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SCIENTIFIC MEMOIRS,
Pa <}
| ‘SELECTED FROM
THE TRANSACTIONS OF
FOREIGN ACADEMIES OF SCIENCE
AND LEARNED SOCIETIES,
AND FROM
¢
FOREIGN JOURNALS.
EDITED BY
RICHARD TAYLOR, F.S.A.,
FELLOW OF THE LINNZ AN, GEOLOGICAL, ASTRONOMICAL, ASIATIC, STATISTICAL,
AND GEOGRAPHICAL SOCIETIES OF LONDON ;
HONORARY MEMBER OF THE NATURAL HISTORY SOCIETY OF MOSCOW,
UNDER SECRETARY OF THE LINNZAN SOCIETY.
VOUT
LONDON:
PRINTED BY RICHARD AND JOHN E. TAYLOR,
RED LION COURT, FLEET STREET.
:
“sou BY LONGMAN, ORME, BROWN, GREEN, AND LONGMANS; CADELL; RIDGWAY
AND SONS; SHERWOOD, GILBERT, AND PIPER; SIMPKIN AND MARSHALL; B.
; FELLOWES; S. HIGHLEY; WHITTAKER AND CO.; AND J. B. BAILLIERE, LONDON:
ia —AND BY A. AND C. BLACK, AND THOMAS CLARK, EDINBURGH; SMITH AND
SON, GLASGOW :—MILLIKEN AND SON, AND HODGES AND M’ ARTHUR sDUBLIN :
h — DOBSON, PHILADELPHIA :—-AND GOODHUGH, NEW YORK.
1841.
oy.
oh
ior
ti
“Every translator ought to regard himself as a broker in the great intellectual
traftic of the world, and to consider it his business to promote the barter of the pro-
duce of mind. For, whatever people may say of the inadequacy of translation, it is,
and must ever be, one of the most important and meritorious occupations in the great
commerce of the human race.””—Goethe, Kunst und Alterthum.
PREFACE TO THE SECOND VOLUME.
eee
IN the Advertisement to the Seventh Part of the Scientific
Memoirs the Editor has already acknowledged the assistance
' afforded to the work by the British Association for the Ad-
vancement of Science, concurring, as it has done most efficiently,
with the other public bodies and individuals by whom the suc-
cess of the undertaking had been promoted. It is now his
pleasing duty to state, that the support thus given having af-
forded an opportunity for the plan and objects of the work to
become more generally known, the sale has been so far increased
as to give an improved prospect of its permanence; and that a
portion of the Third Volume is already in the press.
Of the Memoirs contained in Part VIII. the following have
been received from the Committee of the British Association for
procuring the translation and publication of Foreign Scientific
Memoirs, viz. :—
The Galvanic Circuit investigated Mathematically. By Dr.
G.S. Oum. Continuation.
Besse. on the Barometrical Measurement of Heights.
RupBeErG on the Expansion of Dry Air.
WeseER on a Transportable Magnetometer. With a Plate.
Wesex on the Magnetic Term-Observations for 1839 of the
German Magnetic Association. Extract. With a Plate.
Goutpscumipr on the Observations 6f Magnetic Declina-
tion at Gottingen. |
The continuation of the translation of Ohm’s Memoir has
iv PREFACE.
been paid for out of the grant at the disposal of the Committee ;
as have the Plates for the two Memoirs of Professor Weber.
The translation of Rudberg’s experiments has been presented
to the Committee by Professor W. H. Miller, of Cambridge ;
and the translation of the Memoirs of Bessel, Weber, and
Goldschmidt, by Major Sabine; and by the Committee to the
Editor.
The Editor has also to acknowledge the valuable assistance
which he has received from Professors Miller and Wheatstone
in the revision of the translation of Ohm’s Memoirs, and of
Professor Graham and Richard Phillips, Esq., for similar
services with regard to the Chemical Memoirs. To the friendly
and zealous cooperation of Major Sabine he is also most espe-
cially indebted.
Red Lion Court, Fleet Street,
Feb. 20, 1841.
CONTENTS OF THE SECOND VOLUME.
ite AF sult,
PART V.
Page
Art. I.—Electro-Magnetic Experiments, forming a Sequel to
the Memoir on the Application of Electro-Magnetism to the
Movement of Machines; presented to the Royal Academy
of Sciences of St. Petersburg. By M. H. Jacos1, Doctor
of Science, and Professor at the University of Dorpat....... I
Art. Il —Results of the Observations made by the Magnetic
Association in the year 1836. Gottingen: Edited by Cari
Frizepricu Gauss, and WILHELM WEBER. ........ seit PD
Pemaioductton's-by Prot. GAussts.veresc0csonsscssesctercevncsdsdosnsocessete 20
2. Remarks on the Arrangement of Magnetical Observatories, and
Description of the Instruments to be placed in them; by Prof.
Weber ....... Sone Sse tree maeuniadodentneneene aay racseaassesenecetcabenese 25
3. Method to be pursued during the Terms of Observation; by Prof.
Mela Seirteeaceaeecseesarsceenesatsdevdadusteedclos ee Rydeasnaadesel seas oSemas 42
4. Extract from the Daily Observations of Magnetic Dailisinsion
during three years at Gottingen; by Prof. Gauss..............see0e0e 54
5. Description of a smal] portable Apparatus for Measuring the Abso-
lute Intensity of Terrestrial Magnetism ; by Prof. Weber ......... 65
6. On the Graphical Representations, and Table of Results; by Prof.
(27 TES daowoande asain OS aaPa EE Ac sao -eeebsaSackcodd Meee edn hase sah 87
Arr. J11.—On the Combinations of Ammonia with Carbonic
Acid. By Hernricu Roser, Professor of Chemistry in the
Bere ew EE LICINRTY OSes Ue he OS rs Se Pe SOA ASE 98
PART VI.
Art. [V.—Memoir on the Polarization of Heat. By Mace-
SINDEN LONE 2S 8 225 clas SS mundi wtomon lta he 2a, esse aL
Arr. V.—General Theory of Terrestrial Magnetism. By Cary
Frrepricu Gauss, Professor in the University of Gottingen 184
Arr. WE
the Changes in the Intensity of the Horizontal Portion of the
Terrestrial Magnetic Force. By Cari Frieprich Gauss 252
vi CONTENTS.
Art. VII.—Observations on the Arrangement and Use of the
Bifilar Magnetometer. By Wirnetm WEBER .......... 268
Art. VIII.—Contributions to our Knowledge of Phytogenesis.
By Dr. M. J. ScHEEIDEN £2... 1. 00. 2-0 ee ole oe Cee 281
PART VII.
Art. IX.—Supplement to the Treatise entitled “ General Theory
of Terrestrial Magnetism.” By Cari Frirpricn Gauss,
of the University of (Gottingen. . ....\.. ... ness =enee 313
Arr. X.—On the Method of Least Squares. By J. F. Encke,
Director of the Astronomical Observatory at Berlin ...... Si
Arr. XI.—On the Theory of the Formation of Aither. By
Heryricu Rose, Professor of Chemistry in the University of
BROTURD eo d wispy oon og ont 6 3 wegen art ge 370
Art. XII.—Determination of the Axes of the Elliptic Spheroid
of Revolution which most nearly corresponds with the ex-
isting Measurements of Arcs of the Meridian. By F. W.
BESSEL ©. 0. c:-} 871°35
10 871.0 | 871-60 |
20 8724 | 871-95)
30 872.9
The second column contains the several notations ; the third,
the partial results ; 870°80 is the mean between the first and third
notation, and therefore corresponds to 10" 19’ 40", and so forth.
It is pleasing to perceive in this example, chosen from a time of
rapid change in the declination, how a practised observer can
recognize with certainty the changes occurring in 10 seconds.
Observation on the 25th March, 1837, at 0» 5'. By Dr.
Goldschmidt.
Om 4 3Q" 847°3
39 847-2 ‘
46. | S478) |. 8ta oe
53 848-7 847.95 |
5 0 848 9 £2? \847-91
7 848-1 847°85
14 847-0 cae)
21 346.9 | 84770
28 847°3
The first partial result in this case is obtained from the com-
bination of the first and fourth notations ; the second from that
of the second and fifth, &c.
In this example the submultiple of the approximate time of
vibration is an integer number; where this is not the case, the
time must be divided into unequal parts, which has, however,
no disadvantage, provided such an arrangement is made, that
the notations to be combined shall always have for the in-
terval to which they correspond the same approximate value of
the time of vibration, and that the time, and also its portions,
shall be registered. Thus, for instance, the observations in
the astronomical observatory, with a bar of 25 pounds in weight,
having a time of vibration of 43%-14, must be arranged according
:
| GAUSS AND WEBER ON TERRESTRIAL MAGNETISM. 49
‘ to the following scheme,—taking the approximate value at 438,
;| dividing it into four parts, and deriving the final result from
| five partial results.
o> 4/17!
| 28
39 0 4! 38"-5>
| 49 49 5
5 0 5 0°5 $0 5! OMI
1] 105
22 21 +5
32
43
The first column contains the times of notation; the second
the times to which the partial results severally correspond: it is
obviously unimportant that the final result, if accurately taken,
falls at 0" 5! 0""1. If the final result is based on six partial re-
sults, then the following scheme is adopted:
0» 4! 19"
22
33 0» 4! 33-55
44 43 “5 |
55 aS ae
Aes Bon eh
16 16 5
27 26 +5
38
48
The advantage of this modification in the mode of observing is
most evident, when it is desired to follow the course of the mag~
netic declination more closely than at intervals of 5 minutes.
These intervals, sufficient for the ordinary progress of the changes
of declination, are in fact too large for the examination of the greater
and more rapid changes; and it was in this view, and because
shorter intervals could scarcely be generally adopted through-
out the terms of 24 hours, that subordinate terms were added,
each of two hours’ duration, in which the observations were
to be made at intervals of 3 minutes. As, however, the sub-
ordinate terms occasioned some difficulties, and, as they have
hitherto brought to light but few phenomena of correspond-
ing importance, it has been decided to discontinue them. The
Same object can be attained even more effectually in another
manner. The rule of observing at every 5 minutes is retained ;
but if at any time rapid changes of declination occur, the obser-
VOL. II. PART V. D
50 GAUSS AND WEBER ON TERRESTRIAL MAGNETISM,
vations are made at every 24 minutes, as long as it may appear
desirable to do so. An example is added :
10" 22' 0” | 875-0
10 8748 | 875-50)
20 8760 | 875:95 |
30 8771 | 876-40 + 876-27 for 10" 22! 30”
40 8768 | 87660 |
50 8761 | 876-90)
23 0 877°]
Observers in general are requested to pursue the course here
pointed out whenever occasion may require it; and, in such case,
it cannot be doubted that, whenever changes of such magnitude
occur, a body of corresponding observations in close detail will
be collected, and will furnish interesting conclusions respecting
these remarkable phzenomena.
If observers, instead of a clock beating seconds, are furnished
with time-pieces marking other divisions of time, they must ar-
range their observations in an analogous manner, corresponding
to the beats of the time-piece. The observations with a chrono-
meter are more difficult than with a clock, particularly if the
second hand is not truly centred, as is sometimes the case.
It may be well to add some general precautions for unprac-
tised observers.
It is of the first importance that the movement of the needle
should be perfectly free. Spiders sometimes get into the box,
and attach their web to the needle. This may be so fine as pos- —
sibly to escape observation with the eye. Previously to each
term, therefore, the finger should be passed carefully round the
needle on every side. Any impediment which may exist to free
motion will diminish the time of vibration of the needle. The
most minute spider’s thread has a very considerable effect in
this respect, of which a curious example will be related in its
_place.
In night observation it is necessary to illuminate the scale,
which, at Gottingen, during the term-observations, is done by
means of two Argand lamps. There is always an upward cur-
rent of heated air above the flame, and, therefore, if one of the
lamps is placed near and below the telescope, such a current
passing before the object-glass will impair the distinctness of
vision, and cause the divisions of the scale to appear tremu-
lous and undulating. This inconvenience frequently occurred
GAUSS AND WEBER ON TERRESTRIAL MAGNETISM, 5
at Gottingen in the first observations ; but has completely ceased
since each lamp has been provided with a copper chimney, di-
rected to the side.
As in the term-observations several observers are required,
there may be a considerable difference in the distance at which
distinct vision is obtained by the several individuals. Ifa short-
sighted person comes to the telescope adjusted for a long-
sighted person, some alteration will be required for distinct
vision. The use ofa concave glass would be inconvenient and un-
advisable, on account of the considerable loss of light. The mere
sliding of the eye-tube is not sufficient, as, although the image
of the scale might thereby be rendered distinct, the cross threads
would remain indistinct, and would have a parallax in respect
to the image of the object. It would be necessary, therefore,
(with the construction which the telescopes employed in these
observations usually have) that the cell containing the cross
threads should be moveable in the eye-tube, and that it should
be brought nearer to the lens in the eye-piece ; but this requires
a practised hand, takes time, and for other reasons is not to be
recommended for the present case. The difficulty may, however,
be got over in a very simple manner, if the following plan be
adopted. The eye-tube in the telescope, and the cross threads
in the same, are to be so adjusted previous to the observations,
that the most short-sighted among the observers can see perfectly
distinct both the image of the scale and the cross threads ; when
_ a longer-sighted person arises in turn, he has merely, without
displacing the eye-tube or the cross threads, to draw out the
glass nearest the eye so far that he can define perfectly well
the cross threads, and with this a completely distinct vision of
_ the image of the scale is necessarily connected. A short-sighted
person coming in turn has merely to make an adjustment in the
contrary way.
For the purpose of proving the undisturbed state of the tele-
scope, a mark is employed, which is placed at such a distance
i; that it may be seen distinctly with the same position of the
_ eye-piece as is required for the distinct vision of the image of
the scale ; this consists, in the Géttingen observatory, of a small
vertical line on the northern wall*. Previously to the commence-
* With respect to this arrangement, I may here observe that a mark for the
verification alluded to must be considered as indispensable. Previously to
the building of the present Gottingen magnetic observatory, it was doubted
D 2
52 GAUSS AND WEBER ON TERRESTRIAL MAGNETISM.
ment of the observations, the telescope must be directed towards
the mark, and this examination must be repeated from time to
time ; and if a deviation is indicated in the optical axis, it must be
again brought back to its original vertical plane. If the precau-
tion is taken to note two other divisions on the wall, one on
either side of the mark, they will furnish the means of estima-
ting the amount of the requisite correction. But it should be
remembered that these divisions, though they may be made to
correspond exactly with the divisions of the scale, will not have
exactly the same value in seconds. If no such auxiliary marks
have been made, the amount of the correction must be judged of
by the eye, in parts of the divisions of the scale itself.
The observations are made at the vertical thread; the hori-
zontal thread serving merely to indicate nearly the middle of the
former. In order that it should make no difference whether the
parts of the scale appear somewhat higher or lower in the field
of view, the cross threads must have such a position, that a
fixed object, seen on their crossing, remains accurately on the
vertical thread, when the telescope is moved somewhat up and
down. The mark also serves for this verification, which, how-
ever, need not be frequently repeated when the position is left
unchanged.
The plumb-line suspended from the centre of the object-glass
must be so near the scale that the image of both may appear with
the same distinctness in the telescope, and that thus the division
covered by the line may be precisely determined. The scale
must be so placed that its zero must correspond with the plumb-
line, or the division which does so correspond must be taken as
an arbitrary zero. The verifying the undisturbed state of the
scale should be repeated from time to time in the course of the
whether it was not better to place this mark on an insulated pedestal in the
interior of the room, than on an exterior wall exposed to the weather. The
latter was decided on, as otherwise either the distance of the observer from
the needle must have been diminished,—or the advantage of seeing distinctly
the mark and the scale with the same position of the eye-piece be given up,—
or the room must have been made of a greater length, which was not possible
in the place fixed on. ‘lo have a separate foundation for a mark was regarded
for many reasons as objectionable. Moreover, the fear that the place of the
mark might be perceptibly altered by the influence of the weather on the wall,
was regarded as of little importance, considering the solid construction of the
building, and the small height of the mark above the foundation; and espe-
cially as it was in our power to repeat, as frequently as desired, the measure-
ment of the angle between the mark and a church spire seen through the
northern window. The experience of three years justifies the propriety of
this arrangement.
GAUSS AND WEBER ON TERRESTRIAL MAGNETISM. 53
observations ; it is, however, not requisite, when a small change
is found, to bring back the scale to its former position; it is
sufficient to note down in the registry the point of division cor-
responding to the plumb-line.
It may probably not be superfluous to draw attention to one
or two points of comparatively minor importance. It has been
supposed, that the magnetometer and telescope are so arranged
that the mean position of the magnetic declination corresponds to
about the centre of the scale. However, at times of consider-
able variation, this centre frequently gets entirely out of the field
of view, and then the above method of verification will no longer
answer. If at such a time the verification appears necessary,
the quieting bar must be made to perform an exactly oppo-
site office to that which it generally serves; namely, to give the
magnetometer a vibration of sufficient extent to reach, and even
to go rather beyond, the spot required, and thus to allow the
plumb-line to appear in the middle of the field, at that part of the
vibration where the motion is slow, and where consequently the
corresponding division of the scale can be determined with accu-
racy. It is obvious that if such cases occur in the course of a
periodical series, the magnetometer must be again quieted in
time for the next observation, and, consequently, skill in the use
of the quieting bar is of great moment.
When the declination falls very nearly in the centre of the scale,
unpractised observers must be on their guard not to confound
the plumb-line with the vertical line of the telescope. In our
apparatus both resemble one another so much, that with a very
quiet state of the needle, a mistake is very possible, and did,
indeed, once occur. When there is danger of such a mistake,
it may be expedient temporarily to remove the plumb-line.
With respect to the form of communication, some persons
are accustomed to send in the observations im full, others the
partial and final results only, and several merely the latter. The
last may be sufficient, if the calculations have been revised, and
the communicated numbers collated ; but the observations them-
selves should be preserved, in case a reference should be wished ;
and when unusually great changes occur, communication, in full
detail, is most desirable. Besides the results of the observations,
it is always proper to notice, in connection, the value of the parts
of the scale (or the measurements on which the determination is
founded), the time of vibration, the correction and rate of the
54. GAUSS AND WEBER ON TERRESTRIAL MAGNETISM.
clock, the name of the observer, and remarks on such observa-
tions as may be somewhat doubtful. An early communication
is always greatly to be desired. Gauss.
Hil.
Extract from the daily Observations of Magnetic Declination
during three years at Gottingen.
To discriminate the regular changes of declination, amidst
those incessant changes of greater or less amount, which we call
irregular, i so far as their occurrence seems unconnected with
any periodical rules, requires a great number of observations on
a fixed plan, persevered in for a length of time, in order to deduce,
by suitable combinations, mean values, freed as far as possible
from the influence of those anomalies by which the individual
declinations are affected. In general, in this part of the globe,
the declination increases during the forenoon, but the increase
is unequal on different days ; it even sometimes happens, though
rarely, that at the usual hour of maximum, the declination is
less than it was during the earlier part of the same day. The
cause of the morning increase may be in operation every day;
but its influence is sometimes increased, sometimes diminished,
and sometimes entirely masked, by other irregular intervening
forces. Observations on a single day, or continued for a few
days only, cannot therefore determine either the amount of the
effect due to the regular cause, or its inequalities at different
seasons. For this, mean values, taken from a great number of
days, are required. The same is the case with those progress-
ive changes which take place in one direction for a very long
time ; these we call secular, because they require a long series of
years to amount to many degrees. Single observations, repeated
after an interval of only a few years, even though performed on
the same day, in the same month, and at the same hour, can
afford us no certain knowledge respecting them; but mean
numbers, obtained by continued observations, allow us to an-
ticipate, at the end of very few years, what it would otherwise
take many tens of years to fix with any considerable degree of
approximation.
With this view, from the very commencement of the observa-
tions to be performed at our Magnetic Observatory, I have in- -
cluded among them the daily determination of the absolute de-
GAUSS AND WEBER ON TERRESTRIAL MAGNETISM. 55
clination at the same hour. In order to be able to calculate
more easily on the possibility of a long and continuous perseve-
rance, by which alone labours of this kind can be of value, I
have at first rather chosen a limited plan than attempted to
combine too much at once. On this account only two observa-
tions are made daily; at eight in the forenoon, and one in the
afternoon, according to mean time. These hours, which were
most easily compatible with other duties, are also suitable
ones, because in the regular course of the magnetic movements
the position of the needle at 1, p.m. is never far from the maxi-
mum of declination, and during the greatest part of the year, the
hour of minimum is not far from 8, A.M. Observations at fixed
hours of apparent solar time would, it is true, have been more in
accordance with nature; but the much greater facility of an ar-
rangement made according to mean time, renders it deserving
of preference in this case, where the chief point is to secure a per-
severing continuance in one and the same principle.
A regular register was commenced on the Ist of January, 1834 ;
but the first two months and a half have been omitted in the
following extract, because during that time it was frequently
necessary to wind up the suspension-thread, whereby changes
were produced in the torsion which were at first not sufficiently
attended to. From the 17th of March a stronger suspension-
thread was employed, consisting of 200 fibres, of which the point
of no-torsion had been previously accurately determined ; when-
ever changes were subsequently made in respect to the thread,
or to any other circumstance connected with the elements of
reduction, the necessary corrections, or modifications of those
elements, have each time been applied. During the first months
various sufficiently practised observers took part with me in the
observations ; but since the Ist of October, 1834, they have been
regularly made by Dr. Goldschmidt, his place having been only
occasionally supplied, when necessary, by other expert observers.
I have already communicated in the Géttingen Gelehrten
Anzeigen, 1834, p. 1269, and 1835, p. 345, the monthly means
deduced from these determinations up to January, 1835: they
are now given for three entire years.
iL
56 GAUSS AND WEBER ON TERRESTRIAL MAGNETISM.
Mean value of the Westerly Magnetic Declination at
Gottingen.
8, A.M. 1, P.M.
° ° i /
1834. March, secondhalf.| 18 38 16:0 | 18 46 404
prilee yeti 5 etree 36 69 47 38
WER Sedo aatigd 2) 36 28:2 47 15°4
Wane wes scons eee 37 40:7 47 59-5
Vily ..asaessecesee 37 57°5 48 19:0
INapuIsti re cine etemtels 38 48:1 49 11:0
September ........ 36 58:4 46 32:3
Octdtter: csc.cc sas 37 184 44 47:2
November ........ 37 38:4 43 43
December .......- 37 54:8 41 32-7
1S8e. anusnye. setae 37 51°5 42 14:4
February.....5.5.: of. 68'D 42 29:4
March sViiisanects 34 47°5 44 55:2
Aprils gine tren stet eiete 32 57:7 46 31°6
Ma Vics aererseesteais 32 13:4 45 17°71
Junie: Peer eeacees 32 56:4 44 41°3
Ditaliyiacteneaetiaiet acta 34 8:0 44 42:8
AUBUStesee 00056 ne 34 12:4 46 56:8
September ........ 33 21:2 44 27-6
OctObEE ie: ties: 33 23:0 43 5:3
November .......-. 36 15°3 43 49°5
December ........ 35 25:9 40 19:1
1836, January ........-- 35 24 40 346
February...... sees 33 26-7 41 15:2
Wharchisepstetnsenute 31 1:4 43 16:4
April’. .csc- cers 26 32:9 43 42°6
May csc sreescinss 28 0:8 44 37:2
JUNE: aie siastectenetas 27 351 42 52:4
July ...cceccconeee 26 54-2 42 26:0
August ........00. 25 42-4 41 45:0
September .....+ «+» 26 146 40 59:6
October .....-00-- 27 34-0 40 32:8
November .......- 29 21:0 36 54:3
December ....«-.- 29 13-7 35 46:8
1837. January ....++--«- 27 35:3 37 46:2
February ec es ceessee 27 356 36 28:3
IMarchieti. siekaseree 25 44.2 39 42
Some combinations of these observations may now be noticed.
The difference between the declination of the morning and
afternoon has one sign all through in the monthly means; the
dependence of its magnitude on the season of the year will be
perceived in the following tabular view:
GAUSS AND WEBER ON TERRESTRIAL MAGNETISM. 57
1834—1835. | 1835—1836. | 1836—1837. | Mean.
i / i U i“ I u
el ....... 10 569 13 339 17 97 13 53°5
Waves ices. 3's 10 47:2 13 37 16 36-4 13 29:1
DUNG: 0:50:00 10 18°38 11 44-9 15 17°3 12 27:0
ini SSeenee 10 21°5 10 34:8 15 31°8 12 9-4
August...... 10 22:9 12 44-4 16 26 13 3:3
September... 9 33:9 V1: 6:4 14 45:0 11 48-4
October...... 7 28°38 9 42:3 12 588 10 3:3
November .. 5 25:9 7 34:2 Loe 6 51-1
December.... 3 37:9 4 53:2 6 33:1 5 1-4
January ..... 4 22:9 5 32:2 10 10-9 6 42-0
February .... 5 25:9 7 48:5 8 52: 7 22:4
Marchese ccs| 10° 7-7 12 15:0 13 200 ll 542
Mean.... 8 142 10 28 12 54:3 10 23:8
It will be perceived that, not only in the mean values, but
also in each of the separate years, the difference has been smallest
in December ; and this is what we might expect, as those changes
which vary according to the time of the day must necessarily be
ascribed to the action of the sun, although as yet we know not
how this action is effected. It may at first appear surprising,
on the other hand, that the differences are not greatest at the
time of the summer solstice, but appear smaller in June and
July than in April, May, and August, especially as the coinci-
dence of all three years in this circumstance affords a presump-
tion that it is not accidental. It must not, however, be over-
looked, that in the months immediately following the solstice,
the time of the minimum of the declination is earlier, and there-
fore the whole increase would be sensibly greater than the change
reckoned from 8 o’clock.
It is further observable that in each month the differences are
greater in the second year than in the first; and again, in the
third year greater than in the second. But these differences are
by far too great in amount to admit of our considering them as
parts of a secular increase, and it is rather to be expected that
by continuing the observations for several years we shall not
fail to discover a fluctuation. But, in any case, we hereby learn
that one year may differ from another in respect to the effect
of the sun on the earth’s magnetism, somewhat in the same
way that one summer or one winter differs from another in
temperature. On this account also we shall only arrive at an
accurate determination of the mean values by observations con-
tinued for several years.
58 GAUSS AND WEBER ON TERRESTRIAL MAGNETISM,
It has been already stated that exceptions sometimes occur on
single days, when the difference between the forenoon and after-
noon declinations may have the opposite sign. But such ex-
ceptions are rare; during the three years’ observations only
fourteen cases of the kind have occurred; or, on an average,
one in 79 days. I give them in this place, together with the
amount by which, on each occasion, the declination at 8, a.m.
exceeded that at 1, P.M.
U a“ i i
1834. Aug. 15 6 80 1835. Nov. 8 3) 42-2
Dec. 24 3 43-0 Dec. 8 18 35°6
Dec. 25 0 38-2 1836. Jan. 20 0 46:3
Dec. 26 2 20:3 July 20 5 88
1835. Jan. 30 0 23:8 Nov. 9 ll 95
Feb. 7 0 32-5 1837. Feb. 13 4 10
Oct. 4 0 43-1 Mar. 14 1 22-6
Of these fourteen exceptions, twelve, as might be expected,
occur in the winter months, and only two in the summer months ;
the small regular action of the sun in the former being more
easily exceeded by an anomalous movement than could be the
case in regard to the far greater regular action in the summer
months.
To try how far the secular variation might be recognised in
the present observations, the monthly means of the first year
have been compared with the corresponding ones of the second,
and these with those of the third year. Among the forty-eight
comparisons thus obtained (for the incomplete month of March,
1834, has been excluded from this as well as from all the other
combinations), forty-seven give a decrease, and only one an
increase, which is therefore characterised in the following table
by the sign —.
Yearly Decrease of the Declination.
First Year. Second Year.
Mean
8, A.M 1, P.M 8, A.M 1, P.M
i] 1
April...... 3 92 | 0322 | 6248 | 2490 | 3138
May .... 4 14:8 1 58:3 4 126 0 39:9 2 46-4
SHINE voces: 4 44:3 3 18:2 5 21:3 1 48:9 3 48:1
DULY sae. 3 49°5 3 36:2 7 138 2 16:8 4 141]
August 4 35°7 2 14:2 8 30:0 5 11°8 fa
September . 3 37:2 Dwi Ad 7 366 3 28:0 4 4]
October....| 3 55:4 1 41:9 5 49:0 232°5 3 296
November . 1 23:1 |—0 45:2 6 54:3 6 55:2 3 36:8
December..| 2 28:9 1 136 6 12-2 4 32:3 3 36:7
January... 2 49:1 1 39:8 7 27:1 2 A8-4 3 41:1
February ..| 3 36:8 ] 14:2 5 55°] 4 46:9 3 52:2
March :...| $8 46:) 1 38:8 Tle 4 12:2 3 46:6
| Mean... | 3 308 1 42:2 6 21°7 oO mune 3 462
| |
jo!
47° 42!
Uy — Us = 71° 49)
69° 21!
46° 12!
990 947!
R, = 450
R, = 350 - millimetres
ft =6"6/
=
=
H
es
Sew
_~
Hou i il
= 101°0 sre
bahay millimetres.
p 142000 milligrammes.
From these may next be calculated,
> = + (23° 9! + 290 27!) = 11° 24"-00
v, = ¢ (47° 42' + 46° 12!) = 23° 28'50
v, = + (71° 48! + 69° 21/) = 35° 17/25
If now we take the second and the millimetres as the funda-
mental units of time and space in our calculation, we may deduce
from the ascertained values of Ro, R,, Ras Vp, Vy» Va» the following
values of A, A’, B, B', B", viz.
tang 11° 24’ tang 23° 2e''5 |, tang 35° 197"25 _385°54
S
|
A =—~7508 3508 3008 =jou >
Zs _tang 11° 24! tang 23° 28'5 = tang 35° 17'"25 __384'86
450° 350° 300° 10% 3
Ppa 1 _ 20362
= 750° * 350° * 300° 10 °
1 1 1 20977
| ee je =e
B' = 350° + 350° + 300° — 10 °
1 1
yrs 1 20855
450 * 350% + 3900 = 0% *
From these 7 is calculated:
_; 385°54 + 2°0855 — 384°'86 + 2: 0277 10°
~ 2° 9:0362 + 20855 — (20277)?
or
7 = 87650000.
GAUSS AND WEBER ON TERRESTRIAL MAGNETISM. 83
Finally, from this value of 7, and from that of ¢, determined by
observation, may be deduced the value:
By ctciey _ 5:0641
tVr ~~ 667° 8765000 =—:10” *
This number suffices for the comparison of all intensities mea-
sured with the same instrument, however the magnetic condition
of the apparatus may have varied.
Further, the number 7, which expresses in absolute measure
the resulting intensity of the earth’s magnetism, may be ascer-
tained by deducing from the observations the value of C, and
multiplying the former number by its square root. C is calcu-
lated from the observed values of a, 6, and p, the mass of the mil-
ligramme being taken as the unity of mass:
C = 9-8696 + LOL + 17°5° = 0°1227 10
= 9° coger pert + 142000 = 0°12272 + 10
“=
whence 7 is deduced
T = 5:0641 . 0712272 = 1°774.
5. Examination of the result.
This number 1°774, expressing the intensity of terrestrial
magnetism on the 18th of January, 1837, possesses, as an
absolute measure, the advantage of being directly comparable
with the results obtained in 1834 with the magnetometer of
the Gottingen magnetic observatory, published in the Géttingen
gelehrten Anzeigen of that year. They will be found in part
128, (with the account of the newly-constructed building, and
of the instruments, as well as of the first experiments performed
there). They are as follow:
Pyenpoicd es Se Heres a. ek. ots
— 20 . : : ° : 17740
— 271 . ; : : z 1°7761
Two apparatus destined for the same purpose can hardly be
more dissimilar than the small apparatus above described, and
the magnetometer. It results from the comparison, that the
intensity of the terrestrial magnetism in Gottingen has under-
gone hardly any alteration from 1834 to 1837.
We have also a direct comparison of this number obtained
for Gottingen with the result of observations with a third ap-
paratus, differing widely from both the others made at Munich,
April Ist, 1836, viz. 1-905, and with the number found for
F2
84 GAUSS AND WEBER ON TERRESTRIAL MAGNETISM.
Milan, with the magnetometer of that place, in October, 1836,
viz. 2°61839.
To gain a clear idea of the import of these numbers, the de-
termination and application of which have been hitherto under
consideration, imagine a number of small steel bars, perfectly
alike, and each weighing about 23 grammes, or 4 of an ounce.
Imagine further a balance, of which the length of the arms
bears to 1 metre the same proportion that 1 metre bears to
the space of descent in 1 second (204 millimetres nearly) ; sup-
pose one of these steel bars to be attached in a parallel direc-
tion to the horizontal beam of the balance, in such manner that
the equilibrium is not thereby disturbed. Then render all the
steel bars (including the one attached to the balance) equally
magnetic, and to such a degree that when another of their
number is placed vertically beneath the scale at the distance of
1 metre from the attached magnet bar, ;15,th of a milligramme
must be placed in the scale to preserve equilibrium. When
the magnetism of all the bars has been regulated in this man-
ner, place one of the bars horizontally, and at right angles to a
small compass needle, 1 metre from the centre of the needle
beneath, taking care that as the compass needle is deflected
from the magnetic meridian, the bar be also turned so that they
may preserve their rectangular position. Lastly, calculate how
many such bars are required that their united force may deflect
the compass needle 90°; the number of bars gives the terrestrial
magnetism in thousandths of its absolute measure.
We may conceive in like manner the number which repre-
sents the absolute measure of the terrestrial magnetism to repre-
sent the number of these bars reckoned in thousands, the forces
of which must be united to cause, at a distance of a metre, a
deviation of 90°. This would require at
Gottingen the force of . . . 1775 bars
MICA. ee Nal) CT
Brae ese) coe ee ot ee
6. On the Advantages of the Dimensions selected for the small
Measuring Apparatus.
Before concluding this article, we have to discuss the accuracy
of which the absolute measurement of intensity with the appa-
ratus described is susceptible, and on what it is founded. It
has been already remarked, that the absolute intensity can be
GAUSS AND WEBER ON TERRESTRIAL MAGNETISM. 85
measured with the accuracy it deserves only with the magneto-
meter. It is therefore unnecessary to state that such extreme
accuracy cannot be attained with the small apparatus. And in
order to obtain with it a good approximation, it must combine
all the advantages of which it is susceptible.
The difficulty of an accurate measurement of intensity, with
other instruments than the magnetometer, is thus stated in the
memoir “ On Terrestrial Magnetism and the Magnetometer +”
“ In all cases, if the elimination is to be satisfactory, the ex-
periments must not be performed at too small distances ; conse-
quently the effects are always comparatively small, and the
means previously in use are inadequate to measure them with
the necessary precision. It is this difficulty which has called
for, and has given rise to the construction of a new apparatus,
which may with propriety receive the name of magnetometer,
since it serves to execute, with an accuracy equaling that of the
most delicate astronomical determinations, all measurements—
both of the force of magnetic needles, and of the intensity of the
earth’s magnetism (at least its horizontal portion). The (hori-
zontal) direction of the earth’s magnetic force is determined ac-
curately with it to within one or two seconds of arc; the com-
mencement and termination of a vibration is observed with it to
within a few hundredths of a second of time, and consequently
more accurately than the passage of stars behind the wires of a
transit.”
There are two circumstances, chiefly, on which the accuracy
of an absolute measurement of intensity depends; first, the
magnitude of the deflection produced; secondly, the delicacy of
the instrument in measuring this deflection. In constructing an
apparatus for this purpose we may therefore follow two different
paths: we may either make the amount of deflection the main
object, and pay only as much attention to the means of mea-
surement as may be consistent therewith ;—-or we may attend
chiefly to accuracy in the means of measurement, and let the
amount of the deflection be the second object. The latter plan
leads to much greater accuracy than the former, for this rea-
son: the amount of deflection soon attains a limit, on account
of the necessary condition of a considerable distance between
the deflecting bar and the needle, so that the deflection produced
86 GAUSS AND WEBER ON TERRESTRIAL MAGNETISM.
must always be small. If, however, all pretensions to great
accuracy of measurement are relinquished at the outset, by
making the magnetic needle play on a pivot, instead of sus-
pending it by a silk thread, the friction of the point renders
fineness of measurement quite illusory, and the former much
less advantageous plan is the only one that remains open; the
endeavour must then be to adopt the arrangements and pro-
portions best suited to produce the greatest possible deflection.
This is the express object of the small size of the apparatus de-
scribed, and not merely to render it light and convenient of
transport.
That the small size of the apparatus does actually allow of a
great amount of deflection is evident by the result ; for in the
experiments above mentioned all the measured angles exceeded
20°: it is easy to explain the reason.
1. The distance of the deflecting bar from the needle must be
relatively great, but need not be absolutely so: it must at least
be three or four times greater than the length of the deflecting
bar, or of the magnetic needle.
2. By diminishing in proportion all the linear dimensions of
the apparatus (viz. the dimensions of the magnets, and their
distance apart), the angular magnitudes, of which the deflection
is one, remain unchanged ; therefore such proportional reduc-
tion in the size of the apparatus, causes no loss in the amount of
the deflection to be measured.
3. But if instead of diminishing in equal proportion all the li-
near dimensions of the apparatus, we diminish only the length of
the magnets and their distance apart, the breadth and thickness
of the deflecting bar being little or not at all diminished, then
we even gain an increase in the angular magnitudes, and it only
remains to know how far this increase may be carried.
The limit depends on a single circumstance, viz. on the
breadth and thickness of the deflecting bar, with a given length.
Experience has shown, that neither the breadth nor the thick-
ness of the bar ought to exceed the eighth part of its length.
It follows that the greatest deflection may be produced by a
magnet bar, of which the breadth and the thickness are equal,
and of which the length is eight times greater than either, and
acting upon a magnetic needle, placed at a distance equal to
three or four times the length of the bar; the length of the
needle must not exceed that of the bar.
GAUSS AND WEBER ON TERRESTRIAL MAGNETISM. 87
From this rule then we obtain the most advantageous di-
mensions of such an apparatus, by knowing the limit in re-
spect to thickness, which is determined by the nature of the steel.
