º
º
ºº º
º º
º º
- º
º
- Tº
-
º
º
º … .
º tº
-
---
º
T
º
º
º º
º º
º º
º º º
º º
º T º
º º
º º
º º º
-
T-
º
ºº
º:
-T-
- º
º
º
º: º
º:
º
º
-
º
º
º:
º
--
|
*** -
ººz.
º
--
-º-
º
º
º
º
º
- º º
- º º
º º º º º º
º º º
º - -
º º - º º
º
º
º º º
º
º
º
º
º: - º
º |
º º -
. -
º º
º:
º
º
º
º º º
º - -
º º
º
º º
º
º
º
|
º º -
º º
| º
-
º º
º º
º º
º º
º
º
- º --
º º
º
- º
º
º
º
º
- º
---
º º
º
* -
º º
º º
-
-
º
º º
º
- º
---
º º
º
- |
º
º
º
º
º
º
T
º
º, sºoºººº-
_ FC Z. C. E.
-
º
º
-
º º
º
- º
º º º
º - º
º º º
º
-i.
…
---
º
º
º - -
º
-- º
--
º
º
|
-
º
º
-
º
!º
º
º
-
| -
º
-
T = 3 º
ALUMINU M.
º
-
º
º
- - -
--
º
--
-
º
…
º
º
|
--
º
º
º
tº
º
º
º
º
º
º
| -

TX f < 3
4+2,
i
;
| 00042
COUNTER ELECTROMOTIVE FORCE
in
THE ALUMINUM RECTIFIER.
ALBERT LEWIS FITCH.
A dissertation submitted in partial fulfillment
of the requirements for the degree of Doctor of
Philosophy in the University of Michigan.


TABLE OF CONTENTS.
++
Measurement of the Counter E.
M. F.
I. Introduction.
l. Historical Review— — — — — -- - - - - - - - - - - - - - - - - - - -- -l.
2. Other metals used -------------------------- ºl.
3. Electrolyte S ------------------------------- l.
4. other factors - - - - - - - - - - - - - - - - - - - - - - - - - - - - -- l.
5. The orie S advanced — — — — — — — — — — — — — — — — — — — — — — — - - - 2.
6. Condenser action — — — — — ---------- - - - - -- - - - --- 2.
7. Object of this investigation --------------- 3.
II. The First Study.
l. Apparatus -
a . Disk — — — — — — — — — — — — — — — — — — — — — — — — — — — — — — — — — — — — 3.
b. Motor connections - - - - - - - - - - - - - - - - - - - - - - - ,4.
C. Cell used - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 4.
d. SWitches — — — — — — — — — — — — — — — — — — — — — — — — — — — — — — — — 5.
e . Other instrument, S used - - - - - - - - - - - - - - - - - - 5.
2. Operations --------------------------------- 5.
3. Advantage S of this method ------------------ 7.
4. Data and discussion ------------------ ------08.
a . Table I. ------------- - - - - ------- - - - - - - - - 8.
b. Table II. ------------------------------- 9.
III. The Second Study --------------------------- 10.
l. Reasons for this study ---------------- - - - - 10.
2. Apparatus --------------------------------- 10.
3. Operations -------------------------------- ll
4. Circuit, S - - - - - - - - - - - ------- - - - - - - - - - - - - - - - - ll.
5. Measurement of the time of open circuit -- 12.

TV.
7. Curve of counter E. M. F. and time of open circuit -- 13.
Theory Proposed ------------------- - - - --------------- 13.
l. Derivation of the formula - - - - - - - - - - - - - - - - - - - - - - - - - 14.
2. Determination of the constants — — — — — — — — — — - - - - ------ 18.
3. Computation for constants ------------------------- 29.
4. Discussion of the formula ----- - - - - - - ----------- — — — 21.
5. Explanation of the curves ------------------- - - - - - - 24.
Plates
l. 1.-- 1 - - - - - - - - -- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 25.
2. l -- 3 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 26.
3. l- - 4 - - - - - - - - - - - - - - - - - - - - -------- - - - - - - - - - - -- - - - - - - - 27.
4. 2--1 — — — — — — — — — — — — — — — — — — — — — — — — — — — — — — — — — — — — — — — — — — — — — — 28.
5. 2.--2 ------------------------------- - - - - - - - - - - - - - - 29.
6. 2.--3 — — — — — — — — — — — — — — — — — — — — — — — — — — — — — — — — — — — — — — — — — — — — — — 3C .
7. 2.--4 ---------------------------------------------- 3l.
8. 2.--5 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 31.
9. Calibration curve for set, s l and 2 - - - - - - - - - - - - - - - - 32.
10. Calibration curve for set 4 ---------------------- 32.
ll. 4- -l - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -------- - - - - - - - 33.
12. 4- -2 - - - - - -------- -------------------------------- - - 34.
l3. 4- -3 - - - - - ---------------------------------------- 35.
14. 4.--4 --------------------------------------------- 35.
lö. 5-–l ------------------------------ - - - - - - - - - - - - - - - 36.
16. 5-–2 ------------------------ - - - - - - - - - - - - - - - - - - - - - 37.
17. 5-–3 --------------------------------------------- 38.
VI. Discussion of Curves — — — — — — — — — — — — — — — — — — — — — — — — --------
1. Difference from other cells — — — — — — — — — — — — — — — ----------
2. Consequences of this view - - - - - ------------ - - - -----
3. As a rect, ifier - - - - - - - - ----- - - - - - - -------- - - - - - - - - -
4. Set 4 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - ---------- -
5. Set 5 - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
VI. Summary -------------------------------------- --------
VII. References -----------------------------------------

COUNTER ELECTROMOTIVE FORCE IN THE ALUMINUM RECTIF IER.
INTRODUCTION.
Historical Review.
The anomalous action of aluminum in the electrolytic cell was f i r St.
discovered by wheatstone in 1855. Soon after this, Buff found that an
electrolytic cell one electrode of which was aluminum would rectify
the alternating current. Among the other men who have been interested
in this cell may be mentioned Ducretet (10), Hutin and Leblanc (lb),
Montpellier (21), Nodon (25), Guthe (12), Greene (13), and Schulze (28––34).
The last named of these has perhaps done the largest amount of work
of any. His articles have appeared from time to time in a number of
magazine S.

Other metals used.
The earlier experimenters with this cell confined themselves to
the study of aluminum but later investigation (31) has shown that
many other metals possess this same property to a greater or less
degree. Among these athere)may be mentioned iron, nickle, cobalt, mag-
nesium, cadmium, tin, bismuth, zirconium, tantalum, etc.
Electrolytes.
A great number of electrolytes may be used in the rectifier. The
most commonly used are the alums, phosphates, and carbonates; however
Graetz and Pollak have shown that any electrolyte Which Will liber-
ate oxygen on electrolysis may be used more or le SS Satisfactorily.
Other factors influencing the cell's action.
It has been found that the ability of the cell to rectify alter-
nating current depends upon the current density at the aluminum
2.
the electrons are with difficulty forced thru.
anode (23), the inductance and resistance of the circuit (27), and its
temperature (31). The cell rectifies best when the current density
is high and the inductance, resistance, and temperature are low.
The ories advanced .
Several theories have been advanced to explain the action of this
cell. The earlier theory known as THE SOLID FILM THEORY ascribes this
action to the electrolytic deposition and decomposition of a solid
film of Some oxide or hydroxide of aluminum on the aluminum anode.
The deposition takes place While the current flows in one direction
and being a high resistance material the film soon grows to a thick-
ness which shuts off the current in that direction. The de composition
takes place when the current is in the opposite direction and per- ~
mits the current to flow unimpeded from the electrolyte to the elec-
trode . -
In 1902 Guthe (12) first gave us the later theory, known as THE
GAS FILM THEORY. This theory ascribes the action to a film of oxygen
gas which is spread over the solid layer. The free electrons of the
metal are forced thru the gas film by the very high potential grad-
ient with very little difficulty when the aluminum is the cathode,
but when the current reverses, and the aluminum is the anode, no such
- º
- --- *.
tº ſº
thing can take place for there are no free electrons in the electro-
-
lyte. Instead, the current must be carried thru the film by the ions
of the electrolyte and these being relatively large as compared to
Condenser action.
It has been known for a great many years that the aluminum cell
acts to a certain extent like a condenser. Schulze (31) states that
a cell 40 x 40 x 40 cm. With both plates of aluminum had a capacity
of 5,000 mſd. On 160 volts alternating current of a frequency of 50




