Mean Temperature Difference and Heat
Transfer Coefficient in Liquid Heat
Exchangers
ALLANP. COLBURN,E. I. du Pont de Nemours & Company, Wilmington, Del.
Where the over-all coeficient of heat transfer,
combined function of heat transHE rate of heat flow bevaries throughout a heat exchanger,the
fer Coefficient a n d t e m p e r a tween twofluidsina heat
ture difference r a t h e r t h a n a
lation of heat transfer by use of the logarithmic
exchanger has customslogarithmic mean of the
rily been e x p r e s s e d a s b e i n g
equal to the product of thearea
mean tenLperature difference m a y lead to conperature d i f f e r e n c e and some
assumed function of the heat
siderable error. For the special case where
of the exchanger, the temperais a linear function of temperature, the simple
transfer coefficient.
ture difference between the two
relationship has been derived that the heat transAfter developing the above
fluids averaged with respect to
method
of design, it was felt
the length of area of the exf e r rate is equal to the logarithmic mean of
desirabletofind
procedure
changer, and a coefficient of heat
UlAt2 and UzAt1, the subscripts indicating
of d e t e r m i n i n g a p a r t i c u l a r
transfer. Where the coefficient
v a l u e of t h e h e a t t r a n s f e r
terminal conditions. A f a m i l y of curves is also
of heat transfer can be assumed
provided f o r this case, which indicates the !emcoefficient which could be used
as constant throughout the apperature to be used with the heat transfer coeflcient
with the logarithmic mean of
p a r a t u s , it was early demonthe terminal temperature differthat the logarithmic
calculated by a logarithmic mean temperature
ences to give also the Same remean of the temperature differences between the hot and cold
difference* Two
examples illustrate the
sult as Equation 1. A specific
liquids a t the two ends of the
application of theseprocedures.
t e m p e r a t u r e was derived a t
which to compute the heat transapparatus is the correct average
fer coefficient to be used with the logarithmic mean of the
to be used.
For liquids, experimental data have more recently shown terminal temperature differences. This derivation is given
a t the end of the paper. The resulting formula is too comh
that the coefficient of heat transfer varies ~ i t temperature
and thus with length of the exchanger, so that the logarithmic plicated to be easily used and so has been represented by a
mean of the terminal temperature differences is not the family of curves given by Figure 1. The ordinate is given
correct average value. To make a correct design for such as the fraction of the temperature rise or fall of either fluid
a case, it has been necessary to apply a graphical solution which should be added to the lower terminal temperature of
using values of temperature difference and coefficient of that fluid to give the correct temperature for calculating the
heat transfer occurring a t small temperature intervals. heat transfer coefficient. The abscissa of the curve is equal
To avoid this laborious procedure, it has been common prac- to the ratio of the temperature difference a t the cold end
tice to accept the error (of variable magnitude) incurred by of the heat exchanger to the temperature difference a t the
employing a logarithmic mean temperature difference and hot end. The parameter is expressed in two ways. For
some arbitrarily chosen average value of the coefficientof heat design purposes, the following parameter may be used:
transfer. Since the over-all heat transfer coefficient in most
liquid heat exchangers is found to approximate a linear relaC' = u 2 - c ' 1
u1
tionship with the temperature of either heat transfer medium,
it was thought desirable to make an integration for the general F~~interpretation of experimental data where the terminal
case for the purpose of determining what values of heat values of heat transfer coefficient are not known, it is necestransfer coefficients and temperature difference should be sary to use the parameter:
generally used. A derivation has been carried out with the
C - tz - t l
assumption that the heat transfer coefficient is a linear funcl/b
ti
tion of temperature for the cases where both heat transfer
mediums are exchanging sensible heat, or where one medium where b = temp. coefficient of heat transfer coefficient in formula:
U = a (1 bt)
is exchanging sensible heat and the other is a t a constant
temperature, such as a condensing or boiling fluid. This
Thus, in interpreting experimental data, the observed value
derivation is given a t the close of the article. The resulting
of heat transfer coefficient which has been calculated by use of
equation is:
a logarithmic mean temperature difference should be corUiAtz - UzAti
related with the properties of the fluid at the temperature
&/A =
(1)
UI At2
indicated by this family of curves. It is necessary only to
2.3 log uz At1
estimate the temperature coefficient of the heat transfer coThus when the heat transfer coefficient is a linear func- efficient to do this. The variation of the factor, F , with the
tion of temperature, the rate of heat flow divided by the area, parameter, C, is not very great, so that even a rough value
& / A , is equal to the logarithmic mean of U2Atl and U1At2, of C will permit a fairly accurate determination of the correct
where 77 and At are the over-all heat transfer coefficient and temperature.