The thickness of the bar must not amount to much more
than 12} millimetres, as otherwise the steel cannot be properly
hardened and magnetized throughout. We thence obtain the
following dimensions of the deflecting bar, as those which com-
bine the greatest advantages, namely, for its breadth and thick-
ness 121 millimetres, and for its length 100 millimetres. We
have also the length of the magnetic needle 100 millimetres,
and the smallest admissible distance between them, 300 milli-
metres.
By following these rules we obtain an apparatus, with which,
in mean latitudes, the smallest deflections to be measured ex-
ceed 22°, as in the experiments related. At greater distances
from the magnetic poles of the earth, this deflection becomes
somewhat smaller; nearer to the magnetic poles it is much
larger. Therefore, if these deflections can be accurately mea-
sured to within a tenth part of a degree, a final result can be
obtained to within the 200th part of the force itself; sinceall other
measurements required in the determination of the absolute in-
tensity can be made with greater accuracy. This result, it is
true, is far inferior to that which can be obtained with the mag-
netometer ; but such results may still be of great utility in the
absence of more accurate determinations.
WEBER.
V.
Explanations of the graphical representations, and of the
table of results.
In Plates [V.—-IX. are given the graphical representations of
the changes of declination during six terms, amounting, in all,
to forty-six curves, from fourteen stations, viz. Berlin, Breda,
Breslau, Catania, Freiberg, Gottingen, the Hague, Leipzig,
Milan, Marburg, Messina, Munich, Palermo, and Upsala. The
graphical representations begin with the November term of 1835,
when the Association was strengthened by the accession of seve-
ral new and zealous cooperators. The representations of two
terms of the year 1836 have been omitted, viz. those of March
and May, as the changes they present are comparatively less in-
teresting than those of the two terms of January and July, be-
88 GAUSS AND WEBER ON TERRESTRIAL MAGNETISM.
tween which they occur; and the number of six terms, fixed on
as the rule for the annual publication, is completed by the addi-
tion of an extra term in August.
Of the apparatus employed, three are exactly similar to those
at Géttingen, but of smaller dimensions; namely, that of Dr.
Wenkebach, first used at the Hague, and subsequently at
Breda; the travelling apparatus with which M. Sartorius of
Waltershausen, and Dr. Listing, observed in Palermo, Catania,
and Messina; and the apparatus already mentioned at p. 22, in
the Berlin Magnetic Observatory, which latter, however, will be
shortly replaced by a larger one, of Meyerstein’s. The other
apparatus in Breslau, Freiberg, Géttingen, Leipzig, Milan, Mar-
burg, Munich, and Upsala, are all alike.
The participators in the observations represented in the six
terms, as far as the names have come to our knowledge, were
as follows :
In Berlin, besides Prof. Encke, MM. Bremiker, Galle, Madler,
and Wolfers.
In Breslau, besides Prof. V. Boguslawski and his sons, MM.
Bratke, Brier, Dittrich, Héniger, Jacobi, Isaac, Klingenberg,
Koch, Kérber, Kiintzel, Maywald, Miiller, Dr. Pappenheim,
Reichelt, Reisern, Ribbeck, Riemann, Roedsch, Wiedemann,
and Wilde.
In Catania, Dr. Listing, MM. Sartorius von Waltershausen,
and Zobel.
In Freiberg, besides Prof. Reich, MM. Felgner, Neubert,
and Walther.
In Géttingen, MM. Briss, Lieut. Engelhard, Dr. Goldschmidt,
Meyerstein, Schréter, Dr. Stern, Lieut. von Stolzenberg, Prof.
Ulrich, Dr. Wappius, Dr. E. Weber, and Prof. W. Weber.
At the Hague, (in the September term,) besides Dr. Wenke-
bach, MM. von Cranenburgh, Rueb, and Simons.
In Leipzig, besides Prof. Mébius, MM. Brandes, Faber, Hiilse,
Kiihne, Michaelis, Netsch, and Zunck.
In Milan, besides M. Kreil, MM. Capelli, Stambucchi, and
Della Vedova.
In Marburg, besides Prof. Gerling, MM. Beck, Deahna, Eich-
ler, Fliedner, Hartert, Hartmann, Ise, Kutsch, Landgrebe, Lotz,
and Oppermann.
In Messina, Dr. Listing, MM. Sartorius von Waltershausen,
and Tardy.
GAUSS AND WEBER ON TERRESTRIAL MAGNETISM. 89
In Munich, besides Prof. Steinheil, MM. Hierl, Lamont, Lip-
-polt, Meggenhofen, Mielach, Pauli, Pohrt, Recht, Schleicher,
Schréder, Siber, and Zuccarini.
Other observations of some of these six terms have also come
to our hands, but too late for insertion in the plates; this is the
more to be regretted, as, for the most part, they accord with the
others in a very interesting manner. The results of the obser-
vations made at Upsala, in the September term, 1836, which are
of this kind, are printed in the sequel. The Milan observations
of November, 1835, which were also received after the curves for
the six other stations had been drawn on stone, were inserted
below them; but for this circumstance, their place would have
been between the Munich and Palermo observations. The Gét-
tingen observations have required no process of reduction, being
drawn in accordance with the divisions of the scale as indicated
in the margin, the height of each square being taken as two divi-
sions of the scale in all the terms, with the single exception of that
of January, 1836. The changes during that term are the greatest
which have been hitherto observed, and rendered it necessary, in
order not to increase the height of the page too much, to allow
three divisions of the scale for each square. Increasing numbers
always denote an advance of the needle from right to left,—in
other words, diminishing westerly variations. The observa-
tions at Breslau, Freiberg, the Hague, and Leipzig, where the
divisions of the scale are nearly of the same magnitude as in
Gottingen, have been drawn according to the same proportion.
The distance between the curves is an arbitrary quantity in each
case, determined solely by its fulfilling the one object of keeping
them at a convenient distance apart.
For those stations where the value of the divisions of the scale
differs considerably from that at Gottingen, the original numeri-
cal results were multiplied in each case by a common factor, ex-
pressing, as nearly as possible, in convenient numbers, the pro-
portion to the Gottingen scale. Thus, the various curves in each
term are represented very nearly according to a common scale.
In the January term alone the scale of representation is somewhat
more unequal, the cause of which does not merit any mention in
this place, as it suffices to know the scale for each curve. In
the three first terms the height of each square corresponds to
the following values of arc, viz. :
90 GAUSS AND WEBER ON TERRESTRIAL MAGNETISM.
November, | January, July,
1835. 1836. 1836.
“a “i “
[a op ee opcepre 42°01 63°01 42°01
Gottingen. ...| 42-25 63°38 42:25
IErIU 2 cis oe s _- — 42:24
Breblau''::25-. 4 a -- 42:40
Leipzig ..... 41°34 63°01 41°34
Marburg ....| 42°20 60°28 42:20
Munich... 41°86 55°82 41°86
IMinlerte cfs: che he 40:27 60°40 41°33
Balernos. 6 oi 42:07 — —
(CaLanity 9. <7s-0.s — 41°56 —
Messina..... — — 43°06
For the three last terms, the value of the divisions of the scale,
and the proportion, according to which they have been inserted
in the plates, are stated in the table of numerical results.
The curves are all drawn according to Géttingen mean time,
(indicated at the top of each plate,) or at least very nearly so, and
therefore contemporaneous movements appear all in one vertical
line. The order in which the several curves are arranged in
each plate was principally regulated by convenience as to the
curves fitting into each other.
The following remarks may be added in regard to particular
terms :
On the 28th of November, 1835, and during the following
night, the observations at Palermo were much disturbed by an
exceedingly violent Sirocco-wind, so that at one time they had
even to be suspended for an hour and a half; and at other times
only partial and uncertain determinations could be obtained. It
is probable, therefore, that many of the apparent movements
were not real magnetic changes. Nevertheless, we Wetermined
not to exclude this curve; as the latter part of it, from the
morning of the 29th November, when the storm had nearly
passed over, offers a sufficiently satisfactory accordance with the
stations to the north. I take this opportunity of mentioning that,
according to all our experience hitherto, the most violent storms
of wind appear to be wholly without influence on the magneto-
meter, provided only the instrument is effectually protected
from any effect of their direct mechanical action. Very frequently,
either an extremely quiescent state of the needle, or a very regu-
lar and uniform progress, has been remarked in the Magnetic
GAUSS AND WEBER ON TERRESTRIAL MAGNETISM. 91
Observatory of Gdéttingen, during the prevalence of the most
violent storm. If any one, however, were inclined to infer from
such experience, that storms in the atmosphere, on the other
hand, counteract or enfeeble the magnetic forces, such an idea
would be dispelled by what took place during the term of Janu-
ary 1836. During this term a very violent storm prevailed at
Gottingen, and at many other stations ; and several observers in
other places accompanied the results which they communicated,
by the expression of a fear that from this circumstance the un-
usually large movements shown by the magnetometer might
offer but little accordance. Nevertheless, the harmony of the
curves from the various stations was so complete (see the repre-
sentations in Plate V.) that it might have been termed wonder-
ful, if the same thing had not been manifested before by so many
experiments. As with wind storms, so it is with ¢hunder storms,
which, even when close at hand, exercise (as attested by several
cases which have occurred here and at other places) no percep-
tible influence on the magnetic needle*.
A letter from M. von Humboldt, received in August, 1836, con-
tained the information that, from the 10th to the 18th of August,
the magnetic changes would be observed uninterruptedly every
quarter of an hour at Reikiavik, in Iceland, by a practised
French astronomer, M. Lottin, with Gambey’s apparatus, and
expressed the wish that corresponding observations might be
made on one or on some of those days with magnetometers. In
consequence an unusual term was fixed for the 17th and 18th
of August, and as far as the shortness of the time allowed, seve-
ral members of our Association at other stations were invited to
take part in it. This unusual term was observed in Upsala,
the Hague, Gottingen, Berlin, Leipzig, and Munich, in exactly
the same way as the usual terms; and if the graphically re-
presented observations in Plate VII. exhibit exceedingly in-
teresting changes, we have only to regret that the place reserved
at the top of the plate for the Iceland observations is vacant, as
we have not been able to obtain the slightest information re-
specting the result of the French Icelandic observations.
The September term presents a case which may be noticed
somewhat in detail, as it confirms, in a very instructive man-
* There is, of course, no question here of experiments in which the atmo-
spheric electricity is conducted to the earth by means of a conducting wire
passing through a multiplier surrounding the needle.
92 GAUSS AND WEBER ON TERRESTRIAL MAGNETISM.
ner, what has been stated at p. 50. In the register of the
Marburg observations, which on that occasion were made in
the absence of Prof. Gerling, and at the hours of 120™, 12h5m,
and 12" 10", there appeared an unusual irregularity, which ex-
cited the suspicion, that about 12"5™ a spider had prevented the
free motion of the needle by attaching a thread; and this sus-
picion was increased by the circumstance, that from 12 10™ to
the end, the changes of the needle were exactly similar to those
which resulted from observations at other stations, but appeared
proportionally much smaller than could have been expected from
the experience of other terms. Prof. Gerling was requested, on
his return to Marburg, to examine the apparatus carefully, and
the result is contained in a letter from the Professor.
The examination took place on the 5th of November, up to
which time no one had entered the room of observation since
the September term. In the first place the position of the
needle was determined and found as follows :
at 34 33m . . . 445°63
Bide 15. Toe ASS
OF fh alt xe Ah
Upon this the needle was set in moderate vibration by means
of the moderating bar, and hence a time of vibration of 17 seconds
was found, being nine seconds less than the usual duration: the
lidof the case was then carefullyremoved, and avery minute living
spider was noticed on its under surface ; a very small, and nearly
imperceptible, thread was thought to be observed hanging to it:
further, a number of small, black point-like bodies were found
in the box, which, under the microscope, proved to be the dead
bodies of gnats ; and finally, in one corner of the box, a regular
undisturbed web, of such fine texture, that without the reflexion
of the light it would hardly have been perceptible. From all
these circumstances it may be supposed that the spider had
been some time in the box.
When the finger had been passed round the magnet bar in
all directions, new observations of the time of vibration gave
again the former value of 26 seconds. The position was also
found to correspond to much lower numbers on the scale,
namely,
gh 45m. AG1°45
Aba he wt er ASd 4G
Eh sata Setar: ad 1
GAUSS AND WEBER ON TERRESTRIAL MAGNETISM. 93
Of course, however, these observations could not furnish an
accurate determination of the amount of error introduced, as the
declination may have. altered during the interval, which amount-
ed to more than an hour.
In the graphic representation the second half of the Marburg
curve has been drawn on a reduced scale, the reduced divisions
representing 28 on the Marburg scale.
I may here mention a second case of a similar kind. The
time of vibration of the magnet bar in Breslau, which, in March
1836, amounted to nearly 3°2 seconds, had from that period to
November gradually increased, making altogether an increase of
about 0-4. This is no unusual circumstance, as all magnetic
bars in the course of time lose some part of their force, though
in very various degrees dependent on the unequal tempering of the
steel and other circumstances. But, from November 1836, to
January 1837*, a decrease in the time of vibration of 1°27 took
place. Prof. von Boguslawski, who informed me of this remark-
able circumstance, seemed inclined to attribute it in part to an
increased intensity of the terrestrial magnetism. I did not doubt,
however, that the cause must be sought in the immediate neigh-
bourhood of the magnet bar, probably in some impediment to
its free motion, and this supposition was verified by the follow-
ing letter of M. Boguslawski :—
** You were right in your supposition as to the cause of the al-
teration in the time of vibration. By a slight accidental dis-
placement of the box, the edge of the small aperture through
which the suspension thread passes, had been brought near the
thread, though by no means into contact with it. However, some
of the finer fibres of the silk must have been touched thereby, for
when it was again made to pass quite through the centre of the
aperture, the time of vibration was found almost identical with
that formerly observed.”
This is perhaps the place for some remarks on the movements
themselves, which are here represented during six terms.
In the three summer terms, (Plates VI. VII. and VIII.) not-
withstanding all the great anomalies, the regular diurnal move-
ment is clearly seen in the curves, ascending during the hours
* Probably during the interval no determinations of the time of vibration
had been made.
94 GAUSS AND WEBER ON TERRESTRIAL MAGNETISM.
after noon, and descending in the following hours of the fore-
noon; there is, on the other hand, scarcely a trace of this in the
three winter terms, Plates IV. V. and IX. All our experience
shows that partial or even total obliteration of the regular move-
ments by the irregular is a verycommon occurrence. In theyears
1834 and 1835 some terms occurred in which the regular course
was not at all obscured by any considerable anomalies, although
there was no want of smaller ones. But what renders the ano-
malous oscillations so remarkable, is their extraordinary coinci-
dence, generally even in the smaller instances, at different sta-
tions; nay, commonly at all the stations, only in dissimilar pro-
portions of magnitude. It is quite unnecessary to demonstrate
this agreement in individual instances : a view of the representa-
tions of the six terms will speak sufficiently for itself.
We cannot at present decipher these enigmatical hierogly-
phics of nature: we must first endeavour to procure from the
most diversified sources, authentic, numerous, and minutely faith-
ful copies, in the confident hope, that when these rich materials
are accumulated, the key to their hidden meaning will not be
long wanting. In the mean time I may be allowed to add a few
remarks, which may assist in the formation of a more correct
judgement concerning them.
First, it must not be forgotten that these anomalies are but
comparatively small modifications of some of the effects of
the great terrestrial magnetic force; that we must distinguish
between the force itself and these supervening alterations ;
and that nothing in the present state of our knowledge obliges
us to ascribe both to the same or to similar causes. There-
fore those who think it probable that these anomalies are
the effects of electric currents, or of action, perhaps far beyond
our atmosphere, (which view we leave entirely to its own merits)
may continue to do so, without having to relinquish on that
account the old view, of a force, residing in the solid portions
of the earth, or rather being the collective action of all its mag-
netized particles. If, according to the opinions of some phi-
losophers, the interior of the earth be supposed still in a fluid
state, the constantly advancing solidification, and the conse-
quent thickening of the solid crust of the earth, would offer the
most natural explanation of the secular variations of the mag-
netic force.
But we willingly leave the uncertain ground of hypothesis,
:
GAUSS AND WEBER ON TERRESTRIAL MAGNETISM. 95
and return to facts. By far the greater number of the ano-
malies are found to be smaller at the southern stations, and
larger at the northern. For instance, the remarkable ascent of
the curve, on the 30th January, 1836, between 94 25™, and 9%
40™, amounted in Catania to 6! (reduced to parts of arc) ; in Milan
to 12’; in Munich to 134’; in Leipzig to 16’; in Marburg to
20'; in Gottingen to 26’; and at the Hague to 29’. Some-
thing, it is true, must be deducted from this inequality, due
to the circumstance that, at the northern points (where the
horizontal portion of the terrestrial magnetic force has a weaker
intensity than at the more southern ones,) similar disturbing
forces must produce greater effects; but the difference of the
horizontal intensities at the Hague and Catania is very small
in comparison with the inequalities observed; and it is there-
fore certain that the energy of the disturbing force was weaker
the further we follow its action towards the south. With all the
uncertainty under which we labour with respect to the nature of
such disturbing forces, we cannot doubt that they have some
definite source in space; and, as we must necessarily suppose
those which produced the above-mentioned phzenomena to have
their seat to the north or to the north-west of the places of obser-
vation, (without venturing to define more precisely from so few
data,) the northern districts, as far as we may venture to draw
any such conclusions from experiments which embrace but a
comparatively small portion of the earth’s surface, appear to be
the great focus, from whence proceed the greatest and most
powerful actions.
A closer inspection of the data hitherto collected leads us
to recognise, in the different successive movements, considerable
variations in respect to their proportional magnitudes at dif-
ferent places, even when the similarity in other respects is un-
equivocal: thus, for instance, at one place, the first of two move-
ments, following one shortly after the other, is the largest; at
another place the reverse happens. We are therefore compelled
to admit that, on the same day, and in the same hour, various
forces are contemporaneously in action, which are probably quite
independent of one another, and have very different sources ; and
the effects of these various forces are intermixed, in very dissi-
milar proportions, at various places of observation, relatively to
the position and distance of these latter; or these effects may
pass one into the other, one beginning to act before the other has
96 GAUSS AND WEBER ON TERRESTRIAL MAGNETISM.
ceased. The disentanglement of the complications which thus
occur in the phenomena at every individual station, will un-
doubtedly prove very difficult ; nevertheless, we may confidently
hope that these difficulties will not always remain insuperable,
when the simultaneous observations shall be much more widely
extended. It will be a triumph of science, should we at some
future time succeed in arranging the manifold intricacies of the
phznomena,—in separating the individual forces of which they
are the compound result,—and in assigning the source and mea-
sure of each. Now and then we find at some places a small
change, without any apparent counterpart at any of the other sta-
tions. Such occurrences ought not to be at once looked upon
as evidences of local magnetic action. In so great a mass of
numbers an error may sometimes take place. Cases have fre-
quently occurred to us where a revision of the original observa-
tions, when these were in’our hands, has shewn an error of cal-
culation in the reduction, or an evidently accidental error in the
writing. In other cases, in which we had received only an ex-
tract of the observations, a reference to our correspondent has
led to a similar conclusion. As, however, it is impracticable to
discuss all such cases by correspondence, those observers who
do not communicate the original observations are requested,
when they discover such cases in the curves representing them
(as, for instance, at Leipzig, on the-26th of November, 1836,
for 64 15™ Géttingen mean time), to refer to the original re-
gister. If errors are thus discovered, they can be corrected in
a following number. Even when the original papers do not
decidedly indicate any error, yet we cannot have perfect assu-
rance with respect to cases which rest only on a single set of ob-
servations : it may happen, even to a practised observer, to write
down in the same set repeated erroneous decimals. By such
a conjecture, (somewhat hazarded it is true,) the above-men-
tioned number 11°69 would be reduced to 6°69, and thus corre-
spond with the others.
But supposing the case of such an insulated movement to be
established beyond all doubt, it does not follow that it is to be
considered as local in the most limited sense. As the source of
every anomaly must have its seat somewhere, it may be that
the disturbing force is in the neighbourhood of the station it-
self. If feeble, its action may still be perceptible at that station,
on account of its proximity, and may disappear (2. e. be no longer
Lda oe pmpet antes
GAUSS AND WEBER ON TERRESTRIAL MAGNETISM. 97
perceptible) at all the other places of observations, because they
are too remote. It appears, therefore, at least for the present,
that there is no reason for admitting among the anomalies other
than quantitative differences. Connected with this, it may be
very useful, in many cases, to have two or more stations situated
within a moderate distance of each other.
It would have been desirable, for example, to have had obser-
vations during the September term of 1836, at Augsburg, where
the simultaneous observations are now regularly made. We
should, in that case, have been able to form a decided opinion
on the subject of the movement at 2 10™, everywhere sensible
indeed, but which, at Munich, appears to have been of re-
markable magnitude.
Note.
In the original work the observations made at the different sta-
tions in the several terms are printed in tables, and graphical
representations of them are contained in six Plates. Much care
has been taken to make the plates which are annexed to this
translation faithful copies of the originals. It has not been
thought necessary to republish the tables ——Enir.
VOL, II, PART V. G
98 HEINRICH ROSE ON THE COMBINATIONS OF
ArRTIcLE III.
On the Combinations of Ammonia with Carbonic Acid. By
Hernricu Ross, Professor of Chemistry in the University of
Berlin.*
[From Poggendorff’s Annalen, vol. xlvi., part 3.]
AN accurate examination of the combinations of ammonia with
carbonic acid appeared to me to be important in several respects.
Since the ultimate component parts of these combinations are
exactly the same as those of animal substances, it was reason-
able to suppose that they might easily combine in other propor-
tions, and form new or already known combinations. It also
appeared to me of importance to become acquainted with the
properties of the anhydrous carbonate of ammonia, so as to be
able to compare it with the other anhydrous salts of ammonia,
The examination, however, of these combinations has not af-
forded such results as I had expected. Carbonic acid and am-
monia seem to belong to the last combinations into which sub-
stances containing oxygen, hydrogen, carbon, and nitrogen,
become converted ; and if therefore such bodies produce during
their decomposition, by means of increased temperature, carbo-
nate of ammonia, it is because the atoms of the elements in the
carbonate of ammonia produced, are united in such a manner as
to form combinations which are less easily decomposed, and, as
it were, more stable, than the combinations consisting of these
simple bodies generally aret. Neither did I find that the anhy-
drous carbonate of ammonia possessed any remarkable properties
analogous to those by which the anhydrous is distinguished from
the hydrous sulphate ofammonia. However, I discovered in my
experiments on the combinations of ammonia with carbonic acid
a fact which to me appeared worthy of attention; for, although
these combinations are less decomposable than other bodies
which consist of the same elements, yet carbonic acid and am-
monia have little affinity for one another, and this is the rea-
* Translated by Mr. William Francis.
+ Something similar occurs with grape sugar. A great number of organic
substances are convertible by the action of very dilute acids into grape sugar,
a substance scarcely decomposable, at least by weak acids,
ore
a
AMMONIA WITH CARBONIC ACID. 99
son why they can both combine in the most varied proportions.
The number of these combinations is in fact surprising. I have
prepared several of them, the existence of which was previously
unknown. It would, however, have been easy for me to have
greatly increased their number by further examination, but I
have contented myself with indicating the possibility of the ex-
istence of a great number of such combinations, since their pre-
paration and examination would occasion more trouble than the
subject appeared worthy of.
The reason of the great number of these combinations arises
less from the weak affinity which carbonic acid has for ammonia,
than from the circumstance that the various combinations have
a great tendency to form double salts with each other. I have
attempted to consider several salts which carbonic acid forms
with ammonia as double salts combined in certain proportions,
by which the number of the more simple combinations is limited.
Hitherto we were acquainted with only the following com-
binations of carbonic acid with ammonia in a solid state: 1.
the anhydrous neutral carbonate of ammonia, NH® + @; 2. the
sesquicarbonate of ammonia, 2 NH? + 3C + 2H, or rather
the sesquicarbonate of the oxide of ammonium, 2 NH‘ + 3 G ;
and 3. the bicarbonate of ammonia, NH? + 2C + 2 H, or
NH‘ 426 4 HL a
~ With respect to the analysis of the combinations of the car-
bonic acid with ammonia, the proportions of the ammonia and
carbonic acid were determined directly, the water by the loss.
The determination of the ammonia may be effected with the
greatest accuracy. The carbonate of ammonia was placed in a
vessel which could be closed with a stopper, and a mixture of
equal parts of muriatic acid and alcohol added; after the com-
plete disengagement of all the carbonic acid, the solution was
diluted by the addition of very strong alcohol (90 — 95 p..c:).
Upon this an excess of a solution of chloride of platina, and
then zether to nearly the amount of one fourth the volume of the
alcohol, was added. The ammonio-chloride of platina is quite
insoluble in a mixture of strong alcohol and zther, and may be
collected without loss. I let it completely settle at the bottom
of the stoppered bottle for twelve hours, and washed it out witha
mixture of alcohol and zther. After desiccation it was cautiously
exposed to ignition in a platina crucible. The salt was placed
with the filtering paper in the crucible, and not as is usually done
G2
100 HEINRICH ROSE ON THE COMBINATIONS OF
with other precipitates, which are to be heated, taken out of the
filter; the crucible was then closely covered with the lid, and ex-
posed for a long time to a moderate heat, which was gradually
raised to redness. This was continued until all the muriate of am-
monia had evaporated. The crucible was then left to cool, the lid
taken partly off, and the coal of the paper reduced in the usual
way to perfect ash. If this precaution is not taken, and if the salt
is heated too much at first, some undecomposed salt and metallic
platina may be mechanically carried away with the vapours of
the muriate of ammonia. From the weight of the metallic platina
the ammonia in the salt is deduced. The determination of the
ammonia may be effected in this way with great accuracy, much
more so indeed than that of the carbonic acid.
The determination of the carbonic acid may be effected by
two methods. The most accurate is to convert it into carbonate
of barytes, and to determine from the weight of this salt that of
the carbonic acid. The carbonate of ammonia was dissolved in
cold water in a bottle, which could be closed air-tight, and a so-
lution of chloride of barium was added to it; if the combination
underexamination does not consist of the neutral carbonate of am-
monia, some pure liquid ammonia is added, after which the flask
‘is closed, and left to stand at least for twelve hours, or longer.
Care must be taken not to use too little water for the solution,
and especially to test the ammoniacal fluid by a solution of the
chloride of barium, to see whether it is free from carbonic acid.
I have usually distilled the ammonia previous to the experiment
over quick lime. The liquid, after the twelve hours’ repose, was
then passed through a filter, during which communication with
the air was avoided as much as possible, and boiling water being
poured upon the carbonate of barytes, it was filtered with the
exclusion of air. This was frequently, and for a long time, washed
with boiling water, but not until the water that passed through
was no longer rendered milky by sulphuric acid, the residue not
being quite insoluble in water. Repeated trials can alone deter-
mine when it is time to leave off the washing. The carbonate of
barytes must not be filtered for some hours after precipitation,
and until it has entirely settled. Ifit be filtered sooner, carbonate
of barytes is deposited from the clear filtered liquid, even when
no communication with the air has taken place.
When dry, the carbonate of barytes is heated. There is no
need to fear, that by burning the filter any of the carbonic acid
AMMONIA WITH CARBONIC ACID. 101
of the carbonate of barytes is expelled ; the strongest heat that an
alcohol lamp, with double current of air, is capable of producing,
may be applied without occasioning any loss.
A solution of chloride of calcium cannot be employed with the
same advantage as one of chloride of barium for precipitating the
carbonic acid. The carbonate of lime, it is true, does not form so
bulky a precipitate as the carbonate of barytes; but a portion of
the precipitate adheres so firmly to the sides of the vessel, that it
is impossible to separate it completely by mechanical means.
The heating of the carbonate of lime has also its disadvantages,
as it then loses a portion of the carbonic acid.
In determining the carbonic acid in the neutral combinations,
it was precipitated by chloride of barium without any addition of
ammonia. In this case also the whole must be left to stand for
some time after precipitation before the carbonate of barytes is
filtered. When the solution of the neutral carbonate of am-
monia is very weak, no precipitate is produced for some time by
the chloride of barium, which is characteristic of the neutral salt.
The liquid separated from the carbonate of barytes is then satu-
rated with ammonia, in order to see whether any small precipi-
tate would follow, which in general was the case; it was occa-
sioned by the impossibility of obtaining the carbonate of ammo-
nia always perfectly neutral. This precipitate, although filtered
perfectly without exposure to the air, was nevertheless always
more considerable than it should have been, and the amount of
carbonic acid in the salt thus appeared to be greater than it really
was.
The second method of determining the carbonic acid was by
measuring it in the state of gas. A weighed quantity of
the salt was decomposed in a graduated cylinder under mercury
by means of muriatic acid, in which shortly previous to the ex-
periment some carbonate of ammonia had been dissolved, in
order to saturate it with carbonic acid. When the salt could
only be employed in the form of powder, it was wrapped up in
bibulous paper. This method, however, gave, even when all.
circumstances had been most carefully taken into consideration,
less accurate results than by means of the carbonate of barytes.
In general I obtained somewhat less carbonic acid than I ought.
As, however, it is more quickly and easily performed, I have
chiefly made use of it to ascertain to what known combinations
of ammonia and carbonic acid any salt might belong.
102 HEINRICH ROSE ON THE COMBINATIONS OF
1. The Neutral Anhydrous Carbonate of Ammonia.
It is well known that the neutral carbonate of ammonia is ob-
tained by mixing dry ammoniacal gas with carbonic acid gas,
and that both gases combine slowly, and only, (whichsoever of the
two may be present in excess) as Gay-Lussac* first discovered,
in the proportion of one volume of carbonic acid gas to two of
ammoniacal gas. The properties of the anhydrous carbonate of
ammonia obtained in this way are nevertheless almost unknown.
Dr. John Davy +, who last experimented on the combinations of
ammonia with carbonic acid, confirmed the previous experiments
of Gay-Lussac, without however subjecting the combination to a
more accurate examination. He states that it possessed the
property of being decomposed without effervescence by a neutral
solution of chloride of calcium, and formed with it a neutral
fluid.
I have only repeated the experiments of Gay-Lussac with the
intention of learning whether, with an excess of ammoniacal gas,
the two gases combined in the proportions above mentioned.
I conveyed the carbonic gas into an excess of ammoniacal gas,
and obtained the following results :
1, 29°7 vol. carbonic acid gas, combined with 61 vol. of ammoniacal gas
2. 24:9 a : - : : : 49°75
3. 20°1 : : ; : 38°15
The small differences are easily explained, by what I have
on another occasion mentioned respecting the mixture of two
gases which combine to form a solid body{. The volume of the
absorbed carbonic acid gas in the first experiment is evidently
smaller on this account than it should be, because the carbonic
acid gas was mixed with too great an excess of ammoniacal gas ; in
the second this was less, and in the third experiment still less.
Since the combination of ammonia with the carbonic acid gas
is formed very slowly, no vapour is observed when a glass rod
moistened with ammonia is held over a carbonated alkali, from
which the carbonic acid is disengaged by sulphuric acid, as is
always the case when volatile acids, such as muriatic acid, sul-
phurous acid, nitric acid, acetic acid, &c. are disengaged from a
fluid by sulphuric acid.
* Mémoires de la Société d’ Arcueil, tom. ii. p. 211,
+ Edinburgh New Philosophical Journal, vol. xvi. p. 245,
¢ Poggendorft’s Annalen, vol. xlii. p. 417.
AMMONIA WITH CARBONIC ACID. 103
To obtain the combination in great quantities, considerable
portions of the dried gases were brought into contact, in large
vessels, which had been filled with dry air. The combination
adheres so firmly to the sides of the vessels, especially when
they have been artificially cooled externally, that it is frequently
possible to obtain it in no other way than by breaking them.
It is only when no external refrigeration has been applied to the
vessels that a portion of the combination can be obtained in a
pulverulent state. I therefore subsequently caused the two
dried gases to pass through several glass tubes, which were kept
cool at their outer surface, in order to obtain larger quantities of
the neutral salt. These tubes were then cut, and the salt depo-
sited in them taken quickly out. On preparing the salt in this
way, it was observed that on the combination of the two gases a
very considerable increase in temperature takes place.
If in the preparation of this combination the greatest care is
not taken to avoid every trace of moisture, which, with great
quantities, it is very frequently difficult to effect, small admix-
tures of the hydrous combinations of ammonia occur with the
anhydrous carbonate.
1:3425 gramme of the neutral anhydrous carbonate, dissolved
in water, gave with a solution of chloride of barium 3:321 grm.
of carbonate of barytes. The liquid filtered from it, treated with
ammonia, gave a slight precipitate, the weight of which was not
determined. 1°444 grm. of the combination, treated in the
manner previously described with muriatic acid, alcohol, chloride
of platina and zther, gave 3°461 grm. of heated metallic platina.
The carbonate of barytes obtained corresponds to 55°45 per
cent. carbonic acid in the combination, and the quantity of pla-
tina to 41°69 per cent. ammonia. Ifwe consider that a very small
quantity of the hydrous bicarbonate of ammonia was contained
in the combination, as would seem from a precipitate, although
an inconsiderable one, being produced in the solution precipi-
tated by chloride of barium and filtered, the compound formed
agrees with the calculated formula NH® + C, according to which
56°31 per cent. carbonic acid is combined in the salt with 43-69
per cent. ammonia.
It results from this examination, that in the solution of the
anhydrous carbonate of ammonia, its constituents can be quan-
titatively separated by the same re-agents as in the case of the
solutions of the hydrous combinations of ammonia with carbonic
104 HEINRICH ROSE ON THE COMBINATIONS OF
acid. The anhydrous carbonate of ammonia is therefore differ-
ently circumstanced in this respect from the anhydrous sulphate
of ammonia, the constituent parts of which cannot be separated
‘by the same re-agents as those producing this effect with the
corresponding hydrous salts. Neither does the anhydrous car-
bonate of ammonia in solution differ in its action with all the other
re-agents from the other salts of the carbonate of ammonia, only
that (which arises from its composition) the carbonic acid of the
anhydrous neutral salt is entirely precipitated by solutions of the
chloride of barium, and of the chloride of calcium, whilst this takes
place in the solution of the other known combinations of carbonic
acid and ammonia only after the addition of ammonia.
The anhydrous carbonate of ammonia is very easily soluble in
water. In the solid state it smells like free ammonia. This is
peculiar to all the combinations of carbonic acid with ammonia ;
but the greater the quantity of carbonic acid they contain, the
weaker is the ammoniacal odour. It is not perceptible at first
in the recently prepared combinations with excess of carbonic
acid, and not till they have been preserved in a vessel for some
time unexposed to the air. In the combinations, with more car-
bonic acid than contained in the neutral salt, this peculiarity
may be ascribed to the circumstance that they do not volatilize
undecomposed ; in the anhydrous neutral salt, however, this is
not the case, for it may be sublimed without changing its com-
position.
The neutral carbonate of ammonia is exceedingly volatile, and
probably the most so of all the combinations of ammonia with
carbonic acid. If exposed to the air, it disappears entirely in
a short time. When sublimed, a very powerful ammoniacal
odour is diffused, which, however, entirely arises from the volatili-
zation of the undecomposed salt. 0°569 grm. of the sublimed
salt, treated with chloride of platina, gave, after heating the pla-
tina salt obtained, 1°4656 grm. of metallic platina. 0°930 grm. of
a second quantity of the sublimed salt gave, with a solution of
chloride of barium, 2°267 grm. carbonate of barytes. Ammonia
still producedaslight precipitate of 0-046 erm. carbonate of barytes
in the filtered liquid, corresponding to 1°11 per cent. of carbonic
acid. The quantity of the platina answers to 44°79 per cent. of
ammonia, and that of the carbonate of barytes to 54°64, or, rather,
55°75 per cent. of carbonic acid, whence it evidently results that
the salt had undergone no change from sublimation.
AMMONIA WITH CARBONIC ACID. 105
Since the salt undergoes no change in its composition by sub-
limation, and volatilizes at a low temperature, it was easy to de-
termine the specific gravity of its vapour. This was performed
according to the well-known method of Dumas*. ‘Two expe-
riments gave the following results :
Weight of | weight of
edad) testis | Tae" | Temoae-| Seer] “atthe | there | Stet
mubepheric siete melting. theair. |harometer. globe. neglected. calculated.
Grammes, | Grammes. Lg eee cab. Cub.
1. | 62-408 | 62-099 |176-25c| 15°C. | 750° | 602-73 | 0-75" | o-9048
II.| 61-6765 | 61:383 |140 8°75 7531 597 6:5 08936
But one vol. carbonic acid = 1°52400
Two vols. ammonia. . = 1°18240
2°70640
The calculated specific gravity of a volume of the vapour of
the neutral carbonate of ammonia is consequently 0°90213, which
coincides particularly well with the result of the first experiment,
which was performed with great accuracy, and it agrees also pretty
fairly with the second.
The gaseous constituents in the vapour of the carbonate of
ammonia are consequently combined without condensation.
For the first experiment a salt was taken, as it had been ob-
tained by the method above mentioned. For the second expe-
riment, on the contrary, a sublimed salt was employed. It is
hence evident, that, as already proved by the analysis of the sub-
limed salt, its composition does not undergo any change by
being sublimed once or even twice.
These experiments, however, disagree with those of M. Bi-
neaut. who alleges that he had observed that the gaseous product
obtained by exposing the salt to heat retains its gaseous property
at a temperature which is lower than that at which it is formed.
But his statement of the specific gravity of the vapour coincides
with the results obtained by me, although he determined it in an
* The calculation was made according to Poggendorff’s formula (Annalen,
vol. xli. p. 449), having regard to the cireumstance, that the gas of carbonic acid
gas is lighter than the atmospheric air, the P of the formula, consequently the
entire last member (p. 453) was taken negatively.
4 Annales de Chimie et de Physique, vol. \xvii. p. 240.
106 HEINRICH ROSE ON THE COMBINATIONS OF
apparently very uncertain way, by keeping the salt for a long
time in contact with a measured volume of atmospheric air and
leaving it to evaporate in it; he then treated the few cubic cen-
timetres of the mixture alternately with dry oxalic acid and with
potash, and thus obtained the volume of the ammonia and of
the carbonic acid*.
