John Almon.

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and Resistance of a Oalvanic Circuit. 47

In oompnting these figares I made use of the values of col«
umns (a), after having raised objections against them. But it
seems to me that I thereby did not unduly increase the results^
attributing them as I do to the full difference of intensities, and
to the difference of temperature as proceeding from the second
intensity and the lowest. Oonsidering this circumstance as
chiefly affecting the results of columns (a), it appears also evi-
dent that the increase of resistance within this column is not so
much the result of difference of temperature, as of difference of
intensity, since the influence of intensity starts from 1*982 in
table VII, and 0'7844 in table vni, while the influence of tem-
perature starts in correspondence with intensity 1*8008 in table
VII, and 0*6068 in table Viii.

There is another circumstance connected with table Viii, the
experiments having been made with a circuit containing con-
stantly 200 centimeters of thin copper wire, as an addition to the
internal resistance. If the resistance of this copper wire, and
the true internal resistance are calculated separately, by means
of combining the two first intensities with each of the following
ones, there result values contained in columns (Cu) and (B).
Both of them show the same ratio of increase as column (a), con-
firming the fact as exhibited in table y. Thus far, the addition
of the 200 centimeters of copper wire to the internal resistance
proper, does not seem to modify the ratio of increase.

The experiments for tables vii and Viii, still were rather un-
satisfactory, showing too great irregularities. To avoid them, if
possible, and with a view to get a clue to the understanding of
the matter, I undertook another series of experiments, with as
much care as I could afibrd, and the instruments at my command
would allow. I made four pairs of observations, two for each
end of the swinging needle alternately, and took the mean value
of them. The battery was a Bunsen's ; the diluted sulphuric
acid containing rather much sulphate of zinc, and the nitric acid
having been used for a short time. Using such acids my object
was plainly to get results about facts of ordinary occurrence. I
tried the battery first without any unnecessary addition of other
resistances than the platinum rheochord, and afterwards with an
addition of 25, 50, 100, 150, 200 centimeters of thin copper wire.
The results of these observations, calculated in the same way as
explained for tables vii and viii, are recorded in tables ix to
XIV. I did not succeed, the results remaining irregular, prob-
ably partly from constant faults of the instruments, and of the
location of the tangent compass within about 15 feet distance
from an iron stove, and within about five feet distance from about
five pounds of iron which could not be removed. I therefore had
to content myself with these results, and to use them with caution.

In table ix, the mean of the first three values of column (a)

Digitized by



H. Haug on the Ekctrihmotive Force

is 3'21 ; the mean of the last three values of the same column
is 6'34:. The increase is in the ratio of 1 to 1-975. Leaying out
the value of column (6), as too low, but taking the mean of the
six mean values to the left of column (5), from 17'81 to 23'08
there being three small and three large values, we get an in-
crease of internal resistance from 3'21 to 18*51, or from 1 to 5*77.
This increase is due to the reduction of intensity from 1*8422 to
0*0581, and to the reduction of temperature of the unit of resis*
tance, from dark red heat of the 6 cm. of platinum wire, to
about the temperature of the air.

It may be well to examine with some detail this series of ob-
servations. The battery was in such a state that the direct inten-
sity decreased rapidly during the short time necessary for 4 pairs
of observations of the needle. The intensity with any length of
platinum wire in the circuit, was variable too, becommg dimin-
ished with short length, and increased with great length of the
wire. The examination of the following figures will give an
* idea of the amount of this variation of intensity. They are the
mean values for the first, respectively for the second two pairs of
observations :

Cent, of plat.

Cent of plat


wirA in thik

wiio 111 me




wrJro III 1.16


Firat Later.




•1487 -1441





•1267 '1259





•1118 -1180





•1000 '1016





•0898 -0919





•0814 -0840





•0748 -0774





•0705 -0726





•0652 -0677





•0608 -0684





•0567 0585

Owing to this change of intensity, it would be necessary to
calculate upon the first observations rather than upon any later
ones, or upon some mean values. If I do so, I get m column (a),
801 and 5*89 as mean values, with an increase from 1 to 1*957 ;
instead of the above values 8*21 and 6*84, with an increase from
1 to 1'975. The true ratio of increase is therefore somewhat
less than calculated from the table, and this holds good for the
whole ratio of increase.