temperature difference, respectively, a t the ends of the apThe new method of designing heat exchangers is based
paratus. This method is a new departure in the design of on the assumption that the coefficient of heat transfer is a
heat transfer apparatus in that it uses a logarithmic mean of a linear function of the temperature of either fluid and, since
T
u,
u
~
+
+
- -
873
874
INDUSTRIAL AND E N G I N E E R I N G CHEMISTRY
this is the case in many instances, the method is often exact.
For example, the heat transfer coefficient of water in turbulent flow is often expressed as a linear function of t as
by Equation 4. Typical equations for heat transfer coefficients for fluids in turbulent flow in general, as exemplified
by Equation 2, have a temperature relationship dependent
on the viscosity-temperature variation of the fluid. Several
of these have been plotted and found to give very nearly
linear temperature relations. For some special cases,
however, the coefficient of heat transfer may not be a linear
0.8
0.7
Ob
0.5
F
04
of the heat transfer coefficients of the aniline and of the
water a t the two ends of the apparatus are calculated by
Equations 3 and 4. A film coefficient of 1000 is to be used
to allow for the thermal resistances of the metal pipe and any
deposit collecting thereon. The water fdm coefficients were
adjusted to the basis of the inside diameter of the pipe and
then over-all heat transfer coefficients were determined from
these two film coefficients and the assumed pipe resistance.
Heat transfer coefficients were calculated also at various
temperatures suggested by previous methods of determining
an average heat transfer coefficient. A graphical integration
was finally made from values of heat transfer coefficients
and temperature differences a t various temperature intervals.
The graphical integration is made by Equation 10, for
which values of 1/UAt are calculated a t regular intervals
of t. Then the area under a curve of l/UAt vs. t between
the ordinates tz and tl is equal to A/wc. Values of At a t any
values of t are calculated directly from a heat balance between the two streams, as indicated by Equation 6. Values
of U are determined from values of the film coefficients calculated a t each temperature interval. The film coefficient for
the cooling aniline is obtained from the Dittus and Boelter
type of equation for cooling liquids:
k
h = 0.0262
a2
O i
OC
where h
002
005
0.1
0.2
0 5 l>b*h
2
5
10
FIGURE1. PLOT
F = factor which multiplied
gives temperature associated
logarithmic mean At.
A t s = temperature
A t h = temperature
tt
OF
F
VS.
20
k
d
so
Atc/Alh
by temperature rise, 17 - ti, and added to
with heat transfer coe5cient, U ,based on
difference at cold end
difference at hot end
function of temperature, and a design based on a logarithmic
mean of UIAtz and UzAtl will not be correct. A design
based on a logarithmic mean temperature difference and the
heat transfer coefficient corresponding to the temperature
indicated by Figure 1 will be found to be a close approximation, as indicated by the examples given. It is therefore
recommended in design work, where it is doubtful whether
or not U is a linear function of t, that designs be made on
both bases with the knowledge that the correct value lies
between the two, being generally closer to the result determined from the coefficient of heat transfer a t the special temperature. In the following examples a solution by direct
use of Equation 1 will be termed method 1, whereas the application of Figure 1 and a logarithmic mean temperature
difference will be termed method 2.
An attempt was also made to derive the correct relationship for the case where the heat transfer coefficient is a
parabolic function of temperature-i. e., U = ai"-but a
differential equation was obtained which could not be integrated for the general case.