Although the solution of the anhydrous carbonate of ammonia
does not act differently towards the re-agents from the hydrous
combinations of ammonia with carbonic acid, yet the combina-
tion, in its solid state, is distinguished on account of the absence
of water, by its action upon several substances, from the sesqui-
carbonate of ammonia.
If dry muriatic gas is passed over the anhydrous carbonate of
ammonia, no action is perceptible in the cold, even when the gas
is left for a long time in contact with the salt. But if, during the
passing, the ammoniacal carbonate is heated at one spot only for
a moment, it decomposes there, and the heat gradually diffuses
itself through the whole combination ; and when it ceases, there
is no longer any carbonic acid combined with the ammonia,
and it has changed, naturally, without any disengagement of
water, into hydrochlorate of ammonia. The common sesquicar-
bonate of ammonia is decomposed, even in the cold, by muriatic
gas, with disengagement of heat. Water is formed by a slow
disengagement of the carbonic acid at the upper surface of the
glass sphere in which the mixture is contained.
The anhydrous carbonate of ammonia is at first not at all af-
fected by gaseous chlorine; after an action of several days only
does it gradually change, without any formation of water, into
muriate of ammonia, in which case carbonic acid and nitrogen
gas must necessarily escape. No formation of chloride of nitro-
gen takes place. The common sesquicarbonate of ammonia gra-
dually changes, with perceptible disengagement of water, into the
muriate of ammonia. If the salt is employed in pieces, they de-
compose very slowly, and, when taken out of the apparatus, ef-
fervesce with acids. Even in this case no production of chloride
of nitrogen could be observed ; however, the experiment was not
continued until the salt had completely decomposed. The ex-
ternal portion of the salt, and the fine powder, had become per-
fectly converted into muriate of ammonia, without having indi-
* Annales de Chimie et de Physique, vol. Ixviii. p. 434.
AMMONIA WITH CARBONIC ACID. 107
cated any trace of chloride of nitrogen. When the anhydrous
carbonate of ammonia is treated with dry sulphurous acid, it
assumes, even in the cold, a pale yellowish colour. If it is
heated in an atmosphere of sulphurous acid gas, it changes en-
tirely into an orange sublimate of anhydrous sulphite of am-
monia. The solution acts with acids, solution of the nitrate of
silver, and solution of chloride of mercury, &c., quite in the
same way as the solution of the anhydrous sulphite of ammonia,
which has been directly prepared from dry ammoniacal gas and
dry sulphurous gas*. When the common sesquicarbonate is
treated with dry sulphurous gas, no change is perceptible in the
cold. But if the salt be slightly heated in the sulphurous gas,
a yellow sublimate of anhydrous sulphite of ammonia is pro-
duced on the first action of caloric; but if the heat is continued,
a white sublimate of the usual hydrous sulphite of ammonia is
formed. If the whole is left to cool, and then suddenly heated
anew, the same phenomena occur, and this may be repeated
three or four times in the same way. But at last only white
sublimate of anhydrous sulphite of ammonia is apparent. This
decomposition of the salt into anhydrous and hydrous sulphite
of ammonia is very easily explained if we regard the sesquicar-
bonate as being composed of anhydrous carbonate and of hydrous
bicarbonate of ammonia.
When the anhydrous carbonate of ammonia is treated in the
cold with dry sulphuretted hydrogen gas, no effect is produced.
On the application of heat sulphuret of ammonia is formed with-
out any evolution of water. The sesquicarbonate is likewise not
affected by sulphuretted hydrogen gas in the cold, and even
when heated it changes with difficulty, and partially only, with
production of water, into sulphuret of ammonia; the greatest
portion of the salt, however, may be sublimed in sulphuretted
hydrogen gas.
An important difference between the anhydrous neutral and
the hydrous sesquicarbonate of ammonia, is manifested in their
respective actions with anhydrous sulphuric acid. When the
vapours of this acid are passed over some powdered sesquicar-
bonate, it is decomposed, even when kept cold by a refrigerating
mixture, with effervescence and evolution of carbonic acid, and
the common hydrous sulphate of ammonia is formed. The neu-
* Poggendorft’s Annalen, vol. xxxiii. p. 235.
108 HEINRICH ROSE ON THE COMBINATIONS OF
tral anhydrous carbonate of ammonia, on the contrary, loses, by
the action of the vapour of the anhydrous sulphuric acid, its
carbonic acid, without any effervescence, and is converted into
anhydrous sulphate of ammonia. -
The neutral carbonate of ammonia may be prepared from the
common sesquicarbonate in various ways, but not in a dry state.
There is no way of obtaining it crystallized from asolution. The
solutions of all the combinations of ammonia with carbonic
acid, which contain more carbonic acid than the neutral salt,
lose, when heated, carbonic acid, and are converted into the neu-
tral combination ; while the solution of this latter, evaporated at
the common temperature, (in vacuum either over sulphuric acid
or hydrate of potash,) loses ammonia, and changes into super-
carbonates.
When the solution of the sesqui- or bi-carbonate of ammonia
is boiled for a short time, it acquires the property of being thrown
down entirely by an excess of a solution of the chloride of ba-
rium, or the chloride of calcium ; so that pure ammonia produces
no precipitate in the liquid filtered from the carbonated earth,
nor even an opalescence. In the solution, therefore, there is a
neutral combination of carbonate of ammonia. If the boiling is
continued, the salt volatilizes entirely from the solution.
M. Hiinefeldt* has shown, that when solid sesquicarbonate is
subjected to distillation along with alcohol, on the boiling of
the alcohol the carbonic acid escapes as gas; a portion of the
alcohol then passes over, upon which a sublimate of a solid salt
volatilizes with the remainder of the alcohol, at first adhering to
the neck of the retort, and finally passing into the receiver with
the vapours of the alcohol: this salt is the neutral carbonate of
ammonia. I have frequently repeated this experiment in various
ways, and convinced myself of the correctness of the fact. If
the sublimed salt is dissolved in water, the solution is com-
pletely precipitated by a solution of the chloride of barium or
the chloride of calcium in excess, and in such manner that no
milkiness is produced by an addition of ammonia to the solution
filtered from the carbonated earth.
It is, however, impossible to dry the neutral salt moistened
with alcohol without its changing in its composition and losing
some ammonia. When I dried it as quickly as possible by
* Journal fiir praktische Chemie, vol. vii. p. 25
AMMONIA WITH CARBONIC ACID. 109
means of bibulous paper, and then precipitated the solution of
the dried salt by chloride of barium, I obtained from 1:042 grm.
of the salt only 1°714 grm. of carbonate of barytes, which only
answers to 36°87 per cent. carbonic acid in the salt. When,
however, some ammonia was added to the filtered liquid, and the
precipitate formed protected from the action of the air, I ob-
tained 0°688 grm. carbonate of barytes, corresponding to 14°80
per cent. of carbonic acid in the salt.
I then attempted to dry the neutral salt, by placing it immedi-
ately in vacuo over sulphuric acid. The salt, it is true, became
dry, but was no longer perfectly neutral, for its solution gave,
after precipitation by the chloride of barium, a precipitate with
ammonia. It is, nevertheless, the best method of drying the
salt without its composition being considerably affected.
When I attempted to desiccate the salt moistened by alcohol
over a considerable quantity of the hydrate of potash in vacuo,
it remained moist although I kept it for more than a week under
the air pump. The hydrate of potash became, it is true, carbo-
nate at its surface, but a great quantity of ammonia was evolved
in the gaseous form during the pumping.
The moist salt was then placed in a basin filled with fused
chloride of calcium, and this again put imto a larger basin
containing hydrate of potash, and the whole then quickly placed
inavacuum. The chloride of calcium became covered with car-
bonate of ammonia; the remaining portion of the salt was dry,
but after desiccation was no longer neutral.
I obtained a similar result when I employed quick lime in-
stead of the hydrate of potash. When I brought this, as was
the case with chloride of calcium, warm into the vacuum with
the moist salt, the greater portion of it volatilized and deposited
itself on the chloride of calcium; the small quantity of the salt
remaining was not neutral.
I then placed the moist salt with another combination of chlo-
rine of easy solubility in alcohol in vacuo. I chose for this
purpose pulverized bichloride of mercury. The carbonate of
ammonia remained moist, but the chloride of mercury attracted
some of it, and did not dissolve entirely in water, the solution
being opalescent. I obtained a remarkable result when I placed
‘the moist salt under the air pump with quick lime and the ace-
tate of lead. The carbonate of ammonia volatilized sooner than
the alcohol with which it was moistened; it combined with the ace-
110 HEINRICH ROSE ON THE COMBINATIONS OF
tate of lead, forming a tumid, white pasty mass, which effervesced
with acids, and dissolved in water, leaving carbonate of lead be-
hind. The alcohol was left in the fluid state, and contained
some, although very little, ammonia. For this, and most of the
other experiments, the sesquicarbonate was distilled with anhy-
drous alcohol.
It appears to result from these experiments that the carbonate
of ammonia combines with some salts, and that it has towards
these, even when they are soluble in alcohol, a greater affinity
than alcohol towards them. However, this affinity does not
seem to be very considerable, and probably occurs only under
peculiar circumstances, perhaps not without the presence of a
trace of water or alcohol, or at the common pressure of the
atmosphere. For when I placed some anhydrous fused chloride
of calcium, and some fused acetate of soda, in bottles which con-
tained anhydrous neutral carbonate of ammonia, which had been
prepared from a mixture of the carbonic and the ammoniacal
gases, none of it was absorbed by the fused salts, not even when
they had been moistened with some alcohol or water. The same
is the case with fused chloride of calcium, which absorbs none of
the usual sesquicarbonate of ammonia, when both are placed
together in vessels. If, therefore, under certain conditions, the
carbonate of ammonia appears to combine with some salts, this
affinity cannot be compared to that which pure ammonia exhibits
towards a great number of salts.
The experiments above mentioned, of drying the neutral car-
bonate of ammonia moistened with alcohol, were modified in
various ways, but I never succeeded in obtaining a dry, unde-
composed salt. The result was either that the salt remained
moist or volatilized previous to desiccation, or that when it did
become dry the salt was no longer neutral.
If the sesquicarbonate is distilled in a similar manner with
ther, the phenomena are nearly the same: a considerable evo-
lution of carbonic acid gas takes place during the distillation of the
ether, but a far smaller quantity of carbonate of ammonia escapes
with the ether than with the alcohol. The sublimed mass is
the same neutral salt as that obtained with alcohol, and like it
cannot be obtained pure in a dry state.
The only method by which I succeeded in obtaining a dry
neutral carbonate of ammonia, besides that of preparing it
from a mixture of carbonic acid gas with ammoniacal gas,
AMMONIA WITH CARBONIC ACID. 111
was by the sublimation of a mixture of anhydrous sulphate of
ammonia and carbonate of soda. If every trace of moisture is
avoided, a product is obtained as pure as by the mixture of the
gases.
The impossibility of combining the anhydrous neutral carbo-
nate in any way with the quantity of water which is requisite to
convert the ammonia into the oxide of ammonium is in so far a
very remarkable circumstance, as the carbonate of ammonia
dissolved in water exhibits quite the identical properties which
the carbonate of the oxide of ammonium would present, and,
moreover, does not differ essentially in its other relations from
other combinations of carbonic acid with ammonia, in which
the latter may be regarded as the oxide of ammonium. Berze-
lius’s view of considering the ammoniacal salts, on account of
their water, as salts of the oxide of ammonium, is so plausible,
and has justly been adopted by so many chemists, that the
composition and properties of the anhydrous carbonate of am-
monia do not suffice to render this view less probable. It must,
therefore, be regarded as a body of a peculiar kind, belonging,
with respect to its composition, to a class with the anhydrous
combinations of ammonia with sulphuric acid and sulphurous
acid, which latter, however, essentially differ in their properties
from the carbonate of ammonia, in so far as these ammoniacal
salts vary considerably in their action upon re-agents from the
corresponding salts of the oxide of ammonium, and indicate in
the most evident manner the distinction between combinations
of ammonia and those of the oxide of ammonium. The most
important distinction which exists between the anhydrous neu-
tral carbonate and the hydrous combinations of ammonia with
carbonic acid, which contain more carbonic acid, is that the
former may be sublimed undecomposed, which is not the case
with the latter.
It must be here mentioned that I have also prepared some
anhydrous combinations of ammonia with oxy-acids, which,
dissolved in water, did not differ, in their properties, from their
corresponding salts of the oxide of ammonium, and in this respect
are analogous to the carbonate of ammonia.
Il. The Neutral Hydrous Carbonate of Ammonia.
The experiments mentioned in the preceding section show
that it is not possible to combine the neutral anhydrous carbonate
112 HEINRICH ROSE ON THE COMBINATIONS OF
of ammonia with the quantity of water which exactly suffices to
change the ammonia into the oxide of ammonium.
I was much surprised at obtaining a hydrous neutral carbo-
nate of ammonia in an unexpected manner. For if the sesqui-
carbonate of ammonia of commerce is exposed in a retort to a
very gentle heat, and if the neck of the retort is connected with
a longish glass tube, the other end of which is immersed in mer-
cury, a disengagement of pure carbonic acid gas is first perceived,
and in that part of the glass tube furthest from the heated retort a
crystalline salt is deposited, the solution of which, in water, is so
entirely precipitated by a solution of the chloride of barium, or
the chloride of calcium, that ammonia produces no opacity, or
at least only a very slight one, in the liquid separated from the
carbonate of the earth. This salt is the most volatile of the solid
products, which are produced during the distillation of the ses-
quicarbonate; if a gentle heat is applied for some time to the
retort, the salt melts, and other combinations are formed and
sublimed, which will subsequently come under our notice.
If the sesquicarbonate is exposed to a stronger heat, but little
of the neutral salt is produced. It is therefore necessary to ap-
ply a very gentle heat, and only to employ for examination the
products which are deposited in the part furthest from the heated
portion of the retort. When this is not carefully attended to, a
mixture of other combinations is obtained.
A mixture of sal-ammoniac and carbonate of soda gives, when
exposed to heat under similar circumstances, the same salt. With
this distillation, at first only ammoniacal gas escapes, as will be
subsequently shown.
1:609 erm. of the sublimate, treated after having been dis-
solved with the chloride of barium, gave 3596 grm. of carbonate
of barytes: and 0°860 grm. of the sublimate, prepared in the
same way, gave, when treated in the manner above mentioned,
with alcohol, «ther, muriatic acid, and chloride of platina,
1:942 germ. of metallic platina. This corresponds to the fol-
lowing composition :
Carbonic acti eles os S09
Ammoniae ee wertecis ee Yo ee DT
W ate? Hite Wesaihiyl ravilen =) 2": LORS
100°00
The composition of this salt is yery remarkable ; only half the
AMMONIA WITH CARBONIC ACID. 113
quantity of water necessary to convert the ammonia into the
oxide of ammonium is present. A composition calculated ac-
cording to the chemical formula C + NH?* + 2 H, gives in the
hundred,
Garbonicacid iw 2b. o Uso. 50°52
AMTTOMIAKEe RL... UA tue oO oe2O
WERE rma? st ce oe EP LO:28
100°00
On repeating the experiment I obtained from 1°420 grm.,
3°288 erm. of platina, and from 0°390 grm., 0°837 grm. of car-
bonate of barytes; and after an addition of ammonia, also
0:059 grm. This answers to the following composition :
@Wanbonic- acid. 26 2s Se bg
AITO Ia tee hy ea eee ee | 426
Water ptt BEML BE 14) Sy dt REAM «C0
100°00
It sometimes happens that it is difficult to obtain the salt per-
fectly pure. That its solution is not entirely precipitated by a
solution of chloride of barium, but that, after the precipitation,
a slight precipitate is still produced by ammonia, is almost al-
ways the case even with the solution of the anhydrous neutral
salt.
The hydrous neutral carbonate of ammonia can, without
changing very essentially in its composition, be again sublimed.
1°552 grm. of the twice sublimed salt gave, treated in the man-
ner above mentioned, 3°692 grm. of metallic platina; and 0°446
grm. by means of chloride of barium, 1°009 grm. of carbonate of
barytes ; a precipitate of 0°077 grm. was nevertheless produced
by ammonia. This answers to 41°37 per cent. ammonia, 50°71
per cent. carbonic acid, and also 3°87 per cent. carbonic acid in the
precipitate caused by ammonia. We see clearly, that this salt,
by the double sublimation, had changed in a small degree into a
combination containing more carbonic acid, though it remained
doubtful whether this was in consequence of the renewed action
of heat, or on account of the attraction of moisture.
I then sublimed the first sublimate which had been obtained
from two pounds of the sesquicarbonate, not less than five times, in
order to see whether, by this means, it might entirely lose its water,
and change into an anhydrous salt. The renewed sublimations
VOL. II, PART V. H
114 HEINRICH ROSE ON THE COMBINATIONS OF ?
were effected in such manner that only the most volatile sublimate
of each operation was employed for the following sublimation :
0:619 grm. of the obtained product gave 1°441 grm. of metallic
platina, and from 0°552 grm. 1:288 grm. of carbonate of barytes
were obtained by the chloride of barium ; the liquid filtered from
it gave, with ammonia, 0°068 grm. more. This corresponds to
40°48 per cent. ammonia, and 52°30 per cent. carbonic acid; and
the last precipitate obtained 2°76 per cent. carbonic acid. The
salt then does not become anhydrous by frequent sublimation.
If we admit that the composition first obtained is the correct
one, and that the other salts contained a slight mixture of a
combination, with a larger proportion of carbonic acid, then in
fact this composition must appear a very remarkable one, for it
is not favourable to the ingenious hypothesis proposed by Berze-
lius, that ammonia is changed into the oxide of ammonium by the
reception of 1 atom of water, and is thus converted into a base.
I shall, however, subsequently endeavour to show that the neu-
tral anhydrous carbonate of ammonia has great tendency to
form double salts, especially with the bicarbonate of the oxide
of ammonium. This tendency it appears to evince also towards
the simple carbonate of the oxide of ammonium, which does not
seem to exist independently in a solid state. The most probable
view which we may therefore take of the composition of the
neutral hydrous carbonate of ammonia is, that we should look
upon it as a combination of the carbonate of ammonia with the
carbonate of the oxide of ammonium, (G + NH’) + (C NH%).
If the anhydrous neutral salt, obtained by the mixture of the
two gases, is not well preserved and protected from moisture, it
appears to change into the hydrous neutral combination. On
analysing such a salt, which had been sublimed, I obtained
from 1°259 grm., 2°929 grm. of metallic platina, and from 0°784
grm. 1°844 of carbonate of barytes. This answers to 40°46 per
cent. ammonia, and 52°72 per cent. carbonic acid.
It is surprising that the formation of the neutral carbonate of
ammonia, during the distillation of the common sesquicarbonate,
or a mixture of sal-ammoniac and dry carbonate of soda, has
escaped the attention of chemists. I must, however, remark,
that John Davy mentions in his paper* that his brother had
obtained, on exposing the sesquicarbonate to heat, a salt which
* Edinburgh New Philosophical Journal, vol. xvi. p. 257.
AMMONIA WITH CARBONIC ACID. 115
possessed a decided ammoniacal odour, deliquesced when ex-
posed to the air, and, as he believed, contained more ammonia
than the known combinations. John Davy confirmed this ex-
periment, and adds that it is more volatile than the last, and
that probably it is hydrous carbonate of ammonia. I did not
find that the hydrous neutral salt deliquesced in the air ; but the
salt, it is true, becomes moist, and remains so if the distillation
is continued for any length of time, and water passes over.
III. The Sesquicarbonate of Ammonia.
This is the salt which occurs in commerce. I have analysed
it several times, and found that, if it had not effloresced at its
surface from the action of the atmosphere, and had not changed
into the bicarbonate, it generally had, but not always, the compo-
sition which R. Phillips has assigned to it. The analyses were
performed with quantities which had been obtained from various
manufactories.
2-143 orm. of salt gave 3°530 grm. of metallic platina; 1:113
grm., however, of another quantity, 1-965 grm. of platina. The
first quantity answers to 28°66 per cent., and the last to 30°70 per
cent. of ammonia. The quantities of carbonic acid, which were
determined in the gaseous form by means of muriatic acid over
mercury, varied quite as much.
0°607 grm. gave 155 cub. centim.; 1°480 grm., 399°44 cub.
centim.; and 1°419 grm. of the salt, 403 cub. centim. carbonic
acid gas. This answers to 50, 55, 53, 40, and 56°23 per cent.
carbonic acid in the salt.
These differences are explained by the modes of preparing the
salt. When it has been prepared directly by sublimation from
carbonate of lime and sal-ammoniac, or from sulphate of ammonia,
then it is sesquicarbonate of ammonia. When, however, it has
been once more sublimed in the manufactory, probably in order
to purify it, it has changed into $-carbonate of ammonia, of
which we shall speak hereafter.
The calculated composition of the sesquicarbonate, according
to the formula 3 CG +2NH? + 2H, is
Ammonia! 3) 2 219 Jo 109 28°92
Carbonic-acid sv 2) 2" 2) 55°91
Waters Oy) sat. ogrreaed 6°17
Se
100°00
116 HEINRICH ROSE ON THE COMBINATIONS OF
We tind that there is sometimes in commerce a salt that con-
tains about 31 per cent. ammonia, 51 per cent. carbonic acid.
This is 2 of carbonate of ammonia.
The composition of the sesquicarbonate of ammonia is such
that it may be conceived as a combination of anhydrous neutral
salt, and hydrous bicarbonate of the oxide of ammonium (C +
NH°) + (2C + NH‘ + H); or if it is thought that the anhy-
drous neutral salt cannot exist in combination with hydrous
salts of the oxide of ammonium, we might consider the for-
mula (© + NH‘) + (2 C + NH‘) to be the more correct.
Perhaps the preference might be given to the first formula,
partly because the bicarbonate of the oxide of ammonium can-
not be prepared alone, but is mixed with water, and at least
with 1 atom of water; and partly because, as will be shown here-
after, anhydrous neutral carbonate of ammonia is volatilized
when exposed to the air from the sesquicarbonate, and leaves
behind hydrous bicarbonate of the oxide of ammonium.
This view is, in a great measure, confirmed by some recent
experiments of Scanlan, and some earlier ones of Dalton*. They
found that if the sesquicarbonate of ammonia is treated at the
usual temperature for several times with less water than is ne-
cessary to dissolve it completely, the first saturated solutions
had a greater specific weight than the last. In the same degree
that the specific gravity of the solutions decreased, they lost their
ammoniacal odour ; the last solution gave crystals of the bicar-
bonate. They hence concluded, that either the sesquicarbonate
is a mixture of two salts, or that the water exerts an action upon |
the salt similar to that it is usually imagined to have on some
salts of bismuth, and that it decomposes it into two salts of two
dissimilar degrees of saturation. Should, however, the last action
take place, the salt of more difficult solution would remain in the
form of a powder, which is not the case, for it is left as a skeleton.
The crystalline structure of the salt evidently shows that it is
not a mere mixture, but is composed according to fixed propor-
tions, which is also confirmed by analysis. But the experiments
above mentioned prove that it is a double salt composed of 1 atom
of neutral, and 1 atom of the bicarbonate of ammonia, both which
constituents may be separated by water, according to their solu-
bility in it. _ This separation, from the two salts being perfectly
*The Atheneum, 1838, No. 565, p. 596.
AMMONIA WITH CARBONIC ACID. 117
soluble, never more than approximates. When I, in the manner
already mentioned, poured a little water upon the sesquicarbonate,
I could not manage to obtain pure carbonate without a small
mixture of dissolved bicarbonate ; for, as I precipitated the solu-
tion with a solution of the chloride of barium, the filtrated liquid
was rendered opalescent by ammonia.
The affinity between the two constituents in a double salt
varies. The carbonate of ammonia is combined so feebly with
the bicarbonate in the sesquicarbonate of ammonia, that water
alone may cause a separation of both constituents. We find
something similar in several double salts which are composed
of a salt difficult, and of one easy of solution. Of the Bro-
gniarti (Glauberit), a crystalline double salt of sulphate of
lime and of sulphate of soda, the latter dissolves in water and
leaves the sulphate of lime undissolved. In the same manner,
according to Stromeyer, sulphate of potash and sulphate of mag-
nesia is dissolved from the polyhallit of Ischl, by water, whilst sul-
phate of lime is left. According to Bauer, from the artificially
prepared combination of carbonate of potash and carbonate of
lime, water dissolves the first salt and leaves the last undis-
solved*; whilst, according to Boussingault, the Gaylussite, oc-
curring in nature, which is similarly composed, withstands the
action of the water, and is only easily decomposed by it when it
has lost its water by being heated}.
Most of the other double salts, likewise composed of a salt
easy and of one difficult of solution, are not at all decomposed
by water. Common alum dissolves equally in water, without
the readily soluble sulphate of alumina being separated by it
from the sulphate of potash, which is of more difficult solution.
The bisulphate of potash, which must be considered as a double
salt, consisting of sulphate of potash and hydrate of sulphuric
acid, acts in a similar way towards water; it also dissolves in
water without decomposition. But between the two examples of
double salts there is this difference, that, from the last salt alco-
hol separates the insoluble sulphate of potash, and dissolves the
hydrate of sulphuric acid, whilst the alum resists the decompo-
sition by aqueous alcohol, though the sulphate of alumina is
soluble, and the sulphate of potash insoluble, in it.
The carbonate in the sesquicarbonate of the ammonia can
* Poggendorff’s Annalen, vol. xxiv. p. 367. t Ibid. vol. vii. p. 99.
118 HEINRICH ROSE ON THE COMBINATIONS OF
also be separated from the bicarbonate, not only by water, but
also by being preserved in vessels from which the air is not en-
tirely excluded. The more volatile carbonate gradually disap-
pears entirely, and the less volatile bicarbonate is left quite free
from the carbonate. This succeeds especially well if the sesqui-
carbonate is employed pulverized in the way above mentioned,
and if the atmosphere in which the vessel is situated be not too
moist. The remaining bicarbonate of the oxide of ammonium
contains 1 atom of water; the volatile carbonate of ammonia is
consequently anhydrous, and contains no oxide of ammonium, on
which account, as remarked above, the latter can hardly be con-
sidered to exist in the common sesquicarbonate.
The double salts, which the carbonate of ammonia forms with
the bicarbonate, are, however, in so far of an uncommon kind, that
whereas in general the simple salts which form the constituents
in other double salts are of one and the same degree of satura-
tion, this is not the case here. We must, however, certainly
distinguish two kinds of double salts. In the double salts of one
kind, which form the majority, the simple salts are of the same
degree of saturation ; in them, generally half, or another defi-
nite portion of one base is replaced by an equivalent of another
base, and the one salt consequently cannot act in them the part
of an acid or a base towards the other, which was formerly the
view taken with regard to the composition of these combinations.
In the second kind of the double salts, on the contrary, both the
combinations of which they consist are not of the same degree
of saturation ; in these double combinations one constituent part
may be considered as the acid, the other as the base. Certain
combinations of carbonic acid, of silicic acid, and of other weak
acids with bases, belong to this class; and also the property
of boracic acid to dissolve, when melted, all substances of acid
and basic properties, depends on the tendency to form double
salts of this second class.
In the combinations of the carbonate and of the bicarbonate
of ammonia, which also belong to this class of double combina-
tions, the carbonate is naturally the base, and the bicarbonate the
part which replaces the acid. The tendency which the carbonate
has to form a double salt with the bicarbonate, when sal-ammo-
niac or sulphate of ammonia is subjected with the carbonate of
1 me oradry carbonated alkali to distillation, rests in part on this
circumstance; that the carbonate of the oxide ofammonium, C +
AMMONIA WITH CARBONIC ACID. 119
NH+4, which ought here to be formed, does not seem to exist in a
solid state of itself, as has already been remarked. On this
account, at the beginning of the heating, ammonia is disengaged,
and this escapes, in common, with so much water as would be ne-
cessary to convert it into the oxide of ammonium, whilst the ses-
quicarbonate of ammonia is formed. From 3 atoms of carbonate
of oxide of ammonium, which ought to evolve from the mixttre
when heated, 1 atom of carbonate of ammonia is formed, and 1 atom
of hydrous bicarbonate, which two form the double salt, and it
disengages 1 atom of ammonia and 1 of water. 3 C + 3NH? +
3H =(C + NH®) + (2C + NH* + H) + NH? +H. Ifthe
products of this operation are received in the order in which
they are produced, over mercury, pure ammoniacal gas is first
obtained, which is wholly absorbed by muriatic acid; and af-
terwards come the products, which appear during the sublima-
tion of the common sesquicarbonate, of which we shall speak
further on. As the sesquicarbonate can be evaporated only
with the disengagement of carbonic acid gas, this gas is found
amongst the products of the sublimation ; there is, however a de-
finite interval between the disengagement of the ammoniacal gas
and of the carbonic acid gas. The latter first begins to escapewhen
the evolution of the ammonia has entirely ceased, and when the
glass cylinder, in which the gaseous products are received, begins
to be covered with a thin incrustation of the carbonate of am-
monia, and at the same time water passes over. When all the
gaseous products are received together in one glass cylinder, over
mercury, the ammoniacal gas which first goes over gradually
combines with the carbonic acid gas which subsequently passes
over.
IV. Sesguicarbonate of Ammonia with a larger proportion of
Water.
If the common sesquicarbonate is exposed for some time to a
very gentle heat, in a retort, the neck of which is connected with a
long glass tube, the following appearances occur : at the very
beginning carbonic acid gas is disengaged, and then the hydrous
neutral carbonate of ammonia sublimes, which, as the most
volatile of the solid products of sublimation, consolidates in that
part of the glass tube furthest from the retort. The nearer to the
retort the sublimate adheres, the more the solution is precipitated
120 HEINRICH ROSE ON THE COMBINATIONS OF
by ammonia, after having been treated with chloride of barium,
and the precipitated mass filtered.
The salt in the retort continually becomes moister, whilst the
sublimate in the neck of the retort increases, and begins to be
deposited in the body of the retort. At last a clear liquid only
is left in the retort, from which, when the heat is over, a
salt crystallizes, in the form of tables, in great quantity. The
bulb of the retort must be broken, in order that the crystals may
be well separated and obtained pure from the original mass.
If the mass is preserved for a long time in closed vessels, a
quantity of tables of the same salt is deposited from it, of more
beautiful and distinct crystalline structure. This deposition of
crystals continues for some weeks. When it ceases, the mass
contains only neutral carbonate of ammonia in solution ; by means
of a solution of chloride of barium it is thrown down so com-
pletely, that ammonia produces no precipitate in the filtered li-
quid.
The salt sublimed in the neck and in the body of the retort,
as well as that crystallized from the solution, are two combina-
tions hitherto unknown. This sublimed salt will be treated of in
the following section.
The crystals of the salt from the solution have the form of
thin six-sided plates. On account of their thinness and rapid
efflorescence the angles could not be measured. No cleavage
could be observed.
Since this salt may be obtained in distinct crystals, it is con-
sequently free from foreign mixtures; and the various analyses
agree better with one another than is the case with those of the
sublimed and non-crystalline combinations of carbonic acid with
ammonia, and are more in unison with the calculated result.
1°904 germ. gave 2°594 erm. of metallic platina ; 1°816 grm., witha
solution of chloride of barium, treated with an addition of am-
monia, gave 3°674 grm. of carbonate of barytes. This corresponds
to the following composition :
IATMINOUIAN \—> sa >
ef! — eB! Prt BP
which equation, for 6 = 0, i. e. when it is not intended to take
into consideration the influence of the ates passes into
a
—x 70
1 >, anid @) tor? gy
A eae 3 (2 ee ‘).
It is easily aces that the ats of the second member to
the right in the equations which have been found for the deter-
mination of wu, becomes smaller and smaller as the time increases,
* See Journal de l’ Ecole Polytechnique, cap. xix. p. 53.
OHM ON THE GALVANIC CIRCUIT. 477
and that it at last entirely vanishes ; the permanent state of the
circuit has then occurred. This moment can, as is evident from
the form of the expression, be retarded by a diminished power of
conduction, and in a far greater degree by an increased length of
the circuit.
This expression found for w, however, holds perfectly only
so long as the circuit, which we have supposed, is not induced
by any external disturbance to change its natural state. If
the circuit is at any time compelled by any external cause, for
instance, by deductive contact at any place, to approximate to
an altered permanent state, the above method has to undergo
some changes, which I intend to develope on another occasion.
I will, moreover, observe, that it is in this last class of galvanic
circuits, in which the peculiar phenomena of dry piles, and, in
general, of circuits of unusually great length, have to be sought
for; to which class likewise belong the circuits of very great
length employed in the experiments of Basse, Erman, and Aldini,
if the influence of their greai length be not annulled by an in-
creased goodness of conduction, or by an increased section.
C. Phenomena of the Electric Current.
24. According to what was advanced in paragraph 12, the
magnitude of the electric current, in a prismatic body, will in
general be expressed for each of its places by the equation
Bc cage
d x’
where S denotes the magnitude of the current, and ~ the elec-
troscopic force at that place of the circuit whose abscissa is 2,
while represents the section of the prismatic body, and x its
power of conduction at the same place. To connect this equa-
tion with the general equation found in § 18 for any circuit,
composed of any number of parts, we write it thus:
du dy
dy dw
S=xo
and substitute for a the value = resulting from that general
equation, and for - the value = easily deducible from the
same paragraph, both which values are valid for each place,
478 OHM ON THE GALVANIC CIRCUIT.
situated between two points of excitation, we then very simply
obtain
A
iz
where L denotes the entire reduced length of the circuit, and A
the sum of all its tensions. By means of this equation we ob-
tain the magnitude of the electric current of a galvanic circuit, —
composed of any number of prismatic parts, which has acquired _
its permanent state, which is not affected by the surrounding
atmosphere, and the single sections of which possess in all their
points one and the same electroscopic force; in this category .
are comprised the most frequently occurring cases, on which
account we shall dissect this result in the most careful manner.
Since A represents the sum of all the tensions in the circuit,
and L the sum of the reduced lengths of all the individual
parts, there results, in the first place, from the equation found,
the following general properties relative to the electric current
of the galvanic circuit.
I. The electric current is decidedly of equal magnitude at all
places of a galvanic circuit, and is independent of the value
of the constant c, which, as we have seen, fixes the intensity
of the electroscopic force at a determined place. In the
open circuit the current ceases entirely, for in this case the
reduced length L acquires an infinitely great value.
II. The magnitude of the current, in a galvanic circuit, re-
mains unchanged when the sum of all its tensions and its
entire reduced length are varied, either not at all, or in the
same proportion; but it increases, the reduced length re-
maining the same, in proportion as the sum of the tensions
increases, and the sum of the tensions remaining the same,
in proportion as the reduced length of the circuit dimi-
nishes. From this general law we will, moreover, particu-
larly deduce the following. F
1. A difference in the arrangement and distribution of the
individual points of excitation, by a transposition of the
parts of which the circuit consists, has no influence on the
magnitude of the current when the sum of all the tensions
remains the same. Thus, for instance, the current would
remain unaltered in a circuit formed in the order copper,
silver, lead, zinc, and a fluid, even when the silver and lead
Ss =
OHM ON THE GALVANIC CIRCUIT. 479
change places with each other; because, according to the
laws of tension observed with respect to metals, this trans-
position would, it is true, alter the individual tensions, but
not their sum.
2. The intensity of a galvanic current continues the same, al-
though a part of the circuit be removed, and another pris-
matic conductor be substituted in its place, only both must
have the same reduced length, and the sum of the tensions
in both cases remain the same; and vice versd, when the
current of a circuit is not altered by the substitution of one
of its parts for a foreign prismatic conductor, and we can
be convinced that the sum of the tensions has remained the
same, then the reduced lengths of the two exchanged con-
ductors are equal.
3. If we imagine a galvanic circuit always constructed of a
like number of parts, of the same substance, and arranged
in the same order, in order that the individual tensions may
be regarded as unchangeable, the current of this circuit in-
creases, the length of its parts remaining unaltered, in the
same proportion in which the sections of all its parts in-
crease in a similar manner, and the sections remaining un-
altered, in the same proportion in which the length of all
its parts uniformly decrease. When the reduced length of
a part of the circuit far exceeds that of the other parts, the
__ magnitude of the current will principally depend on the
dimensions of this part ; and the law here enounced will
assume a much more simple form, if, in the comparison,
attention be solely directed to this one part.
The conclusion arrived at in II. 2. presents a convenient
means for the determination of the conductibility of various
bodies. If, for instance, we imagine two prismatic bodies,
whose lengths are / and /’, their sections respectively w and a’,
and whose powers of conduction are x and x’, and both bodies
possess the property of not altering the current of a galvanic
circuit when they alternatively form a portion of it, and both
leave the individual tensions of the circuit unchanged, then
l I!
Tap ee
consequently
480 OHM ON THE GALVANIC CIRCUIT.
the powers of conduction, therefore, of both bodies are directly
proportionate to theirlengths, and inversely proportionate to their
sections. If it is intended to employ this relation in the deter-
mination of the powers of conduction of various bodies, and we
choose for the experiments prismatic bodies of the same section,
which indeed is requisite for the sake of great accuracy, their
lengths will enable us to determine accurately their conductibi-
lities.
25. In the preceding paragraph we have deduced the magni-
tude of the current from the general equation given in § 18,
A
u=yy-Ote
and have found that it is expressed by a the coefficient of y.
i ye ae ar
To ascertain the value rf it is in general requisite to possess
an accurate knowledge of all the single parts of the circuit,
and their reciprocal tensions; but our general equation indi-
cates a means of deducing this value likewise from the nature
of any single part of the circuit in the state of action, which
we will not disregard, as it will be of great service to us here-
after. If, namely, we conceive in the above equation y to be
increased by any magnitude Ay, and designate by A O the
corresponding change of O, and by Au that of u, there results
from that equation
Au= >A fy AO,
A Auw+AO0_
L Ay i
we find, therefore, the magnitude of the electric current by
adding to the difference of the electroscopic forces at any two
places of the circuit the sum of all the tensions situated between
these two places, and dividing this sum by the reduced length of
the part of the circuit which lies between these same places. If
there should be no tension within this portion of the circuit,
then AO = 0, and we obtain
A_ Aw
i ey.
26. The voltaic pile, which is a combination of several similar
and we thence find
OUM ON THE GALVANIC CIRCUIT. 481
simple circuits, merits peculiar attention in this place, from the
numerous and varied experimental results obtained by its
means.
