Abraham Clark Freeman John Proffatt.

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•963


1088


-986


•953


1069


-975


•944


1053


•964


•936


1039


•965


•927


1001


•929


•904


•983


914


•893



Isometrics.



Ap Volume.



1-000 '
-984
•971 ,
-959
-948
•938
•929
-921 !|
•913 '
•906 i I
-899 1 1
•881 I'
-870 I'



28" 1-00

65 310 I

100 600

^85 1300 .

Rate -12" per atmosphere.



Table 24.
Isothennals of alcohol, referred to unit of volume at 28" and 150 atm.



310" 185"



100"



65"



28"



Isometrics.



Ap Volume.



p=0

150

250

350

450

550

650

750

850

950

1060

1160

1460

1650



29
63
47
37
29
24
19
16
12
09
06
00
96



1-229 '

1-193 ,

1166

M42 !

1-122 I

1105|

1-089

1-075

1-063

1-051

1^041

1013

0^997



•087


1-035


•071


1-024


-057


1-014 1


-044


1004


-033


•996 '


•022


•988


•013


•980


•004


•973


•996 !


•966


-988


•960


•980


•954


•961 ;


•9:<8


•949


•928



l^OOO'
•991
•983
•076
•969
•963
•956
•951
•945
-940
•935
•921
•912



28"
66
100
185





367

740

1470



10



Rate -lO^ per atmosphere.



32. Isothermals computed. — From these results the actual
isothennals of the above substances can be constructed. To

recapitulate: the volume decrement i;/ V=ln{l+9dpW^j refers
in afi cases to unit of volume at the temperature of tne isother-
mal and under the initial pressure p^. The compressed
volume is therefore 1—^ (1+9??/?)*/^ ; and if in consequence
of the observed thermal expansion at jp,,, the volume at tf be
Vq^ the actual isothermal is

* Special measurement, made later.



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Reloition to Pressure and Temperature.



603



^ep^^e{'^-H\+9^p)y^) (5)

referred to the initial temperature O^.Vq^a directly measured.
Hence the only hypothesis occurring in equation (5) is equa-
tion (2). In tables 28 to 28 I have given the value of Vq^ com-
puted conformably with equation (5), for the temperatures of
observation. If these results be constructed graphically, the
conditions subject to which pressure and temperature must
vary, in order that Vq^ may remain constant are given by draw-
ing horizontals. In the supplementary tables certain isometric
data are inscribed.

Tjlble 26.
Isothermals of Diphenjlamine, referred to unit volume at 66° and atm.



Isometrics.



5=



j>=

100

200

300

400

600

600

700

800

900

1000

1300

1600



SIO*'


186** j

1


1-235


1-093


1-211


1-082


1-191


1-071


1173


1061


1167


1-063


1-143


1-044


1-130


1-036


1-119


1-029


1-108


1-022


1098


1-016


1089


1010


1-064


-993


1-060


•983



100**



1-012
1006 I

•999

•993 I

-988

-982

•976

•972

•967

-962

•958

-946

•938



1-000
•994
•988
•982
•977
•971
•967
•962
•967
-963
•949
•937
•930



9

66
100
186





190

1200



1.00



Rate '09" per atmosphere.



Table 26.
Isothermals of Thymol, referred to unit volume at 20*" and 20 atm.



03S



j>= 20

120

220

320

420

520

620

720

820

920

1020

1320

1620



310**



•329
-279
•242
-212
-188
•167
-148
-131
-116
-103
•091
-059
•040



185-


100"


66'' '

1


1-162


1-076


1-042


1-145


1-066


1036


1-129


1-057


1028


1-116


1-049


1021


1-103


1-041


1016


1-092


1033


roo9


1081


1026


roo3


1-072


1-020


•998


1-064


1-013


-993


1-055


1-007


-988


1-047


1-002


•983


1-026


-986


•970


1-014


-977


-961



28°



1000
•994
-998
•982
•977
•972
•967
•962
-967
•963
•949
•987
•930



Isometrics.



e


Ap


Volume.