EXAMPLES
A. WHEREU Js PRACTICALLY
A LINEARFUI~CTIOK
OF 1.
An exchanger is to be designed for 21,000 pounds of aniline
per hour which is to be cooled from 125' to 25" C. with clean
cooling water a t 20' C. To give an optimum aniline velocity
of around 4 feet per second, a convenient apparatus is found
to be a 2-inch standard pipe jacketed with a 3-inch standard
pipe: A convenient water rate is 5 feet per second through
the jacket, or 23,100 pounds per hour, resulting in an outlet
water temperature of 65" C. The length of the exchanger
will be determined by the required heat transfer area. Values
Vol. 25, No. 8
=
=
=
c =
p =
and
G
=
dG
(x) (--)
C,LI
0,3
0.8
film coefficient
thermal conductivity
inside pipe diameter
sp. heat
viscosity
mass velocity (all in self-consistent units)
Values of most of the variables are nearly constant through
the apparatus. Thus k = 0.103 pound-Centigrade unit per
hour per square foot per ( " C./foot) a t 125' C., and 0.108
a t 25" C.; c = 0.55 a t 125" C., and 0.5 a t 25" C.; d =
(0.207/12) foot; and G = (250 x 3600) pounds per hour
per square foot, Thus k and c vary in different ways with
t , so that (kO.7 cO.3) in Equation 2 is essentially independent of
temperature. For this case Equation 2 becomes:
581
h
= a
where p
(3)
4;
= pounds/hour/foot ( p = 2.42 z,'where z is in centipoises)
Values of the viscosity of aniline and calculated aniline film
coefficients, h,, are given in Table I.
OF ANILINEAND CALCULATED
TABLEI. DATAON VISCOSITY
ANILINEFILMCOEFFICIENTS
ta
125
120
110
100
90
80
70
60
50
40
30
25
tw
65
62.8
58.3
53.8
49.3
44.8
40.3
35.8
31.3
26.8
22.3
20
za
110.5
0.44
0.49
0.59
0.72
0.87
1.1
1.35
1.7
2.13
2.72
3.52
3.95
1.03
1.09
1.19
1.32
1.45
1.63
1.81
2.03
2.27
2.56
2.92
3.09
ha
565
533
490
441
401
357
322
287
256
228
199
188
hw
1960
1930
1870
1800
1740
1680
1610
1560
1500
1440
1375
1340
U
305
295
280
262
246
228
212
195
179
164
148
141
At
60
57.2
52.7
46.2
40.7
35.2
29.7
24.2
18.7
13.2
7.7
5
(l/L'At) X 10'
5.47
5.93
6.79
8.29
10.00
12.50
15.90
21.20
29.85
46.15
87.9
142.0
Water film coefficients are calculated by the equation:
h, = 240 (1
0.0127t) UO.~/DO.*
(4)
where t = water temp., " C.
u = water velocity, feet per sec.
D = equivalent diameter, or clearance, inches
+
+
Since u = 5 and D = 0.699, hw = 935 (1 0.0127t), based on
outside diameter of pipe. Then based on inside diameter,
h, = 1073 (1
0.0127t), values of which are included in
Table I. Including a coefficient of 1000 to take care of the
pipe and scale resistances (for clean liquids), over-all heat
transfer coefficients are calculated a t each temperature and
+
August, 1933
I N D U S T R I A L AN D E N G I N E E R I N G CH E MI ST R Y
included in Table I. Values of l / U A t were computed for
each temperature and plotted on Figure 2. The area under
the curve between tl = 25" and ts = 125" C. is found to be
0.02.5 = A/(wc). Since w is 21,000 pounds per hour, and c,
the specific heat, is 0.525, A is 0.025 X 21,000 X 0.525 =
275 square feet of cooling surface, obtained by the graphical
integration, which is the correct value of area for this problem.
t
A, COOLING
ANILIYIZWITH
FIGURE2. EXAMPLE
KATER
U = heat transfer ooe@qient0
t = temperature of aniline
C.