If A represent the sum of the tensions of a closed galvanic
circuit, and L its reduced length, the magnitude of its current
is, as we have found,
A
L
Now, if we imagine m such circuits perfectly similar to the
former, but open, and constantly bring the end of each one in
direct connexion with the commencement of the next following
one, in such a manner that between each two circuits no new
tension occurs, and all the previous tensions remain afterwards
as before, then the magnitude of the current of this voltaic com-
bination, closed in itself, is evidently
nA
nL
consequently equal to that in the simple circuit. This equality
of the circuit, however, no longer exists when a new conductor,
which we will call the interposed conductor, is inserted in both.
If, namely, we designate the reduced length of this interposed
conductor by A, then, when no new tension is produced by it,
the magnitude of the current in the simple circuit will be
A
L+W
and in the voltaic combination, consisting of n, such elements
a ao ctoass
“
nL+A vip A
therefore in the latter circuit it is constantly greater than in
the former, and, in fact, a gradual transition takes place from
equality of action, which is evinced when A disappears, to where
the voltaic combination exceeds 7 times the action of the simple
circuit, which case occurs when A is incomparably greater than
nu. If by A we represent the relative length of the body upon
which the circuit is to act by the force of its current, then from
the observations just brought forward it results that it is most
advantageous to employ a powerful simple circuit when A is
very small in comparison to L; and, on the contrary, the voltaic
pile, when A is very great in comparison with L.
482 OHM ON THE GALVANIC CIRCUIT.
But how must, in each separate case, a given galvanic appa-
ratus be arranged so as to produce the greatest effect? Let us
suppose, in solving this problem, that we possess a certain mag-
nitude of surface ; for instance, of copper and zinc, from which
we can form, according to pleasure, a single large pair of plates,
or any number of smaller pairs, but in the same proportion,
and, moreover, that the liquid between the two metals is constant-
ly the same, and of the same length, which latter supposition
means nothing more than that the two metals between which
the liquid is confined retain, under all circumstances, the same
distance from each other.
Let A be the reduced length of the body upon which the
electric current is to act, L the reduced length of the apparatus
when formed into a simple circuit, and A its tension; then,
when it is altered into a voltaic combination of x elements, its
present tension will be # A, and the reduced length of each of
its present elements x L, accordingly the reduced length of all
the 2 elements z* L, consequently the magnitude of the action of
the voltaic combination of # elements is
vA
Fo METRY, %
when
2VA.L
ip Se = We hence see that the apparatus in form of a
This expression acquires its greatest value
simple circuit is most advantageous, so long as A is not greater
than L; on the contrary, the voltaic combination is most use-
ful when A is greater than L, and indeed it is best constructed of
two elements when A is four times greater than L, of three ele-—
ments when A is nine times greater than L, and so forth.
27. The circumstance that the current always remains the
same at all places, affords us the means of multiplying its ex-
ternal action, as in the case when the current influences the
magnetic needle. We will, for perspicuity, suppose that, im
order to test the action of the current on the magnetic needle,
each time a part of the circuit be formed into a circle of a given
radius, and so placed in the magnetic meridian that its centre
coincides with the point of rotation of the needle. Several
such distinct coils, formed of the circuit in exactly the same
manner, will, taken singly, produce, on account of the equality
of the current in each, equally powerful effects on the magnetic
.
OHM ON THE GALVANIC CIRCUIT. 483.
needle; if we imagine them, therefore, so arranged near one
another, that though they are separated by a non-conducting
layer, they are yet situated so close together that the posi-
tion of each one toward the magnetic needle may be regarded
as the same, they would produce a greater effect on the magnetic
needle in proportion as their number increased. Such an ar-
rangement is termed a multiplier.
Now, let A be the sum of the tensions of any circuit, and L
its reduced length ; let also A be the reduced length of one of
the interposed conductors formed into a multiplier of » convolu-
tions; then, if we represent the reduced length of one such
convolution by a, A = A, the action of the multiplier on the
magnet needle will be proportional to the value
nA
CL aix
But the action of a similar coil of the circuit, without the multi-
plier, is, according to the same standard,
A
LL
and we will suppose the portion of the circuit, whence the coil
is taken, to be of the same nature as in the multiplier; accord-
ingly the difference between the former and the present effect
is
nu—(L+na) A
i a e
which is positive or negative according as x L is greater or less
than L + na. Consequently the action on the magnetic needle
will be augmented or diminished by the multiplier formed of n
coils, according as the n times reduced length of the circuit,
without interposed conductor, is greater or less than the entire
reduced length of the circuit with the interposed conductor.
If 7 A is incomparably greater than L, the action of the mul-
tiplier on the needle will be ;
A
=e
To this value, which indicates the extreme limit of the action
by means of the multiplier, whether it be strengthening or
weakening, belong several remarkable properties, which we will
briefly notice. It is constantly supposed that the multiplier is
formed of so many coils that the magnitude of its action may,
484 OHM ON THE GALVANIC CIRCUIT.
without committing any sensible error, be considered equal to
the limit value.
Since the action of a coil of the circuit is ay while the ac-
L
tion of the multiplier, in connexion with the same circuit, is
Neen : é ;
= it is evident that the two actions are in the same ratio to
each other as the reduced length a and L; if, therefore, we are
acquainted with the two actions, and with one of the two re-
duced lengths, the other may be found, and in the same manner
one of the two actions may be deduced from the other, and the
two reduced lengths.
Since the limit of the action of the multiplier is 2, it in-
creases when A is invariable in the same proportion as the sum
of the tensions A in the circuit increases; we may, therefore, by
comparing the extreme actions of the same multiplier in various
circuits, arrive at the determination of their relative tensions.
At the same time we perceive that the extreme action of the mul-
tiplier increases, when several simple circuits are formed into a
voltaic combination, and, indeed, in direct proportion to the
number of the elements. In this manner it is always in our
power, in cases where the multiplier in connexion with the |
simple circuit produces a weakening effect, to cause it to in- |
dicate any increase of force whatever. |
If we call the actual length of a coil of the multiplier J, its
conductibility x, and its section w, then A= = and conse- | !
quently the extreme action of the multiplier
xW. TY?
whence it results that in the same circuit the extreme actions of
two multipliers of coils of equal diameter, are in the rativ to |
each other of the products of their conductibility and their sec- |
tion. These extreme actions are, therefore, in two multipliers, |
which differ only in being formed of two distinct metals, in pro-
portion to the conductibility of these metals; and when the |
multipliers consist of similar convolutions, and of one metal,
their extreme actions are proportional to their sections. !
But all these determinations are based upon the supposition |
that the action of a portion of the circuit on the magnetic |
OHM ON THE GALVANIC CIRCUIT. 485
needle, under otherwise similar circumstances, is proportional
to the magnitude of the current. But long since direct ex-
periments have established the correctness of this supposi-
tion.
28. We will now proceed to the consideration of a multiple
conduction existing at the same time. If, for instance, we
imagine an open circuit, whose separated extremities are con-
nected by several conductors, arranged by the side of each
other, it may be asked, according to what law is the current
distributed in the adjacent conductors? In answering this
question, we might proceed directly from the considerations con-
tained in § 11 to 13; but we shall more simply attain the re-
quired object from the peculiarity of galvanic circuits ascertained
in § 25, in which case we will, for the sake of simplicity, sup-
pose that none of the former tensions is destroyed by the open-
ing of the circuit, nor a new tension produced by the conductor
which is introduced.
For if a, 2’, ’, &c. represent the reduced lengths of the con-
ductors brought into connexion with the extremities of the open
circuit, and « the difference of the electroscopic forces at the ex-
tremities of the circuit, after the conductors have been intro-
duced, the same difference will also occur at the ends of the
single adjacent conductors, since, according to the supposition
we have made, no new tension is introduced by the conductor.
Since now, according to § 13, the magnitude of the current in
the circuit must be equal to the sum of all the currents in the
adjacent conductors, we may imagine the circuit to be divided
into as many parts as there are adjacent conductors; then, ac-
cording to § 25, the magnitude of the current in each adjacent
conductor, and in the corresponding part of the circuit, will re-
spectively be
2 a a a
ru, YI!’ nP
whence, in the first place, it results that the magnitude of the
current in each adjacent conductor is in inverse ratio to its re-
duced length. If we now imagine a single conductor of such
nature, that, being substituted for all the adjacent conductors
in the circuit, it does not at all alter its current; then, in
the first place, «, according to § 25, must retain the same
value, and, if we designate by A the reduced length of this
conductor, must moreover be
VOL. Il. PART VIII. 2K
&c.,
486 OHM ON THE GALVANIC CIRCUIT.
1 1 1 ]
A We deg a
From the preceding explanations we may conclude, that
when A denotes the sum of all the tensions, and L the entire
reduced length of the circuit without adjacent conductors, the
magnitude of the current, while the adjacent conductors are in
connexion with the circuit, will be expressed in the circuit itself
by
A .
L + A’
in the joint conductor, whose reduced length is a, by
puso,
eee A”
in the joint conductor, whose reduced length is 4’, by
pete ole,
L+A ‘2?
in the joint conductor, whose reduced length is a", by
Beate
L+A ‘A
and so on, where for A its value obtained from the equation
1 1 |
RET PTE
has to be placed.
29. That in the above the galvanic current is found to be of
equal magnitude at all places of the circuit, arises from the
value of as deduced from the equation
being constant. This circumstance no longer happens if we
start from the equations given in § 22 and 23. In all these
du. ae Shae sous
cases Ts is dependent on 2, which indicates that the magnitude
of the current is different at different places of the circuit. We
may hence draw the conclusion, that the electric current is only
of equal intensity at all places of the circuit, when the circuit
has already assumed a permanent state, and the atmosphere
has no sensible action upon it. This property likewise appears))
best adapted to enable us to find out, by experiment, whether
OHM ON THE GALVANIC CIRCUIT. 487
the atmosphere exercises a perceptible influence on a galvanic
. circuit, or not, we will therefore enter into this case at greater
length.
Since, according to § 12, the magnitude of the electric cur-
rent is given by the equation
du
Ss =xX*w. ax’
we have only in each separate case to obtain the value of _
from the equation found for the determination of the electro-
scopic force, and to place it in the one above. Thus, for a cir-
cuit which has assumed its permanent state, but upon which
the surrounding atmosphere exercises no sensible influence,
according to § 22,
; Th l—e—Bt © %. Bt 4 e—Bi?
where a represents the tension at the place of excitation, and 6
the sum of the electroscopic forces immediately adjacent on
both sides of the place of excitation. We hence obtain
eft 4 efx et — e—ha
— nop (ga ae eae
This expression gives the magnitude of the current at each
place of the circuit ; but the law, according to which the alvera-
tion of the current at various places of the circuit is effected,
may be rendered more easily intelligible in the following man-
ner. If, for instance, we differentiate the equation
du
N) = EG eat
we obtain the equation
dS. du.
hen = X*w ada 3
and by multiplying both together,
ds8 d*u
Be du x2 wo d -
2
If we now substitute for nas its value 6” u, as obtained from
P ad?u
the equation 0 = da
— Bu, we have
488 OHM ON THE GALVANIC CIRCUIT.
and we hence obtain by integration
S? = c2 + x? a? 8’ ¥,
where ¢ represents a constant remaining to be determined. If
we designate by w the smallest absolute value which w occupies
in the circumference of the circuit, and by S! the corresponding
value of S, and determine, in accordance with this, the constant
c, we obtain
S? =* S/?2 = x2 w B? (u? ae we
It may easily be deduced from this equation, that the current of
a circuit, which is influenced by the atmosphere, is weakest
where the electroscopic force, without regard to the sign, is
smallest, and that it is of the same magnitude at places with
equal but opposite electroscopic forces.
APPENDIX.
ON THE CHEMICAL POWER OF THE GALVANIC CIRCUIT.
On the Source and character of the Chemical Changes in a Gal-
vanic Circuit, cnd on the Nature of the Fluctuations of its Force
dependent thereon.
30. In the present Memoir we have constantly supposed that
those bodies, which are under the influence of the electric cur-
rent, remain unchangeable; we will now, however, take into
consideration the action of the current on the bodies subjected
to it, and the alterations in their chemical constitution thence
resulting in any possible manner, as also the changes of the
current itself produced by reaction. If what we here give
does by no means exhaust the subject, nevertheless our first
attempt shows that we are advancing in this path towards im-
portant conclusions respecting the relation of electricity towards
bodies.
To proceed on sure ground, let us return to what has been
enounced in § 1 to 7, and connect our present considerations
with those expressions and developments. We will suppose,
therefore, two particles, and designate by s their mutual di-
stance, by w and w! their electroscopic forces, which we admit
to be of equal intensity in all points of the same particle ; then,
as may easily be deduced from what has been previously stated,
OHM ON THE GALVANIC CIRCUIT. 489
the repulsive force between these two elements is proportional
to the time d¢, to the product ww’, and, moreover, to a
function dependent on the position, size, and form of the two
particles, which we will represent by F’; we accordingly ob-
tain for the repulsive force between two particles the expres-
sion
F’ uw dt.
If we here proceed in the same manner as in § 6, and signify
by the moment of action x' between two places, the product of
g', which expresses the force produced under perfectly deter-
mined circumstances between both, and its mean distance s', so
that
ae cesitg!s,) 2"
and determine g' by putting vu =w' = 1 in the expression
F’ uw dt, and extending the action to the unit of time, we have
x = b's,
whence it follows that
!
jae
a vr
Let us now imagine, as we did in $ 11, the prismatic circuit -
to be divided into equally large, infinitely thin discs, and call
M’, M, M, those immediately following one another, which
belong to the abscisse w + dx, x7, vw —dzx; then, according to
what has just been shown, the pressure which the disc M!
exerts on the disc M is
F’ uu dt;
and if we admit that the position, size, and form of the particles
remain in all discs the same, the counter pressure, which the
disc M, exerts on the disc M, is
IY uu, di:
the difference between these two expressions, viz.
F’ u (Ww —u) dt,
gives accordingly the magnitude of the force, with which the
disc M tends to move along the axis of the circuit. This force
acts contrary to the direction of the abscisse when its value is
positive, and in the direction of the abscissz when it is ne-
gative.
If we substitute for w!—w its value proceeding from the deve-
lopments given in § 11 for w' and w, the expression just found
changes into the following:
490 OHM ON THE GALVANIC CIRCUIT.
du
2 F’ U aig: dxd if:
and if we take, instead of the function F’ dependent on the na-
I
ture of each single body, its value oT? this expression, since s!
is evidently here d 2, changes into
du
2 x! U has dt 3
or if we reduce the moment of action x’, referring to the magni-
tude of the section w, to the unit of surface, and at the same
time extend the action to the unit of time, into
du
2x wu ae
where the present x’ represents the magnitude of the moment
of action reduced to the unit of surface. If we write this latter
expression thus :
in which x denotes the absolute power of conduction of the
circuit ; and if we substitute for x w dm, by which, according to
dx
the equation (4) in § 12, the magnitude of the electric current
!
is expressed, the sign S chosen for it, and 7 instead of ~ 5 16.18
changed into
2ius.
We hence perceive that the force, with which the individual
discs in the circuit tend to move, is proportional, both to their
innate electroscopic force, and to the magnitude of the current ;
and that this force alters its direction at that place of the cir-
cuit. where the electricity passes from the one into the opposite
state. And here occurs the circumstance which must not be
overlooked, that this expression still holds, even when the elec-
troscopic force u of the element M is changed in the moment
of action, by any causes whatsoever, into any other abnormal
U, while the electroscopic forces of the adjacent particles con-
tinue the same; only that in this case the value U must be
substituted for wu in the expression 2iuS. It must also be ob-
served, that the expression 2iuS which we have found refers to
the whole extent of the section w, which belongs to that part of
OHM ON THE GALVANIC CIRCUIT. 491
the circuit which we have especially in view; if we wish to
reduce this motive force of the circuit to the unit of surface,
we must divide that expression by the magnitude of the sec-
tion w.
With respect to the causal relation between the law of electric
attractions and repulsions, and that of the diffusion of electricity,
or respecting the mutual dependence of the functions x and
x' on each other, we will, for the present, not enter into any
further inquiries, as shortly an occasion will present itself for this
purpose. We will here content ourselves with the observation,
that the above mode of explanation has arisen from the endea-
your to render the similarity of the mode of treatment in the
doctrines of electricity and heat very obvious.
31. Without pursuing any further these conditions to an ex-
ternal change of place of the parts of a galvanic circuit, let us
now turn to those changes in the qualitative state of the circuit
which are produced by the electric current, i. e. in the internal
relation of the parts to each other, and which derive their ex-
planation from the electro-chemical theory of bodies. Accord-
ing to this theory, compound bodies must be considered as a
union of constituents which possess dissimilar electric states ; or,
in other words, dissimilar electroscopic force. But this electro-
scopic force, quiescent in the constituents of the bodies, differs
from that to which our attention has hitherto been directed, in-
asmuch as it is linked to the nature of the elements, and can-
not pass from one to the other, without the entire mode of ex-
istence of the parts of the body being destroyed. If we con-
fine ourselves, therefore, in the following considerations, to
the case where changes, it is true, occur in the quantitative re-
lation of the constituents, and where consequently chemical
changes of the body, composed of these constituents, also occur,
but where the constituents themselves undergo no alteration
destroying their nature, we are able to show the validity of all
the laws above developed of electric bodies with reference to
their reciprocal attraction and repulsion, only the transition of
the electricity from one particle to the other entirely disappears
in the consideration of chemically different constituents. A di-
stinction here exists with reference to electricity exactly similar
to that which we are accustomed to define relative to heat, by
calling it sometimes latent, sometimes free heat. For the sake
of brevity, we will in like manner term that electroscopic force
492 OHM ON THE GALVANIC CIRCUIT.
which belongs to the existence of the particles, which therefore
they cannot part with without at the same time ceasing to
exist, the electricity bound to the bodies, or latent electricity,
and free electricity, that which is not requisite for the existence
of the bodies in their individuality, and which therefore can pass
from one element to the other, without the individual parts
being on that account compelled to exchange their specific
mode of existence for another.
32. From these suppositions advanced in electro-chemistry,
in connexion with what was stated in § 30, respecting the mode
in which galvanic circuits exert a ditferent mechanical force on
discs of different electrical nature, it immediately follows that
when a disc belonging to the circuit is composed of constitu-
ents of dissimilar electric value, the neighbouring discs will
exert on these two constituents a dissimilar attractive or repul-
sive action, which will excite in them a tendency to separate,
which, when it is able to overcome their coherence, must pro-
duce an actual separation of constituents. This power of the
galvanic circuit, with which it tends to decompose the particles
into their constituents, we will call its decomposing force, and
now proceed to determine more minutely the magnitude of this
force.
Employing for this purpose all the signs introduced in § 30,
we will, moreover, imagine each disc to be composed of two
constituents, A and B, and designate by m and m the latent
electroscopic forces of the constituents A and B, supposing the
disc M to be occupied solely by one of the two, entirely ex-
cluding the other, in the same manner as u represents the free
electroscopic force present in the same disc, and equally dif-
fused over both constituents. If we now admit, in order to
simplify the calculation, that the two constituents A and B,
before and after their union, constantly occupy the same space,
and designate the latent electroscopic force, corresponding to
each chemical equivalent, contained in the disc M, and pro-
ceeding from the constituent A, by mz, then n (1—z) expresses
the latent electroscopic force present in the same disc M, but
originating from the constituent B: for the intensity of the
force diffused over a body decreases in the same proportion as
the space which the body occupies becomes greater, because by
the increased distance of the particles from each other the sum
of their actions, restricted to a definite extent, is diminished in
OHM ON THE GALVANIC CIRCUIT. 493
the same proportion. But when two constituents combine, by
both reciprocally penetrating one another, each extends beyond
the entire space of the compound, on which account the inten-
sity of the force proper to each constituent decreases by com-
bination, in the same proportion as the space of the compound
is greater than the space which each constituent occupied before
the combination. Consequently if z denote the relation of the
space which the constituent A, in the disc M, occupied pre-
vious to combination to that space which the compound in the
disc M occupies; and also, since we admit that both consti-
tuents, before and after the combination, occupy the same ex-
tent of space, 1—z will denote the same relation relatively to
the constituent B; then, since m and n designate the electro-
scopic forces of the constituents A and B previous to combina-
tion, mz and n (1 — z) will represent the latent electroscopic
forces of the constituents A and B, which correspond to each
chemical equivalent of the disc M; and, at the same time, it
follows from the above, that the variable values z and 1—z can-
not exceed the limits 0 and 1.
In order to ascertain the portion of the free electricity w per-
taining to each constituent, we will assume that it is distributed
over the single-constituents in proportion to their masses. If,
therefore, we represent respectively by « and £ the masses of
the constituents A and B, on the supposition that one alone, to
the exclusion of the other, occupies the entire disc, then « z and
6 (1 —z) will represent the masses of the constituents A and B
united in the disc M ; consequently the portions
aUzZ TB Wien
az+PB(l—z) — a : ql 25
of the free electricity wu appertain to the constituents A and B;
instead of which, for the sake of conciseness, we will write
aUz,and@U (1—2).
If we now take into consideration what was stated in § 30,
respecting the motive force of the galvanic circuit, it is imme-
diately evident that the tendency of the constituent A to move
along the circuit, is expressed by
2i(m+aU) ZS,
or that of the constituent B by
2i(n+6U) (1—2z)S.
494 OHM ON THE GALVANIC CIRCUIT.
In both cases a positive value of the expression shows that
the pressure takes place in an opposite direction to that of the
abscisse; a negative value, on the contrary, indicates that the
pressure is exerted in the direction of the abscisse. To deduce
from these individual tendencies of the constituents the force
with which both endeavour to separate from each other, we
must remember that this force is given by the twofold differ-
ence between the quantities of motion which each constituent
would of itself assume, were it associated to the other by no
coherence, and those quantities of motion which each con-
stituent must assume were it strongly combined to the other.
We thus readily find for the decomposing force of the circuit
the following expression :
; mB—ne@
a aes atk id Geka 5
from which we learn that the decomposing force of the circuit
is proportional to the electric current, and also to a coeffi-
cient dependent on the chemical nature of each place of the
circuit.,
If this expression has a positive value, it indicates that the
separation of the constituent A takes place in a contrary di-
rection to that of the abscissa, that of the constituent B in the
direction of the abscisse ; but if this expression has a negative
value, it denotes a separation in the reverse direction. It is
besides evident, at first sight, that the decomposing force of
the circuit is constantly determined by the absolute value of the
expression,
If « = B, the decomposing force of the circuit changes into
4i.z2(1—z) (m—n).S.
Ifmz+n(1—z) = 0, i.e. if the latent electroscopic forces,
existing in the united constituents, are equal and opposed; or,
what is the same, if the body, situated in the disc M, is per-
fectly neutral, in which case m and n have constantly opposite |
values, we obtain, for the decomposing force of the circuit, the
following expression :
mn
47. ;
m—n
The form of the general expression found for the decompos- |
ing force of the circuit shows that this force disappears ; first, |
when S = 0, i.e. when no electric current exists; secondly, |
OHM ON THE GALVANIC CIRCUIT. 495
when z=0, or z = 1, #.e. when the body to be decomposed is
not compound ; thirdly, when m 8 —nz=0, i. e. when the den-
sities of the constituents are proportional to the latent electro-
scopic forces which they possess, which circumstance can never
occur with constituents of opposite electric nature.
All the expressions here given for the decomposing force of
the circuit refer to the entire section belonging to the respective
place ; if we wish to reduce the value of the decomposing force
to the unity of surface, the expression must be divided by the
magnitude of the section, to which attention has been already
called in § 30, in a similar example.
33. If this decomposing force of the circuit is able to over-
come the coherence of the particles in the disc, a coherence pro-
duced by their electric opposition, this necessarily occasions
a change in the chemical equivalent of the particles. But such
a change in the physical constitution of the circuit must,
at the same time, react on the electric current itself, and give
rise to alterations in it, with which a more accurate acquaintance
is desirable, and which we will therefore spare no trouble to
acquire.
For this purpose we will imagine a portion of the galvanic
circuit to be a homogeneous fluid body, in which such a decom-
position actually takes place; then, at all points of this portion,
the elements of one kind will tend to move with greater force
towards one side of the circuit than those of the other kind;
and since we suppose that, by the active forces, the coherence
is overcome, it follows, if we pay due attention to the nature
of fluid bodies, that the one constituent must pass to one side,
those of the other constituent, on the contrary, towards the
other side of the portion, which necessarily produces on one
side a preponderance of the constituent of one kind, and on
the other side a preponderance of the other kind of constitu-
ent. But as soon as a constituent is predominant on one side
of any disc, it will oppose by its preponderance the movement
of the like constituent in the disc towards the same side, in con-
sequence of the repulsive force existing between both; the de-
composing force, therefore, has now not merely to overcome
the coherence between the two constituents in the disc, but
also the reacting force in the neighbouring discs. Two cases
may now occur; the decomposing force of the electric cur-
rent either constantly overcomes all the forces opposed to it,
496 OHM ON THE GALVANIC CIRCUIT.
and then evidently the action terminates by a total separation
of the constituents, the entire mass of the one passing to the
one end of the portion, and the entire mass of the other consti-
tuent being impelled towards the other end of this portion; or
such a relation takes place between the forces in action, that the
forces opposing the separation ultimately maintain the decom-
posing force in equilibrium; from this moment no further
decomposition will occur, and the portion will be, in a remark-
able state, a peculiar distribution of the two constituents oc-
curring, into the nature of which we will now inquire. If
we call Z the decomposing force of the current in any disc of
the portion in the act of decomposition, Y the magnitude of
the reaction by which the neighbouring discs oppose the de-
composition by the electric current, and X the force of the
coherence of the two constituents in the same disc, then evi-
dently the state of a permanent distribution within the supposed
portion, will be determined by the equation
x VS Z's
and it is already known, from the preceding paragraph, that
mB—ne S:
az+B(l—z)° ”
or if we substitute x & for S,
Z=4i2 (1—2)
du. mB—na
BZ=4xuo7.tz (1 — z) ree hee,:
Before we proceed further, we will add to what has been
above said the following remarks. At the limits of the por-
tion in question, we imagine the circuit so constituted, that
insuperable difficulties there oppose themselves to any further
motion ; for it is obvious that otherwise the two extreme strata
of both constituents, which it is evident could never of them-
selves arrive at equilibrium, would quit the portion in which
we have hitherto supposed them, and either pass on to the
adjacent parts of the circuit, or from any other causes separate
entirely from the circuit. We will not here follow the last-
mentioned modification of the phenomenon any further, al-
though it frequently occurs in nature, as sufficiently shown by
the decomposition of water, the oxidation of the metals on the
one side, and a chemical change of a contrary kind occurring
on the metals at the other side of the portion hitherto less ob-
OHM ON THE GALVANIC CIRCUIT. 497
served, but placed entirely beyond doubt by Pofi’s remark-
able experiments on the reaction of metals. Besides, we will
direct our attention to a difference which exists between the
distributioh of electricity above examined, and the molecular
movement now under consideration. If, for instance, the same
forces, which previously effected the conduction of the electri-
city, and there, as it were, incorporeally without impediment
strove against each other, here enter into conflict with masses,
by which their free activity is restricted, a restriction which,
whether we regard the electricity de se ipso as something mate-
rial or not, must render their present velocities, beyond com-
parison, smaller than the former ones ; therefore we cannot in
the least expect that the permanent state, which we at present
examine, will instantaneously occur like that above noticed,
arising from the electric distribution ; we have rather to expect
that the permanent state resulting from the chemical equiva-
lent of both constituents, will make its appearance only after a
perceptible, although longer or shorter time.
After these remarks, we will now proceed to the determina-
tion of the separate values X and Y.
34. To obtain the value X, we have merely to bear in mind
that the intensity of coherence is determined by the force with
which the two adjacent constituents attract or repel each other
by virtue of their electric antagonism, and consequently, as was
shown in § 30, proportional to the product of the latent electro-
scopic forces mz and n (1 — 2) possessed by the constituents of
the disc M, and is, moreover, dependent on a function to be
deduced from the size, form, and distance, which we will desig-
nate by 4 4. Accordingly, when we restrict the coherence to
the magnitude of the section w,
X=—49mnz (1—2) wo.
We have placed the sign — before the expression ascertained
for the strength of the coherence, since a reciprocal attraction
of the constituents only occurs when m and n have opposite
signs; when m and have the same signs, the constituents
exert a repulsive action on each other, which no longer pre-
vents, but promotes the decomposing force. After this re-
mark it will at first sight be evident that a positive or negative
value must be ascribed to the function $, according as the ex-
pression taken for the decomposing force z is positive or nega-
498 OHM ON THE GALVANIC CIRCUIT.
tive; the sign of the function $, therefore, changes when the
direction of the decomposition is transposed from the one con-
stituent to the other. The nature of the function ¢ is as little
known to us as the size and form of the elements on which it is
dependent; nevertheless, we may, in our inquiries, regard its
absolute value as constant, since the size and form of the cor-
poreal particles, acting on each other, must be conceived to be
unchangeable so long as the two constituents remain the same,
and the supposition that the two constituents constantly main-
tain for every chemical equivalent the same volume, renders
attention to the mutual distance of the chemically different
particles unnecessary, as regard has already been paid, when de-
termining the electroscopic forces in the disc M, to the relative
distances of the elements of each constituent.
35. To determine the magnitude of the reaction Y, which in
the disc M opposes the latent electricity of the neighbouring
discs to the decomposing force, we have nothing further to do
than to substitute in the expression for Z instead of wu, the sum
of all the latent electroscopic forces in the disc M. Since now
the sum of these latent forces is m z+ (1—2z), we obtain for
the determination of the force Y, which is called into existence
by the change in the chemical equivalent of the constituents,
and which opposes the decomposition, after due determination
of its sign, the following equation:
Y=4n0 52. i(n—m).2 (1-2). POO.
If now we substitute for % Y and Z the values found in the
equation
X+Y=Z,
we obtain, after omitting the common factor 4z(1—z), and
az+ 6 (1—2)
multiplying the equation by , as the condition of
i(mB—na)
the permanent state ia the chemical equivalent of the two con-
stituents, the equation __
du omn
ati (mB —n a)
ae
x. [zz+B (1—2)] @
which, when we put
OHM ON THE GALVANIC CIRCUIT. 499
SMM ing (XO mn
i(mB—na) Lae x! (m B—n a)’
passes into
du dz
oY + bo [2248 (1—2)]—x0(n—m) 5%. (5)
This equation undergoes no change, as indeed is required by
the nature of the subject, when m, a, z, and n, 8, 1 — z are re-
spectively interchanged, and, at the same time, the sign of ¢
is changed, as according to the remark made in the preceding
paragraph, must take place, since by this transformation the
direction of the decomposition is transferred from one consti-
tuent to the other.
36. In order to be able to deduce from this equation the
mode of the diffusion of the two constituents in the fluid, 7. e.
the value of z, we ought to know the power of conduction x, and
the electroscopic force u at each point of the portion in the act
of decomposition, the values, however, of which, are themselves
dependent on that diffusion. Experience, as yet, leaves us in
uncertainty respecting the change of conductibility, which
occurs when two fluids are mixed in various proportions with
one another, and likewise with respect to the law of tensions,
which is followed by different mixtures of the same consti-
tuents in various proportion; for, if we do not err, no ex-
periments have been instituted relatively to the latter law, and
the law of the change produced in the conducting power of
a fluid, by the mixture of another, is not yet decidedly esta-
blished by the experiments of Gay Lussac and Davy. For this
reason we have been inclined to supply this want of experience
by hypothesis. We have, it is true, constantly endeavoured to
conceive the nature of the action in question, in its connexion
with those with whose properties we are better acquainted ;
but, nevertheless, we wish the determinations given to be re-
garded as nothing more than fictions, which are only to remain
until we become by experiment in possession of the true law.
With regard to what relates to the change in the power of
conduction of a body, by mixture with another, we have been
guided by the following considerations. We suppose two adja-
cent parts of a circuit of the same section w, whose lengths are
» and w, and whose powers of conduction are a and 4; then,
when A is the sum of the tensions in the circuit, and L the re-
duced length of the remaining portion of the circuit, the mag-
Ox w
500 OHM ON THE GALVANIC CIRCUIT.
nitude of its current, which results from the above-found for-
mulz, is
If now a conductor of the length v + w, aud of the power of con-
duction x with the same section, being taken instead of the two
former, leaves the current of the circuit unchanged, then must
wy we oF e
aw be. woe?
whence we find
ab (v +)
LS eer
bv+aw
But it is perfectly indifferent for the magnitude of the cur-
rent, whether the entire length v be situated near the entire
length w, or any number of discs be formed of the two, which
are arranged in any chosen order, if only the extreme parts re-
main of the same kind, as otherwise a change might result in
the sum of the tensions, consequently also in the magnitude
of the current. If we extend this law, which holds for every
mechanical mixture, likewise to a chemical compound, the above
value found for x evidently gives the conducting power of the
compound, where, however, it has been taken for granted that
the two parts of the circuit, even after the mixture, still occupy
the same volume, for v and w are here evidently proportional
to the spaces occupied by the two bodies mixed with each
other.
If we now apply this result to our subject, and therefore
put, instead of v and w, the values z and 1 —z, which express
the relations of space of the two constituents in the disc M, we
obtain, when a denotes the conducting power of the one consti-
tuent A, and 6 the same forthe constituent B; further, x the
power of conduction of the mixture of the two contained in the
disc M, the following expression for x,
Sait ab
~ a+(b—alz
37. Having thus determined the power of conduction at each
place of the extent in the act of decomposition, there only re-
mains to be ascertained the nature of the function uw at each
such place; and since all tensions and reduced lengths in the
OHM ON THE GALVANIC CIRCUIT. 501
part of the circuit, in which no chemical change occurs, are
unalterable and given, it is, in accordance with the general
equation given in § 18, which likewise holds for our present
case, only requisite for the perfect knowledge of the function u,
that we are able to determine the tensions and reduced lengths
for each: place within the extent in which the chemical change
takes place.
But evidently the reduced length of the disc M is
dx.
aay )
or if we substitute for x its value just found,
a+ (b—a)z Be
abw
we accordingly obtain the reduced length of any part of that
extent, if we integrate the above expression, and take the limits
of the integral corresponding to the commencement and end of
the part. If now we bear in mind that the integral
Cri Oz
Sf abw
may also be written thus:
whe b—a d
bw ia aba Sf 7° al
when / represents the length of the part, over which the in-
tegral is to be extended, and zwdwz expresses merely the
space which the constituent A in the disc M occupies; con-
sequently /zwdaz, the sum of all the spaces which the con-
stituent A fills in the part whose reduced length has to be
found, it is obvious that the reduced length of the entire
portion, in the act of decomposition, remains unchangeable
during the chemical change, since, as we have supposed, each
constituent maintains, under all circumstances, constantly the
same volume. The same result may also be directly deduced
from what was advanced in the preceding paragraph ; however,
this unchangeability only relates to the reduced length of the
entire portion; the reduced length of a part of it does not in
general depend merely on the actual length of this part, but
likewise on the contemporaneous chemical distribution of the
constituents in the extent, and must therefore, in each separate
ease, be first ascertained in the manner indicated.
VOL, 11, PART VIII. 21
?
502 OHM ON THE GALVANIC CIRCUIT.
38. We have lastly to determine the alteration in the _ten-
sion of the circuit, which is produced by the chemical altera-
tion of the extent, which has hitherto been considered. For
this purpose we assume, till experience shall have taught us
better, the position, that the magnitude of the electric tension
between two bodies is proportional, first to the difference of
their latent electroscopic forces, and secondly to a function,
which we will term the coefficient of the tension, dependent on
the size, position and form of the particles which act on each
other at the place of contact. Not only from this hypothesis
may be deduced the law which the tensions of the metals ob-
serve inter se,—nothing further being requisite than to assume
the same coefficient of tension between all metals placed under
similar circumstances,—but it likewise affords an explanation
of the phenomenon, in accordance with which the electric
tension does not merely depend on the chemical antagonism of
the two bodies, but also on their relative density, and can for
this reason exhibit themselves differently, even in different tem-
peratures. For the same reasons which we have already men-
tioned in § 34 on the determination of the coherence which
occurs between the two constituents of a mixed body, we shall
likewise admit here, in the circumference of the chemically
variable extent as constant, the unknown function dependent
on the size, form and position of the particles in contact, and
designate it by ¢’. Since now the latent electroscopic force in
the disc M, to which the abscissa # belongs, is expressed by
n+ (m—n) 2,
and that in the disc M', to which the abscissa # + da belongs,
by
n+(m—n) z+ (m—n) dz,
the tension originating between the discs M and M’ is
—¢' (m—n)dz;
consequently the sum of all the tensions produced through-j
out a portion exposed to chemical change
4! (m—n) (22!)
when 2’ and 2” represent those values of z, which belong to the
comméncement and end of the extent in question.
But the tension of the circuit undergoes, besides the change}
just explained, a second one, from the extremities of the che-j
OHM ON THE GALVANIC CIRCUIT. 503
mically changeable portion, which are in connexion with the
other chemically unchangeable parts of the circuit, undergoing
a gradual change during the decomposition till they arrive at
their permanent state, giving rise at those places to an altered
tension. If, for instance, we call ¢ the value of z, which
belongs to all places of the extent in question, before chemical
change has begun in it, and designate the coefficient of the ten-
sion occurring at the extremities of this extent, supposing that
it is the same at both ends, by ¢”, and moreover express by p
and y the latent electroscopic forces of those places of the che-
mically unalterable part of the circuit which are situated adja-
cent to the chemically changeable extent, the tensions existing at
these places can be determined individually. They are, namely,
previous to the commencement of chemical change, the fol-
lowing:
$" [w — (n+ (m—n) $)], and
$" [(n + (m—n) 8) —»]5
and after the permanent state in the decomposition has been
attained, if we, as above, let 2’ and 2” be those values of z
which belong in this state to those places, they are the fol-
lowing :
4" [w— (n+ (m—n) 2')], and
$" [(m + (m —n) 2") — 9],
_ their sum is therefore in one case
. $" (u—»),
and in the other
o! (4 —») + 9" (m—n) (2" —2/) 5
consequently the increase of tension at those places is
$! (m—n) (2! —2').