On the other hand, if the decrease of intensity with the time,
is mainly to be assigned, as probabl;^ will be maintained, to some
polarization having taken place, which, from the high direct in-
tensity to the next with 6 cm. of platinum wire in the circuit,
will he kept for some time near its maximum ; then the inten-
sity with 6 cm. of rheochord wire is lower than it would be,
had the circuit not been closed, directly and constantly, previous
to the observation with 6 cm. of platinum wire, since this low

Digitized by


and Resistance of a Galvanic CircuiL 49

intensity cannot possibly prodnoe the maximtim of polarization.
Aasuming therefore the intensities with 6, 8 and 10 cm. of pla-
tinum wire too low, the mean value in column (a) would become
yet smaller than 8*01, and the ratio of increase of resistance
therefore greater than 1*967, if not greater than 1*976. And
this again holds good for the whole ratio of increase.

Considering all these circumstances, I think that my discussion
of the combined results, from table Yi, is not much at variance
with the truth, and that my figures do not exaggerate the facts
in any hi^h degree.

There is an other point to be oonsidered. The decrease of
intensity with 6, 8 and 10 cm. of rheochord wire in the circuit
amounts to a mean of 0*0018. When the circuit is closed di-
rectly, this decrease of intensity, for about the same time, amounts
to 0*1484, that is, to many times more than the difference of in-
tensities amounts to. Tne intensity 1*6089 within the circuit
closed directly, is the mean value of two pairs of observations, ^
one for each end of the needle, being respectively 1*6846 and *
1*4238, with a decrease of 0*1612. This rapid decrease of inten-
sity would justify starting the calculation of column (a) from
the direct intensity 1*6846 instead of from any later intensity, or
firom any mean value. If I do so, and compare this intensity
with the first intensities given above, the mean values for the
first and for the last three figures of column (a) become 2*80, re-
spectively 6*58, the ratio of increase being 1*998 against 1*976
mm the table. And the whole ratio of increase of resistance

would become ^r^^^^'l*^ times greater than was resulting

from the table. This increase, due to the greater direct inten-
sitv started from, exemplifies however the intensive degree of
influence of the intensity of the current upon the internal resist-
ance, as compared with the influence of the temperature of the
unit of resistance.

I sappose, after all, that one may possibly consider the great
ratio or increase of internal resistance as figured fix)m table ix, to
be the consequence, to a great extent of polarization to which
any inconstancy of a battery is usually assigned, and the battery
was in fact rather inconstant. But apart &om my above rea-
soning to the contrary, I can refer to table i, the experiments
fi>r this table having been made with a battery the acids of
which had been used for but a very short time. The degree of
constancy of this battery may be judged from the fact that the
compass needle was at 60*8^ at the beginning of the experiments
and at 60*2° one hour later, during which time the battery had
been in use, except for very few jninutes. Now, if I combine
the intensities for several great resistances in the circuit, and
take the mean of three consecutive values, I get 16*66, 19'46|

Am. Jwjr. Sgl— Sbcoud Sibxxs, Vol. XLIII, No. 137.— Jan., 1867.

Digitized by VjOOQIC


H. Haug on the Electro-motive Force

24'97, 17*92, as internal resistances. The mean valae of all of
them is 19 6, and the internal resistance as calculated from the
direct intensity, and that with 8 cm. of platinum wire in the cir-
cuit, being 3*48, there results an increase from 1 to 5'6{)4, with-
out the platinum beinc red hot, against 5*77 of table ix, with
the platinum wire red hot indeed. At any rate the polarization
cannot play a great part in the results of my experimenta

Comparing the results of tables ix to ziY, I get from the mean
values the following

Thble of ratio of increate of Internal Reaittanee, with eoMtant addition of differ^
ent Unfftkg of copper wire in the eiraiit.

Lenirih of eopper
wire in the

Resistances of colamns (a)



ratio of












25 cm.