A t = temperature differencibetween aniline
and water
By method 1, (UAt),.,. = logarithmic mean of UI At? and
U z Afl, or of 141 >(: 60 and 305 X 5 or 4050. Since Q =
21,000 X 0.525 (12.5 - 25) = 1,103,000 P. C. U. per hour,
d = 1,103,000/4050 = 273 square feet.
By method 2, At,/Ath = j/60 = 0.0833. C = ( Cz - Vl)/U1
= (305 - 141)/141 = 1.16. ThenfromFigure 1, F = 0.253,
( t z - t l ) / ( t z - t i ) = ( t z - 25)/(125 - 25) = 0.253; t z =
50.3" C.; and Lrz = 180. The logarithmic mean At of 5
and 60 = 22.2, so ZJ, Ati.,. = 180 X 22.2 = 4000. Then
1 = 276 square feet.
Figure 2 shows a plot of the calculated over-all heat transfer
coefficient against temperature of the aniline and indicates
how nearly U varies as a straight-line relationship with t.
A summary of the resulting calculations is giyen by Table
111. The two recommended methods give results on both
sides of the correct graphical integration, with method 2 being
closer. Either method, however, gives results checking the
correct cooling surface within one per cent. Any of the previously applied approximation methods would have been considerably on the unsafe side.
B. WHEREU Is KOTA LIKE.4R FUNCTIOK
OF t . Straw
oil is to be heated from 80" to 200" F., flowing a t an average
velocity of 3 feet per second through a standard 2-inch horizontal pipe using steam a t 227" F. in a jacket outside the
pipe., The oil has a mean specific heat of 0.47, a mean specific
gravity of 0.85, and a mean thermal conductivity of 0.078 in
English units. The viscosities of the oil are 18 and 4 centipoises a t 80" and 200" F., respectively, and a plot of viscosity
vs. temperature on logarithmic paper may be considered a
straight line. The outside and inside diameters of the pipe
are 2.38 and 2.07 inches, respectively; the thermal conductivity of the pipe is 35 in English units. Since the oil side resistance is controlling, the heat transfer coefficient on the steam
side will be assumed constant a t 2150.
In this case the heat transfer coefficient does not vary as
the 0.8 power of Reynolds number, since the Reynolds
number is near the critical value. Values of the oil film codG
efficient, h,, are obtained from a plot of
rs. P
given by Figure 3.
The equation for the over-all coefficient is:
?,/ (T))"'
-1 _U
873
1
0.154/12
1
2150 (2.38/2.07) + 35 (2.19/2.07) + %
= 0.000751
+ -ho1
(5)
Table I1 gives calculated values of over-all coefficient, temperature difference, and of l / U A t a t various temperature
intervals. Figure 4 shows a plot of U vs. t and of 1/UA2
m.t. The area under the latter curve from t = 80" t o t =
200" F. is found t o be 0.0321 = A/wc. Since w is 13,350
pounds per hour and c is 0.47, A = 0.0321 X 13,350 X
0.47 = 202 square feet, which is the correct solution for this
problem.
By method 1, (UAt),.,,. = logarithmic mean of GI At? and
V2 At,, or of 21 x 27, and 69 x 147 = 3340. Since Q/A
= 13,350 X (200 - 80) x 0.47 = 753,000 B. t. u. per hour,
A = 753,000/3340 = 225 square feet.
By method 2, Atc/& = 147127 = 5.43. C = (Cz Ul)/Ul = 2.27. From Figure 1, F = 0.54; then t, =
145' F., U,= 54.5. The logarithmic mean At = logarithmic
mean of 27 and 147, or 70.7. U , Ah.,,.= 3850. A = 196
square feet.