If we add this change of the tension to that above found, we
obtain for the entire difference of the tension, produced by the de-
_ composition until the commencement of the permanent state,
(@" = 4!) (m—n) (2! —2),
which, if we substitute @for $' — 9', changes into
® (n—m) (2 —2’).
If now we represent by S the magnitude of the current, and by
A the sum of the tensions in the circuit, before any chemical
change has commenced, by S’ the magnitude of the current,
after the permanent state has been attained; lastly, by L the
2u2
_
504 OHM ON THE GALVANIC CIRCUIT.
reduced length of the entire circuit, which, as we have seen, re-
mains under all circumstances the same, it results
, A—® (n—m) (2"— 2) |
ae ss
3
Ss
‘ : A. ;
or, if we write for iis equivalent S,
®@ (n--m) (2 —2’)
Sie Sin py Tse ie
2 ae
so that, therefore, eli) Az) designates the decrease
L
produced in the magnitude of the current by the chemical al-
teration. .
39. After all these intermediate considerations, we now pro-
ceed to the final determination of the chemical alteration in
the changeable portion, and the change of the current in the
whole circuit produced by this chemical alteration, where, how-
ever, we have constantly to keep in view only the permanent
state of the altered portion. If we substitute in the equa-
du
dz
have just found, is solely dependent on the fixed and unalter-
able values of z, and therefore has to be treated in the calculation
ab
a+(b—a) 2
tion (& ) given in § 35, for xw its value 8’, which, as we
as a constant magnitude; further, for x its value
given in § 36, this equation changes into
or if we place 8+ PwB=, and Pw (« —f) =Q, into
abw(n—m) dz
ORR het at eae ae
from which, by integration, we deduce the following :
(6—aB—aO | iy 2+02z
abw(n—m) S a+ (b—a)2’
where ¢ represents a constant remaining to be determined. If
we designate by x the abscissa of that place of the chemically
changed portion for which has still the same value, which,
previous to the commencement of the chemical decomposition,
belonged to each place of this portion, for which therefore z =§,
OHM ON THE GALVANIC CIRCUIT. 505
and determine in accordance with this statement the constant c,
our last equation acquires the following form :—
Oe ROL, ieee
a+(b—a)z at+(b—a)t"
where e denotes the base of the natural logarithms. The fol-
lowing consideration leads to the determination of the value x.
Since, namely, € represents the space which the constituent A
occupies in each individual disc of the changeable portion pre-
vious to the commencement of the chemical decomposition, if
we denote by / the actual length of this portion, /§ expresses
the sum of all the spaces which the constituent A occupies on
the entire expanse of the changeable portion ; but this sum
must constantly remain the same, since, according to our suppo-
sition, no part of either of the constituents is removed from this
portion, and both maintain, under all circumstances, the same
volume, even after chemical decomposition has taken place ; we
obtain, therefore,
Mr I Zaz,
where for z is to be substituted its value resulting from the pre-
vious equation, and the abscisse corresponding to the com-
mencement and end of the changeable portion are to be taken
as limits of the integral.
These two last equations, in combination with that found at
the end of the previous paragraph, answer all questions that
can be brought forward respecting the permanent state of the
chemical alteration, and the change in the electric current thus
produced, and so form the complete base to a theory of these
phznomena, the completing of the structure merely awaiting a
new supply of materials from experiment.
40. At the conclusion of these investigations we will bring
prominently forward a particular case, which leads to expres-
sions that, on account of their simplicity, allow us to see more
conveniently the nature of the changes of the current produced
by the chemical alteration of the circuit. If, for instance,
we admit a = 4, and a=, the differential equation obtained in
the preceding paragraph changes into the following :
0= 2 dx—aw (n—m) dz,
whence we obtain by integration
506 OHM ON THE GALVANIC CIRCUIT.
aw (n—m)’
when x designates the value of x, for which s = %. Since in
this case the value of = constantly changes to the same amount
on like differences of the absciss, the abscissa x, which belongs
to its mean value {, as it was at all places of the changeable
portion previous to the commencement of the chemical decom-
position, must be referred to the middle of this portion. If,
therefore, 2! and z!', as above, represent the values of z, which
correspond to the commencement and end of the variable por-
tion, and / the actual length of this portion, it follows, from our
last equation, that
and
piety Giang dS,
aw (n—m)
and from these two equations results
(a—m) (2! — 2!) = Bs 2
aw
or, if we put, instead of ae by which here nothing further is
expressed than the unchangeable reduced length of the chemi-
cally variable portion, the letter A, the following :
(n— m) (2"— 2!) = . 2is5
If we place this value of (7 — m) (z'' — 2’) in the equation found
ah & (n—m) (2! — 2’)
g ag — 2mm nA),
and at the same time substitute for = its value S’+ wa, we
obtain
)
s=8— 5 (8+ 4a),
an equation, the form of which is extremely well suited to indi-
cate in general the nature of the change of the current pro-
duced by the chemical alteration, and the expressions of which
coincide exceedingly well with the numerous experiments I
have made on the fluctuation of the force in the hydro-circuit,
and of which only a small part have been published*.
* Schweigger’s Jahrbuch, 1825, Part 1 and 1826, Part 2.
r
we
ARTICLE XIV.
Selections from a Memoir on the Expansion of Dry Air. By the
late Professor F. RuDBERG.
[From Poggendorff’s dnnalen, B. 41. 8. 271.]
AMONG the constants in physics there is certainly not one
which is usually considered to be determined with greater preci-
sion than the expansion of dry air, or of dry gases generally, under
a constant pressure, between the standard points of the thermo-
meter scale. The numerous experiments made by Dalton and
Gay Lussac, almost at the same time, about the beginning of
the present century, appeared to show, beyond all doubt, that
the amount of this expansion from 0° to 100° C., under a con-
stant pressure, was 0°375 of the volume of the air at 0°. Their
great skill in experimenting, and the magnitude and number of
the services they had rendered science, left no room for any
doubt as to the accuracy of this result; consequently, for more
than thirty years in all computations in which the expansion of
gas occurs, it has been assumed to be 0°375.
The constant in question is undeniably of the greatest im-
portance in Physics, since it forms the basis of all methods of
measuring temperature ; it is used in the explanation of most of
_ the phenomena caused by heat; and lastly, is requisite in the
reduction of many observations in Physics and other sciences;
as, for example, in determining the velocity of sound, in the
measurement of heights by means of the barometer, and in com-
puting astronomical refractions. This being the case, it will no
doubt appear surprising, that the value of this constant, which
has been employed up to the present time, is erroneous to no
small amount, since, as will be shown in this memoir, it appears
to be not more than from 0°364 to 0°365, instead of 0°375.
The change of volume produced by heat can be determined,
either by heating cold air and measuring the increase of its vo-
lume, or by cooling warm air and determining the diminution
of its volume. I have adopted the latter method, as being by
far the most accurate.
In most of the experiments, a glass globe, having a neck
made of thermometer tube A B C (fig. 1.), and capable of con-
508 RUDBERG ON THE EXPANSION OF DRY AIR.
taining from 120 to 150 grammes of mer- E
cury, was used for containing the air. After
the end of the tube had been fitted into a
hole in a cork at one end of a cylinder, D E,
containing chloride of calcium, the air was
dried, either by heating the globe strongly over
a spirit-lamp, and then suffering it to cool,
and repeating the process at least fifty or sixty
times ; or else by connecting the end E of the
cylinder with an air-pump, and exhausting and
re-admitting the air fifty or sixty times. I have ke
not observed any difference between these two
methods of drying air, but have found one as x
effectual as the other. The chloride of cal-
cium was fused at a red heat, then poured out
upon a cold plate of metal, and as soon as it
became solid, broken to pieces, and put into F
bottles with ground stoppers while red hot.
The globe having been dried in this manner, and remaining
in connexion with the chloride of calcium tube, a small opening
being made in the cork at E for the air to escape through, was
suspended by means of a cork G cut in two, in the boiler F, the
upper part of which, as described in my memoir on the construc-
tion of thermometers (Poggendorfi’s Annalen, B. 40.), consists
of two concentric cylinders, so that the globe and the greater
part of the tube were surrounded by steam. After the water
had been boiling three quarters of an hour, or an hour, the cy-
linder D E was removed, and the boiling continued for about
ten minutes longer. The height of the mercury in the barome-
ter was then observed, and the tube sealed, the water being kept
boiling freely in the mean while.
After the ball had been weighed with a balance, which turned
with one-tenth of a milligramme, it was firmly fixed to the arm
Q (fig. 2.) of a steady support, with the tube passing through
a hole, in a metal dish H. The arm Q was then so far de-
pressed, that the point of the tube was deeply immersed in
the mercury of the trough T. Lastly, the point of the
tube was broken off, and in order that all the mercury re-
quisite might enter, the ball was suffered to remain in this
situation several hours, almost always all night, although I
had convinced myself that not more than.a quarter of an hour
=
RUDBERG ON THE EXPANSION OF DRY AIR. 509°
at most was requisite, with even the smallest of the tubes which
I employed.
Snow was now placed on
the metal dish H, and the
globe surrounded with it
on all sides. The water
produced by the melting of
the snow escaped through
the tube L. As soon as
the snow began to melt,
fresh snow was carefully
added, so that the tempe-
rature of the globe was
kept at 0° for about two
hours, and sometimes even
longer. When by this
means I was certain that
all the mercury had ac-
tually entered which at 0°
could be forced in by the
pressure of the atmosphere,
I closed the fine opening
of the tube with a very soft mixture of wax and turpentine,
which was prepared for that purpose in a little spoon of iron.
At the same instant the barometer was observed, in order to de-
_ termine the existing pressure of the atmosphere; the snow was
then carefully removed, and the difference of altitude between the
surfaces of the mercury within and without the globe measured.
For this purpose the measuring apparatus N M K was pre-
pared. Upon the whole, it depends upon the principle employed
in measuring the height of the mercury in Fortin’s barometers.
A slider M, embracing tightly the vertical bar, is moved up or
down by a screw P, and therefore also the cylindrical ring N,
and screw K, which are connected with it. The ring N having
first been made accurately horizontal, was depressed, surround-
ing the globe, till its under edge coincided with the surface of
the mercury in the globe, and the screw K S turned till its point
§ just touched the surface of the mercury in the trough. It is
evident that the difference of altitude between the under edge
of the ring and the point S was equal to the difference of alti-
tude of the two surfaces of the mercury. After the contacts had
510 RUDBERG ON THE EXPANSION OF DRY AIR.
been made as accurately as possible, the measuring apparatus
was removed, and the globe, the extremity of the tube being
closed with wax, as has been already stated, lifted out of the
trough. The difference of altitude of N and S was then accu-
rately measured, by means of two graduated scales, placed at
right angles to each other, and the globe, with the mercury
which had been forced into it, weighed after the wax had been
removed.
When this was accomplished, the tube was bent at the end,
so that it could be dipped into a vessel of mercury, the globe
filled with it, and all the air expelled, by carefully boiling. When
cold it was placed in snow, and completely filled with mercury
at 0°. When no more mercury could be introduced (this was
known to be the case by the thread of mercury showing itself at
the extremity of the tube), a clean empty vessel was placed un-
derneath, to receive the mercury that ran out; the globe taken
out, and placed in the boiler. The mercury that escaped be-
tween the temperatures of 0° and temperature of boiling deter-
mined by the height of the barometric column, was weighed,
and the weight of this, added to the weight of the mercury re-
maining in the globe, consequently gave the weight of mercury
contained in the globe at 0°. From these two weights, and the
true expansion of mercury, the true expansion of the glass may
be calculated.
Let uw be the volume of the globe at 0°, and therefore the vo-
lume of the mercury contained in it at that temperature; / the
height of the barometric column, in centimetres, at the instant
the tube was sealed; T the corresponding temperature of the
vapour of boiling water; 100 A the true expansion of dry air
from 0° to 100°; 100 G the expansion of glass in volume from
0° to 100°. At the instant the end of the tube was closed with
wax, let v be the volume of the air contained in it; g the weight
of the mercury contained in it; & the height of the mercury in
the barometer ; / the height of the surface of the mercury in the
globe above the surface of the mercury in the trough; p the
weight of the mercury contained in the globe at 0°. The vo-
lumes, pressures, and temperatures of the air at the time the
tube was sealed, and at the time it was closed with wax, were
asu(1+GT), v; h,k—J; T°, 0° respectively, therefore
{VAG T), > bet
HAS) =A (1+ AT).
RUDBERG ON THE EXPANSION OF DRY AIR. bit
But
Therefore
(AA PES ae dahl IE NE
i gaged h
Let 7’ be the weight of the mercury expelled from the globe
when heated from 0° to T’°; 7 the weight of the mercury ex-
pelled when heated from 0° to 100°; 100 M the true expansion
of mercury from 0° to 100°; 8, 0! the weights of a unit of volume
of mercury at 0° and 100° respectively. Then
wen 3
100: "Ty,?
(1 +100 M) = 4;
the volume of the mercury at 100° = uw (1 + 100 M); the volume
of the globe at 100 = u (1 + 100 G); therefore the volume of
the mercury at 100° expelled = u.100 (M — G); therefore
bu
. , — rie ptr tei Enid tg
its weight r = J'u. 100 (M S) Shoe Mn (M — G)
_ p-100(M—G)
Sats 100M * Therefore the true expansion of glass from
0° to 100°
100 G = 100M — zl 4+ 100M).
‘The value of the true expansion of mercury is here assumed to
be known. This may be done with confidence, inasmuch as it
has been determined, quite independently of the expansion of
glass, by the masterly experiments of Dulong and Petit. They
found 100 M = 0:0180180. Therefore
100 G = 0:018018 — 1:018018 re
__ The following table exhibits the values of 100 M — 100 G for
the glass employed, which was potash glass, from the manufac-
tory at Reymyra. The first fifteen results were obtained from
globes used in experiments upon the melting-points of easily
fusible metals; the remainder were obtained from the globes
used in determining the expansion of air. They show that the
same kind of glass, though made at different times, and there-
fore in different meltings, possess the same expansibility.
512 RUDBERG ON THE EXPANSION OF DRY AIR.
"015732 "015720 "015732 "015713
*015744 7015761 *015706 °015697
"015754 °015730 OLS jak *015751
"015744 *015711 "015741 015744
"015723 °015737 "015753 *015726
"015735 015720 *015762 "015736
The mean of the twenty-four results gives the difference be-
tween the true expansion of mercury and the expansion in vo-
lume of potash glass, 100 M — 100 G = 0-015733. Hence
the true expansion in volume of the potash glass of Reymyra
from 0° to 100°,
100 G = 0°002285.
In the following table of the results of nine observations, p
and p — q are expressed in grammes, and A, &, / in centimetres.
p- p-4Yy. h. k. 1. Re 100 A.
166°6891 . 1383:1409 . 76°528 . 74:277 . 3:98 . 100°20 . 0:3643
173°4432 . 1381-7215 . 76°362 . 77:°584 . 3°81 . 100718 . 0°3654
183°4963 . 148°2124 . 75°702 . 75:965 . 4:69. 99°89 . 0:3644
154-2360 . 120°6356 - 77°230 . 75-910 . 3:50 . 100°45 . 0:3650
174-6862 . 134-9876 . 77:985 . 77:748 . 3°81 . 100°73 . 0°3653
187:4650 . 144:9009 . 76-444 . 76°474 . 3°81 . 100°16 . 0°3636
198:8099 . 172°7273 . 76°442 . 76°271 . 11:70 . 100°16 . 0°3651
184:4872 . 146°6123 . 75°811 . 75°342 . 5°25 . 99°93 . 0°3643
191:1037 . 178-9558 . 75°779 . 76°105 . 16°65 . 99:92 . 0:3645
The value of 100 A. in the sixth line is too small, in conse-
quence of the loss of a globule of mercury in one part of the
experiment. The mean of the preceding values of 100 A. is
0°3646.
Two other experiments were made with cylinders of glass. It
was found impossible to boil the mercury contained in them, on
account of the smallness of the bore of the tubes which formed
their necks. The results are therefore considered less accu-
rate.
Dp p-4y h. k. 1. ii 100 A.
1158°902 . 946:516 . 76°773 . 76°789 . 7°80 . 100°28 . 0:3646
1196:992 . 991:695 . 76°313 . 75°470 . 7:92 . 100°12 . 0°3662
Meant) J7ieiseseonedasseercest seansacsbene 0°3654
Two other observations were made without previously drying
the air with chloride of calcium, in which, however, an exami-
nation with a microscope showed that there were no visible drops
of water in the globe. These experiments were made merely
RUDBERG ON THE EXPANSION OF DRY AIR. 54S"
for the purpose of seeing how great an error might be introduced
by neglecting to dry the air completely. The results are,
De rg. h. ke Ll. T. 100A.
166:4746 . 128°0336 . 75°166 . 75:049 . 4:21 . 99°69 . 0°3840
139-2725 . 106°1248 . 75-964 . 75-201 . 4°325 . 99:99 . 0°3902
The experiment was repeated with the ball used in the last of
the above observations, the air having first been perfectly dried.
It gave the following results :—
p p-¢@. h. k. 1. T. 100A.
1392725 . 107:8192 . 76:440 . 76°185 + 3°725 . 100°16 . 0°3652
From the whole of these observations, I can come to no other
conclusion, than that the expansion of dry air, and without
doubt of all other dry gases, from 0° to 100°, is not 0:375, but
only from 0°364 to 0°365 of the volume of the gas at 0°.
514
ARTICLE XV.
Second Series of Experiments on the Expansion of Dry Air
between 0° and 100°. By the late Professor F. RupBEre.
[From Poggendorff’s Annalen, B. 44. 8. 119.]
SINCE the publication of my experiments on the expansion of
air (Poggendorff’s Annalen, B. 41.8. 271.), I have had an appa-
ratus constructed, by the aid of which one such experiment may
be made in the short space of an hour and a half, or two hours.
The mean of the results which it has given agree perfectly with
those I had previously obtained. I here communicate a short
description of the apparatus, and the values of the expansion
which it has afforded.
The construction of the apparatus enables us to determine
the pressures of a given mass of dry air at 0° and at 100°, the
spaces occupied by the air in
the two cases differing only by
the expansion of the receiver.
The dry air is contained in
the cylinder A B, which com-
municates through the slen-
der tube DE with the wide
tube F, which, together with
a second tube H I, about 50
centimetres long, and open at
both ends, is cemented into
the lid of the box G. The
box contains a leathern bag
for holding mercury, the ca-
pacity of which, as in a baro-
meter, can be altered by means
of the screw K, so thut the
mercury may be elevated or
depressed in the tubes. A
fine line is traced with a dia-
mond point on the slender
tube D E at C, up to which
the mercury is screwed, as
RUDBERG ON THE EXPANSION OF DRY AIR. 515.
well when the air in the receiver A B is cooled down to 0°,
as when it is heated up to the boiling point of water. In order
to measure with accuracy the altitude of the mercury in the
tube, a brass scale H I, divided into millimetres, is attached to
the tubes. The line which marks the commencement of the
divisions at C is so long, that it passes behind both tubes, and
thus the altitude of the extremity of the column of mercury in
the tube HI, above the mark on DE at C, is easily deter-
mined.
The air in the receiver AB was dried before the tubes were
cemented into the box, in the following manner. The lower end
of the tube F was drawn out to a capillary point, and connected
with a very wide tube filled with chloride of calcium, which
communicated with an air-pump. After the air had been fifty
times exhausted and re-admitted, the capillary point was sealed
and the tube cemented into the box G, which had been pre-
viously filled with dried mercury, and lastly, the sealed end
broken off under the surface of the mercury.
The capillary depression of mercury at C was determined by
experiment before the narrow tube DE was joined to the re-
ceiver, and found equal to 1°85 centimetres.
The tube F was taken of large diameter, in order to receive the
air as it expanded on being heated from 0° to 100°, and so ob-
viate the necessity of continually screwing up the mercury.
The calculation and the method of observing are both equally
simple. When the air in the receiver AB is cooled down to
0°, and the mercury is screwed up to C in the tube D EK, let the
mercury stand at M inthe tube HI. At the same instant let
h be the altitude of the mercury in the barometer. Let the al-
titude of the mercury in HI, above the mercury in DE, or
C M = &, and let / be the capillary depression of the mercury
in DE; then the pressure of the air in the receiver AB will
be A+k—J. When afterwards the air is heated up to the
boiling point of water, and the mercury is screwed up to C in
the tube D EK, let the mercury stand at Pin the tube HI. At
the same instant let A! be the height of the mercury in the baro-
meter, and the difference of altitude of the mercury C P =X’;
then the pressure of the air in the receiver will be h! + k' — 1.
Let T be the temperature of steam corresponding to the baro-
metric height h', 100 A. the expansion of air from 0° to 100°,
and 100 G. the expansion of glass in volume*from 0° to 100°;
516 RUDBERG ON THE EXPANSION OF DRY AIR.
then
W+k—l
1+AT= er oa, (1+GT).
In the above expression the altitudes /!, k', h, k need not be
connected for temperature, because the experiment is completed
in the short space of an hour and a half, during which the tem-
perature of a room will undergo no sensible variation. The only
reduction to 0° requisite, is that of the barometric height /!, in
order to deduce from it the temperature T.
The experiments which I have made up to the present time,
with the above-described apparatus, under very different baro-
metric pressures (from 752™™92 at + 17°°4 to 783™™72 at
+ 18°), gave for 100 A. the follewing values :—
0°3640 0°3640 0°3653
0°3648 0°3656 0°3640
0°3641 0°3643 0°3664
0°3648 0°3648 0°3645.
The mean value of 100 A. is 0°36457. Since this mean value
is the same as that given by my former experiments made in a
manner entirely different, I venture to consider it as fully esta-
blished,—that the true expansion of dry air between 0° and
100° centigrade, is only from 0°364 to 0°365 of its volume at 0°.
ArTicLeE XVI.
On Barometrical Measurement of Heights. By ¥. W. BessEu.
{From the Astronomische Nachrichten, Nos. 356, 357.]
l.
THE atmosphere of the earth is known to be composed of
the nitrogen, oxygen, and carbonic acid gases, and of aqueous
vapour. These constituents are supposed to exercise no che-
mical action on each other; and arbitrary quantities of them,
mixed together under circumstances of equal temperature and
pressure, occupy spaces equivalent to the sum of the spaces that
they would severally occupy. Were we to assume that the
constituents of the atmosphere are mixed in the same propor-
tion at all times and at all altitudes, we might dispense with the
knowledge of what that proportion is, in treating of the condi-
tions of their equilibrium; but if we desire to preserve the
freedom of founding our investigations on other suppositions
also, we must not pass by in silence the mode in which the con-
stituents are combined.
The proportion of the three gases may not always be exactly
the same at a given point of the earth’s surface; but the altera-
tions which take place are so small, that they are only discover-
able by chemical experiments frequently repeated ; we cannot.
therefore, regard the proportion as determinable by observation for
each particular case, and we must assume a certain proportion.
According to Berzelius, the spaces occupied by the three
gases, in the order in which they are named above, are to each
other as
77°96; 21°15; 0:07 ;
or, one volume of dry atmospheric air at the surface of the
earth contains
v =0°78605 nitrogen gas
v, =0°21325 oxygen gas
v,, = 000070 carbonic acid gas.
The same great chemist has given the densities of these three
gases, under the pressure which gives to the mixture the den-
sity D, viz.:
VOL. 11. PART VIII. 2M
518 BESSEL ON BAROMETRICAL
Nitrogen gas = 0:9691 D=¢.D
Oxygen gas =1:1026 D=d, D
Carbonic acid gas = 175260 D = d, D.
These six numbers require to be slightly altered, in order that
they may correspond to the relation
Pevd + 0,4, +0, dy « eet. UO)
Designating by M, m, m, m,, the masses, and by D, 4, 3, 8),
the densities of the mixture and of its constituent parts, we
have, on the supposition of equal distribution in the space,
Di: M 0 sm = 2): m, = 5/2 ys See oe)
further, if P, p, p,, p, denote’ the pressures which the mix-
ture and its constituent parts, the latter taken separately, exert
on the unit of surface of the enclosing space, we have by Ma-
riotte’s law,
| beat go oo age)
Pt Oy et = 210,
P:d,D = pyiby
and also
Pol = 9.0 =p) 2) — pire Oy
thus
s=vdD; § = 9,4, Ds; 8, = 0, 4, D.
Introducing these values of 8, 8, 8, into the above proportion
(2.), we obtain
m=vdM, m,=v,d,M, m,=v,d,M,
and aa M=m-+m,+m,, we have also the relation (1). To
satisfy this relation I have slightly altered d and d,, making the
first 0°9711, and the second 1°1048.
Biot and Arago determined the density of atmospheric air
(é. e. the mixture of the three gases) at the surface of the earth,
at the temperature of melting ice, and under a pressure of a
column of mercury of the same temperature in the 45th parallel
of latitude of 336°905 Parisian lines, to be 10466°8 times less
than that of mercury. Under the aforesaid circumstances, there-
1 <
fore, D = 104668"
As the temperature increases, the specific elasticity of the air,
or the space which a given quantity of air occupies, increases
also, the pressure remaining equal. Gay Lussac arrived at the
remarkable result that the specific elastic force of all gases and
a Hees
MEASUREMENT OF HEIGHTS. 519
vapours alters equally with equal changes of temperature, and
that the alteration is proportional to degrees of the mercurial
thermometer. If the elasticity at the temperature of melting
ice be 1, and its alteration for a change of temperature corre-
sponding to one degree of the thermometric scale = f, its value
for a given amount of the thermometer is
E=1 + kt.
For the temperature of boiling water Gay Lussac found E
= 1°375.
Besides the three gases the atmosphere contains aqueous va-
pour, which is present in variable quantities, determinable only
by experiment in each particular case. I propose to return
hereafter to this part of the subject ; but I will first consider of
atmospheric air unmixed with aqueous vapour.
2.
Barometric measurements of height rest on a comparison of
the observed pressure of the atmosphere at different heights,
with the expression denoting the conditions of its equilibrium.
Although this expression has been developed in the Mécanique
Céleste, and in several subsequent works, I shall not omit its
development here; as it will enable me to introduce a small
alteration, as well as to connect what I have further to say.
Mariotte’s law requires that to produce equilibrium the density
(8) of the air should be in the direct ratio of the pressure (p)
which it experiences, and which it consequently exerts in
return, and in the inverse ratio of its elastic force; or that
be constant. The air is here supposed to be constituted
alike at all altitudes. If we take for the measure of p the
pressure exerted on an unit of surface, by a column of mercury
of 336°905 Parisian lines, at the temperature of melting ice, at the
_ Surface of the earth in the latitude of 45°,—for the measure of 8
_ the density of mercury at the temperature of melting ice,—and
_ for the measure of E the specific elastic force of air at the same
temperature,—and if we make 6 = D for p= 1, and E = 1, we
have
Bi HTD Lites 5) hye ea pole v0 OR)
The pressure of the air at an elevation 2 above the surface of
the earth, or at a distance a + 2 from its centre, is the sum of
the pressures of all the strata above x. A stratum between the
2m 2
520 BESSEL ON BAROMETRICAL
elevations x and 2 + dz has for every unit of its surface the
mass ¢.d a; therefure it exerts on this unit the pressure
(s) ®(—2.) aa,
aQ+ea@
in which (g) is gravity at that part of the earth’s surface which
is perpendicularly beneath the point to which » and 8 belong,
expressed in terms of gravity in the latitude of 45°. But in
order that the diminution of pressure, caused by taking away
this stratum from those above 2, may be obtained in terms of
the measure applied to p, the above expression must be divided
by that measure, which then gives
ee PG) 10 ( a ) ;
Oe ar505 Nag a)
or, if we prefer the use of the toise to that of the Paris line,
dp= —O~ ( g \Vde.. (4.)
336°905 a4+2
If we eliminate ¢ by combining the two equations, we obtain
dp __ _ (g) 864.D ( a ) dx
Bian 336°905 ates HK
By the integral of this equation the values of p at two different
elevations above the surface of the earth, v = h, and 2 = i’, be-
come comparable with each other ; or, if we denote them by P
and P’, and employ Briggs’s logarithms, of which the modulus
IS fy
in P(g) 864. Dom a _ daz.
= Bi 336°905 i ( lol Be
or if we write
336-905 34 Tes eee
Seiwa Ta te ee
then
P 1 ht a 2 dz
lg =-7/, (—-) Boe . (5.)
The integration, which still remains to be performed, requires
that we know the relation between w and E, or the law according
to which the observed heights of the thermometer + and 7’, cor-
responding to the temperature of the air at the two heights, pass
into each other. We do not know this law in every case, and
we have, therefore, no ground for assuming the change of tem-
perature to be otherwise than proportioned to the change of ele-
.
?
MEASUREMENT OF HEIGHTS. 521
vation. In order to correspond approximately to this view, and
at the same time to give the integral the most simple form pos-
sible, Laplace assumes
iy gee ee
a+e2
to be constant for all corresponding values of ¢ and 2, and deter-
mines the constant i, so that it may satisfy the two observed
temperatures t and 7’. Hence
(l+2)?+iX=(l ieee on (1+ k7')?+7H!
ah ah!
See Gah thon
2k (r — 1) )(a+a2t*)
H’—H ;
where I have written X, H and H’ for ——
We obtain thereby
i=
and
= fa) dr= — AG +k?) dt;
and further,
GQ \a a2 Qk
(-,) meee ghee
whence the integral taken from h/ to i is
[re
ee ee
i ae
We have thus, in accordance with Laplace’s assumption of the
law of the change of temperature, transformed the formula (5.)
into
Ee 1 H'—H
log = T oS
1+k
(6.)
t+!"
2
3.
I have hitherto considered the air as dry, and have still to
take into account the aqueous vapour which it always contains.
Tf, in a circumscribed space, the mixture of the dry constituents
of the atmosphere exert on the circumscribing surface the pres-
ure p, the aqueous vapour the pressure p,, aud if the specific
gravities of the two be respectively denoted by D and d, D, and
of the moist air which results from their mixture by Di, then
according to equation (1.),
522 BESSEL ON BAROMETRICAL
RN ANE
SrA: oD!
and
aye = P;
amet, pp;
thus
i = TL + Pp, ca
PtP,
or if, to avoid introducing a new sign, we denote the whole press-
ure (=p + p,) by p
Di=D {1-2 (—d)f veers
For moist air, therefore, the equation (3.) is changed into
6.E = {p —p,(1—d)} D,
and its combination with (4.) gives
O=dp + yp tS share Ge
To integrate this equation, we must know the dependence
which py, has on the other variable magnitudes. If in a parti-
cular case we have no observation determining the amount of
aqueous vapour contained in the air, we must found our calcu-
lation on the supposition either of a mean state of the atmo-
sphere, or of one which may appear more suitable to the actual
circumstances. I will first examine the case in which we may
suppose that at every point of the atmosphere there exists a de-
terminate portion of the maximum quantity of vapour which
it can receive in accordance with its temperature. If this maxi-
mum of vapour exert the pressure (p,), I then assume
P= (Pi)>
where by a I understand a constant factor not greater than unity,
the value of which is to be determined hereafter.
The expression for (p,), at the given ¢ of the centesimal scale,
deduced by Laplace (Méc. Céi., iv. p. 273.) from the experiments
of Dalton, in the unit of pressure chosen in the foregoing article,
= 1¢ (t — 100) 0-0154547— (¢ — 100)? 00000625826.
For which we may also write
(p,) = 0°0067407 .10 t:0°0279712 — t? 0°0000625826 rier (9.)
We have thus, conformably to the supposition,
p,= «6 10%'— °F,
:
MEASUREMENT OF HEIGHTS. 523
where 6 = 0:0067407
a = 0°0279712
c = 0°0000625826.
If we now multiply the differential equation (8.) bv
1 fax
1oF
we can integrate the product, namely,
- Oa ree ah © dX
‘Pp pl ? [p,r0 E
Laplace’s assumption of the law of the change of temperature
between two elevations, at each of which the temperature is given
by observation (Art. 2.), is
If we substitute this, and also the expression above given of
(p,), we have
2k 2k
i t — )t—c#?
C=p.10 i” ,? Bib a) 106 *—7i) dle
a a
By this equation we obtain the relation between the pressures of
the atmosphere P and P’ at the heights A and A’, namely,
Sp Lae - eae
mao. fi) — Pl 1g. vi
t—cf
_ 2%B(1—d)k -#)
ari sy ae dt.
If we write T for 1 (r + 7’), and T + z for ¢, then the integral
still to be sought is changed into
2k
2k
Tare i 4(¢—7) — —2cT z—c.2x?
mad ate fT ae gh ) dz.
= ales’ :
If, for brevity, we write
A(r—%) 2k
= ees} a@— 7 .—2cT Ju—cx?
EC hf OS eee ) dz,
—
ad Sie e/)
We have thus,
524 BESSEL ON BAROMETRICAL
or
2k Qk f(s — 0
—-7.(r-7 — ae =
Pio * aa +7, 10 rh Ga pe
whence it follows that
Re ow) Pay Tap? PP 4 ee
~ Pv [47 PP + wv] +4’
and if we take the Briggs’s logarithms of both numbers of the
equation, and develope fully to uw? inclusive,
2k P u
pt ee ps 7 (Ee
10
but according to the relation between the temperatures and the
elevations in Art. 2,
whereby we obtain
PS) ee ei u
log PY Li VCP) eae oe
The integral occurring in the expression for u is found by deve-
loping the Sextet ee into a series
SN {14% 2 (a—74-2e)*-2¢n | +8...
In order to estimate in some measure the amount of the second
member of this series, we may assume that the centesimal ther-
mometer falls a degree for every 85 toises of elevation. Then
is this member for H' — H = 2.1000 toises, and for T = 0,
= n?.0°0093 for small differences of elevation; it is therefore
an inconsiderable part of the first member; and even for the
greatest accessible elevations it does not amount to a tenth part
of it. The supposition as to the distribution of aqueous vapour
in the atmosphere, on which the present calculation rests, has
far more uncertainty; on which account I think there can be
but little interest in adhering strictly to it by means of a compli-
cated calculation. I therefore simplify it by assuming
_ 2aB(1—d,)k (r—7)
ins li
According to Berzelius d, = 0°62, and it has been snown above
that
lot? -¢™
MEASUREMENT OF HEIGHTS. 525”
6 = 0:0067407,
2k(r—7') H'—-H
a oe by 2
Hence
Hi (ror* oF 0-002s6l ;
I 1+kT
and we obtain, by the substitution of this expression in equa-
tion (10.),
H'—H 0°002561 | aT—cT?
be = raat 4i-* very Van
If we wish to found the calculation of the difference in height
of two points, where the pressures and temperatures of the air
have been observed, upon the supposition of a mean state be-
tween dryness and saturation, we must make 2 =}. But if we
have not an immediate determination of the quantity of aqueous
vapour on such occasions, we may obtain in particular cases,
by taking other circumstances into account, greater exactness
than by making « = 3. If, for example, rain falls throughout
the whole space between the two elevations, then a = 1. If
the two points are far distant from the ocean, and in a coun-
try known to be particularly dry*, it will be more suitable to
take less than}. In order to give a direct view of the infu-
ence of aqueous vapour on barometric measurement, I will de-
velope it further. The increase, which is occasioned in a differ-
ence of elevation computed on the supposition of dry air, by
‘the introduction of the consideration of the aqueous vapour,
according to equation (11.), is
aw
~ law
where w is written for
0°002561. oT_er?
(H’— H)
TP Py 10 :
If we neglect the square of this quantity, and make
(HH
P= P1lo—VU+kN),
which can only occasion an error of the order w®,
‘
H’—H
. 95 9/7 M1LeT™
eae — 102! +E) | 1077? -¢T™
* Such is the case in a great part of northern Asia, as we learn from
Adolphe Erman’s Reise, vol. ii. p. 67, where we have not only the fact, but the
geographical relations of which it is the consequence.
526 BESSEL ON BAROMETRICAL
and thence the influence of the aqueous vapour
H’—H
=a aS (H'—H) 1077 + #7) | 19aT—eT.. . (12)
If we assume the pressure in this formula at the height A = 1, |
or the height of the barometer there = 336,°905, and k =
0°00375, we find the quantities to be multiplied into a@ for dif-
ferent values of H' — H and T as they are given in the follow-
ing table.
T=2(r + 2).
H’-H. 0°. 10°. | 20°,
ve T T Hic
500 1:36 2°55 4-64
1000 2:90 5-41 9°83
1500 4-62 8-61 15-60
2000 6°55 12°18 22:02
2500 8-70 16°15 29°14
3000 11-10 20°15 37:02
From these numbers we may judge of the influence on the
result which may be occasioned by an uncertainty in the value
of « in any occurring case.
4.
Since the invention of Daniell’s Hygrometer and of August’s
Psychrometer, we have the means of ascertaining at all times,
with ease and sufficient exactness, the quantity of aqueous
vapour contained in the atmosphere. The observation of the
psychrometer at both elevations, in addition to those of the
barometer and thermometer, is readily made, and dispenses —
with any arbitrary supposition in regard to the moisture, as_
that of the thermometer does in regard to the temperature of
the air. I will, therefore, examine the rules of calculation
which are applicable in cases where the psychrometer has been
observed.
The psychrometer rests on the comparison of the heights r,
and + of two thermometers, one with a moistened bulb, and the
other with a dry bulb. If the greatest pressure which aqueous
vapour at the temperature ¢ can exert be denoted by ¢ #, and
the height of the barometer in Parisian lines by 4, the existing
pressure of the vapour
eg ee eae
~ 7! 336°905 (m—+)
where, if the value of r be positive, m = 640; and if negative
MEASUREMENT OF HEIGHTS. 527
(in which case the moistened bulb is coated with ice), m = 715.
This formula is given by August, the inventor of the psychro-
meter, and rests on the comparison of experiments with certain
physical considerations*.
The expression for ¢¢ for different values of ¢ is deduced by
August from observations on the pressure exerted by aqueous
vapour at different temperatures, employing a mean result,
which Kimptz has derived from the observations of Dalton, Ure,
Schmidt, and Artzberger. But these, with the exception of
the two first-named series, are so little accordant with each
other, that it may be doubtful whether all the four should be
combined. I prefer to adhere to the expression already given,
which Laplace derived from Dalton’s observations, to which
those of Ure approximate. It is my opinion generally that
formule which are well known and extensively applied ought ~
not to be altered until the necessity for the alteration becomes
decided, which is by no means the case in the present instance.
