has been sub-
stantiated by further investigations.   In conclusion, I would ex-
press my obligation  to the gentlemen who have assisted me  in the
labor of the investigation which  on  account of the large number
of analyses has been very great and  could not have been conclu-
ded so soon  had it not been for their great  industry and zeal.
* This Journal, voL xviii, p. 229, 
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