TABLE11. CALCULSTED T7ALCES AT \-.<RIOCS TEMPERATURE
IXTERVALS
1
t
80
90
100
110
120
130
140
150
160
170
180
190
200
z
18.0
15.0
12.5
10.8
9.3
8.2
7.2
6.4
5.8
5.25
4.80
4.40
4.00
DG/ir d k hD/k
h
263
47.5 21.5
219
65.6 29.7
183.5 8 2 . 1 3 7 . 1
158
93.2 42.1
136
104.8 47.4
120
114.2 51.6
105
123.0 55.6
9 3 . 5 128.7 5 8 . 1
8 4 . 6 138.8 6 2 . 7
7 6 . 6 146
66.0
7 0 . 1 150.5 68.0
6 4 . 2 156.0 7 0 . 5
58.4 161.8 73.0
l/h
1 / C T - t Lr(T
147
137
127
117
107
97
87
77
67
57
47
37
27
- t)
U
Figure 3 shows a curve of heat transfer coefficient us. temperature which is considerably concave downward. A comparison was again made of area determined by the use of
various methods as shown by Table 111. For this case,
method 1 recommended herein gives an area too large, and
8
6
4
3
2
3
4
5
20
6
30
r
FIGURE
3.
CIENTS
FOR
TRANSFER
COEFFIHEaTIXG HEAVYA N D
MEDIUMOILS
HEAT
method 2 gives one slightly too small. The reason for this
difference can be seen by examination of Figure 4. The first
method is based on the assumption that U follows the dashed
straight line A. Method 2 assumes that U is expressed by
the dashed straight line B which is a closer approximation to
the true curve. The true curve will practically always lie between A and B so that the true area will be between the areas
computed by the two methods given herein when U is not a
linear function of t.
I N D U S T R I A L -4S D E N G I N E E R I N G C H E M I S T R Y
876
TABLE111. COMPETED
AREAS F R O N
A
ERROR
-4
5%
.
-
Integrating:
= Q/Uat
B
ERROR
%
Correct method:
Graphical integration
275
...
202
..
Recommended methods:
Method 1
273
- 0.7
225
11.4
Method 2
276
0.4
196
-2.9
Methods previously used:
U at t n ~ and
. ~ At 1. m.
227
-17.5
202
0
L'w. and At 1. m.
223
-18.9
249
16.8
Gay. and Atav.
152
-49.7
192
-5 0
U at ( t a
At I. m.) and A 1. m. . .
...
191
-9.4
a Subscript BI. indicates arithmetic average of terminal values, 1. m . indicates logarithmic mean, s indicates surface temperature for case B where the
surface temperature is constant.
Vol. 25, No. 8
1
Simplifying by use of Equation 7 and rearranging:
f,
-*
a(1
- t,
+ bti) (Tz - t z ) - ~Tz( -+l t btz)
(Ti z
-A
ti)
+
~ ( l btz)) = A
- (15)
(In m
i a(l
btl)
wc
Substituting, U1 = a(1 btl); U z = a(1 bt2);
*
Atl = Ti - tl; and Atz = T2 - tz
+
+
+
?VIATHEMATICAL DERIVATIONS
SOLUTION
OF CORRECT
VALUESOF HEATTRANSFER
CoEFFICIENT AKD MEAK TEMPERATURE
DIFFERENCE
TO BE
USEDIK DESIGNING
LIQUIDHEATEXCHANGERS.
Assumptions: (1) The over-all heat transfer coefficient, Lr,
is a linear function of temperature t; i. e., I; = a (1 bt),
where a and b are constants, and t is the temperature of one of the
fluid s t r e a m s . T h e
specific heats are constant, and heat losses
are negligible.
(2) The derivation
is limited to the follomi n g c a s e s : (a) T w o
heat transfer mediums
in countercurrent flow
are changing in temperature in such a way
that t h e d e c r e a s e in
sensible heat of one is
equal to the increase in
s e n s i b l e h e a t of the
FIGURE4. EXAMPLE
B, HEATIKG other; or (b) One heat
transfer medium is a t
OIL WITH STEAM
a constant t e m p e r a U = heat transfer coe5cient
t = temperature of oil, F.
t u r e , such as a conA t = temperature difference between
steam and oil
densing vapor or boiling liquid, and the
other is changing in sensible heat as indicated by a temperature rise or fall:
+
Combining Equations 16 and 6 gives:
SOLUTION OF TERlPERlTURE TO BE U S E D I S DETERMINING
A PARTICULAR VALUE OF HEAT TR.4KSFER COEFFICIEKT
WHICH,WHENGSEDWITH A LOGARITHMIC
MEANTEMPERATURE DIFFERENCE,
GIVES SAMERESULTAS EQUATION 1.