3.
cycle 5 per Second. It was possible, he states, to take an alternating
current of 250 amperes thru this condenser. But one must not go too
far in likening this cell to an ordinary leaking condenser as Greene .
(13) has shown. -
Object of this investigation.
This investigation was undertaken to determine if a more careful
study of the counter electromotive force, which is produced when the
current enters at the aluminum, would throw some light on the action
Of the cell as a condenser and also on the theories advanced.
THE FIRST STUDY.
Apparatus.
Disk.
The first study was undertaken with the apparatus as shown in Fig. l.
D is a disk designed for this work and made in the Engineering Shops
of the University of Michigan. It is a solid hard rubber disk of ap-
proximately 31 cm. radius. Firmly fastened to this disk are three con-
centric rings of brass. The inner ring R, has an inner radius of 12
cm. and an outer radius of 16 cm. It is made in one solid piece. The
second ring R, has an inner radius of 19 cm. and an outer radius of
23 cm. It is divided into Sectors ranging in magnitude from 5 degrees
to 35 degrees. The outer ring Rs has an inner radius of 26 cm. and
an outer radius of 30 cm. It is divided into sectors ranging from
3.75 degrees to 28 degrees. Each sector on each ring is connected
electrically to a binding post on the back of the disk. On the cir-
cumference of the disk is a steel tire. The disk is mounted on the
shaft of a Roth motor, designed to run at 2, 000 R. P.M. on 220 volts
direct current. This disk is enclosed in a wooden box supported on
sliding arms so that the box can be brought as near as desired to

4.
the disk and then clamped fast. The front of this box holds the brush
C Ontact, S B, , B, , B, , made of spring steel with brush contacts of sheet
C Opper". B, and B, are bolted directly to the box and allow the brushes
fastened to them to bear on the rings R, and Rs. B, is a moveable brush
contact, Supported on a brass rod bent at right angles and passing
thru the box front at a point directly in line with the center of
the motor Shaft. A long brass pointer P is fastened to this brush
holder by heavy brass nuts and plays over a protractor of 8 inches
radius divided into quarter degrees. On the back of the disk, the sect-
ors are connected as is shown by the dotted line. -
MO t, or connections.
The mot, or is connected With it, S field over the 22C volt, direct,
current power line and its armature over the storage battery. By
this arrangement, any desired speed up to 2,000 R. P.M. is attainable
by varying the number of cells of the storage battery.
As shown in the diagram, S.B. is the storage battery to furnish
current to the cell C. This cell is composed of a lead plate with
an area of approximately 90 sq. cm. and an aluminum Wire .258 cm.
in diameter and 10 cm. in length, immersed in a saturated solution
of sodium phosphate. The lead is the same grade as is used in the
Chemistry Department in qualitative chemical experiments and is a-
bout 99% pure. The aluminum wire was tested and found to contain .27%
iron and considerable silicon in the form of Silicate S. It is about
99% pure. Both electrodes are heavily coated with a good grade of
Sealing wax where they emerge from the solution to eliminate surface
effects which were found to be present when the electrodes were not

coated.

Switches.
S, and §2. make an eight pole double throw switch. Sg is a double
pole double throw switch of the tilting type. A slight movement dis-
connects one side and connects the other. The two sides are electric-
ally connected as ShoWn. S., and S - are single pole switches. All these
SWitches are made of heavy copper.
Other instruments.
R; and R. are high grade Leeds and Northrup resistance boxes each
having a total resistance of 21, lll .5 ohms. G is a Leeds and North-
rup high sensibility galvanometer With a resistance of 1600 ohms.
This galvanometer is fitted with a concave mirror of 40 cm. focal
– length. The source of light, a single filament carbon lamp, and the
Scale of translucent celluloid are arranged to Slide on two guides,
one on either Side of the gaivanometer. By this arrangement, the Whole
System of light, and scale can be moved back and forth until the pos-
ition for the best focus is obtained. H. R. is a high resistance box
in series with the galvanometer. All resistance was cut out of this
box before readings were taken. L is a carbon lamp inserted to cut
down the current when the switch was first thrown. A is a Weston
ammeter with . Cl ampere divisions.
A suitable voltage was obtained over the storage battery termin-
als with S, S, open and S, thrown to the right. S, and Sº were both open.
The sum of the resistances R." and R' was kept at 21, loo ohms. Then
When S, Sa was thrown up the current flowed from the storage battery
around a divided circuit. R' and R; form One circuit, and the Other
is thru S, , S, , C, A, T, and back to S. B. When this current, as shown by
the ammeter, had dropped to . Cl ampere, Sz Was closed, cutting out all
6.
resistance in series with the cell, and when the current had again
dropped to . Cl ampere the ammeter A was cut out of the circuit, by
closing Ss. The cell was left directly across the storage battery
for a time and then the motor Was Started. When the motor had attain-
ed full speed, S, was thrown to the left, cutting the cell off from
direct connection to S.B., and closing the circuit thru the rotating
disk during one half of each revolution. The current then flowed from
S. B. to E down the wire at the right to F then to B, . From B, it
flowed thru the disk to the Wire on the back and around to R, thence
to B, N, I, O, to S, and thru C back to the storage battery. By this
2.
arrangement, the cell was placed across the battery one half the
time and for a sufficiently long time during each revolution to
bring it back to its former State. However as soon as the last sec-
tor connected to this wire had passed B2 the circuit, thus establish-
ed was broken and the cell was left on open circuit until the sector
on R, which was connected to this wire came under B, . The cell Was
then placed over a fraction of the storage battery voltage equal to
_R.' W, , where V, designates the storage battery voltage and r"
FT. F. FF'

designates the storage battery resistance. Since r is so very small
as compared to R, and R, it may be neglected and was in all comput-
at ions. Current, then flowed from S.B. thru B.E.,H.R.,8,9,8, ºr to
the moveable arm r, thru B. , the wire and ring R, to N, I, O and thru
the cell back to the storage battery. The resistances in R, and R!
were adjusted until the galvanometer showed no deflection when H. R.
was all out, the sum of R, and R. being kept at 21, 100 ohms. Then the
counter electromotive force of the cell equalled R.' V,
Fºr-Fºr-Fr"
The time of open circuit was computed from the position of the
pointer on the protractor. The moveable arm r was moved to a new
\ .


7.
position as indicated by the pointer and a new reading taken. The
position of the pointer for zero time of open circuit, was found by
connecting a dry cell and ammeter in series with B2. and Ps and ro-
tating r backward until the contact was broken.
Sg Was kept thrown to the right all the time except. When readings
Were actually being taken. This placed the cell across the Storage
battery most of the time and When not directly over the storage bat-
tery it still was placed across it one half the time thru the disk.
Advantages of this method.
This method has some decided advantages over the method used by
Greene (13). The cell was placed directly across the storage battery
terminals when readings were not actually being taken, thus insuring
a much more steady state in the cell than if the cell were connect-
ed only thru the disk. When the cell was connected to the battery
thru the disk, it was connected for a much longer time thaºcula
attain. The counter electromotive force was measured directly against
the applied voltage thus making R, and R! : R. more nearly equal than
if a standard cell had been used. Also any slow change in the appli-
ed voltage has much less effect on the final results if our measure-
ments are taken against it directly than if We must compare both
applied voltage and counter electromotive force to a third source.
The readings could be taken at an average of one per minute or less
and the period of open circuit could be changed without stopping the
nearly
motor, thus insuring a mueh morea constant speed. Since the armature
battery
current was from the storage Awe could control the speed within wide
limits. The slower speed enabled us to take readings for much longer
periods of open circuit than if the motor had run at 2, 000 R. P. M.
The points on the curve of counter electromotive force and time of
8.
open circuit, could be plotted as closely as desired, the only limit
being the accuracy of placing the pointer. On so large a protractor
3. S W 3 S used, it was found that this could be done to . l degree.
Data and discussion.
Table I.
Speed, 300 R. P. M.
Electrolyte, Saturated solution of sodium phosphate.
Applied voltage, 97 volts.
Time of closed circuit, read at end of readings, T.
Time of open circuit in seconds, t .
Counter E. M. F., V, in volts.
T------- l. 5 hrs. --4. 1 hrs. --5. 5 hrs. --25 hrs.
t V V V V
. OCOOOC 97. O 97. C 97. O 97. O
. CCO278 95.4 96.1 96.5 96.8
. OC1945 94.7 95.2 96.2 96.5
. OC472 93.3 94.8 95 - 6 96. l
. OC 752 92.3 94.4 95.2 95.7
. Cl31. 90.3 92.8 94.2 95. 1
. Cl86 88 - 5 91. 2 93.4 94.5
. C297.5 85.8 89. 6. 91.8 93.3
. C408 83. 6 85. 6 90.3 92. l
. C520 81.8 84.9 89. O 91. O
. O631 79. 8 83.9 87.6 90. O