The researches since made by Arago on the same subject were
confined to the elastic force of aqueous vapour at very high tem-
peratures, and we cannot be sure that a formula of interpolation,
which represents those satisfactorily, is applicable in much lower
degrees of temperature.
By applying Laplace’s expression, we obtain the pressure
exerted by the aqueous vapour contained in the atmosphere ac-
cording to the formula which has been already given.
| (7 ne i) b,
Fee tre
m— 7;
Pp, = 00064707 .10%% —¢°77 — 0:0016562
and if we divide it by
| (p,) = 00064707 . 1077 ~°”,
or by the pressure which the vapour would exert if the air were
saturated with it, we obtain the proportion denoted above by a,
thus:
atr,—cr?
(13.) Beare = 02455 a Se SSRI
10¢7-°¢ m— t, 10¢7-¢7
To facilitate the calculation of « I subjoin a table, the first sec-
tion of which is for all values of ¢ from — 20° to + 30°, con-
log 10°'- °" = ft,
* Poggendorff Ann, der Physik, vol. Ixxxi. p. 69, and vol. xc. (xiv. of the
new series), p. 137.
528 BESSEL ON BAROMETRICAL
and the second section
0°2457
log : 10-2#+e? — Ye.
We obtain thereby
log A=fr,—fr
log B = log A + Wr, + log (r — 7) + log 4,
and «, which is sought, = A — B.
ip ft. Yt. Es ft. yt.
—20°/ 94155] 9, | 71086 |, |+5°| 01383 | |. | 64493 | |
—19 | 94459 | || 70788 5 | 6 | 01656 Bs + | 64227 | as
—18 | 94762 7-491 | 7 | 01927 6:3963
302 | 296 | 271 264
—17 | 9:5064 7.0195 8 | 02198 63699
300 295 | 269 262
—16 | 9:5364 69900 9 | 02467 6:3437
299 293 «| 268 261 |
—15 | 9:5663 69607 10 | 0-2735 63176
298 292 266 260
—14 | 9:5961 69315 11 | 0-3001 62916 |~_ |
297 290 | 265 258
—13 | 9:6258 68925 12 | 0:3266 6:2658
~~ | 295 " | 290 264 257
—12 | 9:6553 6:8735 13| 0:3530|~ | 62401
294 288 | 263 256
—11 | 95847 | O 6:8447 ia 14 | 03793 | 3.5 | 62145 oe
4 4 vo
—10 | 9:7140 68160 15 | 0-4055 61890
292 285 260 253
—9| 97432 6°7875 16 | 0-4315 | ~ | 61637
290 285 259 252
— 8 | 9-7722 67590 17 | 0:4574 61385 | ~~
289 283 258 251
— 7 | 9:8011 6:7307 18 | 0:4832 61134
288 282 257 249
— 6 | 9:8299 67025 19 | 0:5089 6-0885
287 280 255 249
— 5 | 9:8586 66745 20 | 0:5344 6-0636
286 279 254 Q47
— 4| 9:8871 66466 21 | 0:5598 60389
284 278 253 246
— 3| 99155 | 0), | 6618s a 22 | 05851 | 9 | 60143 is
— 2| 99438 65911 23 | 06102 5:9899
282 276 | | 95) 243
— 1] 9-9720 65635 | 974 | 24| 06353 5:9656
280 | (6:5361 249 242
0 | 0-0000 bs — | 25 | o-6602 59414
279 | § 65842 | 272 247 241
+ 1] 00279 ahi 6°5570 a 26 | 0-6849 an 59173 | og
2| 0:0557 6-5299 27 | 0:7096 58934
277 270 245 239
3 | 0:0884 6-5029 28 | 0-7341 58695
275 _. | 268 | 244 "| 937
4 | 0-1109 6-476] | 29 | 0-7585 5:8458
o74 268 243 235
5 | 01383 64493 30 | 0-7828 5:8223
If we determine in this manner the values of « for two eleva
tions, they will seldom be found of equal amount; as the la
B33) =
MEASUREMENT OF HEIGHTS. 529
of the transition of the one to the other is not known, we
are compelled to decide arbitrarily, and it seems to me most
suitable to take the mean of the two values of « to be applied in
the calculation of the formula (11.).
5
It appears to me needful to examine more closely the dif-
ferent suppositions by means of which I have obtained the for-
mula (11.). The first assumption in all researches relating to
the pressure and density of the atmosphere at undetermined
heights, is that of its equilibrium. That this is not strictly cor-
rect, is not now said for the first time. Its incorrectness is shown
both in the oscillations of the barometer around its mean height
at each point of the earth, and in the difference of this height
at different points strictly at the level of the sea. The know-
ledge of this difference was first obtained by an investiga-
tion by Adolphe Erman in 1831*, in which he showed, partly
from his own observations made in his travels round the earth,
and partly from the observations of others in Northern Asia
and America, and on board the Russian corvette Krotkoi com-
manded by Captain Hagemeister, first, that in the zones of
the trade winds, the barometer stands higher at the boundary
most distant from the equator than at the boundary which is
nearest to it; and secondly, that the mean height of the baro-
meter is different in different meridians. The first result rests
on observations collected in passing eight times through the
gone of the trade winds; and has since been corroborated in
Herschel’s astronomically-memorable voyage to the Cape of
Good Hope. ‘The second result rests on a comparison of ob-
servations made in the Atlantic and Pacific Oceans; the differ-
ences amount to several lines, and leave no doubt that the mean
height of the barometer at the level of the sea is different at
different points of the earth’s surface, and depends on the geo-
graphical latitude and longitude of the place.
_ The oscillations of the barometer, which may be regarded as
accidental, must cause single barometrical determinations of a
difference of elevation to deviate from the mean of several de-
terminations; but the mean diversities, which depend on the
longitude and latitude, if not known, must produce errors,
which will not disappear in the mean even of many observations,
* Poggendorff, Ann. der Physik, vol. xcix. (xxiii. of the new series), p. 144,
530 BESSEL ON BAROMETRICAL
except in the case when the two points, of which the difference
of elevation is to be measured, are in the same perpendicular.
It follows, from the knowledge we have obtained of these diver-_
sities, that barometrical determinations of the difference of ele-
vation of two points, even if resting on observations repeated
for years, remain the more doubtful the more distant the points
are from each other. If we imagine surfaces surrounding the
earth in which the mean pressure of the atmosphere is equal,
then all we obtain by the barometer is the determination of dif-
ferences of elevation relatively to these surfaces; but whether —
the surfaces at which the two points are situated differ more or
less from parallelism with the surface of the earth, remains
wholly unknown to us, whilst we are ignorant of the function
of longitude and latitude which determines their relative posi-
tion. This opens a new view in regard to observations on the
pressure of the atmosphere; we have to examine for all points
of the earth the height of the [atmospheric] surface at which a
determinate [mean] pressure is found; but we cannot as yet
determine more nearly, the amount of uncertainty arising from
the assumption of this height being everywhere the same.
Also the uncertainty, arising from the oscillations considered as
accidental, cannot be given more nearly; and even if, for the
purpose of learning them more correctly, we were to make long-
continued observations at points at different elevations, the dif-
ferences which might appear could still only be regarded as
caused by the combination of these causes with other as un-
avoidably erroneous assumptions.
The constitution of dry air has been assumed such as it was
supposed to be at the time that Biot and Arago obtained for its
density the determination given in the first section. If the pro-
portion of oxygen were to be altered by x hundredths, its den-
sity would be changed by x . 0:001337, and a difference of ele-
vation computed under the assumption of D= would
1
10466°8
require to be altered in the ratio of 1: 1+.0°001337. Hum-
boldt and Gay Lussac, in nineteen days, between the 17th
Nov. and 23rd Dec. 1804, found no sensible alteration in the
proportion of oxygen, which seems to justify the assumption of
a constant proportion in the two principal constituents of the
atmosphere.
In the meatime, however, it is known that Dalton has con-
MEASUREMENT OF HEIGHTS. 531
sidered it probable that each of the constituents of the air is
compressed by its own superior strata alone, and not by the
whole superincumbent mass; consequently, that at different
heights each constituent possesses the density which it would
have if it existed alone. Hence it must result, that the propor-
tions of the mixture would vary with the altitude, and the rela-
tion of the atmospheric pressure at different heights would differ
from the older assumption adopted in Sect. 2. Barometrical
measurements of heights have been proposed as a means of de-
ciding between the two assumptions. The attention, which the
opinions of so eminent a physicist as Dalton deserve, requires
that I should follow out his supposition also.
The formula (6.) then is no longer correct for the air generally,
but only for each of its constituents ; it applies to each of these
according as the specific gravity of each is taken instead of that
of the atmosphere itself. If we call the pressure exerted by
the three constituents of the air, at the elevations h and h,
=P; Pj P,, and p', p/, p,|, and their specific gravities D d, Dd,
D d,, and if for brevity we denote by U,
eto Ei ete
Bil Sylysprkyd
then, according to formula (6.),
gp =p .10—%4
—Ud
p= p10 4
—Ud
Pil = Py 10 ‘i
and as
P=p+p,t+ Dy
Pi= pl + p/ + pil
p=vP; p,=v,P3 py, =v,P;
therefore
P= Pv. 10-974 v,.10- U4 4-4,.107 0%}
or
P= P.107Y {9,108 4-9 4.9, 1080-4) 4» 19UA-4) }
instead of which, we may write for brevity
Me eg. 2 (14.)
The quantity , at all accessible elevations, differs little from
1, as is shown by the following table, calculated according to
the values given in the 1st Section, viz.
S32 BESSEL ON BAROMETRICAL q
v = 0°78605 d =0°9711
v, = 0°21325 d, = 1°1048
v,, = 0:00070 d,, = 1°5260
U. yp. Log y.
0-0 1:6000000 0:0000000
G1 10006840 0365
0:2 1-0008334 1148
0:3 1-0007444 3232
0-4 | 1:0013135 5701
0°5 1-0020375 8840
If the relation of P’ to P has been obtained by observation,
and if the U proportionate to the difference of elevation be
sought, this table shows that, according to Dalton’s views, it
will be found somewhat greater than according to the older sup-
position, and in a proportion given by the table, the numbers of
which progress nearly as the square of the argument. If we are
willing to be content with an approximation which scarcely dif-
fers from the truth in all cases of probable occurrence, we may
develope (14.) further. We have
P
U = log 5 + log;
and if for log y we write the first member of its development, or
: |
i {o (l—d)*? +, (1 —d)"+ 2, (1— a,)° } = U?.0:003675,
and for U, its expression,
H'—H wa Biitg H'—H
Fa+kT) FP TV +e
The alteration which the adoption of Dalton’s view of the con-
stitution of the atmosphere produces in the values of H! — H
calculated on the older supposition, is therefore
, (=H
Ui+ kT)
and if H' — H = n. 1000 toises
n*.OF-391
= a Teer . ° . . . . . (153)a
This difference is much too small for us to hope to obtain by
barometrical measurements a decision for or against the reason-
2
0°003675.
0003675,
MEASUREMENT OF HEIGHTS. 530
ing on which it is founded: it is far exceeded by the constantly
existing disturbances of the equilibrium of the atmosphere, as
well as by the uncertainty of the law (applied in the 2nd Sect.)
of the variation of temperature between two heights at which
the thermometer has been observed. Even the geometrical
measurement of the difference of elevation could scarcely be made
with sufficient certainty to determine a quantity so small as that
upon which a decision between the two assumptions would de-
end.
4 6.
The necessary following out of Dalton’s supposition, in its
relation to barometrical measurements of altitude, gives me an
occasion of expressing my own view of this much-discussed sub-
ject. The supposition rests principally on the comportment of
aqueous vapour when mixed with air, and when by itself.
A fluid brought into an empty space gives off vapour until
the vapour has attained a density dependent on the temperature
of the space. Dalton has determined this density, in the case
of the vapour of water, for all degrees of temperature between
freezing and boiling water; and has shown by indubitable ex-
periments, that the vapour attains precisely the same density
when the space is occupied by dry air, of any density whatso-
ever, as when it is originally a vacuum. Every attempt to in-
crease the density, when the temperature remains the same, fails.
If the space, when filled with the densest vapour consistent with
the temperature, be contracted in the ratio of 1 : 1 — », a part
of the vapour, proportioned to the whole as 2: 1, is converted
into fluid: precisely the same change takes place if a space filled
with the densest vapour consistent with the temperature, and
containing air of any density whatsoever, be contracted in the
same proportion: in such case the air undergoes no correspond-
ing change, but merely an increase of density in the ratio of
1—n:1. This is the pure result of Dalton’s experiments.
They show a difference between vapour and air, assigning to
yapour a maximum of density dependent on temperature, which
does not exist in the case of air. They show further, that the
forces at the surface of the fluid, which cause it to rise in va-
pour in a vacuum, are not counteracted by the pressure of the
air in contact with it. In respect to the latter point, I may re-
mark that Poisson derived from phanomena of another class,
i, é. the capillary, that the density at the surfaces of fluids is in-
VOL. II. PART VIII. 2N
534 BESSEL ON BAROMETRICAL
finitely small. Whether all gases have a maximum of density
dependent on temperature (as is known to be the case with car-
bonic acid gas), so that they only differ from vapours by the
amount of the maximum (or specifically), cannot at present be
decided, and is not here touched on.
So long as vapours have a less density than the greatest
they can attain in the respective temperatures, they are not
physically different from gases; they follow Mariotte’s law; and
Gay Lussac has shown that they possess the same expansibility
by temperature which is common to all gases. So long, therefore,
as they have not attained the maximum of their density, they
comport themselves, whether alone or mixed with gases, pre-
cisely as gases do. A pressure does not produce a change of
state in them any more than in gases: that change first takes
place, equally whether they are mixed or unmixed, whenever an
attempt is made to cause their density to exceed its maximum.
This can be done by lessening the space in which they are con-
tained, in which case the gases, if present, remain unchanged in
consequence of their unlimited compressibility. If, further, a
space is filled with a gas which exerts a pressure p upon an unit
of surface, the introduction of another gas, which if alone would
exert the pressure p, on the same unit, produces no other phy-
sical consequence than that this unit now sustains the pressure
p+ p,; but it would sustain precisely the same pressure, if, in-
stead of the second gas, a vapour were introduced exerting when
alone the pressure p, Lastly, different kinds of gases mix with
each other, as well as with vapour, in any arbitrary propor-
tions.
There is therefore throughout, no difference between the phy-
sical comportment of a mixture of two gases, and of a gas and
vapour; consequently the circumstances of the second mixture
can teach us nothing which we might not learn from those of the
first. The comportment of the mixture of air and aqueous va-
pour, which Dalton’s experiments have fully manifested, is not,
therefore, more instructive than that of any mixture of two
gases; and a theory which could not be constructed upon the
latter, cannot find support in the former. It could not, there-
fore, have been deduced from the comportment of a mixture o
vapour and air that the air does not press the vapour, unles
for the presupposition that pressure changes vapour into fluid;
for this presupposition, however, there is no justifying fact.
MEASUREMENT OF HEIGHTS. 535
According to this view of our knowledge of vapour, no ground
is afforded for the hypothesis that vapour is compressed only
by vapour, and not by air; and we lose at the same time the
analogy for the similar comportment of the mixture of different
gases. Dalton has adduced, in further support of his supposi-
tion, a circumstance which is independent of the experiments
on aqueous vapour, viz. that a specifically heavier gas mixes
with a lighter one, even though the latter should be placed
uppermost. It is true that Dalton’s hypothesis explains this
fact; but it cannot be maintained that the fact is inconceivable
apart from the hypothesis. The ascent of fluids in tubes which
are wetted by them might, for example, be explained by the
assumption that gravity exerted its action but imperfectly
within the tubes; but we know the true explanation is
different. If I do not mistake, the small amount of the altera-
tion which the constitution of the air undergoes in a space in
which there are many persons, whose breathing must diminish
the oxygen and increase the carbonic acid gas, has been ad-
duced in support of Dalton’s views, as the oxygen must by pre-
ference replace itself from the outward air, and the carbonic
acid gas must pass to the same in preference, if the several con-
stituents of the interior air are compressed only by those of the
same nature without. The first experiments of the kind were
made by Humboldt and Gay Lussae in one of the Parisian thea-
_ tres*; and these gave a diminution of the oxygen of 0:007, with
an imperfectly determined content of carbonic acid gas. Dalton
_ subsequently repeated experiments of a similar kindy in spaces
filled with numerous assemblages, and found the oxygen =
0°20325, whereas in free air he found it 0:2090; there was also
more carbonic acid gas than in the free air, and one case, in
which it was determined, the amount was 0:01. These experi-
ments do therefore show actual alterations in the constitution of
_ the air; and it only remains to examine whether they are Jess
“thm the alterations to be expected according to the older views.
e first-mentioned experiments do not appear to have been
made for the purpose of testing these; and all are deficient in
the exact data requisite for founding a calculation; i. e. the
ubic contents of the room, the air of which was examined,—
the number of persons, and of the lights, and the strength of
* Gilbert’s Ann. der Physik, vol. xx. p. 88.
+ Phi. Trans. 1837, part LI. p. 363.
2N2
the latter,—the communications with the external air,—and the
temperature at different heights. Nor is the case examined
sufficiently simple to be a fit subject for strict calculation. But
to obtain an approximate view, I have proceeded from the rule
adopted in Prussian towns, which prescribes that in buildings,
which are to contain assemblages of people, not less than 100
cubic feet shall be allowed for each person. I have further di-
minished this space by one-third, and have taken Davy’s expe-
riments*, which show that each person diminishes in one mi-
nute the nitrogen by 4°9 cubic inches, and the oxygen by 19°5
cubic inches, and increases the carbonic acid gas by 15:4 cubic
inches. If we assume that the diminution of 9 cubic inches is
compensated by the necessary inpressing of the external air,
on account of the continual augmentation of temperature which
takes place, we find from these numbers that the proportion of
the three gases of the atmosphere given in the first article, viz.
536 BESSEL ON BAROMETRICAL
v = 0'78605
v, = 0°21325 -
v, = 0:00070
will be altered in the course of an hour to
v = 0°78719
v, = 0°20405
v, = 0°00875.
If we deduct from the mixed air the carbonic acid gas, the
proportion of the two other gases is at first as 0°7866 : 0°2134,
and at the end of an hour as 0°7941 : 0°2059. The calculated
result is not so dissimilar from the experiment as to afford
a conclusion that the supposition on which the calculation is
founded is incorrect. It would, indeed, seem as if the com-
parison might rather be alleged against Dalton’s view than
in favour of it. I believe that if we desire decisive experiments
on this point, they would most easily be obtained by observing
the ingress, from pressure, of atmospheric air into a closed
space not air-tight, and filled either with one of the constituents
of the air, or with both mixed in a different proportion from
that in which they exist in the atmosphere. In order to sim-
plify the experiments, and to obtain most conveniently the bases
of their calculation, the space ought not to be the interior of a
building, but that of a bell glass.
* According to Gilbert’s calculation, Ann. der Physik, vol. xix. p. 312.
MEASUREMENT OF HEIGHTS. 537
If no special hypothesis be made as to the molecular consti-
tution of gases and vapours, it is plain that a particle of gas
must press an adjoining particle of similar or dissimilar consti-
tution with equal force (i. e. with the same force with which it
endeavours to expand). Without a special hypothesis Dalton’s
view contradicts the fundamental propositions of aerostatics. But
such a view cannot be maintained unconditionally until proof
is adduced that no supposition, such as is here referred to, is
mathematically possible. On the other hand, the view which I
have developed of the comportment of vapours, does not require
to be justified by a special hypothesis. We may regard, as the
immediate result of experiment, and as the distinguishing mark
between vapours and gases, that the density of vapours cannot
be increased beyond a certain degree dependent on temperature.
But if we desire to enter likewise on the molecular constitution,
it is easily conceivable that there may exist a distance between
the ultimate particles of vapours, in which their attractive force
is equal to the repulsive force arising from the temperature, so
that every decrease of distance renders the attractive force pre-
dominant, and consequently unites the particles.
he
If, notwithstanding what is here said, I have followed Dal-
ton’s view in Sect. 5, in respect to the dry constituents of the
air, I can the less omit to examine the deductions from it in re-
gard to the aqueous vapour. This examination must also be
pursued, if we desire to learn whether the observed distribution
of the aqueous vapour in the atmosphere can be made to tell
for or against Dalton’s hypothesis. I will, therefore, assume
- with Dalton the aqueous vapour in the atmosphere to be pressed
_ only by its own higher strata, or to form an atmosphere by the
equilibrium of its own parts alone. The change of the pressure
of the atmosphere of vapour, corresponding to the increase dx
_ of the elevation z, is according to formula (4.),
_ _ (g) 864.8 ( a )' .
PPi 886905. \a-a) 07?
| or, according to the notation subsequently introduced,
| D)
dp, — wiD aX.
Its density @, until it reaches its maximum, follows Mariotte’s
|
|
538 BESSEL ON BAROMETRICAL
law, or corresponds to equation (3.), which, for the present
case, is
§.E=p,Dd,;
to which must still be added the condition requisite for equili-
brium, that the @ resulting from this equation shall at no eleva-
tion exceed the maximum of density corresponding to the tem-
perature ; or, according to the notation in Sect. IV., that
P, 2 >t.
If we eliminate 8, we obtain
ETS.
P; TR we ee Le ee
a similar differential has already been integrated in Sect. 2,
assuming the variation of temperature between the two heights
at which it was observed, to be that supposed by Laplace. With
this assumption, it follows that
dX 2k
Ligeakd 040 Goa
and thence the integral, reckoned from the elevation h, where r
is the height of the thermometer, and P, the pressure of the
aqueous vapour, is
P,_ d, 2k
le AT ph me te
or
aT Da
oO, SB AD Geo et ee ee
If we assume the pressure P, at the elevation h = «$7, where
a cannot be greater than 1, the conditions to be fulfilled require
that for each value of ¢,
ee La ee
agdr.1l0O =— ot;
or
d, 2k —d, 2k
agv.10 “ #2 ot.10 4 7;
and if for $7, and $¢, we substitute the expression (9.),
d, 2k p d, 2k
ced =7*) Tog ota 100 \Wisi —a) tee
If we suppose ¢ to decrease without limit with increasing eleva-
tion, it would attain a negative value, for which, even with the
smallest value of «, the conditions would cease to be fulfilled ;
MEASUREMENT OF HEIGHTS. 539
but we must not hence conclude Dalton’s assumption as not re-
concilable, under all circumstances, with the existence in equi-
librium of an atmosphere of aqueous vapour of which the den-
sity is always a positive quantity. The decrease of ¢ does not
go on indefinitely, but only as far as the value which it pos-
sesses at the limit of the atmosphere; the formula (9.), which
expresses the condition, is merely an interpolation formula, and
has no justification beyond its more or less satisfactory accord-
ance with Dalton’s experiments made between ¢ = 0, and ¢
= 10)°.
If we take the logarithm of the two quantities, between which
the conditions apply, it follows that
9
lo a =(4. ae ate(r +d) (7 — 2);
and we also know that a 1, so that log « must not be positive.
Hence it follows that the conditions may be fulfilled, or that
the atmosphere of aqueous vapour is possible; also that the
value of « (<1), which determines its density at the elevation h,
remains arbitrary, if
2
= ota —e(r +i) eel ewieee ea
which must be the case up to the limit of the atmosphere ; fur-
ther, that in the opposite case, if even at the height h,
a oes aH. MP Bhi (6)
the existence of an atmosphere of aqueous vapour in equilibrium
is possible ; but its density, at the elevation h, is limited by the
condition that « must be less than
d, 2k
a aate(rt)) (7-9. 2. (21)
_ for the value of ¢ at the limit of the atmosphere. In a parti-
cular case of the decrease of temperature, the atmosphere of
aqueous vapour may be at all elevations as dense as the tempe-
rature permits; this case requires that
dp, a dX dot.
ie) hie. Ey
or, under the supposition of the customary expression for ¢ ¢,
that
540 BESSEL ON BAROMETRICAL
au dX = (a—2ct) (1+ kt) dt.
Hence follows by integration,
k
a(r —2) +(e) (2— £2) —sek (89 — 8) = & (XH);
for which we may also write
x — H = 54 (e-2¢ r) (1+ kr) (r—2)
— (G-e+2ckr) (—#'— Lek al = (223)
If we introduce into this equation the values of I, d, a, c, k
already employed, we obtain the law of the decrease of tempera-
ture, which, on Dalton’s supposition, is alone reconcilable with
an atmosphere everywhere saturated with aqueous vapours.
X —H = 424T0 (1—r .0:00447) (1 + 7.0°00375) (7 — 2)
+ 0™15 (1—7.0°0463) (r —¢)? — 07-003 (7 —Z)*.
If, further, according to Sect. 2, we put
2k H'— 1
i t—et “14+kT’
and designate by (¢) the value of ¢ at the extreme limit of the
atmosphere, the condition (19.) becomes’
H'-H oT! 1 4 eT) {a—c (r+ ()}
r—T od,
> {4247-0 —0T-95 (x + (t))}(1 + KT).
The actual change of elevation, which produces a decrease of 1°
in the height of the thermometer, is much less, or about
= 85 toises; this is irreconcilable, under Dalton’s supposition,
with the saturation of the atmosphere with aqueous vapour at
the surface of the earth. But if the condition (20.) be fulfilled,
or if
H'—H
—r!
< (424T-0—1:9 r) (1+4T);
then, according to formula (21.), after substituting in it the ex-
Qk
pression for —,
mes or: tratetr+()) be-O),
T_T — —————
MEASUREMENT OF HEIGHTS. 54]
or
u HH
(4k) 7 log « < { ——
— [4247-0 — 0795 (r + (2)] (14h 7) | Cray
whence follows
1
— Fog a. (1+)
t—(t)< ! ; "
[424-0 —0°95 (x + (¢))] (1 + 4T)— = a
ao
If, then, we know both the last members of the denominator and
a, we can compute by this formula a value of r—(¢), which, con-
tinuing Dalton’s supposition, exceeds the difference of tempera~
ture between the elevation / and the limit of the atmosphere.
fh
If we take, for example, — = 85 toises and T = 0, and sup-
posethe atmosphere at the surface of the earth to be half saturated
with aqueous vapour, we obtain approximately 7 — (¢) < 135,
which is scarcely equivalent to the usual decrease of temperature
in 1200 toises, not to speak of the limit of the atmosphere ; if
t—(t)= n .13%5, the extreme value of 2 = 47. Dalton’s sup-
position is therefore only reconcilable with a very small quan-
tity of aqueous vapour in the atmosphere, and not with that
which really exists. If we could, therefore, regard as correct
the pre-supposition of the equilibrium of the atmosphere on
which we have proceeded, the presence of a considerable quan-
tity of aqueous vapour in the atmosphere would be a conclusive
argument against Dalton’s supposition. But this equilibrium
never really exists, and I am indebted to Professor Neumann
for the remark, that the density of aqueous vapour ascending
from the surface of the earth must be increased by the resistance
opposed to it by the air.
8.
Icome now to the examination of the supposition, that the
temperature between two elevations at which it has been ob-
served varies according to the law which has been assumed by
Laplace, Sect. 2. The equation between ¢ and X, which enounces
this law, as deducible from Sect. 2, is
oX—-H
se s
Prose
(l+ko*=(1 + ke) oa + (1 + kr’) . (23.)
_ But we have no reason to regard as unreal moderate deviations,
542 BESSEL ON BAROMETRICAL
in the transition of the temperature from r to 7’, from the rule (
prescribed by the equation. It remains, for instance, quite —
doubtful whether between the two elevations the true tempera- ’
ture may not differ from the value which would follow from the —
rule by a quantity amounting to one-tenth part of r—7/. It is
not superfluous, therefore, to investigate further the influence of
such possible deviations.
I will suppose that the true value of
me Apaial
Linger A ype a. a ey
“ 1+kt
where ¢ denotes the height of the thermometer at the elevation a,
corresponding to equation (23.), and « is a constant coefficient,
greater or less according to the amount of the deviation from the
4
: F we. 3 :
law. This expression of fF 8 80 chosen, that it agrees with the —
previous one at the two limits, and that the deviation of the
temperature which it supposes attains its maximum =a (r — 1’)
somewhere about ¢ =4(r +7') orv =i (h +h‘). We obtain
thence
fs ht dv _ — t) (¢-—7’)
(, + =) reat 41- tT— Tv a=
and the integral taken from / to fh’,
en ~= ak(r—a)h
HW —H 2
=the sete} , (408
It does not seem probable that in any case which is likely to
occur the value of a would be i a within any very
; if it should reach either of
narrow limits, as for instance + + 63
these limits, the consequent correction in the resulting difference
of elevation, according to formula (23.), would be
ad galrol alse
= T4kT ° 4000°
So, for example, for a difference of elevation of 1000 toises, for
which + — 7’ is usually 12°, the correction would be about
+ 3 toises. We should be the less inclined to assume that @
must necessarily be very small, as it should not be overlooked
ae
MEASUREMENT OF HEIGHTS. 543
that the temperature of the air observed on a plain or on a height
is always affected by the temperature of the surface of the earth.
Hence we see, were it from this cause only, how little fitted ba-
rometrical measurements of height are to determine questions,
the answers to which depend on small differences between theory
and experiment. Possibly observations made late at night might
agree better together than those made in the day when the
surface of the earth is heated by the sun.
5
It is known that Gay-Lussac found the value here denoted
by & = 0°00375, by experiments agreeing almost perfectly with
each other; and that Dalton found exactly the same result
from his experiments. The object of both these great phy-
sicists was to determine directly the increase which an unit of
yolume of dry air undergoes, when, the pressure remaining equal,
the temperature is increased from freezing to boiling water. The
accordance, not only of the several experiments in each series,
but also of the results of the two series, has caused the determi-
nation of k=0°00375 to be generally regarded as one of the most
certain that we possess: and there would be no reason for doubt
respecting it at this period*, had it not been for recent experi-
ments of Rudberg’s, distinguished by the great care with which
they were conducted, particularly in drying the air employed,
and which give a considerably smaller value for 4, i. e. 0°003648.
Any later determination, contradicting an older one which has
become in a degree classic by its intrinsic weight and by
its general acceptance and use, ought to be accompanied by
a strict examination of the older determination ; and it is only
when such criticism shows grounds for distrusting the older,
that the more recent should be deemed deserving of preference.
Rudberg has not entered into such a criticism. As the dif-
ference between the two values of k cannot be explained by
the accidental errors of the experiments, as is shown by the
* I have myself determined, from my own observation, the value to be em-
ployed instead of k in computing astronomical refractions, and have found it
0°0036438 ; but this value must be different from that of k, and ought to be
less, as shown in the 7th part of my observations, page xi. The research might
have been spared had I possessed observations of the quantity of aqueous va-
pour in the air at the time of each observed refraction. It remedied the diffi-
ty as far as could be done in the absence of a knowledge of the actual acci-
dental state of the atmosphere on each occasion. But it is to be regarded as a
contribution to the knowledge of astronomical refraction, and not as a determi-
nation of the value of k.
544 BESSEL ON BAROMETRICAL
agreement of the partial results in the earlier as well as in the
later series, it indicates a constant error, and there can be there-
fore no propriety in taking the arithmetical mean of the two de-
terminations. I see no other course at present than to employ
both, and to await a future decision on the differences which
may result therefrom.
10.
Having gone through the different assumptions involved in
formula (11.), I return to this formula, and will now show its
application to barometrical measurements of height.
The pressures P and P’ at the elevations 4 and A’, are de-
ducible from the barometrical observations there made. If we
denote one of the heights of the barometer by 4, the temperature
of the mercury and of the scale by which the height is measured
by ¢, and assume that the scale is of brass as is usual, we obtain
the mass of mercury supported by each unit of surface
53242 +¢ 5550
* 53242 + (t) © 5550 + 2”
where (é) signifies the normal temperature of the unit of measure
of the barometer-scale, and where the unit of volume of mercury
at the temperature of melting ice is taken as the unit of the mass.
This mass presses in proportion to the force of gravity to which
it is exposed; or with the force
a 2
Olas.
and the pressure which it exerts is the product of both divided
by the Sele unit of intial (=336!:905). Thus we obtain
53242 + ¢ 5550,
sarees ag a +h 53242 + () 5550 + 2’
and its Briggs’s logarithm in formula 11, with sufficient approxi-
mation,
336°905 (53242 + (?) )
— log b— log Kisser node
1 1 Qe
ae he ae ind sous | oe
If we put for a the geometrical mean of the two semi-diame-
ters of the earth (log 6°5140838, Ast. Nach., 333), and for (¢)
the normal temperature of the French standard foot = 16°25,
then
MEASUREMENT OF HEIGHTS. 545
log P = log b — log 337-008 —¢ . 0:000070095
We obtain thus
H
~ 3760707
H'’—H
3760707
where log J, and log 4/ are substituted for brevity for
log b—t . 0:00007 and log J/—¢’.0°00007. Further, we obtain,
without sensible error,
P
log po log 6, —log 6) +
Vv (PP) = vee,
If we introduce log 4, and log 4/ in (11.), and put 7 for I’,
this equation becomes
(y) (H! — )
as poz
log b, — log 6) = i +k)
; 111+ kT) Lh 0°863 eae
sf ~ (g).3760707 Vv (b'6/) ;
If we change (gy) in the denominator of the second member
into 1, which has no sensible influence, and if we take for «
the half sum of its values at the two points of observation
=4(«+ a’), then the quantity within brackets is
339°17 —kT Deez) 108 ™
LL RCo gee
400°17 V (6,6)) © 39917 —kT
If we designate thenceforward
400°17
1. + kT) S557 — kT i
472:67.10°' —°?
39917 —kT uy WY
the equation gives
log 6, — log b/ Vv
H —H =—2—__=++_- —_____
(9) ._ @t+2/)W
Te Vv (,6/) 3
as
: itt ah Te ah ney ti Rl? he
a ~ ath ab Tat 4 Bil athe
hn? =f? _ logb,—log bd} V
74 aes + a —_ (9) .y : _ @ +a) Ww . (25.)
546 BESSEL ON BAROMETRICAL
This is the most convenient form of the equation (11.) for use. —
It cannot be abbreviated further without giving up the power of |
bringing into the calculation the quantity of aqueous vapour
contained in the atmosphere, as shown by the psychrometer at |
each station. The tables for facilitating the computation may
also be so arranged, as to render quite inconsiderable the labour
of taking the aqueous vapour properly into account.
11.
I will now explain the auxiliary tables. They are construct- —
ed logarithmically, like the small and very convenient tables
of Gauss; but are rather more extensive, because they permit the
result to be computed on either supposition of k = 0:00375 or
= 0°003648, and also because they enable the influence of the
aqueous vapour to be taken into account more completely than
is done by the formula of Laplace.
If we denote
log {log 6, — log b/} by B,
1
pete ULES es eee S 1
Pa (aaaCeTTNT ahlinin on
v (6, 6/)
1
ces NLVPA I) Oe ane nn, oe
(9) A
‘ h!? he
then is the logarithm of he
a a
= B+ logV + log V' + logG.
Table I. contains the value of
9397°74 .400°17 (1 + kT)
399:17 —kT
calculated in the first column for k = 0°00375, and in the last
column for k = 0:003648. Its argument is2'TT=++7, The
second column contains
log V = log
172-67 10°" °
B99 17—k'T ”
a single column is sufficient for log W, as the difference in the
two values of k does not influence the last decimal. If we de-
duct from the tabular value of log W the half sum of the loga-
rithms of 4, and 6/, the remainder is the logarithm of
(a + a’) W
v (6, 6/) 7
log W = log
MEASUREMENT OF HEIGHTS. 547
yee @ =a’ = +; if a different ult be supposed for «
and a!, log (# + al) must be added. Hence is obtained the ar-
ipsent of Table II., which contains log V’. Table III., with
the argument ¢ = the latitude, contains
1
log G = log (—9-0026967 cos 2 e”
which formula rests on the value of the increase of the length of
the seconds pendulum from the Equator to the Poles, deduced
by Mr. Baily from the combination of all the known pendulum
observations. Trans. Ast. Soc. vol. vii. page 94.
The sum of B and of the numbers taken from the three Tables,
2
is = log 4 —h—-——+ | ; to obtain from hence h! — h,
12 2
We must add = and subtract ~ which are both given by Table
IV., which is to be entered with /! and with h.
It may be convenient to recapitulate the notation and rules:
b, U' are the heights of the barometer, read off on a scale divided
into Parisian lines.
t, v' are the heights of the centesimal thermometer attached to
the barometer.
t,t! are the heights of the centesimal thermometer in the free
air.
_@, a! are the degrees of saturation of the atmosphere with aque-
ous vapour.
The calculation of the difference of height of the points where
these observations have been made, requires
1. log b, = log 6 — ¢ .0:00007; log b/ = log d' — #'..0:00007.
2. B= log {log , — log d/}.
3. log V and log W, which, with the argument r + r/, are to be
taken out of Table I.
4. log V', which is given in Table II., with the argument
(a+ a)W
“WV (6, 8]
5. log G, which is given in Table III., with the argument of the
latitude = ¢.
6. The log of the approximate difference of height = B + log V
+ log V' + log G.
log
548 ON BAROMETRICAL MEASUREMENT OF HEIGHTS.
7. The true difference of height is the approximate, + the differ-
ence of the two small corrections which are obtained
from Table IV., with the arguments of the greater and —
lesser height.
I take, as an example, one of D’Aubuisson’s measurements of
the height of Monte Gregorio, above a point at an elevation
h = 128°3 toises (Traité de Géognosie, i. p. 481.). There be-
ing no observation of the psychrometer, I take « = a! = 3.
fe} fo)
i= 329-013, fo LOIS Ds Fie L995
6! = 268°215, 2105, gi =. 9:9
log Gi Polls ft = 1395 log b, = 25 isse half
log b! = 2°42848;. 7.#= 73°5; logd/ = oar geetinere
log = 0°088075
B = 8-94485
Table B=8'94485
I. +7! = 29°85 (k=0:00375) logV =3-99782 logW=0-0397
Il. Arg. = 7°5679....... logVi= 161 *.. 2:4718
III. (Jee. ig ee ae logG = —2 7°5679
2°94496
Approximate height ....... 8797-54
IV. h'= 10078, h=1283 ..... 40°31
hi — h = 879785 .