60 "






100 "






160 "






200 «






The table illustrates the dependence of the ratio of increase on
the manner the directly closed circuit is built up, on the greater
or less intimacy of the contact, etc.

In tables X to XIV, column (Cu) contains the resistances of the
respective lengths of copper wire. The increase of resistance
maintains the same ratio as in the respective columns (a).
Using m«an values, I derive, from comparing all five tables, the
following results.






of copper

at high

resistance of


resistance of



26 cm. length.


2Scin length.

26 cm.





60 "





100 ••





160 "





200 «





The resistance of 26 cm. of copper wire, expressed in .centi-
meters of platinum wire, at high intensity, is rather irregular,
the first value in particular being too great. It is, however, in
agreement with all other facts, safe to say that the resistance
of a given length of copper wire, or the specific resistance, ap-
pears the greater the longer the measured wire is. This is con-
trary to what may be expected from the different influence of
temperature upon the resistances of copper and platinum, exem-
plifying again the supposition that there is some other reason for
the increase of resistance in columns (a), overruling the influence
of difference of temperature. At low intensities, tlie specific re-

* The obMrTatioD with 26 em. of copper and 4 cm. of platioum wire in the
dreoit, gi^ee a ratio of incrtaae oomparatlTelj too great, on account of this length

^^ of platiniun wire hariog been hotter than in any other case.

Digitized by


and Resistance of a Galvanic Circuit. 51

mstance of the copper is actually decre^tsing with the length of
the measured wire, and this seems to indicate that at low inten-
sities, the inflaence of temperature upon the resistance of con-
duetors prevails over anj other reason which, in a galvanic bat*
tery, ana with this method of determination and calculation, may
modify the resistances, actually or apparently.

It was desirable to determine the resistance of the copper wire
at low intensities, without any interference on the part of high
intensities. The last observation of each of the tables xii to ziv,
^ch with 100 cm. of platinum but with no copper wire in the
circuity enabled me to do so. From

1,(1. -I2)
Putting Ii=01900, Pi=80; 13=00882, Ps=100, and afterwards
" =0-1580, " =40; " = " ** = ♦* all from table
XII, and combining them successively with each of the observar
tions with from 50 to 100 cm. of platinum, and 100 cm. of cop-
per wire in the circuit, as per table xii ; and further calculating,
after the same manner, with the corresponding figures of tables
xai and xrv, there result, as the mean values from 12 single
ones, the following resistances :

Length of Resistance of

copper wire. Resistance. 25 cm. iengtb.

100 4*465 M16

160 6128 0-866

200 6-126 0-641

It becomes here more evident that at low intensities the spe-
cific resistance of the copper wire appears to increase with the
intensity, respectively with the temperature produced by it

Of course the above figures cannot be compared with those
given on page 50, since the latter values were derived from the
highest direct intensity. In order to connect the results of both
calculations, I combined first, the intensities 0*8865 and 0*0832,
and afterwards the intensities 0*878 and 0*0882, with each of the
six observations before the last, all of table xii. The values re^
salting therefrom, in columns 1 and 2 of the following table, com*





























Mean, 4*66 4*27

pared with those in columns 8 and 4, which the above mean
value (4*466) is derived from, go again to show a general de«

Digitized by


52 J7« Haug on ike Electro^motive Force

crease of resistance of the copper wire with decrease of observed
intensities, the last horizontal row of figures making the only
exception, if one and the same low intensity is considered. The
values in columns 8 and 4, do not decrease, on account of errors
of observations, I suppose. If calculated for table ziii, column
8 is decreasing, column 4 increasing. If calculated for table xrv,
both columns 8 and 4 are decreasing, from the mean of the first
three values to the mean of the last three.