It, Will be noticed in the above data that the counter E. M. F. is
not only a function of the time of open circuit, but also of the
time of closed circuit. One cannot assume then that this cell Will
assume a constant state and remain there for any appreciable length
of time. Since it took between 10 and 15 min. to take a set of read-
ings, one must conclude that the curve plotted between counter elec-
tromotive force and time of open circuit is not a simple curve as
desired but a sort of composite curve. The error due to the assump-
tion that the cell remains constant during the taking of a set of
readings is larger the shorter the length of time of closed circuit.
F-
24e y
Therefore if one wishes to use such data #t= must be taken after a
time of closed circuit sufficiently long so that the time for taking
the data is negligible. This explains why Some investigators have
had difficulty in reproducing their curves when the period of clos-
ed circuit was a matter of a few minutes. This same variation of
counter electromotive force is noticeable táciº all the range of volt-
age applied from 2 volts to 97 volts. -
Table II.
Speed, 300 R. P. M.
Electrolyte, Saturated Solution of sodium phosphate.
Applied voltage, 2. l volts.
Time of closed circuit, read at end of readings, T.
Time of open circuit in Seconds, t .
Counter E. M. F. in volt S V.
T— — — — — — — — 22 min. -55 min. --l. 5 hrs. -2.25 hrs: 3 hrs. ---4.5 hrs. - 5.5 hrs.
t, V V V V W V V
ÇOOOOO 2.100 2. 100 2. loo 2. loo 2. loo 2. 100 2. loo
. CC222 2. O90 2. O9.5 2. O96 2. Q98 2. O98 2. C98 2. Q98
. OC50 2. O8O 2. O9C 2.092 2. C94 2. Q94 2. O9.5 2. O93
. OC78 2. O'74 2. O85 2. O88 2. O90 2.091 2. O90 2. C90
. Ol33 2. C6C 2. O'77 2. Q8 2. Q83 2. O84 2. C84 2. O82
. Ol&9 2. C48 2. C67 2. O'73 2. O'77 2. O'78 2. C79 2. O'77
. C328 2.013 2. Q46 2. O55 2. O62 2. O65 2. O67 2. O63
. Q466 1.989 2. Q23 2. Q4C 2. O46 2. O55 2. O56 2. O57
. O606 1.963 2. OC 7 2. O20 2. O33 2. C4O 2. C40 2. C37
. O'745 1. 943 l. 990 2. Olo. 2. O21 2. O29 2. O3 l 2. Q27
. O855 1. 930 l. 980 l. 997 2. Cl3 2. O20 2.921 2. C2C
As in Table I it tº feed that, the counter electromotive force
is a function of the time of closed circuit, as Well * time of
open circuit. It Will also be noticed that for corresponding periods
of closed and open circuit this lower voltage has a much larger value
Aora aſ 'ces
Of V/V. . Therefore the time for taking readings makes a greater er-
ror in the lower voltages than in the higher.
A





10.
THE SECOND STUDY.
Reason for second study.
Since the time for taking readings by the former method could not
be decreased, the oscillographic method was devised. This method en-
ables one to take a complete set of readings in about one second.
This eliminates to a large degree the objection to the former method
and also eacºles one to get readings for much shorter periods of
closed circuit.
Apparatus.
The diagram förathe oscillographic arrangement of apparatus is
ShoWn in Figure 2. In this arrangement, the Same disk was used as be -
fore With the same brush contacts and the same electrical connections
on the disk . In the back of the box face, a large screw Was placed
to stop the rotating arm r at the same place each time. As before;
it was arranged to have the cell placed directly across the Storage
battery when readings were not being taken. S., and 5. eight pole
double throw switch. S., and S3 are double pole double throw switches.
C is the rectifier. L is is a lamp for resistance. A is a Weston
ammeter with . Cl ampere divisions. L and A may be cut out of the
circuit by switches S, and S, . R is a Leeds and Northrup resistance
box with a total resistance of l, lll ohms and 0 is the vibrator of
the Siemens and Halake oscillograph. The oscillographic chamber Was
filled With oil to produce the proper damping effect. The cylinder
of the oscillograph is connected directly to the motor shaft which
rotates the disk. This makes the cylinder and disk rotate in exact

Synchronism.


ll.
Operations.
When S3 is thrown to the right, with S, S, down, current comes from
S. B. to B, E, S, , F thru S, to S, and S, then to C and back thru S, to
the storage battery. Current also comes directly from S.B. to S, and
S; by the path B, A. This arrangement enables one to use two electrodes
of different metals in the same cell if desired and still have them
independent of each other. If S, be thrown to the right and S, to the
left, Ala is directly across the storage battery irrespective of how
any other switches of the system may be thrown while Al, depends up-
on the position of Ss. Reversing S, and S3 places A1, directly across
the storage battery While Ala depends upon S., . Both may be thrown
to the right, which places Alpmand Alz in parallel across the storage
battery or both may be thrown to the left placing the electrodes in
parallel thru S, . This is a very desirable arrangement, where one
wishes to experiment with two anodes. However in this work but one
switch was used and one anode. The cell was made of the same mater-
ials and in the same way as in the first study.
When S s is thrown to the left current passes to B, E, S3, B, along
the wire on the back of the disk to R, out at B, to S., thru the cell ºr
and back to the storage battery, while the brush B, is on the sectors
connected by the wire. When the last connected sector has passed Bs
the cell is left on open circuit until the sector on R2 connected
to R, passes under P2 . Current, then flows from S. B. to B, E, Ss, thru
0, R, r and Ba. , then thru the connection on the back to B, and so thru
the cell and back to S. B. It is to be noticed that no matter how the
current comes to the cell it always is in the same direction thru it
i. e. from the aluminum to the lead. If the counter electromotive
force drops after a short period of open circuit, when B2 Come S into




play, there is a difference of potential across the oscillograph and

12.
&#& Requal to the difference of the storage battery voltage and
the counter electromotive force of the cell. This difference of poten-
tial Will be registered on the photographic film on the cylinder of
the O Scillograph.
Measurement of time of open circuit.
A flash is registered on the film Whenever the Small Sector on R2,
which is connected to R, , and R 3, passes under B2. Then if We rotate B2
about its axis the resulting flashes on the film Will be registered
at exactly corresponding point S of the film. Knowing the Speed of
the motor, We can compute the length of time between any two flashes
by measur's ing the distance between them and finding what fraction
it is of the total film length. We know the greatest length of time
of open circuit is always the same Since the rotating arm is stopped
at the same point each time by the projecting screw. This gives a
very good check on the measurement. l mm. distance between flashes
corresponds to . OOC37 see.when the motor is running at 750 R. P. M.
In most case S the Se flashes are very distinct So that one can measure
fairly accurately to Q. OCC2 Sec. If still shorter intervals are de-
Sired, one has but to increase the speed of the motor.
Measurement of counter E. M. F.

(
A calibration curve must be made in order to measure the difference
V.
between the Storage battery voltage and the counter electromotive
force of the cell. This is easily done by removing the cell and con-
necting its terminals together and ther sending current from a known
electromotive force thru the oscillograph and its accompanying re--
sistance. The deflections of the oscillograph are proportional to the


current thru it and therefore proportional to the difference of po-
tential across its terminals. One has but to measure each ordinate
l3.
length and compare it with the deflection for the known difference
of potential. The value of this ordinate subtracted from the applied
voltage gives the counter electromotive force of the cell for that
period of open circuit.
Curve of counter E. M. F. and time of open circuit.
If one plots the counter electromotive force as ordinates and the
time of open circuit as abc is Sae, a curve is obtained which looks very
much like the curve of decay of electromotive force in a leaking con-
denser. But if the equation W = w.e.” is assumed and the value of
c computed for each point of the curve it is found that c is not a
Constant thruout the same curve nor is it the Same in Successive
curves for the same period of open circuit. This leads one to think
that this c depends for its value on the time of closed circuit and
- - C tº
also on the time of open circuit. But the formula V = V, e is de-
- - - * As *4 c – c for-c
rived on the assumption that c is constant in value; # - 3:#-Görar-
/7 of proper ze---g He re. A 22 ce- c. & y 2 fºr a < *, 'ez a f *A c ***** of 2/222 22 or
- ree-ti-agi–e=####-t:#e=triº fºg-rººt=&prºt-critic siegł-e-itrºet š-is rict, desirable .
C & os e a cº-c ºf 2 + . . .
One must rather go back to the initial conditions and build a formula
which will embrace the fact that this counter electromotive force
aeronet.*, the time of open circuit, and on the time of closed circuit.
THEORY PROPOSED.
We have seen that the eurve-of counter electromotive force (pict-
tea against the time of open-circuit depends on both time of open
Circuit, and time of closed circuit. Let us assume with Guthe (12)
and Schulze (31) that the aluminum anode becomes coated with a layer
of some oxide or hydroxide of aluminum and that this solid layer is
Covered With a very thin film of oxygen gas whose thickness depends
on the applied voltage and the time of open circuit. If this layer
of oxygen gas attains a definite thickness for each applied voltage



l 4.
then the thickness of the solid layer must increase with increasing
time of closed circuit, for if one places a milliammeter in the cir-
cuit With the cell and storage battery, it Will be seen that While
the current does attain a very low value in a very short time after
the circuit is closed, it does not remain at that value but is cone
stantly dropping lower and lower. Even after a whole day on closed
circuit, it can be seen that this current is growing smaller and
Smaller, altho at a very slow rate. This solid layer is deposited
electrolytically and therefore its thickness must be proportional
to the quantity of electricity passing thru the cell, which in turn
depends on the length of time the cell is left on closed circuit, .
The drop in counter electromotive force after a period of open cir-
cuit is due to the leakage of electricity thru the combined thickness
of Solid layer and oxygen. It has been shown that this oxygen film
decreases in thickness with increasing time of open circuit (31).
We have here then a clear case of a condenser With a double dielectric
both parts of Which leak slightly and change in thickness, the solid
layer increasing in thickness With the time of closed circuit, and
the gas film decreasing in thickness with the time of open circuit.
Derivation of formula. -
From the theory of condensers we have
i = -dq = -d (CV)
dt, dt,
Where i is the current leaking thru the dielectrics, q is the quantity
of electricity stored in the condenser, C is the capacity of the con-
denser at that instant and V is the difference of potential between
the two plates of the condenser. With a double dielectric we have
t
- § 2" e."
TF(ETIT, era")
the formula C