66


40


1-04


100


410




185


1090




310


1600





\\ Rate -1 1"* per atmosphere.



33. Isomet/ric8. — Some remarks on these tables are essential.
In case of alcohol the curves for 28** to 185° are a family of



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504



G. Barvs — Fhiid Volume cmd iU



like properties. The curve for 310° intersects these at high
pressure. This, however, was suggested in §28, sinoe above
the critical temperature the mean equation (2), is not appli-
cable. The chief result of the table is riven in the supple-
ment, for ^^^='^28^150=1. It appears that (Tand^ as far as 185**

Tablb 27.
IsothermalB of Paraffioe, referred to unit volume at 66" and 20 atm.











!


Isometrics.


e=


310**


186'


100**


66'*




1 1










1


d ^p Volume.


p:= 20


1-241


M08


1-026


1000 1


66 100


120


1-202


1-090


1015


•991 1


100 260


220


1171


1074


1006


•983


185 880


320


1-146


1-060


•996


•976


310 143U


420


1-125


1-047


-988


-968 i




620


1-107


1036


•980


-962 1


Rate 1-3" per atmosphere.


620


1091


1-025


•973


-956 '




720


1076


1016


•966


•950




820


1063


1007


•959


■945 '




920


1-061


•999


•953


•939 1




1020


104*0


-991


-947


•935 '




1320


1-012


•970


•931


•921 ;




1520


•995


-958


•922


•912 I





Tablb 28.
Isothermals of Para-Toluidine, referred to unit volume at 28** and 20 atm.




are linear functions of each other. The rate of change
•10** C. per atmosphere.

Similar remarks apply for ether, where conformably with the
lower critical point, tne high temperature discrepancy is more
pronounced. The rate of variation of d and p for ^^^=^28,100=1
is here '12° per atmosphere.



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Relation to Pressv/re a/nd Temperature.



506



In case of parafl5ne, which is the first substance solid at

ordinary temperature, 'O^^^ shows a somewhat larger variation

of d relative to j?, the rate being 13® C. per atmosphere. The

^ rate for thymol is -ll** per

atmosphere, for toluidine

M- WL m, -10® per atmosphere, for

diphenylamine "09 per at-
mosphera In most of
these cases the expansion
diflSculties, § 14, make the
present results irregular,
particularly in the case
where two or more threads
are observed. At 310® the
behavior is usually excep-
tional, the discrepancy
which shows itself is simi-
lar to the case of ether and
alcohol, but much less pro-
nounced.

In fiffure 4 I have rep-
resented these relations
graphically. It is seen at
once that the errors left
show no march. For di-
phenylamine the distribu-
tion is zigzag; for tolui-
dine and thymol in an
opposite sense for the two
cases.

Taking these results
(0° to 185°) as a whole it
follows with remarkable
uniformity that if temper-
ature and pressure vary
linearly witn each other,
at a rate of about 'l^C.




Eer atmosphere, there will



Kg. 4. laometrics of Ether, Alcohol, Paraffine, be no change of volume.
Diphenylamine, Toluidine and Thymol. More riffOrouslv : if with
a, region of undercooling. ^^^ obs^ed thermal ex-

pa/nsion compressibility be supposed to increase inversely as
the ^st power of the pressure bvnomial (§ 27), th^n temperature
a/na pressure must vary linearly to maintain constancy of
volume. Change of the state of ag^egation is excluded.
The thermodynamic signification of this result has been sug-
gested in § 2. So far as the present results go, 0° to 185**, the



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506 C. Barvs — Fhiid Volume and its

surface Vqj^ will be generated by moving the initial section,
when d is constant, parallel to itself, in such a way that each
point describes an oblique horizontal. It is not to be inferred
that these horizontals are parallel, though within the limits of
the above investigation such a result is nearly given.