An instantaneous value of the heat transfer coefficient,
U,, can be found so that:
[
Q_=
At1
-
" 2.3 log
-4
Substituting,
+
dt
U (T - t )
Xh
or :
dA
=-
wc
+
Ab
a [1
at
A
+ btl [Ti - Btl + ( B - 1 ) t I = -wc
Separating into parts:
u(B
-
1
1 - bTi
+ bBti)
= a(1
mz
(17)
+ bt,); U2 = a(1 + biz)
- a(l
-k btil At?
Afz
Let F
t. -
ti
= t z - 11
F is thus a fraction, which, multiplied by the total temperature rise of one fluid stream and added t o the lower terminal
temperature of the same fluid stream,
gives the t e m p e r a t u r e at which to
c a l c u l a t e the U to be used with a
logarithmic mean At.
Substituting these equivalents in Equation 14, and s i m p l i f y i n g , notingthat
1
btz
k@2
=C
1, and that -= CF
1
btl
1
bt!
+ 1, gives:
FIGURE5. TIP I CAL
TEMPERAT U R E DISTRIBU-
1
F =
+
+
+
TION
+
R
C +logR (C
- - l+ 1) - C
'+
(19)
log R
A family of curves for solving this equation is given by Figure 1 -
(11)
t
(12)
UzAti - UiAtz
2.3 log Uz Ati
Ai
2.3 log -'
,_
dA
(9)
=
~ ( -C
1 bh) At1
(8)
A
U ( L ) = -wc
For the case considered, U = a (1
bt)
Substituting Equations 7a and 11 in 10 gives:
21
u, = a(1 bt,); U1
Equation 17 becomes:
I/
By a heat balance over the differential area, d A ,
dQ = U (T - t ) d A = wcdt
Equation 8 can be rewritten as follows:
Atz
T
ti, ff
TI, T i
U
=
=
=
=
=
NOMENCLATURE
(REFERTO FIGURE
5)
temp. at any point of cold
C.
temp. at any point of hot fluid C.
terminal temp. of cold
k.
terminal temp. of hot fluid, C.
heat transfer coefficient at any point, P. C. U./hour/sq.
=
=
=
=
heat transfer area, sq. ft.
heat transfer rate, P. C. U./hour
rate of flow of cold liquid, Ib./hour
rate of flow of hot liquid, lb./hour
ft./O
A
Q
w
W
c.
August, 1933
C
= sp.
C
=
INDUSTRIAL A S D ESGINEERING CHEMISTRY
heat of cold liquid, P. C. U./lb./" C.
sp. heat of hot liquid, P. C. U./lb./" C.
ACKNOWLEDGJIENT
The writer wishes to acknowledge the valuable criticisms
of W. H. McAdams and to thank him for permission to use
877
the material in example B which was taken from his unpublished notes.
RECEIVED
January 31, 1933. Contribution 119 from
t h e Evperirnental
Station, E. I d u Pont de Kernours 8: Company.
Improved Process for Physical Development
of Plates, Films, and Lantern Slides
ALLANF. ODELL,The du P o n t Tiscoloid Company, Inc., Arlington,
N. J
Attention is directed to the unusual and litfle
to finish one negative a t a time.
HE introduction of the
Finally, the precipitating silver
physical
Of
known merits of the process of physical developmakes the operation unspeaknegatives, which is an
ment. An improz!ed and simplijied process has
ably dirty.
adaptation of the method used
t o d e v e l o p t h e collodion
been worked out which makes Physical detelopComplete descriptions of the
menl as simple and successful in practice as
methods currently in use may
emulsion plates of the middle of
ordinary 7nethods of photographic dettelopment.
be found in the l i t e r a t u r e alt h e l a s t c e n t u r y , has b e e n
has been applied to practically ecery
ready cited, and in a few availascribed by various authors to
The
able t e x t b o o k s (1-4, 18). In
( I h ) , K e u h a u s s ("),
make and type of plate andfilm on the market.