1 5.
in which S is the area of the plates, c' is the dielectric constant
tf
of the substance whose thickness is d', c is the dielectric constant
of substance of thickness d" and C is the capacity. Dividing both
numerator and denominator by c." and placing Sc' = K we have
- 4 TT
* T = −-º-
ăTº gºal
c."
Now let d', c' and d", c." apply to the solid layer and gas film, respect-
ively, and ai-sie call the maximum thickness of the gas film do . If we
as Sume the rate of change in thickness of the gas film proportional
to the thickne SS We have
f :
o” —, t
#"= —cd"; #" = - c dt; integrating, Z log d"-4 - -cAt 7.
- - Ct.
Therefore log d" = -ct or d" = d, e
#
By Substitution in the equation for i, we get
in which h = c do . But we also know that the current leaking thru
11
a high resistance is equal toe the quotient of the electromotive force
over the resistance divided by the resistance :
i = W
-
– c t
r” + Se
Where r equals the resistance of the solid layer and S equals the
Afzva èzzy -
resistance of the maximum gas film. Placiing these values for i errºt,
We have

l6.
If we carry out the indicated differentiation we get
- C t - C t
-K (d.'t he )d V + (-KV c he )
dt, –––– ——
- Ct. 2 - C t
(d" + he ) r” + Se
Simplyfing -
- C t - C ti —ct, 2
–K (d.' * he j div - KV c he = V (d.' * he J .
dt, - Ct
r” + S6
Therefore
- C t - Ct.
-K dy. = (d" + he Jat “ (K c he Jat
V - Ct. - - Ct,
r” + SG d' + he
- – C. t. - C t
= d' dit. - * — he dt. * K. G. he dt
- Ct, - Ct. - C t
rº + SG Y' 4. Se d' + he
Integrating
V - C t - C t
Z-K log V_Z= / d' (-et - log(r. 4 se )) - h log (r se )
V. - r"C os
- - c t *
- K log (d.' + he }_Z
- G t - C t - C
= d.'t * d' log r + se - h log r + se - K log_d 't he
r r"C r” + S CS r” + S GT. H.
Therefore
d' tyr , -ct, (d'/rc – h/cs)
-K log V = log e * r * se
We r” + S )
Simply fing
-at . —ct,
W = W., e (; * Sè -
r” + S
-at, - C tº f
= W., e (A + Be )
Where A = r—, B = s , C
r” + S r” + S
a = d'/rK and f = d'Arc = h/cs.
-K

l'7.
It is easy to find out something of the nature of these last two
values a and f'.
a = d' = g". . . . . 4. It
r"K ST3TS cº sTo
S 4
where s' is the specific resistance of the solid layer. Since we
know s' to be very high a must be very small. Similarly for f,
–4 ºr -,++. ºr , . -- - tº
f = *:: ** = (s'd º/āls ; cº'ch/c"S) = .#Fºr + # #72
4 rp
where s" is the specific resistance of the gas film. This s” must
be higher than s'ºz'the nature of the Substance S. Then We See
- e re/7
that f is negative and stiž1 smaller, than & .
Schulze (31) has given us relative values for some of these quant-
ities. He give S r approximately .02 s, and d' approximately 100 h.
Then A = 1/51, B = 50/51, C = 100/101 and D =
- C t, f'
expand (A + Be ) by the binomial theorem. Yve f^n o'
-ct, f f’ – f Ct. f—l – c t (f -l) f–2 -ct, (f-2) 2 -
(Be 4 A) = B e + f B e A * f (f -l) B e A + - - -
r", -
It was shown above that f is extremely small and A is also small,
therefore we do not introduce any great error if we neglect all terms
after the Second. Factoring, wre here
- Ct. f —f C to f f’-l c t Ct.
(Be 4 A) = e (B + f B e A) = x - Ye
f f’-l. - f' C t
Where X = B and Y = -f BA, and We call e = l since f is so small.
This simplyfies our formula to
". . " - at ct - Ct.
W = W. e (X - Ye ) (C + De )
o
- at Ct - Ct.
e (CX - CYe + DXe - YD)
-
Vº
e
H
-
C.
€
+
K
€

l8.
Which reduce S to
Ct. - C t
W = V. (H - Ge + Ke )
if We place e = l. This last is justified by the very small values
of both a and t.
Determination of constants .
Let us write v, - V, /V. , v, = V, /V, etc. Then we may write
Ct. - C t
v, - H - Ge + Ke
Ct. CAt - Ct. -CAt
v. = H – Ge e + Ke e
Ct. 2 CA t —ct – 2 CAt
v, - H - Ce e + Ke e
Ct. 3 CA t -ct, -3 CA t
v, - H - Ge e + Ke e
nº ſerra /

where A t is taken as a certain definite length of time and t as the
time of open circuit from which we wish to count.
By subtraction we get
ct, CAt —ct, - c.f. t.
A v. = v. - V - Ge (1 - e ) + Ke (e - 1)
ct cat CA t –ct -cat —cAt
A v. = V, - V, F Ge e (l − e ) + Ke e (e - 1)
Then
CA tº -ct, -c At - c.4t, - Ct. CA t – c. At
A v, - e AV, F Ke e (e - 1) - K e e (e - 1)
-ct, -2CAt - - C4 t C4 t
= Ke (e - € – 1 + e )
- Ct. - c.4 t CA t - CAt
E Ke (e - e ) (e - 1)
Therefore
CA t
K = —4 V, t-É.---4 V. --—-
- CA t CA t - CA t

if we begin to count time of open circuit from t = C, since for this
- Ct,
value Of t, e = l.
Similarly
- C A t Ct. CAt c At Ct C4t - CA t
Av, - e A V, - Ge e (1 - e ) - Ge (l − e )e
Ct c 4t 2C4t - CAt
= Ge (e - e º 'º - G + 1)
Therefore
- CAt
G - A V2. " € AV, -
CAt - C A t CA t
(e - € ) (1 - e )
Now since V = V, when t = 0
1 = H – G + K
Orº H = 1 + G - K
By Subtraction. We also get
ct 2 c.4t CAt - ct, -2 CA t – c. At
A v. = V, - V, - Ge e (1 - e ) + Ke e (e - 1)
Then c 4t, —ct - c.4 t –2CA t
Av, - e Av = Ke (e - 1) (e - 1)
CAt CA t
whdrce: K = 4.W. T. & 4 V. - A V4 - 5 *—
- CA t -2C At - CA t - CAt CAt - CAt
(e - l) (e - 1) (e - 1) (e - G )e
But, We found be £o re.
CAt
K = A V, - € A V,
- CA tº c At -CA t
(e - € (e - l)
The refore
CA t -C4 t
A V, - e A v. = Ave - A V.
when ee & - CA tº c.At
4 v. 3 A.V. F (e + G ) = a constant, M.
T-
Then 2 CA t CA t
G - Me + 1 = O


20.
The solution of this last equation gives us the value of c, when We
know the values of At and M. This equation also shows that M must be
the same in all the various curves provided only that We take A tº the
Saſſlé .
Computation for the constant S.
Using the equation just derived for M we obtain the following
values for this constant. The figures in the parentheses are to give
We ree -
the plate from which the data was taken and the subscript on the M
gives the value used for At , thus M, means that At was used as . Clsec
(l--1) (l--3) (2–-l) (2--2) (2–-3) (4--l)
. ll 3.31 3. lo
3
M.5 3. 53 3.36 2.96
M 3. l8 2.87 2. 58 2. 63 2.75 2.93
The mean value of M, ... is 3.23 which gives a value of 84 for c and
the mean value for M, is 2.82 which gives a value of 88 for c. The
mean of these two values, 86, was taken for c in all the following
Computation.
Using the value of c just obtained, and substituting in the formula
for K With At = . Cl9 sec. We obtain



K F AVA - 5
. 1192 AV = Av. - 5. ll.92 A.V.
(. 195 - 5
5. iigg) ( . 195 - 1) . 396
which gives the following values. -
(1--1) (1--3) (1--4) (2--1) (2--2) (2––3) (4--1)
K . 138 . 121 . O215 . 150 . O945 . O568 . 101
(4--2) (5--1) (5--2)
K . Q329 . 265 . O615
In a similar way by using c = 86 and At F . Cl9 se c. We obtain the
following formula and values for G.