COMPBBSSIBILITY INCREASING INVERSELY AS THE SQUARE OF
THE PRESSURE BINOMIAL.

34. Properties of the ^jt^a^ttm*.-— Equation (2) as used in
§ 27, furnished a family of curves which in their ultimate con-
tour necessarily fall below the corresponding isothermals of
the substance under discussion. It is the object of this section
to investigate a similar family, the ultimate contours of which
are above the actual isothermals. This may be done by assuming

<i— /^=/i/(l+vp)', whence

vlV^fApl(\ + yp) ... (6)

In this case, when p = co, v'/ F=/i/i^=2/9, as will be seen in
the following tables. In the actual case,* v/ V, though it can
not be greater than 1, will in all probability eventually ex-
ceed 2/9.

The method of discussion to be adopted is similar to that in
the foregoing section. Let

yo=j^)i>o/(l+J^A) and j/=MPo+l>)A^+^{Po-^P))'
Then y=y'-jro=/^M(H^o;>o)'(l+i^oi?)/(l+^oi>o)); or if

/^=/'o/(l + nPo)' and 1^=^/(1 + Vo/>o) • 0)

equation (6) again results. Hence if po and p are consecutive
pressure intervals between and p-k-poy then the constants
obtained from observations within the interval p, may be
reduced to those applying to the whole interval ^o+/?, by
equations (7), or their equivalents

/i„=/i/(l-vp„)«, y,= v/(l-vp^) . . (8)

According to Mendeleef, Thorpe and Riicker, (1. c), the
volume of liquids in case of thermal expansion may be repre-
sented by F^=l/(1 - ^^), where pressure is constant, Vq the

actual volume at temperature ^, and ^ a constant. Introduc-
ing equation (6) and denoting by F, the volume for pressure p
and temperature 0j F={l-}-(v— //)p)/(l— A^)(H-vp), which for
pressures and temperatures not too great may be put F=
l+{i^—/x)p/{l—k0'\-pp). If, therefore, F= Vc is constant,

* Of. Rucker (Nature, xli, p. 362, 1890). Converging lines of evidence obtained
from optical, electrical and thermal researches show l^at liquids can not be com-
pressed more than '2 to *3 of their normal bulk.



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Relation to Pressure and Temperature.



507



^=~(l-Fe)/*Fe+i?(j<l-Fe)-//)/AF,; so that in case of
constant volume, temperature varies linearly with pressure,
small intervals of variation presupposed. The rigorous deduc-
tion from (6) and Mendeleers equation is A;Fc^=— (1— Fc)+
/i/?/(l+v/?), which is linear in proportion as vp is small com-
pared with 1. In § 33 it was si)own that the relation of 6 and
jP is probably linear throughout great intervals. It follows
that (6) is insufficient for large ranges of pressure. Finally
r^ardiuff Mendeleef s equation, it follows, if B^ and 6 be two
consecutive intervals of temperature, the former measured from
zero, that Fo=l/(l-Mo), K/=l/(l-^(^o+% and F^=H-
F/- Fo=(l+A;»^tfo)/(l-*^), if ^=V(l-*o^o). Thus obser-
vations may be referred to any convenient temperature as a
point of departure.

35. Computation of hyperbolic constants, — Applying equa-
tion (3) to the observations in § 15 to 24, 1 obtained the con-
stants given in table 29. Clearly v must be some function of
fi\ but the observations are now too crude to indicate its
nature. If the ratios of v to ^ be found either graphically or
by computation, the consecutive values show no discemable
march or grouping. Hence I assume this ratio to be constant,
and add its mean value in the table. As before the ether and
alcohol points at 310° are to be excluded, and the discrepancy
is apparent in the ether point for 185°.

Table 29.
Hjperbolic constants. Direct computation.