D’Aubuisson himself computes the height 87977; from Gauss’s
tables we should have 879763. Ifk be taken = 0:003648, we
have 17-26 less. If we take the air as dry, we obtain 3724 less; ;
and if as saturated, 37-28 more. :
BrEssEL.
BESSEL ON BAROMETRICAL MEASUREMENT OF HEIGHTS. 549
TABLE I.
Argument = r + 1’ (Centesimal scale.)
0-00375
log V.
395747 | 9°3501 | 3:95793 20° 3:99014 398971
3°95832 | 9°3646 | 3:95875 21 | 3:99093 | 9:9229 | 399048
3°95916 | 9°3792 | 3-95958 22 | 399171 | 9-9362 | 3-99124
3°96001 | 9:3937 | 3:96040 23 | 399249 | $:9495 | 3-99200
396085 | 9°4083 | 3:96122 24 | 399328 | 9:9628 | 3-99277
399353
3'99428
399406
3-99484
3°96203
3°96285
9:4227
9°4372
396169
3°96253
396337 | 9°4516 | 3-96366 27 | 399561 3°99504
396420 | 9:4660 | 3:96447 28 | 3:99639 399580
396504 | 9°4803 | 3°96529 29 | 399716 399655
3°96587 | 9 4946 | 3-96610 30 | 3:99794 399731
3°96670 | 9°5089 | 3-96690 31 | 3:99871 399806
3-96753 | 9°5232 | 3:96771 32 | 3:99948 399881
396836 | 9°5374 | 3-96851 33 | 4-00025 3°99956
396918 | 9°5516 | 5:96932 34 | 4:00102 400031
3°97012 4:00179
397001 | 9:5657 35 400106
3°970383 | 9-5799 | 3:97092 36 | 4-00255 400180
3°97165 | 9°5940 | 3:97172 37 | 4:00332 4:00255
400408
400484
4°00329
400403
3°97247
3°97329
96080
9:6221
3°97252
3°97332
397411 | 9-6361 | 397411 40 | 4:00560 400477
397493 | 9:6500 | 3:97490 4] | 4-00636 400551
3°97574 | 9-6640 | 397570 42 | 4:00712 400625
3:97655 | 9°6779 | 3:97649 43 | 4-00787 400699
397736 | 96918 | 397725 400863 400772
3°97817 | 9°7956 | 3:97806 45 | 4:00938 400846
3-97898 | 9°7194 | 397885 46 | 401013 400919
397979 | 9°7332 | 397963 47 | 401088 400992
398059 | 9°7470 | 3-98042 48 | 401163 401066
398140 | 9-7607 | 3:98120 49 | 4:01238 4:01139
3°98220 | 9°7744 | 3-98198 50 | 401313 4:01211
398300 | 9-7880 | 3:98276 51 | 401388 401284
3-98380 | 9°8017 | 398354 52 | 401462 401357
398460 | 9°8153 | 3-98431 53 | 4°01536 401429
3:98539 | 98288 | 3:98509 54 | 401611 401502
Sa
401685
3°98619
9°8424 | 398586 55 401574
398698 | 98559 | 3:98663 56 | 401759 401646
3'98777 | 98693 | 398741 57 | 401832 401718
398856 | 9°8828 | 398818 58 | 4-01906 401790
398935 | 9:8962 | 3-98894 59 | 4-01980 | 0-4068 | 4-01862
_———_|
399014 | 9:9096
3:98971
401933
402053 | 0-4189
: VOL, Il. PART VIII. 20
550 BESSEL ON BAROMETRICAL MEASUREMENT OF HEIGHTS:
TABLE Il. TABLE III. TABLE IV.
Ul W /
Argument = Sire Argument = Latitude. eae ais
( Mise ¢
Height | —
Arg. log V’.| Arg. log V’.) Arg. |log V’.|| 4. |log G7] @. |log G’. ||h’and h.
186 | 8:03 | 468 110 | 48 |}— 12} 900 | 0:25
764 | 190 | 8-04 | 479 109 | 49 |— 16|) 1000 |031
7°65 | 194 |8-05 | 490 || 10 | 107 | 50 | — 20]] 1100 | 0:37
7°66 | 199 |8:06 | 502 || 11 | 106 | 51 |— 24]] 1200 | 0:44
7°67 | 204 |8-07 | 513 || 12 | 104 | 52 |— 28] 1300 | 0:52
7°68 | 208 |8°08 | 525 || 13 | 103 | 53 |— 311] 1400 | 0-60
11 |7°69 | 213 |8-09 | 538 || 14 | 101 | 54 |— 35)) 1500 | 0-69
14 |770 | 218 |}810 | 550 || 15 | 99 | 55 |— 39)| 1600 |0-78
17 |771 | 223 |}811 | 563 | 16 | 97 | 56 |— 43} 1700 | 0-88
22 17°72 | 229 |\812 | 576 || 17 | 95 | 57 |— 46} 1800 | 0-99
297 |7'°73 | 234 | 813 | 590 || 18 | 92 | 58 | — 50} 1900 | 1-11
34 |7°74 | 239 |8:14 | 604 || 19 | 90] 59 |— 54} 2000 | 1-22
43 |7795 | 245 |8:15 | 618 || 20 | 87 | 60 |— 57] 2100 | 1-35
T
7-55 | 154 17-95 | 389 || 0| 114] 40 20|| 100 | 0-00
7°56 | 158 |7-96 | 398 || 1 | 114] 41 16|| 200 | 0-01
7-57 | 162 |\7-97 | 407 || 2| 114 | 42 12|| 300 | 0-03
7-58 | 165 17-98 | 417 | 3| 114) 43 8) 400 | 0-05
759 | 169 |7:99 | 427 || 4 | 113 | 44 4| 500 | 0-08
7°60 | 173.|8:00 | 437 || 5 | 112 | 45 0|| 600 | 0-11
7.61 | 177 |8-01 | 447 || 6| 112146/— 41 700 |0-15
7.62 | 181 |802 | 457 | 71 111147/— 8] 800 |0-20
6: 8
9
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cs
55 251 |8:16 | 632 || 21 | 85 | 61 |— 60}) 2200 | 1-48
69 256 |8:17 | 647 || 22 | 82] 62 |— 64] 2300 | 1-62
87 262 |8:18 | 662 || 23 | 79 | 63 |— 67} 2400 | 176
109 269 |8:19 | 678 || 24} 76 | 64 |— 70}) 2500 | 1-91
275 |\8:20 | 694 || 25 | 73 | 65 |— 73)| 2600 | 2:07
28] |8:21 | 710 || 26 | 70} 66 |— 76) 2700 | 2-23
288 |8°22 | 72 2 67 | 67 |— 79|| 2800 |2:40
295 |823 | 744 || 28 | 64 | 68 |— 82] 2900 | 2:58
302 |8°24 | 761 || 29 | 60 7} 69 |— 85]| 3000 | 2-76
309 |8°25 | 779 || 30 | 57 1 70 |— 87|| 3100 | 2-94
316 {8-26 | 798 || 31 | 54] 71 |— 90]! 3200 |3-13 —
323 |8:27 | 816 || 32 | 504 72 |— 92|| 3300 | 3:33)
331 |8:28 | 835 || 33 | 46 | 73 |— 94|| 3400 | 3°54
338 |8:29 | 855 || 34 | 43 1 74 |— 97)| 3500 | 3°75
346 |8°30 | 875 || 35 | 39) 75 |— 99
354 |8°31 | 896 || 36) 35 | 76 |—101
363 |8:32 | 917 || 37 | 31 | 77 | —102
371 | 8:33 | 939 || 38 | 28 | 78 |—104
380 |8:34 | 961 || 39 | 24) 79 |—106
389 |835 | 983 || 40 | 20] 80 | —107
BI III III INI DAS RAPSPASSDSAAMAAAAMA I
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AI TS IN TS
ARTICLE XVII.
On the Anhydrous Sulphate of Ammonia. By Heineicu Rose.
[From Poggendorft’s Annalen, vol. xlix. p. 183.]
In attempting to precipitate the excess of sulphuric acid from
a solution of anhydrous sulphate of ammonia by means of car-
bonate of barytes, I succeeded in obtaining crystals of consider-
able size from the fluid separated from the sulphate and excess
of carbonate of barytes ; these crystals I took for anhydrous sul-
phate of ammonia ; having obtained only a small quantity I did
not subject them to analysis, but employed for this purpose the
indistinctly crystallized mass, which remained with these crystals
after evaporation over sulphuric acid. I found in them only
67°47 per cent. of sulphuric acid instead of 70°03, which, ac-
cording to theory, the anhydrous sulphate of ammonia should
contain*.
I have since separated, in the above-described manner, the
excess of acid from larger portions of the anhydrous sulphate of
ammonia, and have obtained a greater quantity of these crystals.
At the same time I investigated more accurately the action of
water on this salt, which had been carefully prepared, and was
perfectly neutral. After precipitating the excess of acid by car-
bonate of barytes, I satisfied myself that the solution had pre-
cisely the same properties as the salt obtained by treating an-
hydrous ammonia with anhydrous sulphuric acid. I found
also, what I had not been before able to decide with certainty,
on account of the small quantity of the salt employed, that the
solutions do not contain one salt, but two different salts, pos-
sessing very singular properties, and remarkable as to their com-
position+.
I have also submitted the properties and composition of neu-
tral anhydrous sulphate of ammonia to a fresh examination, and
have ascertained some facts which will complete my former in-
vestigations. 1 have called this salt sulphat-ammonf, for reasons
formerly explained; the two salts obtained from its aqueous
* Poggendorff’s dnnalen, Bd. 47, 8. 474.
+ Poggendorff’s Annalen, Bd. 32, S. 81.
t Ebendaselbst, Bd. 37, S. 475.
202
552 ROSE ON THE ANHYDROUS SULPHATE OF AMMONIA. 7
a
solution, I will, at present, denominate parasulphat-ammon, and —
the deliquescent salt; the names of sulphat and parasulphat-
ammon are, however, to be considered as merely provisional; I
shall very readily withdraw them if the ingenious views of Mr.
R. Kane*, which regard ammonia as an amide of hydrogen, —
should be more generally adopted. It is indeed true, that, by
this hypothesis, the phenomena which the compounds of anhy-
drous sulphuric acid with ammonia exhibit with reagents, are
capable of more satisfactory explanation than by other theories ;
but as to the numerous compounds of ammonia with oxyacids
and with water, the opinion of Berzelius, that these combina-
tions contain the oxide of ammonium, is more simple and pro-
bable, because these salts, considered in this light, are analogous
in composition to the salts of other bases.
I, Neutral Anhydrous Sulphate of Ammonia—Sulphat-ammon.
The principal properties of this compound I have described
in a former paper, in which I especially mentioned its action on
the solutions of barytic salts, oxide of lead, strontia and lime,
and chloride of platina. Other reagents, which instantly in-
dicate the presence of ammonia in a solution of sulphate of
ammonia, do it imperfectly in a solution of sulphat-ammon. In
order to determine this point, equal parts of sulphat-ammon and
of sulphate of oxide of ammonium were dissolved each in nine
times its weight of water, and both solutions were tested with
the same reagents; sulphat-ammon is not perfectly soluble in
less water than employed in this experiment.
A solution of sulphate of alumina soon produced crystals of
alum in the solution of the sulphate of oxide of ammonium, but
none were immediately produced in the solution of sulphat-am-
mon ; after some time a small quantity was formed, but much
less than in the sulphate of oxide of ammonium.
A concentrated solution of tartaric acid soon produced a
crystalline precipitate with the sulphate of oxide of ammonium,
and also after a longer time in the sulphat-ammon. A concen-
trated solution of racemic acid, which is a much more sensible
test of ammonia than tartaric acid, produced similar effects ; but
the quantity of precipitate was much greater in the sulphate of
oxide of ammonium.
* Researches on the Nature and Composition of the Compounds of Am-
monia. ‘l'ransactions of the Royal Irish Academy, vol. xix. p. 1.
ROSE ON THE ANHYDROUS SULPHATE OF AMMONIA. 553
A solution of carbazotic acid acted in the same way ; it im-
mediately produced a considerable precipitate with the sulphate
of oxide of ammonium, and to a less extent, and after a longer
time with the sulphat-ammon.
The sulphat-ammon is a homogeneous powder; when exa-
mined by the microscope it does not exhibit any appearance of
crystallization ; like other powders it attracts moisture from the
air, but this is got rid of without any change of properties, by
drying in a water-bath, and by fresh exposure it gains as much
water as before.
Although I have already stated an analysis of sulphat-ammon,
yet having, by a method which I shall hereafter describe, ob-
tained it in larger quantity and of great purity, I have considered
it necessary to repeat the examination. The proofs of the purity
of this salt are not only that it scarcely reddens litmus paper,
but on the contrary renders it blue (after it has been reddened),
but only to a slight degree, and this effect it continues to pro-
duce only when kept in a bottle containing ammoniacal gas.
When litmus paper, which has been dipped in a solution of
sulphat-ammon, sulphate of oxide of ammonium, or most
other soluble ammoniacal salts, is dried in the air, it is red-
dened.
One hundred parts of sulphat-ammon were treated with a so-
Jution of chloride of barium ; the whole was evaporated to dry-
ness, heated to low redness, treated with hydrochloric acid and
water, and there were obtained 203°79 parts of sulphate of
barytes. This is the only method by which the whole of the
sulphuric acid can be eonverted into sulphate of barytes; but
this substance, when so procured, passes through filters, and
requires frequent filtration. The sulphate of barytes obtained
indicates 70-04 of sulphuric acid, which agrees as nearly as pos-
sible with the amount of this acid calculated from the formula
S + N H®, or 70°03 per cent. The results of several analyses,
confirming this composition, will be subsequently stated.
Il. Parasulphat-ammon.
I have thus denominated a remarkable salt, which crystallizes
in large well-formed crystals from the concentrated aqueous
Solution of sulphat-ammon; they may likewise be obtained by
combining sulphat-ammon with anhydrous sulphuric acid by a
method already mentioned. These are the crystals which
554 ROSE ON THE ANHYDROUS SULPHATE OF AMMONIA.
have been described by my brother in Poggendorff’s Annalen,
B. XLVII. 476. These crystals are obtained by evaporating the
solution ; but, like that of sulphate of oxide of ammonium, it is
apt to become acid during the operation, and to have its pro-
perties thereby difficultly recognized ; it is better to evaporate
over sulphuric acid in vacuo. On further evaporating the
mother-water another salt is formed, which differs essentially in
its properties from the larger crystals ; but it is difficult to se-
parate it from them, especially when considerable quantities of
the sulphat-ammon have not been operated upon. This salt
attracts moisture from the atmosphere, which is not the case with
the crystals of the parasulphat-ammon, this when quite dry
suffering no alteration by exposure to the air. Of this salt I
shall treat in the following section.
The parasulphat-ammon is rather more soluble than the
sulphat-ammon ; its solution is neutral to litmus paper. When
also preserved for a long time, so that nothing can evaporate
and crystallize, it remains neutral. When, however, the salt
is moistened with water, it acquires in a short time the pro-
perty of reddening litmus paper, and the solution possesses
qualities and acts differently with reagents from that of the salt
not previously moistened.
The acid reaction, which the salt acquires by moistening,
probably arises from the expulsion of some ammonia by the
water; the carbonic acid of the atmosphere appears also to
exert some action; for if a solution of parasulphat-ammon is
slowly evaporated, cold, over sulphuric acid, in contact with the
air, it often acquires an acid reaction, which is not the case i
the evaporation be performed in vacuo; when the crystals of
this salt are obtained, no attempt must be made to free them
from the solutions by washing with water; they must be dried
only by blotting-paper.
What particularly characterizes the parasulphat-ammon, and
distinguishes it from the sulphat-ammon is, that the solution of
the dry salt is not rendered turbid by the salts of barytes or of
lead, even when they remain long mixed. This property, it is,
however, sometimes difficult to observe, partly because the
crystals may contain a portion of the solution from which they
have separated, and therefore contain the deliquescent salt;
and partly from having been exposed to the atmosphere after
moistening, and then yielding a solution which reddens litmus
ROSE ON THE ANHYDROUS SULPHATE OF AMMONIA. 555
paper; in both these cases the solutions instantly precipitate
the salts of barytes and lead.
If hydrochloric acid and a solution of chloride of barium be
added to one of parasulphat-ammon, it remains also for some
time perfectly clear ; in about twelve hours, however, a precipi-
tate of sulphate of barytes is formed; but it does not occur
without the hydrochloric acid be present.
In the property of not precipitating the solutions of barytic
salts in the cold, the parasulphat-ammon very much resembles
the compound obtained by M. Regnault, by saturating sulphate
of chloride of sulphur S Cl? + 2 s (S Cl) with anhydrous am-
monia*, and which he considered as a mixture of sal-ammoniac
and a sulfamide (S N H’). The solution of this compound oc-
casions no precipitation with the salts of barytes, even when
they have been long in contact. M. Regnault did not succeed
in separating this peteide from sal-ammoniac by crystalliza-
tion ; and he adds, moreover, that the compound which he ob-
tained very soon attracts moisture from the air, which, as already
mentioned, is not the case with the crystals of parasulphat-am-
mon or sulphat-ammon.
The results of analyses prove, likewise, that the crystals can-
not be regarded as an anhydrous sulfamide; 100 parts dissolved
in water, were mixed with a solution of the chloride of barium
and boiled. After some time a precipitate of sulphate of ba-
rytes appeared, but less in quantity and much more slowly than
would have occurred, under similar circumstances, with a solu-
tion of sulphat-ammon. The whole was evaporated to dry-
ness; the residue heated to incipient redness, left 203°64 parts
of sulphate of barytes after treatment with hydrochloric acid
and water; this is equivalent to 70 of sulphuric acid.
The result of this analysis proves that these crystals possess
as exactly as possible the same composition as the anhydrous
sulphate of ammonia or sulphat-ammon, If the sulphur in an
anhydrous sulfamide S N H? was entirely converted into sul-
phuric acid, there would be obtained 80-03 per cent. of sul-
phuric acid from the sulfamide employed.
One hundred parts of crystals of parasulphat-ammon, which
had been formerly prepared, gave, when treated in the same
* Ann, de Chim, et de Phys. \xix., 170.:
556 ROSE ON THE ANHYDROUS SULPHATE OF AMMONIA.
manner, 204°49 parts of sulphate of barytes, equivalent to 70°29
of sulphuric acid. If we were to regard the crystals prepared —
by me, on account of their similarity to the combinations formed
by M. Regnault, as a sulfamide, it must be considered as hy-
drated, S N H? + H.
Since, however, the existence of hydrous amides is not suffi-
ciently proved, and even appears in some respects to be impro-
bable, I have denominated these crystals parasulphat-ammon,
or parasulphammon, on account of their similar per centage
composition with sulphat-ammon.
In the solution of the parasulphat-ammon the ammonia is
still more imperfectly separated by reagents than in a solution
of the sulphat-ammon. In solutions of equal strength, one part
of each salt to nine parts of water, a concentrated solution of
tartaric acid does not effect the formation of supertartrate of am-
monia, even after several days in the parasulphat-ammon, while
a precipitate, though not an abundant one, is produced in the
sulphat-ammon. A concentrated solution of racemic acid occa-
sions, after some time, a very small quantity of crystalline pre-
cipitate in the solution of parasulphat-ammon, and much smaller
than in the solution of sulphat-ammon ; solutions of chloride of
platina, carbazotic acid and sulphate of alumina, react in the
same manner with the solution of sulphat-ammon.
As the presence of sulphuric acid is not indicated in the solu-
tion of parasulphat-ammon by the salts of barytes and lead, this
is also the case, as might be anticipated, with the salts of strontia
and of lime.
I have long hesitated whether the crystals of parasulphat-_
ammon should be regarded as distinct from the sulphat-ammon,
merely on account of their different crystalline forms. It is
well known how difficult it is to obtain perfectly anhydrous sul-
phuric acid; and, if it contain only a trace of water, a corre-
sponding quantity of sulphate of ammonia is formed on satura-
tion with dry ammoniacal gas; and the solution of barytes,
being an extremely sensible reagent for sulphuric acid, it might
easily happen that the solution of sulphat would be slightly pre-
cipitated even in the cold by barytes, owing to its being impure,
on account of the presence of sulphate of ammonia. It is,
indeed, true, that the solution of parasulphat-ammon acts some-
wnat differently from that of sulphat-ammon, with solutions of
ROSE ON THE ANHYDROUS SULPHATE OF AMMONIA. 557
barytes and lead and other reagents, and more particularly with
tartaric and racemic acids; the sulphat-ammon is more spa-
ringly soluble than the parasulphat, and does not so readily
become acid when moistened ; these, however, are circumstances
of too little importance to allow of our regarding with certainty
the parasulphat as a distinct substance from sulphat-ammon,
and isomerical with it.
The following facts led me, however, to adopt this opinion:
when a neutral solution of chloride of barium is added to a cold
solution of pure sulphat-ammon, and the sulphate of barytes is
allowed to precipitate for an hour, the filtered solution, without
being heated again, deposits sulphate of barytes, and this occurs
again after repeating the filtration; this is not the case with the
parasulphat-ammon ; its solution, after the addition of chloride
of barium, remains for months perfectly clear in the cold, when no
acid has been added; in performing these experiments equal
portions of the isomerical salts were dissolved in similar quan-
tities of water.
I consider these different actions as an essential difference be-
tween these substances ; and the following series of experiments
is also decidedly in favour of this difference: 100 parts of sul-
phat-ammon weighed 91°42 after drying in a water-bath; it
was dissolved in cold water, without any acid, and mixed in the
cold with a solution of chloride of barium; in an hour after
mixing, the sulphate of barytes was separated by the filter and
washed, towards the end of the operation, with warm-water ; it
weighed 51°71 parts, equivalent to 18°16 of sulphuric acid:
Hydrochloric acid was added to the filtered solution, and it was
evaporated to dryness; the residue, moderately heated, treated
with water and a little hydrochloric acid, gave 145-7 of sulphate
of barytes, equivalent to 51°16 of sulphuric acid; the whole
quantity of sulphuric acid, therefore, in 100 parts, eli chata to
69°32 parts, approximating very closely to the quantity con-
tained in the sulphat-ammon by calculation.
In supposing that the 18°16 of sulphuric acid precipitated in
the cold, might be derived from an admixture of sulphate of am-
monia with the sulphat-ammon, they would be equivalent to
30°01 of the former salts, and the 51°16 of sulphuric acid ob-
tained by evaporation indicate 73-08 of sulphat-ammon, giving
an excess of 3°06, which the analyses will not admit of.
558 ROSE ON THE ANHYDROUS SULPHATE OF AMMONIA.
The results of two additional experiments are still more deci-
sive of the difference between sulphat- and parasulphat-ammon ;
100 parts of the same sulphat-ammon, as already employed,
corresponding to 91°42 when dried in the water-bath, dissolved,
cold and mixed with a solution of chloride of barium, gave
63°84 of sulphate of barytes, which was separated by the filter
half an hour after precipitation, and are equivalent to 22°41 of
sulphuric acid; in another experiment the sulphate of barytes
separated an hour after precipitation, the sulphate obtained in-
dicated 23°49 of sulphuric acid; the quantity of sulphate of
barytes, obtainable by evaporation, was not determined in either
experiment.
It is evident, from these experiments, that the quantities of
sulphuric acid, precipitated in the cold by chloride of barium,
may differ greatly; the three portions employed were weighed
at the same time from the same quantity of the preparation ;
the greater or less quantity of the sulphate of barytes obtained
in the cold, by a solution of the chloride of barium, undoubtedly
depends not only upon how soon it is filtered, but upon the
quantity of water in which the sulphat-ammon is dissolved, and
the concentration of the solution of chloride of barium.
Were we to suppose, that in the last-described experiments,
the sulphuric acid precipitated in the cold is derived from the
sulphate of oxide of ammonium, there would arise greater con-
tradictions than would attend the results of the first-mentioned
analysis ; for 22°41 parts of sulphuric acid would correspond to
37°03 parts of sulphate of oxide of ammonium. The different
analyses of the sulphat-ammon having constantly given 70°03
per cent., or very nearly, of sulphuric acid, there would be ob-
tained by further treatment 47°62 per cent. of the same acid,
which corresponds to 68 parts of the sulphat-ammon. But in
this case the quantities of sulphate of oxide of ammonium and
the sulphat-ammon would amount to 105°03 per cent., and there-
fore the analyses would indicate an excess of 5:03 per cent.
In the last-mentioned examination of the sulphat-ammon
23°49 per cent. of sulphuric acid were obtained in the cold; if
these indicated 38°81 parts of sulphate of oxide of ammonium,
and if 46°54 parts of sulphuric acid, obtained by evaporating,
correspond to 66°46 parts of the sulphat-ammon, the analyses
would have given an excess of 5:27 per cent.
ROSE ON THE ANHYDROUS SULPHATE OF AMMONIA. 559
Ill. The Deliquescent Salt.
This salt, as already mentioned, is contained in the solution
from which the parasulphat-ammon has crystallized ; if this be
evaporated to dryness over sulphuric acid in vacuo, imperfect
crystals, or crystalline crusts only are obtained, which attract
moisture from the air, and eventually deliquesce ; it is very diffi-
_ cult to obtain this salt perfectly free from parasulphat-ammon ;
it is indeed more soluble, but the parasulphat is not very diffi-
cultly so, which renders it impossible to separate them when
operating on small quantities ; but in larger quantity I effected
their separation in the following manner: I allowed the solu-
tion, which had been evaporated to dryness in vacuo over sul-
phuriec acid partially to deliquesce by exposure to the air; or
added a few drops of water to it, left them for some time in
contact, and then evaporated the small portion of the salt [dis-
solved], again to dryness, as before, and employed it for analysis.
If the solution of the salt contains parasulphat-ammon, and
if it has been evaporated very slowly over sulphuric acid, but
not im vacuo, the crystals obtained from it become, in a moist
state, very readily acid; the crystals of the parasulphat-ammon
must therefore be picked out as much as possible from the
mass evaporated to dryness, then the deliquescent salt must be
dissolved in water, and carbonate of barytes added to the solu-
tion to saturate the free acid, and lastly, the solution must be
again evaporated in vacuo.
The crystals of the salt are too indistinct to admit of their form
being determined, and they are usually mere crystalline crusts,
and any crystals which may be observed with bright faces are
parasulphat-ammon.
The solution of this salt instantly precipitates solutions of
barytes; but, as happens with the solution of sulphat-ammon,
not nearly the whole of the sulphuric acid is thrown down in
the state of sulphate of barytes. When hydrochloric acid is
added to the solution, more sulphate of barytes is precipitated
in the ‘cold, than without such addition; a solution of chloride
of strontium produces immediate precipitation in the solution of
this salt only when very much concentrated ; this distinguishes
the solution from that of sulphat-ammon. If equal quantities
of both salts are dissolved in similar quantities of water, both
the solutions are not precipitated by a dilute solution of a salt
560 ROSE ON THE ANHYDROUS SULPHATE GF AMMONIA. .
of strontium ; after some time, however, if the solutions are not
too dilute, precipitation begins in that of the deliquescent salt,
while that of the sulphat-ammon remains clear. A solution of
the acetate of peroxide [protoxide ?] of lead precipitates the solu-
tion of the deliquescent salt in the same way that it does the —
sulphat-ammon; a solution of chloride of calcium does not
render either solution turbid; both solutions are similarly —
affected by chloride of platina, sulphate of alumina, tartaric
acid, racemic acid, and carbazotic acid.
It is difficult to prevent the solution of the salt from reacting
as an acid upon litmus paper, but it is inconsiderable if the
salt has been carefully prepared.
The salt obtained by evaporating the solution in vacuo was
dried at 212° until it ceased to lose weight ; 100 parts of the dried
salt dissolved in water, mixed with a solution of chloride of
barium, and left in the cold for twenty-four hours, gave 20°42 of
sulphate of barytes. Hydrochloric acid being added to the
filtered solution, it was evaporated to dryness, and the residue
was heated nearly to redness, and treated with hydrochloric
acid. The quantity of the sulphate of barytes precipitated was
166°18 parts; the quantity of sulphate of barytes, precipitated
in the cold, therefore, amounts to scarcely one-eighth of the
whole ; both quantities together gave 64°14 per cent. of sulphuric
acid in the salt; this corresponds to a compound of anhydrous
sulphate of oxide of ammonium, with half an atom of water,
which, calculated according to the formula SN He +3 H gave
in 100 parts i
Sulphuric, acid seis) a! \cpye. tei A
ADAMIONIE,. Jy./\s<>..:8%) (bie, sennetl cee ee
WBbeB icc hpnorcy soils see Seats Malan) ieee ree
100°
On repeating this experiment with a portion of the salt pre-
pared on another occasion by dissolving pure sulphat-ammon, I
obtained, by exposure to cold from 100 parts, after adding hy-
drochloric acid and chloride of barium to the solution, 106°06
parts of sulphate of barytes, and from the residue obtained by
evaporation to dryness, and treating it with hydrochloric acid, .
84:62 parts more of sulphate of barytes were obtained. It will
be seen from these experiments that much more sulphuric acid
ROSE ON THE ANHYDROUS SULPHATE OF AMMONIA. 561
is precipitated from the salt when cold, if mixed with hydro-
chloric acid, than when this is not the case. The quantities
of sulphate of barytes, added together, indicate 65°54 of sul-
phuric acid in the 100 of salt; the slight excess is unquestion-
ably derived from the parasulphat-ammon which the salt con-
tained, because it had been prepared from but a small quantity
of the sulphat-ammon.
When I first prepared the crystals of the parasulphat-ammon,
having obtained but a small portion of it, I resolved not to employ
them for analysis, but to examine the irregularly crystalline
masses obtained by evaporation to dryness, which must consist
of a mixture of the deliquescent salt, and the parasulphat-
ammon*; analyses confirmed this by finding only 67°47 per
cent of sulphuric acid in this mixed substance. The hydrous
sulphat-ammon is perfectly analogous to a salt which I ob-
tained during my investigation of the compounds of carbonic acid
and ammonia‘, and which consists of carbonate of ammonia and
half an atom of water, requisite to convert the ammonia [am-
monium ?] into the oxide of ammonium. The same is also the
case with the hydrous sulphat-ammon. With respect to the car-
bonic salt, I have advanced the opinion that it might be regarded
as carbonat-ammon with the carbonate of oxide of ammonium.
The same view may also be adopted with respect to the hy-
drous sulphat-ammon, by regarding it as a compound of sul-
phat-ammon with the sulphate of oxide of ammonium S AH?
+S N Hi}; the salt may perhaps also be formed by saturating
the first hydrate of sulphuric acid 2 S + H, contained in Nord-
hausen sulphuric acid, with dry ammoniacal gas.
The deliquescent salt unquestionably originates from the
parasulphat-ammonia when dissolved in water, and remaining
for some time in contact with it. Very pure crystals of the
parasulphat-ammon, quite free from the deliquescent salt, when
dissolved in water, and evaporated over sulphurio acid in vacuo,
always yield a considerable quantity of the deliquescent salt,
along with the crystals of parasulphat-ammon. As crystals
of the parasulphat-ammon become acid, when exposed to moist
air for some time, it seemed to me interesting to inquire into
the nature of the alteration which they undergo. Some ex-
* Poggendorff’s Annalen, Bd. xlvii. S. 474.
+ Poggendorfl’s Annalen, Ba, xlvi. S. 3738.
562 ROSE ON THE ANHYDROUS SULPHATE OF AMMONIA.
ceedingly pure crystals of the salt were reduced to powder
and moistened during several hours, by which the salt acquired
an acid reaction, and it was then perfectly dried in a water-
bath; 100 parts of the dry residue were dissolved in cold
water; the solution reddened litmus paper, but not strongly,
and it precipitated solution of chloride of barium. By the
method frequently mentioned, I obtained 198°19 parts of sul-
phate of barytes equivalent to 68°13 of sulphuric acid ; it fol-
lows from this result that the parasulphat-ammon, by moisten-
ing with water, is partially converted into the deliquescent salt.
The acid reaction arises from the presence of free hydrate of
sulphuric acid.
It results from these investigations, that, although the sulphat-
ammon seems to dissolve in water without decomposition ; yet,
when the solution crystallizes, the crystals obtained, notwith-
standing they are similar in composition to the sulphat-ammon,
possess many properties which differ from it. In the solution
of the sulphat-ammon the constituents of water are more readily
combined with it by the action of certain reagents, and the
compound therefore changes more readily. This is the case
with the crystallized sulphat-ammon, or the parasulphat-am-
mon, which resists more powerfully the action of such reagents.
The conditions of the sulphat-ammonand parasulphat-ammon,
may be compared with the vitreous and crystalline state of
certain bodies, in which they exhibit different properties.
The combinations of anhydrous sulphuric acid with am-
monia may be regarded, according to Dr. Kane, as perfectly
analogous to the hydrate of sulphuric acid. By supposing
that ammonia is an amide of hydrogen, and that the amide
combines in a similar manner with other bodies, as oxygen and
chlorine, the amide of hydrogen becomes a body analogous to
the oxide and chloride of hydrogen. But when sulphuric acid
is combined with water or other oxibases, it may possess pro-
perties very different from those which belong to it when com-
bined with the amide of hydrogen. We have, in fact, of late,
become acquainted with a great number of cases, in which the
sulphuric acid, when combined with certain substances, as for
example, with the oxide of ethule, and other bodies of organic
origin, loses some of the peculiarities by which we were pre-
viously accustomed to characterize it, especially that of giving
an insoluble precipitate with barytic salts. But [hypothetical]
ROSE ON THE ANHYDROUS SULPHATE OF AMMONIA. 563.
as this opinion may be, the explanation which Dr. Kane gives
of the compounds of ammonia with hydrous oxacids is equally
so; these are regarded by Berzelius as salts of the oxide of
ammonium, and on this view, the analogy of these salts, with
those formed with other oxibases, is maintained ; as is also the
isomorphism of some salts of potash and the oxide of ammo-
nium; and these opinions were rapidly and almost universally
adopted. But according to Dr. Kane, this numerous class of
ammoniacal salts consists of combinations of acids with two
bases, the oxide and amide of hydrogen; and the sulphate of
oxide of ammonium becomes on this view analogous to several
sulphates, which, at a higher temperature, retain one atom of
water. But the perfect analogy and isomorphism of these am-
moniacal salts with the salts of potash, are thrown into the back
ground by Dr. Kane’s theory, instead of being advanced. Prof.
Graham*, for similar reasons, adopts the opinions of Berzelius
justly, as he acknowledges the importance of the theory of Dr.
Kane.
I will direct the attention of the reader to an analogy existing
between the compounds of sulphuric acid with ammonia, and of
the same acid with bicarburetted hydrogen (the elayl or ztherol
of Berzelius) which was long since pointed out by Dumasf.
The elayl and the ammonium produce, when combined with hy-
drogen, one the hypothetical radicle zthyle, the other the no less -
hypothetical radicleammonium ; both radicles may be combined
with sulphur, chlorine, bromine and iodine: combined with
the elements of water, one yields the base, oxide of zthyle, the
other the base oxide of ammonium. Both bases may be com-
bined with anhydrous oxyacids; both the bicarburetted hy-
drogen, as well as the ammonia, may be united by direct com-
bination with anhydrous sulphuric acid; this acid may likewise
be combined with oxide of ethyle, a compound contained in the
sulpho-tartaric acid and in its salts, and also with the oxide of
ammonium. The sulphuric acid forms compounds also with
elayl (or rather with etherol), as well as with ammonia, which
contain so much water, or its elements, that only half the quan-
tity of the bicarburetted hydrogen or the ammonia can be con-
verted by it into the oxide of zthyle, or the oxide of ammonium ;
the former compound is the oil of wine (sulphate of the oxide of
* Elements of Chemistry. By T. Graham, p. 117.
+ Poggendorff’s Jnnalen, Bd. xii. S. 452.
564 ROSE ON THE ANHYDROUS SULPHATE OF AMMONIA.
ethyle—etherol), the latter the deliquescent salt, contained in the
mother-water, from which the parasulphat-ammon is separated
by crystallization.
Much value, however, is not to be attached to these com-
parisons, for they merely refer to a certain analogy or combina-
tion, which may be even called a remote one, since bicarburetted
hydrogen and ammonia differ with respect to the number of
their elements.
This parallel becomes still more improbable, on account of
the different properties of the substances compared, they pos-
sessing not the least resemblance to each other.
565
ArticLe XVIII.
On a Transportable Magnetometer. By WiLuELM WEBER.
[This article is translated partly from the Resultate aus den Beobachtungen des
magnetischen Vereins im Jahre 1838, and partly from manuscript commu-
nications from M. Weber to Major Sabine.]
A SMALL travelling apparatus for the absolute measurement
of the force of the earth’s magnetism has been described in the
Resultate for 1836*. That apparatus was not a magnetometer,
but rather served as an illustration of the mode in which this
measurement, which had previously been executed only with
a magnetometer, might be made with an ordinary compass
needle.
The degree of accuracy attainable with such a small appa-
ratus, and the occasions on which it ought to be employed, were
examined in the memoir referred to. But for the limitation
imposed by the want of time, or by other external circum-
stances, it would of course be always preferable to use the
magnetometer; the small apparatus being only intended to
serve as a substitute, on occasions when the use of the more per-
fect instrument is impracticable. It is very desirable to reduce
ee. a . aids
_ the number of such occasions as much as possible, by devising
‘means of removing the difficulties which often oppose them-
selves to the use of the magnetometer ; and this will appear the
more desirable, the more we consider the great difference in
the degree of precision attainable by the two instruments; and
the more we reflect on the importance that would be given to
a class of observations in which magnetometers have not hitherto
been used, (namely, those made during distant and extensive
journeys and voyages,) if they could be rendered susceptible of
a higher degree of accuracy, certainty, and completeness.
If the final aim of such observations were simply that of
constructing magnetic maps on which no ulterior investigation
was to be based, the degree of exactness to which such maps
should be carried might be arbitrarily determined; and pos-
sibly such an amount of accuracy as can be obtained without
* Translated in the Scientific Memoirs, Part V.