G = A v. - . 195 A V, - = Av. - . 195 A V.
(5.1192 - . 195) (1 - 5.1192) –20. 2 ſ
which gives
(l--l) (1--3) (l--4) (2--1) (2--2) (2- -3)
G .000.94 . OCC87 . OCC46 . OC 145 . OCC87 . OCC 645
(4--1) (4--2) (5- -l) (5-–2)
G . 20124 . OCC42 . OCCO3 . OCC)695
Discussion of formula .
The formula -
-at, —ct ºf - - © t
V = V, e (A + Be ) (C++ De )
eXpands to
-at, – c t f -f C. t. f—l –ct (f -l) f–2 -ct, (f-2) 2
W = W., e (C + De ) (B e + f B e A + tº-DP e A

* terms in higher powers of A)
which reduces to
Ct, - C t
W = W. (H - Ge Ke )
f - f'C t f’- 1
When We consider f so small that we may place B = l; e = l; B Fl;
* …” B
f’-l. = -1, and We neglect all terms involving powers of A higher than
- - at,
the first, and place e = 1. This means then that we put H = C *PAf,
B
G = - CAf' and K = D. If we express A, B, C and D in terms of the thick-
B - -
nesses of the dielectrics and their resistances, we are able to de-
*ēr”. of *4elec- sº, “ ; 2 or *, *,'es - -
termine H, G and K in these—same=terms and so prove that their values
from curve to curve are what would be expected from the theory.
This seet et substitution gives us
H = d' + h f
I’
d'ºh d" + his
Since r and d' both increase with increased time of closed circuit,
H Should increase . This is ShoWrl in each Set of Curve S.
AlSo We have

22.
and since d' grows; with increased time of closed circuit while h
K should decrease in value as the time of closed
remains unchanged, K
circuit, increase S. This is also shown in each set of curve S.
However, substituting for G. We find
G = -d' r f
dTº Th s
Which should increase in value as time of closed circuit, increases,
since both d' and r increase. It is seen from the tables that G de-
- - 22/2are ºf
creases with increased time of closed circuit. This seeming failure

of the formula is explained/however if we go back and take into ac-
count one more term of the expansion. The formula can be written
2. 2. Ct c t - c t
W = W. (C + DA f * (CA f – DA f – CA f e ) e º De )
© B B 2E* 2E*
c 2 - #2 ºz. .” -
if we include the term Haririg the second power of A and make the same
f -f G t f -1.
substitutions as befoee for B., e , B . This gives us the same

value S for H and K as before, but the value of G is reduced by the
two terms involving the square of A/B. Thus gives
- ct,
H = C + DA f ; G = CA f - DA* f – CA f e ; K = D
B w B 2B2. 2E * -
Now We know K from the formula derived for finding the constants.
This gives us a value of D, but D is equal to l - C, therefore C is
known. We also know H and so can find A. f. Call this quantity X.
- B
We now can Write
Ct.
* e
G = Cx —
x -
f
#
#
#
but since D is ee very small compared to C We can neglect the second
term. This reduces the expression for G to
ct,
G = Cx - C x*e -
2 f
º Ct.
In this expression we know all the terms except e , but this should
- 2
23. Y
remain constant from curve to curve. Substituting the values of G,
o, and x for the second set of curves we find it does prove very nearly
constant.
2--l
G = . OOl45 H = . 85.145 K = . 150 from Table IV.
Therefore C = l - . 150 = .850
H = C + D A f = . 850 + . 150 A f = .851.45
B B
150 A f = .001.45
B
A f = . CC967 = x
B
Therefore 2 ct,
G = .001.45 = (.850) ( .00967) - .. 850 (.00967) e
2 f
Ct.
- e = 170.
ºf
ºn (2-2)-
G = . CCC87 H = .9064 K = . C945 from Table W.
Therefore C = 1 - D = . 9055
H = .90.64 = . 9055 + . 0945
A f = .00953 = x
B
Therefore 2 ct,
G = .000.87 = (.9055) (.00953) - .9958 (.99953) e
2 f
c t
e = l88
f
2- -3)
G = .000645 H = . 94.38 K = . O568 from Table VI. .
Therefore C = 1 - D = .9432
H = .9438 =
.9432 + . 0568 A f
B -
f = . Olć55 = X
#

24.
2 Ct.
G = . Cocò45 = (.9432) ( . Cloë5) - . 9432 (.91055) e
2 f
Ct.
S. = 178.
f
It is to be noticed that the figures in the fourth and fifth decimal
va/azs of ct,
places Should be known accurately in thea H and C for this e to be
- * f
constant. These figures can not be accurately determined from the
curves, hence We ought not to expect more than a rather rough agree-
ment in the values computed.
Explanation of curves. - -
In each set of curves taken one cell was used thruout , so the changes
in the curves are due to the changes in this single cell. The cells
for the various sets of curves were made as nearly as possible exact-
†y alike. The electrolyte was dissolved in distilled water in a larg
bottle, and enough was made at a single time for all the curves shown.
The applied voltage ranges from 10 to 99 volts, and in each set
the change of the curve with time of closed circuit is clearly shown.


25.
PLATE 1--1
Electrolyte, saturated solution of sodium phosphate.
Time of closed circuit 16 min.
Applied E. M. F., V. = 99 volts.
Counter E. M. F. , V.
Time of open circuit in seconds, t .
75C R. P. M.
C = 86 K = . 138 H = . 86.29 G = . COO.94
ct ct, - cit
t V V/V. ct, G Ge Ke V/V, Error
Observed – - Computed
. OC 178 96.9 . 978 . 153 l. 165 . OCll ... ll.90 .981 +3
. OC407 93.8 . 947 . 35C 1. 419 . OCl3 ... O 974. .959 +12
... CO685 92.2 . 931 . 589 l. 802 . OC 17 .0767 .938 +7
. OC814 91.7 . 926 . 700 2. Olé. . OCl.9 . O686 . 93C #4
... CC98 90.6 . 915 .843 2. 323 . OC2]. . O595 . 920 * 5
. Cl15 89. 8 . 907 . 988 2. 686 . OC25 . O515 . 912 +5
. Cl52 88.7 896 L. 31. 3. 706 . OC35 . C373 . 897 +l
. Cl69 88. 7 . 896 l. 45 4.263 .00.40 . C324 . 891 –5
. Cl88 87.7 . 886 1.62 5. C53 . OC48 . O274 . 886 –0
. O2C5 87. 1. . 88C 1.76 5.812 . Q055 . Q238 . 881 +l
. C218 86. 7 . 876 1.88 6. 554 . OC 62 . Q211 . 878 *2
. O275 85.7 .866 2.37 lo .. 70 . ClOl . Cl29 . 863 –3
. O298 85.1. .86C 2.56 l?.94 . Cl21. . ClO'7 .862 +2
. Q322 84.8 .857 2.77 15.96 . Cl50 . CC87 . 857 O
. C335 84.8 . 857 2.88 17.8l. . Cl67 . CO78 .854 -3
. 0355 84.2 . 850 3.06 21.33 . O2CO . OC 65 . 849 -l
3. 22 25.03 . O235 . OC 55 .845 +l
. C374 83.6 . 844

26.
PLATE l-–3.
Electrolyte, saturated solution of sodium phosphate.
Time of closed circuit, 3 hrs.
Applied E. M. F. ,
Counter E. M. F. , V.
Time of open circuit, in seconds, t .
750 R. P. M.
C = 86 K = . 121
t V V/V,
Observed
, co278 96.4 . 974.
. OC389 95.1 . 96.1
. CO648 93.5 .944
. ClO35 91.9 . 928
. Olll 91.4 . 923
. Ol38 90.6 . 915
. Cl67 89.8 . 907
. Q222 88.5 . 894
. Q238 88.3 . 892
. O266 87.5 .884
.0309 86. 7 . 876
. O331. 86. 6 . 875
. Q350 86.1 . 969
- Q374 85.6 . 865
V. = 99 volts.
.0204
= . 8798 G = . COO 87
ct, ot, —ct
ct, © Ge Ke V/V, Error
--- - Computed
. 239 l. 270 - 0010 . C954 .974. O
. 334 1. 397 . COll . C87 . 966, #5
. 557 1. 745 - 001.4 ..d694 .948 #4
. 891 2.438 . CC2C . 0497 . 927 –1
. 955 2. 599 . OC21 - 0466 - 924 +l
l. 19 3.287 - 0027 . C368 . 914 – 1
l. 35 3. 857 . 0.032 . C315 . 908 +l
1.91 6.753 . OC 55 . Clºg .892 -:
2.95 7. 729 . CQ 63 . C167 . 889 -3
2. 29 9.875 . 0091 - 0123 .883 -l
2. 66 14.296 .0117 . oogº .877 ::1
2.87 17.64 . O144 . OC 69 - 872 –3
3.01. 20. 29 .0166 . CC&O . 869 Q
3.22 15. O3 . OC48 - 864 - 1.