Q


^xlO«


vxlO«


Toluldine


//xlO«


vxl0«


e

Paraffine


fixW


pxl0«


Ether








29


169


830


28


56


58


65


85


191


65


228


1030


65


70


413


100


111


475


100


353


1570


100


81


110


185


181


845


185


1028


3870


185


, 146


801


310


368


1510


Alcohol






310


401


1730


Thymol






28


87


243


Diphenylamine




28


68


465


65


111


276


65


.1 61


162


65


69


157


100


182


1630


100


69


285


100


99


553


185


348


1755


185


114


613


185


162


716








310


' 215


889


310


465


2000








Mean


v/// = 4-5.











36. Mean constants. — Utilizing the ratio v///=4'5, I con-
structed the next table. The agreement as a whole is not as
good as were the data for i? and a in § 30.

37. The isothermal band. — With the constants of table 30, 1
computed the actual isothermals, in the way suggested in § 32.
Expansion being directly observed, the only hypothesis intro-
duced is equation (6). The results so obtained are to be tabu-
lated in the manner shown in tables 23 to 28, with which they



Am. Joub. Sol— 1'hird Series, Vol. XXXIX, No. 234.— June, 1890.
33



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508 C. Ba/ni8 — Fluid Volume and its

are to be compared. The two sets of results then exhibited
the upper and the lower limit of the isothermal band, § 25. I
will omit the new results here and confine myself to a state-
ment of the degree of accordance.

Table 30.
Hyperbolic coustants. Mean values. p/V=fip/(l + 4.'6 fip).



Substance.


e


fixW


Substance.

1


d


^xlO*


Ether


29


167


DipheoylamiDe ;


65


64




65


229


1


100


69




100


354


j


185


112




*I86


1220


,


310


216


Alcohol


28


89


Paraeane


66


88




65


115


1 t


100


112




100


163


i


185


181




185


340


' i


310


382


Para-Toluidine


28


59


Thymol


28 ;


66




65


69




65


73




100


86




100 !


97




185


141


i


185 1


162




310


412


,


310 1


481



* Equation begins to faiL

In case of ether the divergence, or the width of the band at
1000 atm. is -4 per cent at 28'', 1 per cent at 65'' and at 100^
At 186° the hyperbole begins to fail. Constructing the
isometrics for /> and tf, when T^=l, it is seen that whereas for
the exponential formula (2) the straight line is predicted as far
as 185* and 1300 atm., this is not the case with the hyperbolic
equation, for which the isometrics are straight only below 100^
and 700 atm.

The conformity of results for alcohol is better throughout
At 1000 atm., the divergence at 28^^ is nil j at 65° it is 2 per
cent; at 100°, 3 per cent; at 185^ 2 per cent When Fc=^l,
the exponential relation is satisfied by linear isometrics as far
as 185 and 1500 atm. The hyperbola admits of this only
below 100° and 700 atm.

Divergences in case of paraffine at 1000 atm. is '1 per cent
at 65°, -2 per cent at 100°, '7 per cent at 186°, 6 per cent at
310°. As far as 185° and 900 atm. both isometrics are linear.
At 310° both show curvature, toward opposite sides of the
common line. The exponential is in better agreement. The
divergence at' 1000 atm. in case of diphenylamine is '1 per cent
at 65^ and at 100°, -2 per cent at 186°, 1 per cent at 310°.
The linear isometrics hold almost to 310°. Thymol at 1000
atm. shows a divergence of *! per cent at 28°, -2 per cent at
65°, 1 per cent at 100°, -6 per cent at 185°, 3 per cent at 310°.
Finally, para-toluidine at 1000 atm. shows a divergence of nil
at 28° and 65°, -3 per cent at 100° and at 185°, 3 per cent at
310°.