Reneral, these
are all
a n d Kogelmann ( 5 ) , b u t t h e
l a t e r de\yelopments i n t h e
Seceral lal)oraforY and technical aPPlicafions Qf
similar and, aside from those
of Sterry ( 1 6 ) and of Neuhauss
Ihe method are pointed out where the process
method are to be found largely
should hai!e an outstanding adivmfage.
(13) which consist of a bath of
in t h e p u b l i c a t i o n s of t h e
hypo, ammonium sulfocyanate,
LumiBres and Seyewetz (9) and
of Luppo-Cramer (10-12). Wall
s o d i u m sulfite, s i l v e r nitrate,
(17) claims that the method applied t o dry plates was first and a developer-reducer, and from one proposed by the
suggested bv Abner in 1878.
Lumihres and Sevewetz (8) of a neutral solution of silver
nitrate and sodium sulfite,'all are made up of baths containADVdNTAGES O F PHYSICAL DEVELOPhlEXT
ing citric acid in high concentration, metol, and silver nitrate,
Physical development, in the sense the term is used today, sometimes with the addition of sodium citrate, sodium sulfite,
is to be distinguished from ordinary methods which are gener- gum arabic, etc.
Most authors have noted that the image from physical
ally employed in all photographic work, sonietimes called
"chemical development" in order to introduce a difference in development is composed of an extremely fine grain, and that
terminology, by the fact that the developing bath contains a the gradation is beautifully exact. The extreme fineness of
silver salt in solution from which colloidal silver is obtained the grain size, coupled with the fact that this grain is formed
by reduction with a suitable agent, also in the solution, and independently of the grain of the original emulsion, constitutes
the production of the negative image results from the deposi- the chief advantage of the method. One may thus use coarsetion of the nascent silver upon the silver nuclei forming or grain superspeed emulsions to obtain fine-grain images. This
originating in the latent image. Both methods are, of course, factor becomes of great importance where enlargements of
chemical, and the developing baths resemble each other by unusual size are to be made from small negatives.
Aside from the many beautiful and useful aspects which
the further fact that they both contain the same developers
as reducing agents. Physical development occurs only when physically developed negatives have from an artistic standthe bath contains one of the usual photographic developers, point ( I J ) , such negatives and prints, or enlargements made
which must function first in some manner by preparing the from them, should have a definite appeal to the scientist and
laboratory worker in nearly any field where photography is
latent image to receive the silver deposit (6,7,12,15).
Physical development has been little used outside the labo- applicable.
ratory, where it has proved a valuable adjunct in research
Wherever reproduction as close as possible to the original
upon emulsions and upon the theory of image formation, and and with an absence of unnatural contrasts is desired, for
information upon the method, while widely distributed intricate detail, and for clean and extraordinarily sharp line
through the literature, is rarely found outside of very re- work particularly for measurements, this type is better
stricted fields. It has so many advantages, however, that it adapted than the ordinarily used methods of photographic
should long ago have been put upon a practical operating development. It should be of value in mierophotography and
basis and introduced as a part of laboratory technic wherever cross-section work especially, in biological work (particularly
photographic requirements are necessary.
photographs from life), and in x-ray work where grain is a
The reasons why this has not been done are readily found in problem and undue contrasts are not desirable; i t should
the difficulties that surround the present methods. Long ex- prove especially valuable in spectrum photography where
posures, up to ten to twenty times normal, are required. The both sharpness of lines and correct comparative densities are
development takes from 6 to 48 hours with ordinary
imDortant.
- negative
emulsions. The bath must be freshly renewed every hour
SIMPLIFIED
PROCESS
FOR PHYSICAL
DEVELOPMENT
or two. The solutions, usually strongly acid, attack the
emulsion, and the most careful handlingis necessary t o avoid
A study undertaken to improve existing methods of physical
marring the surface. It requires all one's personal attention development showed, after repeated experiments with the
T