27.
PLATE l--4.
Electrolyte, saturated solution of sodium phosphate.
Time of closed circuit, 24 hrs. 15 min.
Applied E. M. F. , V, - 99 volts.
Counter E. M. F., W.
Time of open circuit in seconds, t .
725 R. P. M. -
c = 86 K = .9215 H = .979 G = .00046
ct ct, -ct,
t V V/V. ct, e Ge Ke V/V, Error
Observed - Computed
. OC74 9.7. 9 .989 . 636 l. 889 .0009 . Ollá. .989 O
.0102 97.7 . 987 .877 2.404 .00ll .009C . 987 O
. O129 97.5 . 985 l. 11 3.034 . OCl4 . OC76. . 985 Q
. C15C 97.4 . 984 l. 29 3. 633 . OCl." . OC59 . 983 -l.
. O156 97.2 . 982 l. 34 3. 8.19 . OCl8 . OC56. . 983 +1.
. O.199 97.2 • 28%. 1.71 5.539 .0025 . coag Iggo lº
. 0220 97.1 .981 1.89 6.619 ... CO3C . OC33 . 979 -2
. C268 96.9 27° 2.32 °.974 .2946 .co.22 .377 –
.0287 96.4 27# 2.47 11.76 .2954 .cola gº, i.
.0316 96.4 . 974 2. 72 15.18 . OC 70 • CO14 . 97.3 -l
. O34C 96.1 . 971 2.92 18.54 . OC85 - OOlz .972 ºl
- Q368 95.8 'º. 3.1% ºf .9108 .3063 º .
.0384 95.8 *7 3.3° 27.11 .0125 .330s ...; "3

2.
7", / e of 22e z c ºr c 0 , t , 2 & e c oz cºs. -
{2/3-262-044-263. .0%
/.
78
76
.2%
.72
.70
& 3
-8 (a
.8% /
62
.6O
73
,76
.72.


28.
Electrolyte, saturated solution of sodium phosphate.
Time of closed circuit,
Applied E. M. F.,
Counter E. M. F.; W.
= 49
; min. 30 sec.
Volt, S.
Time of open circuit, in seconds, t.
725 R. P. M.
C = 86.
K =
V
. OC 38
.0063
. Cl26
.0142
, Ol'75
.019.7
. C217
.0232
.0268
. C287
.0310
. C332
.0354
. O384
46.7
45.9
44.2
43. 6
43. 1
2.6
42. 3
42. Q
41.6
41.4
4.l.. 3
49.8
40.6
40. 1.
. 150 = . 85.15 G = - 001.45
ct ct, - Ct,
V/V, ct, e Ge Ke V/V,
Observed.--- - - Computed
. 953 . 327 l. 387 . OC20 . 108 . 957
. 937 . 54l l. 718 . OC25 . Q375 . 937
. 902 1.08 2.945 . OC43 . O510 . 899
. 890 l. 22 3. 38.7 . OC49 .0444 . 891.
. 880 1.50 4.482 . OC65 . Q334 . 878
.87C 1.69 5. 419 . OC89 . Q277 . 87Q
. 863 1.86 6.4.24 . OC93 . Q234 .866
. 857 l. 99 7 - 316 . Olć)6 .0205 .860
. 850 2.30 9. 974 . Olá5 . O850 .852
. 845, 2.49 12.00 . Ol'74 .01.25 . 847
.843 2.67 14.37 . Q208 . O104 . 841
. 834 2.85 17. 29 . Q250 . OC87 .835
. 83C 3. C4 2C. 91. . O303 . OC'77 . 829
.820 3.30 27. ll . C393 . OC 55 ... 818
Errºo
+4
O
-3
:l
+2
–Q
+3
+3
+2
+2
–2
+1.
-l.
-2
r
--

PIATE 2- -2
Flectrolyte, saturated solution of sodium phosphate.
Time of closed circuit 9 min. 30 sec.
Applied E. M. F., W. F. 49 volts.
Counter E. M. F., W.
Time of open circuit in seconds, t.
725 R. P. M.
C = 86 K = . O945 H = , 9964 G = .90087
ct, ct - cit,
t V V/V, ct; € Ge Ke V/V, Error
Observed Computed
, 0.028 48. O .980 . 24l l. 273 . OCll . O'742 .980 O
, 0.063 47.6 . 973 . 542 l. 719 . COl. 5 ... O 550 . 960 -13
.0104 46. 38 .945 .895 2.447 . CO21 - 0.386 - 943 -2
. Cl29 45.88 . 936 l. 11 3.034 . OC26 . O312 . 935 -1.
. 0192 45. 23 . 924 1.65 5.2O7 . OC45 . O182 . 920 –4
. 0210 44. 90 . 917 1.81 6. ll . OC 53 . O155 . 917 C
.0262 44. 57 . 910 2. 25 9. 488 . OC83 . O100 . 908 +2
.0284 44.2 . 902 2.44 ll. 47 . OC 98 . OC 83 . 905, +3
. 0314 44. C . 898 2. 7Q 14.88 . Ol29 . OC64 .9CC +2
. 0354 43.86 .895 3. C4 20.91 . Cl82 . OC45 .893 -2
, 0.380 43. 18 . 881 3.27 26. 31. . O229 . OC36 - 887 +6
, 0384 43. 26 . 883 3. 3C 27. 11 . O236 ... CO35 . 886 43

30.
PLATE 2 – “3
| | - -
| | |
- S.
Electrolyte, saturated solution of sodium phosphate.
Time of closed circuit, l hr. 32 min.
Applied E. M. F., W. = 49 volts.
Counter E. M. F. , V.
Time of open circuit, t , in seconds.
725 R. P. M.
C = 86 - K = . C 568 H = - 94.38 G = . CQQ645
ct, ct – c. t.
t V V/V, ot, e Ge Ke V/V, Error
Observed Computed
. OC96 47. 85 . 978 . 825 2. 282 ... CC15 . 02:49 . 967 —ll
, 0.125 47. 36 . 967 l. O'72 2.92.1 ... COlº . Q195 .961. -6
. Cl63 47. C4 .961. l. 4CC 4. C55 ... CO26 . C140 . 955 – 6
. Cl94 46.7C . 952 1. 67 5. 31.2 . OC34 . Q107 .951 -1
, 0211 46. 54 . 950 l. 81 6. llC . OC39 . OC93 . 948 –2
.0228 46. 38 .946 1...96 7. C99 . OC46 ... CO 80 . 947 +l
, 0.240 46. 38 .946 2. C6 7.846 . OC 51. . OC 73 .946 C
.0272 46. 13 . 941 2. 34 10.38 . OC 67 . OC 55 . 943 + 2
. Q281 46. C 5 - 940 2.42 1.1.25 . OO72 . CO 51 .942 + 2
. C323 46.05 - 940 2.78 16. 12 • Q104 . OQ35 .937 -3
,0340 45.88 . 938 2.92. 18.54 . Oll.9 . CO31 . 936 -2
. C355 45. 72 .933 3. C5 21. 12 . O136 . CC27 . 933 O
. C37.2 45. 56 . 931 3.2C 24. 53 . Cl64 . 0023 . 93C -l.
. C384 45.48 . 928 3. 30 27, ll . Ol' 5 . OC21 . 928 O


Plate 2- -4.
Electrolyte, saturated solution of sodium phosphate.
Applied E. M. F. 49 volts
725 R. P. M.
On closed circuit 2 hrs. 50 min.
Plate 2- -5 |
|
S. T-
Same cell as above on closed circuit 23 hrs. 20 min.
1,


7 g /77 e o foyo e º c / r c v å ż / rz s e c o 7 ºs2. .