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Relation to Pressure and Temperature, 509

38. Conclusion, — Summarizing these resalts it appears that

the exponential v/ F=^n(l -{-apy is more in keeping with the
general cliaracter of the isothermals discussed than is the hy-
perbolic form v/V=^/ip/{l + iyp). Both equations appa/renUy
fail at 310°. It is difficult to assign a reason for this. It is
not probably due to occluded air, since the substances were
boiled and introduced into a hot capillair tube. Moreover in
case of mercury (table 3) an air bubble discrepancy would
necessarily have shown itself at 310°. Errors due to the fact
that my curves must be in some small measure isentropic,
would induce too slow a volume variation and hence only em-
phasize the break. There may be dissociation in some of the
above organic substances at this high temperature. Azo-
benzol actually decomposes and turns black at 310°. What
the effect of aissociation may be in modifying the computed
isothennal is not easily conjectured ; for the greater compres-
sibility of the dissociated substances is in some degree compen-
sated by larger initial volumes. Equation (2), however, must
certainly begin to fail. Cf. § 28.

The high temperature break in question would result in case
of inconstancy of temperature in the boiling tube. I did not
test the thermal distribution ; the behavior was such throughout
that I see no reason to suspect inconsistency. Final reference
might be made to the pressure expansion oi the capillary tube.

To throw light on tliese particulars, I made the following
direct measurements with ether, a case in which the high tem-
perature break is most pronounced. Table 31 contains an
example of the results. The isothermal are referred to unit
of volume at 22° and 100 atm. To reduce them to 29° and
100 atm., conformably with table 23, the volumes at 310° are
to be decreased 1*5 per cent. The length of thread at 22° is
only 1*85^, thus enabling me to observe the whole thread at
310°. In other respects the work was done in the manner in-
dicated above to make the different data comparable.

Tablb 31.

Isothermals of Ether. Direct measurement.

0=300'; i,oo=6-00<^»



V


Volume.


Volume.


" i


Volume. Volume.


P


Volume.


Volume.


aim.






aim.




aim.




100


3-30


312


400


1-43 , 1-41


. 700


124


1-23


200


183


1-76


500


1-34 1-32


' 800


1-19


M9


300


1-56


1-62


600


1-28 I 1-26


i 900


116


lie








ft=:22'; iioo=l-84«»»








100


1-00


1-00 ,


j 300


•97 j -97


I






200


•99


•99 ;


400


•96 1 -96


1







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510 C. Bancs — Fluid Volume^ Pressure^ and Temperature,

Constructing the isometric for Y = Y ,^^=1? it will be

seen that the 310° point may be looked for in the region above
2000 atm. Hence, these observed results substantiate the
computed isometric in figure 4, which predicts the correspond-
ing point at 2300 atm. Nevertheless it cannot be too carefully
noted, that if the isometrics for Y =1-2, 1*3, 14, .... be

constructed the break between 185° and 310° remains in full
force, quite in conformity with the other data (alcohol, par-
aflSne, etc.).

The full interpretation of these discrepancies is of great
importance and will therefore be made the subject of my sub-
sequent work. The isometric, curved as above, introduces
certain interesting conditions of maximum volume.

The chief observational discrepancy remaining in the results
is the expansion error encountered in case of substances which
solidify between observations at different temperatures. Hence
the effect of different volumes on the slope of the isometrics
cannot be satisfactorily discussed. Since the compression
measurements retain their value independent of the thermal
expansion, and since the method pursued is such that all nec-
essary measurements for thermal expansion can be made under
atmospheric pressure, the difficulties may easily be rectified.
For by using a bulb and stem arrangement, the purely thermal
data can be supplied with any desired accuracy. This I con-
ceive to be the advantage of the mode of investigation set
forth in the present paper.

Among the important results of the above tables is the fact
that compressibility moves in the even tenor of its way quite
independent of normal boiling points and melting points, pro-
vided of course the conditions are not such that boiling or
melting can actually occur. For this reason compressibility is
particularly adapted for exploring the nature of the environ-
ment of the molecule in its relations to temperature, i. e. for
exhibiting the character of the thermal changes of the molecu-
lar fields of force.