It seems to me that the facts here illustrated, give a new rea-
son for the great difference of the specific resistances of conduct-
ors, as derived by different observers from experiments, under
conditions much varying and either partly unknown, or at least
underrated in their influence. From observations of Davy, Bee-
querel. Ohm, Christie^ Lenz, Fouillet, Buff, Frick, Mtiller, Lamy,
Arndtsen, Matthiessen and Wiedemann, as recorded in G. Wiede-
mann's Galvanism, 1868, I extract the following table of the
extreme values of the conducting power of different metals, for
which the conducting power of silver is taken as 100. The val-
ues vary

For copper between the limits 65*8 and 280*99 ratio 1 to 4-27
*• gold •* " ** 65-2 " 161-8, " 1 *• 2-93

"woo « a a 24-06 ** 98-6, « 1 « 8-88

a tin it u u 11.45 « 47.2^ « 1 44 4-12

" iron " " « 12-36 « 48-9, « 1 « 8-96

" platinum u u u 7.93 u ^q.^^ u 1 « 3-05

*' lead « « u 7.77 4i 03.3^ u I 44 8.15

" antimony a «« 44 4-29 " 6-6, ** 1 " 1-61

" mercury " " " 1-63 " 4-62, « 1 « 2-83

" bismuth ** " « 1-19 ** 1-9, « 1 " 1-6

While the method of calculation of columns (Cu), (B) and (a),
of tables x to xrv^ gave the iq>pearance of the ratio of increase
beinff equal for the whole amount, and every part, of the so-
called internal resistance, the copper wire included, the above
eomputations show that, for low intensities, the copper wire fol-
lows its own rate of increasCr or rather decrease, leaving indeed,
AS was to be expected, the full amount of increase with the true
internal resistance, viz., within the liquids of the battery. In
table XII, the mean of the first three values of the true internal
resistance, in column (R), is 3'66. The same true internal resist-
ance at low intensities, may be calculated either by the formula

W - 1,(1,^1,) '

with the same observations, (Cu) has been calculated, as per page
51 ; or^ the values for (Cu) computed there, and specified in col-
umns 8 and 4, on page 51, may simply be deducted from the cor-
respondiag mean values of the whole internal resistance of table

Digitized by


and Resistance of a Galvanic Circuit. 53

XCL Thus we get (E) at low intensities^ equal 20-90— 4'f)6=
16-24:; and equal 21-99~4-27=17-72 ; with a mean of 16-98.
From 8*66 to 16*98, the increase is as 1 to 464 ; while the in-
crease of the full internal resistance, the copper wire included, is
only from 5*02 to 21*445, or from 1 to 4*27, for the correspond-
ing values of table zii. Here again the influence of the intro-
duction of 100 cm. of copper wire appears as reducing the true
amount of increase of resistance, and it seems safe to recognize
this increase as residing mainly if not entirely, within the liquids.
The contrary result exhibited in columns (Cu), (B) and (a), ia
therefore due exclusively to the method of calculation.

My series of experiments, most of them, show the values for
the internal resistance, after the general great increase, to de-
crease for the lowest intensities. This becomes more visible from
a graphical representation of the course of the internal resistance.
This circumstance may partly depend on constant &ults of the
observations of small denections of the compass needle. But it
seems certainly to depend partly on the circuit being formed with
copper conductors. The influence of the intensity upon the in-
ternal resistance, appears to become constant at low intensities.
Any further variation of the internal resistance will then be due
to the influence of temperature upon the liquids on one side,
and upon the copper conductors on the other side. Now, as the
resistance of the copper increases with the temperature, from 8
to 4 times more than the resistance of the liquids decreases, their
combined result may produce a reduction of the internal resis-
tance, to some extent, with further decrease of intensity.

On page 888 I ought to have mentioned the so-called " Ueber-
^ngswiderstand," or resistance to passage from solids into
liquids, as one of those circumstances which may influence, or
bring fbrth the results of my experimenta However, from what
I could learn about this kind of resistance, I at first could not
make much of it. Fechner represented it as in direct propor-
tion with the intensity of the current (see G. Wiedermann's Gal-
vanismus, vol. i, page 449, which, however, is contradicted by
De la Bive's Treatise, vol. ii, page 402). Such relation would
not harmonize at all with my experiments. Poggendorff found
the reverse to be the case ; but the idea of such resistance was
generally discountenanced, and the polarization was considered
as sufficient to explain the whole matter, in most cases. To be
sure, the existence of such resistance in other cases was acknowU
edged, and Neumann and Wild gave methods to determine it.
Experimenting with a DanielPs battery, Neumann found the in-
crease of this peculiar resistance to be in direct proportion with
the intensity of the current. But I could not form any idea
about the amount of this resistance compared with the common
resistance of the liquids, since I had at hand nothing but a meager