Plate-1 & 2
Calibration curve for Plates 1--l, l--3, l-–4, 2--1,2--2, 2––3, 2––4, 2––5.
Longer ordinate for 10 volts with 50 ohms in series with oscillograph.
Used with Plates 2--1,2--2, 2- -3, 2––4, 2--5.
Shorter ordinate for 19 volts with 100 ohms in series with oscillograph
Used with Plates 1--l, 1--3, l--4.
Plate 4.
Calibration curve for Plates 4--1,4--2,4--3,4--4.
Corresponds to 14 volts with 100 ohms in series with oscillograph.
-





33.
PLATE 4 - -l.
Electrolyte, saturated solution of sodium phosphate.
Time of closed circuit 15 min.
Applied E. M. F. 100 volts.
Counter E. M. F., W.
Time of open circuit in seconds, t.
750 R. P. M.
c = 86 K = . 101. H = .9002 G = . C9124
cit ct, - Ct.
t V V/V, ct, e Ge Ke V/V, Error
Observed - Computed
. OC 58 95. 6 . 956 . 498 l. 645 . OC20 . O61.5 . 960 +4
. OC98 94.2 . 942 . 842 2.321 - 0029 . 0435 . 941 -l
. Cl33 92.9 . 929 1. 14 3. 127 ... CO39 . O323 . 929 C
. Cl'74 91.9 . 919 l. 50 4.482 - 00:56 . 0225 . 917 -2
. C2CO 90.8 .9C8 1. 72 5. 585 . CO69 . Cl31 .9ll +3
. C233 90.2 . 902 2. CC 7. 389 . OC92 . Cl37 . 905. +3
. C27C 89.5 .895 2. 32 10, 18 . C.126 - 0099 .897 +2
. O302 88.8 . 888 2.60 13.46 . Cl67 . OC 75 . 891 +3
. C338 87.8 . 878 2.91 18.27 . C226 . O055 . 883 +5
. C374 87.4 . 874 3. 22 25.03 . 0310 . OC40 . 973 -l

34.
PLATE 4--2
Electrolyte, Saturated solution of sodium phosphate.
Time of closed circuit on 100 volts 15 min. and 75 volts 5 min.
Applied E. M. F. , V. F 75 volts.
Counter E. M. F. , V.
Time of open circuit in seconds, t .
75C R. P. M. -
C = 86 K = . C329 H = . 96.75 G = . CCC 42.
Ct, ct, —ct,
t V V/V, ot, ë Ge Ke V/V, Error
- Observed - Computed -
. Cl22 73. 3 . 978 l. O5 2.858 .0012 . Ollā . 978 O
. Olć 6 73. 1. . 975 l. 425 4. 158 . OC17 . OC 79 . 974 -l.
. Olę0 73. l . 975 L. 635 5. 129 . OC22 . OC64 . 97.2 -3
. O2.19 72.8 . 971 l. 80 6. O50 . OC25 . OC54 , 970 -1.
. C.273 72. 4 . 965 2.35 10.49 . OC44 . OC31 . 966 + 1
. O3Q8 72. C. . 960 2.65 14.15 . OC 59 . OC23 .964 #4
. O332 72. O . 960 2.86 17. 46 . OC 73 . OO19 . 962 £2
. C365 72. C . 960 3. 14 23. lo . OQ97 . CQ1.4 . 960 - O
. C374 72 - C . 960 3.22 25, C3 . ClO5 . OC13 . 958 –2

35.
Plate 4--3
Electrolyte, saturated solution of sodium phosphate.
Applied E. M. F. 50 volts. -
750 R. P. M.
On 100 volts 15 min. , 7.5 volts 5 min. , 50 volts 5 min.
Plate 4 -- 4.
Same cell as above with applied E. M. F. 25 volts.
On 100 volts 15 min. , 75 volts 5 min. , 50 volts 5 min. , 25 volts 5min.




|----- ---------- _ _ _ _ _
o/o e 77 c/rc w Ż ż / rz s e c o 77 o’s4- - - - - - -
ſiitſººrtritººrittº-;2&ć - |-
·HHHHHHHHHHHHHHHHHHHHHHHHHHHHFHHHH
- 1 L l lt-t-t-t-t-t-t-t-tt
+-+-+-+
+-+-+-+-+-+-+-+-+-+-+-+-+-+




36.
Plate
-
| |
| | | || |
| | || | |
1111 | | | | || || ||
__ - | |
|
5'--l.
Electrolyte, saturated solution of sodium phosphate.
Time of closed circuit, 1 min. -
Applied E. M. F., V, - 10 volts.
Counter E. M. F., W.
Time of open circuit in seconds, t .
750 R. P. M. - -
C = 86 K = . 265 H = . 135 G = .00003
ot ot, - C tº
t V V/V, ct G Ge Ke V/V, Error
Observed Computed
. OC22 9. 16 .916 . 189 1.298 -90005 .229 .955 Tº
. ClC7 8. 20 . 820 . 920 2. 509 . OCCl ... 105 . 840 +2C
. Cl42 8. C8 . 808 1. 22 3. 387 . OC Ol . O'78 ... 813 +5
. Cl96 7. 85 . 785 l. 69 5. 419 .0002 . O49 . 784 -l
. O246 7. /8 . 778 2. l.2 8. 330 . OCO2 . O318 . 767 -ll
. 0307 7. 48 . 748 2. 64 14. Ol . OCC4 . Ol&9 . 754 + 6
. O342 7. 48 . 748 2.94 18. 92 . OCQ6 . O140 . 748 -C
. C374 6. 40 . 640 3.22 25. Q3 . OCC8 . O106 . 745 + 1.05


37. A
PLATE 5-–2.
Electrolyte, saturated solution of sodium phosphate.
Time of closed circuit 10 min.
Applied E. M. F. , Wo F 10 volts.
Counter E. M. F. , V.
Time of open circuit, in seconds, t.
75C R. P. M. -
C = 86 K = . C615 H = . 9392 G = . CCO695
- ct, ot, – c t
t V V/V, ot, © Ge Ke V/V, Error
Observed Computed
. OC 76 9. "C . 970 . 654 l. 923 . CC13 - C32C . 97C O
. Cl26 9. 55 . 955 1. C8 2.945 . CC20 . C2C8 . 958 +3
. O.188 9. 52 . 952 1.62 5. C53 . OC35 . Cl22 . 948 - 4
. C218 9. 41. . 941 1. 87 6. 488 . OC45 ... CC95 . 944 +3
. O283 9. 40 . 940 2.44 ll. 42 . OO68 . OC54 . 938 -2
. C32 9. 34 . 934. 2.75 15. 64 . O109 ... CO39 . 932 -2
. C336 9.34 . 934 2.89 17. 99 . Cl2.5 . OC34 . 93C - 4
. C365 9.28 . 928 3. 14 23. 10 . Cl6C . OC27 . 926 -2
. C374 3. 22 25. O3 . Clº 4 ... CC25 . 934

Electrolyte, Saturated solution of sodium phosphate.
Applied E. M. F. lo volts.
On closed circuit, 30 min.
75C R. P. M.
Plate 5.
Jeale for 3
- - - - -
Calibration curve to go with Plates 5––1, 5-–2, 57-3.
Corresponds to 2 volts with 15 ohms in series with oscillograph.
|


/00
| 26
.72
363
. & ?
.630
.7 %
| 72
(o 63
.6 %
, «Ț2.
7 / 77 e of op e 77 c & r c ozi * /77 sec o zºs.
+-+-+-+-+-+
A

39.
Discussion of curves .
It is evident in these oscillographic curves, as in those plotted
from the data taken with the galvanometer, that the curve does not
reach a limiting form. In every case the curve of counter electro-
motive force plotted against the time of open circuit rises With
increased time of closed circuit. It is evident then that this count-
er electromotive force is not due entirely to a gas film as Guthe
supposed. It seems evident also that 3. permanent change must take
place in the cell with time of closed circuit, for the current which
leaks thru the cell does not attain a minimum value but continually
drops lower and lower. Both of these effects are explained if we as-
sume that the cell's action depends upon the thickness of the solid
layer, which increases in direct proportion to the quantity of elec-
tricity passing thru the cell, and also upon the thickness of the gas
layer, which quickly reaches a maximum value for each applied electro-
motive force and then gradually decreases in thickness With the time
of open circuit. The increase in thickness of the solid layer results
in an increase in the resistance of the combined layer, Which account S
for the gradually decreasing value of the leakage current on closed
circuit, and also accounts for the rise of the curves With time of
closed circuit. The decreasing thickness of the gas film results in
a decrease in resistance of the combined layer which in turn accounts
for the drooping curve.
Difference from other cells.
This way of looking at the cell explains why it acts differently
than the ordinary electrolytic cell with both electrodes of Some in-
3 ºc ºf
active substance,as platinum. With inactive electrodes, there will
be no solid layer deposited; for the electrolytically produced oxygen
can not combine with the electrode. In such a cell, the current Will