The above work though confined to relatively low ranges of
pressure was believed to have a more general value for reasons
such as these : instead of tracing the isothermals of a single
substance throughout enormous ranges of pressure, similarly
comparable results may possibly be obtained by examining
different substances, conceived to exist in as widely different
thermal states as possible. For in such a case, since the actual
or total pressure is the sum of the pressures externally applied
and the internal pressure, the total pressure in question vir-
tually varies enormously. This calls to mind the remarks
made in §§ 2S, 34, relative to observations confined to a limited
part of the isothermal.



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Hidden and Penfield — Hamlinitefrom Stoneham^ Me. 511

Finally the work of the present paper may be looked at from
quite a different point of view. Suppose for instance, I regard
tne linear isometric proposed by Ramsay and Young (l. c.) as
an established fact. Then the chief result of the present
work, viz : that the exponential equation (2) if applied to the
observed changes of volume predicts a linear isometric through-
out an enormous range of pressure, affords favorable evidence
of the truth of the exponential equation in question. In
other words, it is probable that along any isothermal compres-
sibility increases inversely as pressure increased by a constant.
The interpretation of this constant cannot now be given.

Since the above work was done, I have succeeded in con-
structing a screw compressor,* by aid of which 2u60 atm. may
be hydrostatically applied with facility. I have also con-
structed gauges suitable for the accurate measurement of such
pressure. The general adjustment is of a kind that all nec-
essary electric insulation of different parts of the apparatus is
guaranteed, so that most of the measurements may be made
electrically. With these advantages I hope to subiect the data
which the above pages have tentatively outlined, to a direct
and more searching test.

Phys. Lab. U. S. G. S., Washington, D. C.



Art. LVII. — On Uandinite^ a new rhomhohedral Mineral
from the Herderite locality at Stoneham^ Me. / by W. E.
Hidden and S. L. Penfield.

Shortly following the announcement of herderitef from
Stonehara, the mineral, which we are about to describe, was
detected by one of us occurring as minute rhomhohedral crys-
tals attached to the herderite and margarodite and associated
with a mineral which was subsequently identified as the rare
beryllium silicate, bertrandite. As the crystals were observed
on only a single specimen and would not have weighed much
more than 0*01 gram, if they could have been successfully
detached from the matrix, it seemed imperative that more
material should be obtained before commencing any investiga-
tion. During the past five years, therefore, we have kept up
a diligent search for the crystals, examining carefully every
available herderite specimen ; we have also informed various

♦ A description of this apparatus will be found in the Transactions of • the
American Academy of the present year, I have now done much work with
ether, tracing the isometrics directly as far as 1850 atro. and something over 215**,
without however being able to reach a decision. May, 1890.

f This Journal, III, xxvii, pp. 73 and 135, 1884.



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612 Hidden and Penfield — Hamlinite from Stoneham^ Me,

mineralogists of the occurrence of a probably new rhombohe-
dral mineral, requesting them to examine the specimens in
their own collections, but as up to the present time no success
has attended our efforts we feel warranted in giving as com-
plete a description as possible of the material in hand. We hope
that in the future sufficient material may be obtained for a
complete chemical investigation. We snail, moreover, con-
sider it a ffreat favor if the readers of this article will carefully
"examine the specimens of herderite which may be in their pos-
session and aid us in securing the necessary material.

The system of crystallization is hexagonal-rhombohedral.
The crystals vary from one to two millimeters in diameter and
are quite flat from the predominance of the basal pinacoid.
They exhibit the forms c, 0001, O ; r, lOlO, 1 and f 0221,-2,
which are developed as shown in the accompanymg figure.
All of the planes are more or less uneven, especially r, which
always yielded a number of reflections
of the signal, so that it was quite im- ^ — ^ "^1....?^
possible to obtain accurate measure- w^^ "^ y^^^\
ments from them. The angle which nST'; ^ y^ 7
was selected as fundamental was f /\f^ \^ ^...-y ,^^^^^^^^^^^^^



Online LibraryAbraham Clark Freeman John ProffattThe American journal of science → online text (page 55 of 59)