Digitized by


5i H. Hang on the Electro-metive Force

report about those experiments. Besides this, the figures given
by Neumann were then (1857) not free from doubt as to their
being increased on account of a possible neglect of a part of the

Apart from all these doubts, I have to confess it, the indis-
criminate use of the formula E=IR was the chief reason of my
neglecting the resistance to passage, " Uebergangswiderstand,''
since the electro-motive force of tne battery seemed to increase
in the same ratio as the internal resistance, and did so indeed if
calculated from column (a), after the common method. Later,

ffuided by the fact of the resistance of the copper wire, if calcu-
ated fix>m low intensities, following its own course, and by the
evident inconsistency of combining intensities widely diroring
from each other, I proposed to calculate the electro-motive force
not with the direct intensity, but with those intensities ever^
higher resistance is derived from. Taking table xii, as a speci-
men, there result from the first and last resistances of 14 col*
umns, the following values for the electro-motive force :


4*31 8-86
4-60 S-tXS






8-77 8-95 916 9*29 984 941 9-48 948 9-58 9'56 958 9-68 9-67 9*62

The mean of the first three values of column (a) is 4*42 ; the
mean of the last six values is 9*67, the ratio of increase therefore
equal 1 to 2*188. I could not venture to determine, without
knowing exactly the influence of temperature, whether or not,
this increase of electro-motive force is due, partly, or exclusively,
to this influence of temperature upon the resistance of the unit
of the rheochord, or to a loss of electro-motive force, which I
suppose to occur at high intensities. But I expect that a closer
investigation of the matter will support my views about this

With the foregoing examination of the electro-motive force, I
hope again to have thrown some new light upon the reason of
differences between the values of the electro-motive force of a
battery, as given by different experimenters, or derived from
different methods. The variations are here not so great as in
ease of the specific resistances ; the electro-motive force of the
Grove battery for instance, varying from 167 (Poggendorff's low-

Digitized by


and Resistance of a Oalvanie Circuit


eit figure) tO"192 Lenz and Saweljev),when the force of Daniell's
battery is taken as 100. The reason for this small amoant of
variation however seems to be obvious. There are less observa-
tions recorded as in the other case, and perhaps mainly such re-
sults which were considered as " reliable," thus excluding ex-
treme values which, under certain circumstances are liable to
turn up.

If I take from the above table, 9'67 as an approximation to
the true electro-motive force of the battery, the internal resist-
ance of the battery, at common temperatures, would result as

^ - ^. =10'9, and the internal resistance would appear to increase

from 10*9 to 21*80, or from 1 to 1*954, and this from some other
reason than the influence of temperature upon the measuring
rheochord wire. These figures however cannot convey a true
idea of the relative importance of the temperature on one side,
and of all the other reasons, if there exist more, for the increase
of electro-motive force, and internal and external resistance, on
the other side, since the simple formula of Ohm does not detail
what is constant, and what undergoes variations in different

What this reason is I am still at a loss to know. I hold that
it is not polarization. It seems very probable that the resist-
ance to passage, '^Uebergangswiderstand," will furnish the key
to the results of my experiments. But it will require other ex-
periments (mite differently arranged and detailed to settle this
question, i think it will no longer do to use Ohm's simple for-
mula, and to permit the intensity of the current, and the tem-
perature produced by it, to influence the determinations of eleo-
tro-motive forces and resistances, to an unknown extent, and
varying vndely according to uncontrolled circumstances*

Tabl» VL

BattMy, anc in dilated sulphuric acid ; gaa coke in properly acidulated solutieii of
bichromate of potash. Both liquids had been used once before.

Ebeo- Com- Tan- lot. Meaa values of

etkord. pass, cent roilat
28<> -4246

Online LibraryJohn AlmonThe American journal of science and arts → online text (page 7 of 102)