I. Tº
drop to a very Small value and remain at that value provided the ap-
plied Voltage is low enough, since the electrodes are unaffected by
the passage of the current. But with an aluminum anode there is always
deposited some of the solid layer, and a rest:#####, drop in current results
Consequences of this view. J
If this view is correct we may use any electrolyte which will pro-
duce oxygen on electrolysis and any anode which easily combines With
this oxygen to produce a compound With a relatively high resistance.
The former has been partially proved by Graetz and Pollak (ll) and
the latter by Schulze (31).
As a rectifier.
When the cell is used to rectify the alternating current, there
is a slight deposit of this solid film every time the aluminum i S
the anode. However when the current reverse S, this deposit is not
de composed by the current; for to de compose& the compounds of aluminum
by electrolysis a rather high temperature is required. As this pro-
cess proceeds, We may reach a stage where the heat produced in the
resistance of this solid film is sufficiently high to raise the temp-
erature of the whole cell to the point, where this solid film begins
to de compose on the reversal. When this temperature is reached, the
cell fails to Work satisfactoray.
Set 4.
Set 4 was taken to show N that the effect, on the cell is due to
the relative thickness of the two layers. Plate 4'--l Was taken after
the cell had been on closed circuit on 100 volts for 15 min. The ap-
plied voltage was then dropped to 75 and plate 4--2 taken, then to 50
and finally to 25. The solid film built up by the 100 volts was large
as compared to what would have been produced by the lower voltages
in the same length of time. This solid film remained on the electrode

41.
thruout the test, but for each applied voltage there is a definite
maximum thickness of the gas film which changes with the applied
voltage. The curves for the lower voltages are what one would get
if the cell had been placed across this lower voltage for a much
longer time.
Set 5. *
Plate 5--1 was taken with lc volts applied for l min. Plate 5-–2
was taken after lo min. of closed circuit and Plate 5-–3 after 30
min. It is seen; there is a rapid change in this cell in the first
few minutes of closed circuit. This great change will explain the
difficulties some investigators have encountered who neglected to
take into account the rapid change in this Solid layer.
Summary.
This investigation has shown that any method of experimentation
-
in Which an appreciable length of time must elapse during the taking
of data, the cell being on closed circuit at least a part of this
time, Will introduce serious errors due to the change taking place
in the cell itself.
So far as the author is aware, no attempt has ever been made to
explain the action of this cell on the theory that the action is |
due to a double dielectric, one part of which changes with the time
of open circuit, and the other with time of closed circuit. This in-
vestigation has shown that Such a theory is plausible and fully ex-
plains all the cases investigated.
The cell does not attain a steady state after a short time of closed
circuit, nor does the single dielectric theory seem plausible.
The theory leads to the conclusion that any electrolyte which lib-
erates oxygen on electrolysis may be used in the rectifier. It also
ShoWS that other metals than aluminum should be available Since it



42.
requires only that the metal form a compound with the liberated ox-
ygen and that this compound have a rather high resistance.
The author is indebted to the University of Michigan for the ap-
paratus provided, to Prof. N. H. Williams for many helpful suggestions,
and to Mrs. Fitch for help in the computations. …

43.
REFERENCES.
l. Atkins M. D.
Physical Review Vol. 13 page lo2.
2. Beet. Z
Wied. Ann. Vol. 2 page 94.
3. Buff'
Ann. de Liebig Vol. 52 page 296.
4. Blondin J. -
Ecl. Electr. Vol. 14 page 293. - -
5. Blond in J. -
Soc. Int. Elect. , Bull. 1 page 323.
6. But, trier M.
Cebtralblatt Accumulatoren Vol. 6 page 56.
7. Bairs to G. E. and Mercer R.
Faraday Soc. , Trans. 7 page l.
8. Carman A. P. and Balzer G. J. -
Physical Review Vol. 30 page 776.
9
Cook S. R.
Physical Review Vol. 20 page 312.
lC). Ducretet
Comptes Rendus Vol. 80 race 280.
ll. Graetz and Pollak -
Elektrotechnische ZS chr. Vol. 25 page 359.
12. Guthe K. E.
Physical Review Vol. 15 page 327.
l3. Greene C. W.
ry
Physical Review. Vol. 3 series 2 page 264.
14. Gordon C. McC.
Physical Review Vol. 20 page 128.



44.
l6.
18.
20.
2
2
23.
24.
r
*
5
26.
27.
28.
Hutern and Leblanc
French Patents #215945
Franchetti A.
Rivista SC 1. - Industriale Vol. 33 page lzl.
Kruger F.
Ann. der Physik Vol. 21 page 7Cl.
Kallir L.
Zeitschr. Electrotechn. Wien Vol. 16 page 602.
Knob lauch E.
Phy S. Zeit Schr. Vol. 3 page 46.
Modzele WSki J. de
Lumiere Electr. Vol. 3 page l87.
Montpellier J. A.
Electricien Vol. 22 page 17.
Mitkiewicz W.
Phy S. Zeit Schr. Vol. 2 page 747.
Mayrhofer G. - -
Elektrotechn. Zeitschr. Vol 21 page 913.

Nordon K,
Electrical World and Engineer Vol. 38 page 68l.
Nodon A. ... "
Comptes Rendus Vol. 136 page 445.
Pollak C.
Comptes Rendus Vol. 132 page lºob.
Paplexi N.
Ann. der Physik Vol. 39 page 976.
Schulze G. ||
Ann. der Physik Vol. 22 page 543.
//
45.
29. Schulze G .
Ann. der Physik Vol. 25 page 226.
5 C. SchUlze C. -
Zeitschr. Elektrochem. VO 1. e page 526.
31. Schulze G.
Zeitschr. ElektrO Chem. Vol . 14 page 333.
52. SchUlze G.
ann. der Physik Vol. 28 page 787.
33. Schulze G.
Ann. der Physik Vol. 25 page 775.
34 . Schulze G. and Lindemann R.
Phys . Zeitschr. Vol. 15 page 254 .
55. Taylor A. H.
- Ann. der Physik Vol. 3 O page 987.
56. Van Laar T. T.
Chem. Zentralbl . 19 O8 l page l O2 l .
57. Walter L. H.
Electrician VO 1 . 7l page l O57.




RULES COVERING USE OF MANUSCRIPT THESEs
IN THE UNIVERSITY OF MICHIGAN LIBRARY
AND THE GRADUATE SCHOOL OFFICE
Unpublished theses submitted for the doctor's degrees and deposited in the
University of Michigan Library and in the Office of the Graduate School are open
for inspection, but are to be used only with due regard to the rights of the authors.
For this reason it is necessary to require that a manuscript thesis be read within
the Library or the Office of the Graduate School. If the thesis is borrowed by
another Library, the same rules should be observed by it. Bibliographical refer-
ences may be noted, but passages may be copied only with the permission of the
authors, and proper credit must be given in subsequent written or published work.
Extensive copying or publication of the thesis in whole or in part must have the
consent of the author as well as of the Dean of the Graduate School.
This thesis by . . . . . . . . . . . . . . . . . . . . . . . . . . . . * * * * * * * * * * * * * * * e s s e e e º 'º e
has been used by the following persons, whose signatures attest their acceptance
of the above restrictions. •”
A Library which borrows this thesis for use by its readers is expected to secure
the signature of each user.
NAME AND ADDRESS DATE
UNIVERSITY OF MICHIGAN
º
º º
º
- ---
º º
- º º º
- cº- -- º
º º º º - º
º º º
ºº:: -- º
º º º |
º º º
º º
º
º
º
º
T
º:
º
º ºº º
º: º
º
º
º
-
- º
º
-
- º º
º º º
- º º
º º º
--~~ º º º º
º º - º º
- - - º º
º º º º º º
º º º º º
º º º: º -T ºº º
º º º º º -
--- º º º º --- º
º º º º º º
- - - º -
º: º --- º
º
º
º
º
-
º º º
º ---
º
º º ---
º
º
- º
º: .
- º º: º º
º º º
º º
º - º º
º | | -º-º:
º º º --> --
º º º
- º º º
º º º
º º
º
…
º º
º
º -
º
º º
º
º
- º º: º,
º º º -
º º º
º º º º º
º: º - º
º - º º
º º º
º º º º
º ---
º
º:
E.
º
º
º º º
º Fº T -
- º º º
º º - º
º - º º º
º º º º …
º - º º
º º º
º º º º - º
º º º:
º sº º sº º
º º
º ºº
º - -
- º
º -
º
º
-
º:º
º
º
º:
º
º º
I º º
º: º º
º: º º
- - º
º
º
*. º
-e-
º
º:
º º
º
---
º
º º
º º
º
º
- º
º
-- º º
-
- º
- -
- ..º.
…tº - - - -
Fºrº. - -
º º º -
º - - T
º º º ---
* --.
- -
º ºs-
º - º
- --- º
-
º º *
º --- -
º ... º. -
º º
º º º T
º º º º º
º º º
- º
º º - º
º
º
º Cº.
º
º
º
º
º
º
º: º
º
º º: º
º º
º º
º
º
º
º
º º
--. --- Tº.
ºnal º: - º
º -
- º
º º - º
º - -
º
Tº
º
º -
º º
º
º
º
º:
-
º
º º:
º: º
º:
º º
---
- º
- º
º º
Tº -
º
- º: -
º
º: º
º
-
º
º
º
º
º
--- º
º
-
º
º
º
º
º
º
-
º
º,
- º
- -
º
-
.…
--
---