VOL, Il. PART VIII. 2P
566 WEBER ON A TRANSPORTABLE MAGNETOMETER. \
the use of magnetometers might be deemed sufficient. But if 5
these maps are not themselves the final object sought,—if they :
are to form the basis of a new investigation,—if determinate —
rules and laws are to be recognised,—if the maps are to serve ‘
as the means of comparing experiment with the general theory
of the earth’s magnetism,—and if the elements of the theory
are to be deduced from them,—then the degree of accuracy
to be demanded is no longer arbitrary, but is determined by the
nature of the subject. A minor degree of accuracy, such as these
maps now possess, has, it is true, served for a first attempt
at such a comparison; but in order that they may afford an
adequate basis for an amended calculation, they must receive
a higher degree of exactness. Such is now the great purpose
of the magnetic observations to be made in distant expeditions,
and it is this which now gives to such expeditions peculiar im-
portance and value.
But the greater the importance which thus attaches to such
voyages and observations, in consequence of the demands of
theory, the more essential it becomes to examine what they are
capable of affording.
Magnetic observations may be made at places widely remote
from each other, either at the same time or nearly so, or alter-
nately, so as to lessen the errors occasioned by regarding them
as simultaneous. At all the stations, or at the more important
at any rate, the observations may be continued with regularity
for at least one or more weeks, so as to afford mean values
freed in some measure from disturbing influences. But it 1
still more desirable to give to such expeditions the advantage
the recent improvements, by furnishing them with magnetome=
ters. This would probably be best accomplished, by the per-
sons who undertake magnetic expeditions making themselves
thoroughly acquainted, both theoretically and practically, with
the whole subject of magnetometric measurements, as they
would then be able to devise for themselves the best travelling
arrangements, But as there are not many opportunities of
acquiring this knowledge, the following memoir may be inter-
esting and useful to persons who cannot study the subj
more thoroughly in other ways.
I proceed to describe a transportable magnetometer, which,
it unites all the advantages proper to magnetometers, with fi
lity of management and compendious construction, appe
'
e
WEBER ON A TRANSPORTABLE MAGNETOMETER. | 567
well adapted for magnetic expeditions and journeys, and is not
more inferior to the magnetometers of fixed observatories, than
good portable astronomical instruments are to the larger ones
used in fixed astronomical observatories. I shall first give
some general remarks on this instrument; then a description of
its several parts; and lastly, observations of the Declination,
and its Variations, made simultaneously with the transportable
magnetometer and with that of the Gottingen Observatory,
and a measurement of the Intensity made for the purpose of
exhibiting its capability in that respect.
§ I. General Remarks.
The transportable magnetometer, figured in half size in
Pl. XXV., fig. 1, requires in general but few explanations, as it
_is only essentially distinguished from other magnetometers by
its small size, and by its more compendious construction. All
the observations which are made with the larger magnetometers
may also be made with the one under consideration ; so that the
absolute declination, the variations of the declination, and the
absolute horizontal intensity, can all be measured by it; the
variations of the horizontal intensity can also be observed, by
suspending the bar employed in the experiments of deflection,
as a bifilar magnetometer. The exactness with which these
various measurements can be made is much greater than has
et been attained in travelling observations; it suffices for all
the purposes of magnetic travellers; and it admits of as much
“accuracy and certainty, in proportion to its size, as do the
largest magnetometers.
The results obtained with the large instrument used in the
Gottingen Magnetic Observatory may be depended upon almost
to the immediate readings, which are to ;1, of a division of the
scale, or to 2 seconds of arc. This supposes the scale to be at
least five meters from the mirror of the magnetometer, as other-
ise the arc value of the divisions of the scale (which are one
‘millimeter long), would be greater. Such a distance would not
answer in journeys, as much time would be lost in bringing all
the parts of the instrument into their proper positions. For
travelling purposes, the distances ought to be limited so as to
admit of the whole apparatus being placed on a table, and they
should therefore be about four times less. Consequently, in
lieu of the 8-inch theodolite, which is required to do full justice
2. Pi2
568 . WEBER ON A TRANSPORTABLE MAGNETOMETER. ‘3
. to the great magnetometers, one of about three or four inches
may be used without disadvantage, being at once more conve-
nient and more ceconomical, and still allowing the measurements
to be depended upon to within from 10 to 20 seconds of are.
In considering the subject further, it will be seen, that admitting
the necessity in the travelling apparatus of diminishing the ob-
servation distance, a diminution in the size of the magnetometer
(which would not be admissible under other circumstances), does
in no degree detract from the accuracy of the observations. For
with a distance four times less, the degree to which the reading
can be depended on (and which it is desired to preserve), is not
affected, though the proportion of the magnetic force of the
magnetometer to external disturbing influences be lessened in
the same proportion. It may be assumed, that the magnetic force
decreases as the cube of the linear dimensions of the bar, and
external disturbing influences as the square, whence it follows
that the bar may be made four times less without diminishing
the dependence to be placed on the readings (which is to about
the one tenth part of one division of the scale). If, with this di-
minution, other arrangements are adopted for guarding against
external disturbing influences more carefully than has been
hitherto found necessary with the larger magnetometers, there
will be no material disadvantage in pushing the diminution in
size somewhat further, having in such case only to preserve the
degree of dependence which may be placed on the readings.
In fact, the length of the bar of 600 millimeters has been
reduced to 100 millimeters; and observation has shown that
the readings may be equally depended upon; with this differ-
ence only, that the divisions, as read off, have a four times
greater value of arc than in the case of the larger magnetome-
ters, so that one division of the scale is equivalent to 80 seconds
of arc instead of 20 seconds. Hence it appears, that by suit-
able arrangements, all the advantages of the magnetometer may
be secured to magnetic expeditions; of course, without that
highest degree of precision attainable only in fixed observa-
tories, where nothing is wanting in construction and arrange-
ment.
The instrument to be described affords these advantages in
respect to the absolute declination and its variations, and still
more in respect to the absolute measurement of the horizonta
intensity; for in the Resultate for 1836, p. 88, it has been
WEBER ON A TRANSPORTABLE MAGNETOMETER. 569
shown*, that if both bars are six times smaller, the deflecting
bar may be brought six times nearer to the magnetometer, with-
out its being necessary to take more exactly into account the
distribution of free magnetism in the bars. If, then, the length
and breadth be diminished, and the thickness be left unaltered,
(the large bars are 600™™ long, 36™™ broad, and 9™™ thick ; and
the small bars 100™ long, 9™ broad, and 9™™ thick,) it follows
that as much may be gained in the small magnetometer, by in-
creasing the angular deflection, as is lost by diminishing the di-
stance of observation. In fact, the experiments of deflection
admit of a precision which leaves nothing to be desired, and
which harmonizes perfectly with the degree of accuracy which
is known to be of easy attainment in the experiments of vi-
bration.
Of course the small magnetometer must be construeted in
such a manner that all its parts may form a solid whole, so that
their relative position may not be liable to be disarranged by
packing, unpacking, or putting up. It must be possible both
to set the magnet bar at liberty, and to secure it again while in
its case, as is done in the common compass, and the torsion of
the thread must not be altered in so doing; the access of air
must be quite cut off even from the mirror, which may be
observed through a thin plate of mica, if a piéce of plane glass
ground parallel is not to be obtained. It is very advantageous
_ to make the case entirely of copper, and even of strong
‘copper-plates, not only for the sake of the increased solidity
given to the whole apparatus, but also because the case will
thus act on the inclosed magnet as a damper, and all the
measurements may be made with much greater rapidity. The
instrument must be so strong and solid, even when used in the
open air, that it may carry two arms, which serve for placing
the deflecting bar at equal measured distances east and west.
These arms being correctly placed, all the preparations for the
; experiments of deflection which would otherwise be necessary,
—namely, placing the measuring bars horizontally, and in a di-
rection perpendicular to the magnetic meridian, and finding
the corresponding points on either side of the magnetometer,—
are spared, and the experiments are rendered much easier, and
require less time.
* Sci. Mem. Pari V. page 86.
570 WEBER ON A TRANSPORTABLE MAGNETOMETER.
§ Il. Description of the several parts.
Fig. 1 represents the vertical section of the magnetometer in
the direction of the magnetic meridian.
The magnetic bar which forms the needle is bored through-
out its length, and the opening which is turned towards the
telescope is provided with a lens, in the focus of which at the
other end there is a cross of wires. This cross of wires is seen
in the telescope, when (as is required for determining the true
azimuth in the measurement of the absolute declination) it is
adjusted to distant objects, and then directed to the lens. This
arrangement was proposed by Airy, to make it possible to dis-
pense with the mirror, and to be able to make, with the same
telescope, and without displacing the eye-glass, the astronomical,
geodesical, and magnetical observations required in measuring
the absolute declination. In making this measurement the
needle must be reversed; but in the reversal the optical axis
must not alter its relative position in respect to the needle ;
this is effected in the closed case by means of a key, turned
on the outside, and causing the needle inside to perform half
a revolution round its axis of length. But this arrangement
is inapplicable to observations which require great changes
in the position of the needle, as in the experiments of vibration
and deflection in the measurement of the absolute intensity. It
therefore appeared advantageous to employ also a mirror, placed
in the same manner as in the bifilar magnetometer, close to the
axis of rotation of the needle, and above the copper case, and
available however great the deflections may be.
The copper case is seen to have three openings: the first is
into a space containing the mirror, and closed towards the
theodolite by a plate of glass, through which the light can pass,
in the direction shown in the plate from the scale, to the mirror,
and thence back to the telescope of the theodolite. The other
two openings are nearly at the same height as the magnetic
needle and the telescope of the theodolite. The light entering
through one of these apertures illuminates the cross of wires
which is stretched across the hindmost end of the hollow needle,
passes on to the lens at the other end, and thence, parallel to
the horizontal direction marked in the figure, to the telescope of
the theodolite with which the cross of wires is observed. The-
needle, bored throughout its length, is made accurately cylin=
WEBER ON A TRANSPORTABLE MAGNETOMETER. 571.
drical, and is inclosed in a cylindrical brass box, on the under
surface of which are two small projections which fit into two
cavities in the copper case when the suspension thread of the
needle is let down. The brass box can be fixed in this position
by two screws brought through the upper part of the copper
case: the box being thus held fast, the needle may first be drawn
out through the opening in the back of the case, and a brass cy-
linder of the same form as the needle, inclosing a weak magnet,
may be placed in its stead, to try the torsion of the thread.
Secondly, for the purpose of measuring the error of collimation,
the needle may be turned in the box round its longitudinal
axis, by means of a key introduced through the aperture in the
back of the case. During the observations the apertures in the
front and the back of the case are closed with a plate of mica
to a against currents of air.
_ Fig. 2 represents a somewhat different and more simple con-
struction of the same instrument; the needle is not hollow,
is not enclosed in a brass case, fal cannot be reversed. This
simplification is admissible when the use of the instrument is to
be restricted to the experiments which are to be made i the
open air, as detailed in the sequel. In this case the mirror is
included in the copper case, and its normal forms a right
angle with the magnetic axis of the needle. The glazed open-
_ ing in the side of the case does not impair its action as a damper,
and the opening may be made of any convenient size.
Fig. 3 represents the outside box, in which the instrument is
_ packed for travelling, and which serves also for suspending the
deflecting bar when it is to be used for the experiments of
vibration. A mirror is fixed to the end of the bar, so that it
may be observed from a distance with a telescope and scale.
The box has a small opening which can be closed with a plate
of mica admitting the light. The figure shows the bar suspended
in the box, and loaded with two cylindrical weights, made of
s, and connected by a silk thread passing over a bar parallel
Ho the needle, to keep the centres of gravity of the two weights
exactly the length of the bar from each other. The weights
serve for the deduction of the moment of inertia.
_ The unifilar suspension of the bar can be changed for a bifilar,
if the variations of the intensity are to be observed. The box
must then be placed relatively to the theodolite and to the mag-
netometer in the manner represented in the ground plan, fig. 4,
namely, so that, according to the rule laid down in the Resultate
572 WEBER ON A TRANSPORTABLE MAGNETOMETER.
for 1837, p. 22*, the line connecting the middle of the bar with
the middle of the magnetometer needle may form with the mag-
netic meridian an angle of 35° 16!. Thus observations of the
variations of the declination and of the intensity may be conve-
niently combined in this manner by travelling observers.
§ III. Examples of Observations and Measurements.
Measurement of the Absolute Declination.
This measurement resolves itself into three parts: 1. The
determination of torsion. 2. The azimuthal determination of
the magnetic axis. 3. The azimuthal determination of the true
meridian. By the azimuth of a direction is here understood
the angle formed by two vertical planes, one in the direction in
question, and the other in the direction of the optical axis of
the telescope of the theodolite, the alidade being placed on the
zero point of the circle.
1. Determination of Torsion.
This determination consists of the measurement of the force
of torsion, and of the angle of torsion.
Force of Torsion.
There belong to the magnetometer two needles, the magnetic
and the torsion needle, which may be suspended to the same
thread, and which differ in the proportion of their magnetic
moments (M, m). Designating by T the horizontal part of the
earth’s magnetic force, the force of torsion is to be compared
with the force M T, as well as with the force m T.
Comparison with the force M T.
In order to reduce the observations to the same time, the
declination was observed in the magnetic observatory simulta-
neously with both the observations.
Observation of thel Observation
Reading of the position of the : : Radius in parts Reduced
Torsion Circle. Magnetometer in the Magnedt of the Scns Observation.
by the Scale. y-
° ’ ° Fe “u
355 6 275-67 18 29 49 2174 275'67
175 6 237-06 18 30 42 237°31
Hence the force of torsion is given in parts of M T
180° 2174 178
* Sci. Mem. Part VI. p. 270.
WEBER ON A TRANSPORTABLE MAGNETOMETER. 573°
Comparison with the force m T.
Observation of the
Reading of the position of Radius
Torsion Circle. Gai ar aah ge Differences, Mean. By eee of
fo} , fheew Bek SBE litcla IY Te ae
269 15 270°77 ?
329 54 10979 ae
269 15 280°91 167-69 2243°5
eu) uh | ie
269 15 282-12
Hence the force of torsion is given in parts of m T
tae 5 FB95)) 16 7°69 7 42-563
PWGOLGS:. onc 2248 e RZ B
Angle of Torsion.
Observation of the
position of Radius
the Magnetometer in divisions of
by Ge Scale. the Scale.
Magnetic needle... 29290 2174
Torsion needle .. 328-67
The distances of the observed divisions of the scale from the
zero point of torsion being designated by v and y, then ~ is the
angle of torsion sought, expressed in divisions of the scale; and
for determining x we have the following equations:
292:90 — x = 32867 — y
12°563 7 = y.
Hence the angle of torsion in divisions of the scale is found,
Ta 3,095
in seconds of arc
309g " "
os - 206265" = 293".
a eo a
From this determination of the force and of the angle of torsion,
the correction on account of torsion to be applied in measuring
the declination is found
1
178
This correction is so small that it may be wholly neglected; the
more so, as, during the time occupied in the measurement, the
declination itself altered two divisions of the scale, so that the
angle of torsion for the time of this measurement almost wholly
disappeared.
- 0G == GG.
574 WEBER ON A TRANSPORTABLE MAGNETOMETER.
2. Azimuthal determination of the Magnetic Axis.
In order to reduce the observations to the same time, the
declination was observed simultaneously in the magnetic ob-
servatory.
Azimuth Observation
Time. : Azimuth
e f the in the Reduced
1839, eee : ‘ of the
April 11. pp reas pecan Azimuth. | Magnetic Axis.
Befor hoe Pere ln Ault 12;
ay \ Li- <¢ 131 22 43| 18 26 2613120 0| o » »
After 131 41 29°5
\ 11 375 |132 259| 18 29 9/132 259
reversal
3. Azimuthal determination of the true North.
Three visible objects were observed, the positions of which,
in respect to the Gittingen Observatory, are given by geode-
sical measurements.
Distance from the Observator
; Be Observed Azimuth of the
Designation :
Azimuth, true North,
of the Objects. |
a South. / West.
33 58 50 ete ual mat)
315.17 5 150 6 14
117 15 15
Hohehagen ..| + 6060:00 | + 12447-70
Gartenhaus ..| + 289°28 - 27°54
|
|
[Oar
|
Jacobithurm..| — 710°70 | + 500- 49 |
As there is no correction to be applied on account of torsion,
we obtain immediately from hence the westerly declination, by
deducting the azimuth of the magnetic axis from the azimuth
of the true north.
150° 6! 14! —131° 41! 29'""5=18° 24! 44/5,
This result corresponds to 115 37™5, 11th April 1839. The
declination observed at the same time in the magnetic observa-
ORS 1g” Zorg",
showing a difference of — 4! 24-5, which probably is only in
part due to error of observation, and is in part caused by the
influence of the copper case surrounding the magnetometer,
which may not be wholly free from iron. Repeated measure-
ments, and comparisons with the observations in the magnetic —
observatory, may serve to deduce such an influence if it exists,
so that it may be taken into account in future measurements.
A second measurement actually gave a similar result, namely,
=
A
WEBER ON A TRANSPORTABLE MAGNETOMETER. 575
1839, April 13. In the open air. In the magnetic observatory.
104 31! 18° 18! O! 1°. 93f Sel
showing a difference of —5' 36". The mean influence of the
copper case in this instrument may therefore be taken as
=—5/.
Observation of the Variations of Declination.
On the 15th April 1839, from 54 25™ to 7) 27™5, the varia-
tions of declination were observed alternately, with the mag-
netometer in the Géttingen Observatory, and with the small
magnetometer. In the following table the four first columns
show the immediate results of observation with the two appa-
ratus. In the final column the observations with the small
magnetometer are reduced according to the proportion of the
value of the scale divisions. The two series of observations are
exhibited graphically in fig. 5, for the purpose of comparison.
It may be seen from this example that the observations of the
variations of declination can be made with a portable mag-
netometer with much accuracy.
: Transportable Magnetometer.
1839. Magnetic 1839.
April 13. Error: April 13, Reading ee ae
-? (w—244'2)
h. m. h. m.
5 25 896-00 5 27:5 244-95 897-44
5 30 895°56 5 32:5 244-20 895°00
5 35 894-66 5 375 244-97 897°50
5 40 896°47 5 42°5 245-20 898-25
5 45 899-56 5 47°5 24618 901-44
5 50 899°52 9 92°5 245-78 900714
5 59 898°78 5 575 246-02 900°91
6 90 900°57 6 25 247°35 905:24
6 5 905°95 6 75 248-04 907-48
6 10 905-00 6 125 249°77 913°10
6 15 916°77 6 17:5 251-77 99°60
6 20 920-00 6 22°5 251:77 919-60
6 25 919-66 6 27:5 251°56 918-92
6 30 916°63 6 325 250°70 916712
6 35 912-72 6 37-5 250°96 916:97
6 40 917-66 6 42:5 251°74 919-51
6 45 927°35 6 47°5 25432 927-89
7 0 941-27 7 25 260°79 948-92
Lo 959-33 ee Jas 265°71 964-91
7 10 964-53 7125 261-27 950°48
7 15 936°38 Ph WA 254-34 927:95
Z 20 922-80 7 225 251-75 919°54
i 25 914-42 7 27-5 250°09 91414
576 WEBER ON A TRANSPORTABLE MAGNETOMETER.
Absolute Measure of the Intensity.
The measurement of the intensity divides itself into four
parts. 1. The determination of torsion. 2. Of the moment
of inertia of the deflecting bar. 3. The experiments of de-
flection. 4. The experiments of vibration. I will confine my-
self in this place, for the sake of brevity, to two parts, viz.
the determination of the moment of inertia, and the experiments
of deflection, which are especially instructive towards a know-
ledge of the instrument. The determination of torsion has
been already spoken of in the measurement of declination, and
the experiments of vibration are so simple and so well known,
that it is sufficient to give their results.
1. Determination of the Moment of Inertia.
The deflecting bar is suspended to a thread or wire, and is
then vibrated: 1) without a weight; 2) with a weight, the mo-
ment of inertia of which is known.
Vibrations without a weight.
Number of Arc of Reduced time
Vibrations. Time. Vibration. of Vibration.
h m. Ss. ° '
0 Gen20s oL27. 8 56 uv
26 7 23 45°49 8 40 6698
61 7 v2] 39:92 8 8 6°695
115 7 33 41°64 7 22 6696
151 7 37 42°80 6 56 6695
186 7 Al 37:19 6 32
Vibrations with a weight.
0 2 18 35°57 8 16 12-058
46 2 27 50°45 6 58 12-039
125 2 43 41°76 5 4 12:019
200 2 58 43:31 3 20
Hence the mean time of vibration without a weight is = 6!"696,
and with a weight = 12-039. For determining the moment of
inertia of the weight we have the following data: 1) the length 7
of the deflecting bar, or the distance apart of the threads which
hang from its two ends and support two equal cylindrical weights ;
2) the mass 2 p; 3) the radius r of the two cylinders.
1 = g3mm-4g
2 p = 500008
Ko= 4mm-60
besigas >
WEBER ON A TRANSPORTABLE MAGNETOMETER. 577:
If the mass of the cylinder were concentrated in its axis, its mo-
ment of inertia would be
1 12 p = 109091000.
If the cylinders revolved only round their own axis, their mo-
ment would be
7? 'p = 529000.
Their moment in the above experiments is to be taken as equal
to the sum of
112 p + 72 p = 109620000.
Whence therefore the moment of inertia of the oscillating bar
may be obtained from the equation
mK w(K +K’)
7? ae 7/2 b)
Vig
where K! signifies the known, and K the desired moment of
inertia, z' the time of vibration with a weight, and ¢ the time of
vibration without a weight, consequently
K = 49103000.
In these experiments the needle was suspended to a thread in
which the force of torsion was so small as to be insensible. The
same series of experiments was repeated with the needle sus-
pended by a wire in which the force of torsion was much greater ;
the result was almost the same as before, namely,
K = 49044000.
Finally, in order to furnish a check, the deflecting bar was
weighed, and its length and radius were exactly measured :
Weight p! = 66670™:
Length 7 = 93mm-4Q
Radius 7 = 5mm 45,
whence its moment of inertia may be calculated. Supposing
perfect internal homogeneity,
K = 7, 1? p! + 17'? p! = 48982000.
The accordance of all these experiments sufficiently shows that
the moment of inertia of even such small bars may be deter-
mined with great precision.
573 WEBER ON A TRANSPORTABLE MAGNETOMETER. 1
2. Experiments of Deflection.
1839, February 13. Double Deflection.
Distance in North . In divisions of
Millimeters. Pole. Readings. the scale. Are values.
— 55675 | E. | 372-95
W. | 13233 | 34062 Lear-os | 5° 30%3
E. | 373-78
— 453-25 | E. | 47591 | ,.-.-
W. | 23-36 tagoa | 44789 10° 9°3
E. | 47658 wid
+ 453°25 | E. 480:04
W. 31-83
E. 480:27
448-21 )
448-44 f 448:32 | 10° 112
455675 | E. | 375-93
w. | 135-06 | 34084 \ 240-82 | 5° 30-0
E. | 375-82 ae
j
Hence the simple deflections vp, v, are obtained for the di-
stances Ro, R, (without regard to signs)
Up = 2° 45! 4/5, for Ry = 556°75
v, = 5° 5! 7/5, for Ry = 453°25.
Consequently, if tang. v be developed according to the powers
of R,
tang. v = 8305800 R~ ® — 4081300000 R~ °
whence (see Intensitas Vis Magnetice, Art. 21, 22),
= = 4152900.
With the comparatively great distance of the deflecting bar
from the needle (equal to from 5 to 6 times the length of the
needle), the determination of the coefficient of the second mem-
ber of this equation (which is to be divided by the 5th power of
the distance) is uncertain, and it is therefore better to dis-
M
ft
R,? tang. vy = 4146600
R,? tang. v, = 4143200,
viz. the mean of which may be taken, consequently,
= = 4144900,
which differs but little from the above value.
regard it. We then obtain for =, two values,
mais
a Oe
WEBER ON A TRANSPORTABLE MAGNETOMETER. 579:
If to the results obtained we add lastly the time of vibration
t, which was found to be
t = 6!-0586*,
and if we assume K = 49073500, we obtain
2
MT = = = 13195000,
consequently
T = 17842.
We are not enabled to test and compare this result further,
as a simultaneous measurement with the large magnetometer
could not be executed at that time. When a new mea-
surement of the earth’s magnetic force is made in the Gottingen
Observatory, the opportunity of comparison thus afforded will
not be neglected.
The improvements, (represented in figs. 2, 6, 7, 8,) which,
since the above was written, I have caused to be made in the
transportable magnetometer, are designed to facilitate the use
of the instrument in the open air, as in travelling it will be rare
to meet with a suitable building free from iron for the execution
of absolute measurements. It is not absolutely necessary that
the whole of the observations for these purposes should be made
in the open air; and on account of the liability to interruption
from weather, it is desirable to reduce the number requiring
this exposure as much as possible. In the improved construc-
_ tion I have given great care and consideration to this part of
the subject, and have found it possible to arrange the obser-
vations in such manner that the greater part may be made in a
room, including those which would be made to the greatest
disadvantage in the open air.
Fig. 6. represents the tripod stand, on which the measuring
apparatus, fig. 7, and the magnetometer, fig. 2, are to be placed
and levelled, as shown in fig. 8. The measuring apparatus,
* The bar having been magnetized afresh for the experiments of vibration
and deflection, had a shorter time of vibration than in the previous experiments
on the moment of inertia.
580 WEBER ON A TRANSPORTABLE MAGNETOMETER.
fig. 7, required for the deflection experiments, consists of a
copper-plate fitting on the tripod, and carrying the supporters
of the deflecting-bar; each of these is formed of two conver-
ging tubes connected at their extremities, from whence proceeds
a third tube provided with a graduation, and on this the deflect-
ing-bar is to be placed: this tube forms also the reading tele-
scope, and has the reading scale attached to it.
Fig. 8. represents the magnetometer placed on the measuring
apparatus, which rests itself upon the tripod: the needle is
suspended in a copper case, which acts as a damper in checking
the vibrations. The mirror close below the needle is directed to
the east. The whole of the eastern side of the copper case can
be removed, to give access to the screw to which the suspension
is fastened, and by which the inclination of the mirror may be
corrected. In the middle of this side is an opening closed by a
piece of plane glass, making a small angle with the vertical,
in order that the reading telescope, which is directed to the
mirror behind the glass, may not see a double image of the
scale.
For the measurement of the absolute intensity the deflection
experiments alone require to be made in the open air; the re-
mainder may be made in a room if more convenient; for if the
magnetism of the needle, which can be ascertained in a room,
be known, the intensity of the earth’s magnetism may be calcu-
lated from that of the needle, and from the experiments of de-
flection made in the open air*. It should be noticed, how-
ever, that the determination of the magnetism of the needle in
such cases requires a complete measurement of the intensity to
be gone through, including both the experiments of deflection
and those of vibration, with and without the weights. The
magnetism of the needle should also be determined either shortly
before, or shortly after, the deflection experiments in the open
air, because it is liable to alteration: and the temperature in
the room and in the air should be as nearly the same as
possible.
The experiments of deflection in the open air require only a
* The experiments of vibration might be made in the open air instead of
those of deflection; but in such case the instrument would afford less cer-
tainty and less convenience.
plas
WEBER ON A TRANSPORTABLE MAGNETOMETER. 58] °
solid foundation, on which the tripod may be placed and le-
velled ; the measuring apparatus, resting on it, carries the de-
flecting bar, the telescope, and the scale, each in its due posi-
tion relatively to the others; and the whole system can be
turned upon the tripod without their displacement. The copper
case of the magnetometer fits into the depression a 3, fig. 8, by
which its position is fixed relatively to all the other parts. The
whole instrument is then turned on the tripod until the middle
_ of the scale is seen in the reading telescope, and it is then ready
for the deflection experiments.
The vernier of the deflecting bar being placed on the zero
point of the graduation of the measuring apparatus, the deflec-
tion of the needle is observed. The deflecting bar is then re-
versed, and the observation repeated. The bar is then removed
to the end of the measuring apparatus, and the vernier set to
1000™™ of the graduated scale, when the deflected position of
the needle is again observed before and after the reversal of the
bar. Let the four observed deflections be called m, m!, n, n!,—
the absolute intensity of the magnetism of the needle, previously
observed in a room, M,—and the arc-value of a division of the
scale, determined also in a room (the torsion being taken into
account), «,—then the absolute horizontal intensity of the earth’s
magnetism will be
2 M
a 008 tan oF
_ where v = } arc-tang. } (m — m! +n —7!) a.
This simple formula may be employed, because the small
dimensions of the needle and bar, relatively to their distance
apart, renders the next member (having the fifth power of the
distance in the denominator) insensible.
Fig. 10 represents the theodolite used in observing the de-
clination and its variations; it is provided with a verification
telescope, having a small scale at the end: a larger scale is
placed above the theodolite, perpendicular to the optical axis of
the principal telescope.
The observation of the absolute declination may be divided
into those parts which must be made in the open air, and those
which may be made in a room. Fig. 11. represents in A the
VOL, II. PART VIII. 2a
§82 WEBER ON A TRANSPORTABLE MAGNETOMETER. :
cross-section of the tube of the magnetometer telescope, and ‘
in BC the scale; between A and BC is a transparent space; —
the theodolite must be so placed that the observer may look with —
the verification telescope through the space D towards the ©
mirror of the magnetometer needle, and perceive the image of —
the scale attached to that telescope; he must first observe the
position of the needle by this scale, and thence determine the
angle ¢ (fig. 12.), which the optical axis of the verification tele-
scope makes with the normal to the mirror of the magneto-
meter; he must then bisect objects of known azimuth with
the principal telescope of the theodolite, and thence find the
angle corresponding on the divided limb to the direction of
the principal telescope relatively to the north.
These are all the observations required to be made in the
open air in determining the declination. The angle x, Fig. 12,
corresponding, on the graduated limb, to the parallel position of
the optical axes of the two telescopes of the theodolite, can be
ascertained in a room; as can also the angle g which the mag-
netic meridian makes with the normal of the mirror belonging
to the needle. Hence we obtain
(x—‘) the angle which the optical axis of the verification te-
lescope makes with the true meridian.
(x —) — 4, the angle which the mirror-normal of the needle
makes with the true meridian.
e—{(x—v)—4$} the angle which the magnetic meridian
makes with the true meridian.
The angle x is found by placing a plane mirror before the
verification telescope, and viewing in the telescope the reflected —
image of a vertical thread suspended over the middle of the —
object glass; a vertical thread is also suspended over the
middle of the principal telescope, and the telescope adjusted to
its reflected image ; the reading on the circle gives the angle x, |
supposing the collimation error of the principal telescope to re-
main unaltered when the eye-piece is adjusted to distant ob-
jects; otherwise the alteration must be sought by reversing the
telescope, and applied as a correction to the reading on the
circle.
The angle ¢ is determined by directing the principal tele-
scope of the theodolite from B (fig. 12.) to C, a second needle
suspended in the wooden case, as represented in fig. 3; the
WEBER ON A TRANSPORTABLE MAGNETOMETER. 583.
verification telescope is directed on the first needle A, in the
copper case as in the open air. The needle C is furnished
either with a collimator or a mirror, and is capable of reversal.
The direction of its magnetic axis is next to be found, 7. e. the
angle »., to which the theodolite must be adjusted, in order that
the optical axis of its principal telescope may be parallel with
the direction of the magnetic axis of the needle ©, whence the
angle eg (= — (x — %) + p) is obtained, if the two needles A
and C are sufficiently distant apart to exert no sensible influ-
ence on each other, so that their magnetic axes may be regarded
as parallel. But if this be not the case, it is easy to determine
the angle v formed by the magnetic axes of the two needles*,
and to add it as a correction to the value, as above, of @; i.e.
g=7—(x— 9) + e+»
The suspension of the needle in the wooden case is so con-
trived, that it may be used either as an unifilar or as a bifilar
magnetometer. This contrivance is represented in fig. 9. The
variations of the declination and of the horizontal intensity can
thus be observed at the same time; the former with the mag-
netometer in the copper case, and the latter with the magneto-
meter in the wooden case. In preparing for the latter observa-
tions, the telescope of the theodolite is to be directed perpendi-
cularly to the magnetic meridian, and the magnetometer in the
wooden case is to be placed in the same direction. The time of
vibration ¢ of the needle, with the unifilar suspension, must be
determined, if not already known, which it will generally be,
from the experiments of vibration belonging to the measure-
ment of the absolute intensity. The unifilar suspension must
then be changed for the bifilar without altering the direction of
the magnetic axis, and the time of vibration must be observed
afresh, the distance apart of the suspension threads being in-
__* From the propositions contained in the Resultate for 1837, page 22 et seq.,
it follows that if A BC = 90°, ACB=a@, and AC =», and if m and m'!
denote respectively the magnetism of the needles A and C,
m—m!
rs T
The value of m and m' must be determined by the deflections 3 and 3! of a
compass needle placed successively east and west at the distance d, namely
mde nl Val
sag Re aaa al
be
y= —sin2e.
$ ae
584 WEBER ON A TRANSPORTABLE MAGNETOMETER. :
creased until ¢’ is about = 0°6871 ¢. The torsion circle must
then be turned until the middle of the scale appears in the field
of view of the telescope, and the time of vibration 2” observed.
The magnetometer is then in the transversal position proper for
observing the variations of intensity, and the value of the scale
divisions may easily be calculated from the observed times of
vibration ¢, ¢', t’; namely, if « denote the arc-value of a division
of the scale in parts of radius, the value of a division of the
scale, in parts of the whole horizontal intensity, is
Fig.
Fig.
Fig.
t? tz {?
mc=,/ (1-25) . Foee:
EXPLANATION OF THE FicurREs, PLATE XXV.
1. a, b,c, dis a vertical longitudinal section of the copper case of the mag-
netometer, with the needle e,f suspended by a silk thread g,h. The
needle is seen to be pierced through its Jength, and provided at the ex-
tremity f with a lens; it is inclosed in a copper tube /, J, m, m, and can
be turned by means of a key o, p, which is accessible by an opening in
the copper case. In doing this the copper tube is held by two screws
g, 7, and two projections s, ¢, The mirror w, v is seen above the copper
case, near the axis of rotation of the needle. A dotted line indicates how
the telescope of the theodolite, fig. 10, is directed, both to the needle and
to the lens at its end f, and also to the mirror uw, v. It is also seen how
the inclination of the mirror may be regulated by the screw w, that
the image of the scale placed above the telescope at a, fig. 10, may
appear in the field of view. This fig. is half the size of the instrument —
itself.
2. represents a magnetometer, which differs from the one just described
in not being adapted for complete measurements of the declination.
The collimator is cmitted, and the needle cannot be reversed. The
mirror @, 6, c,d is inclosed in the copper case, and is parallel to the
plane of the magnetic meridian ; the inclination of the mirror is regu-
lated by the screw at e; the copper case forms an unbroken damper
round the needle, except at the aperture for the suspension thread; the
mirror is observed through a glass plate in one of the sides of the copper
case. This figure is also half size.
3. a, b, c, d, e represents the wooden case, in which either of the instru-
ments shown in figs. 1. and 2. are packed for travelling. The lid, with
the tube a, b, ¢ which is fastened to it, is taken off, the instrument
.
ae -
Fig.
Fig.
Fig.
Fig.
Fig.
WEBER ON A TRANSPORTABLE MAGNETOMETER. 585
placed inside, and the box closed again. When observations are made,
this box serves for suspending a second needle, the time of vibration of
which is required for the measurement of the absolute intensity; this
second needle f, g is provided at both ends with mirrors, one of which
serves for observing the scale. The needle rests on two supports h, &,
attached to a small measuring bar m,n, over which passes a thread
carrying the weights p, g, which serve to increase the moment of inertia
of the oscillating needle. The needle can be turned in the supports h, k,
and may be reversed; rendering it available, in absolute measurements
of the declination, as an auxiliary needle, when the instrument repre-
sented in fig. 2. is used, the needle of which is not reversible. For
this purpose, instead of a needle with a mirror, one with a collimator,
fig. 13, may be placed in h, k. It consists of a magnetic steel tube
a, b, c, d, carrying at the end a, c, an achromatic object-glass ; and at its
other extremity a sliding tube of brass e, f, g, h, provided with a glass
micrometer in the focus of the object-glass. It will be seen also by fig. 3.
that this needle is suspended to two threads, the upper points of attach-
ment of which are r ands. The threads are conducted over a roller x to
give them equal tension, and are united in one from x to v, forming an
unifilar suspension, which may be converted into a bifilar by opening
out the apparatus a, @, y, 3, which is done by pressing down the knob w
by the screw ¢, and disengaging the threads from the pins 2, y, as repre-
sented in fig. 9. Fig. 3. is also half size.
4. A, is the theodolite carrying two telescopes and two scales; one tele-
scope and one scale serve for observing the unifilar magnetometer B,
and the other telescope and scale for observing the bifilar magnetometer
C. The figure gives the angles which the instruments ought to form
with each other.
5. is a graphical representation of the variations of the declination ob-
served on the 13th of April, 1889, at Gottingen, simultaneously in the
magnetic observatory, and with the transportable magnetometer.
6. is the tripod on which the magnetometer, fig. 2, is placed and le-
velled.
7. is the apparatus required for the experiments of deflection. a, b,c, d
is a copper disc which fits on to the tripod, fig.6; e,f, 9, h, and h, l, m, n,
are arms screwed to the copper disc at e, f and /,7; one arm carries the
telescope p, g, to which the scale r, s is attached, and upon which the de-
flecting bar u,v is to be laid; the other arm carries a tube on which the
deflecting bar is also laid, but which could not be conveniently repre-
sented in the figure. Between e, f and 4, J the magnetometer (fig. 2.)
is placed.
8. is a smaller side-view of the magnetometer represented in fig. 2, in
its proper relative position to the measuring apparatus, fig. 7, and rest-
ing on the tripod, fig. 6. In this view the needle is seen only by its
circular cross-section, and the glass plate is shown, in the side of the case
which permits the image of the scale, reflected from the mirror, to be ob.
served with the telescope.
Fig. 9. is explained in the description of fig. 3.
586 WEBER ON A TRANSPORTABLE MAGNETOMETER.
Fig. 10. represents the theodolite with the verification telescope: two scales
are seen, one of which, a, is applied in such manner that its middle —
corresponds to the prolongation of the vertical axis of rotation of the —
theodolite ; the other, b,c, is attached in front of the object-glass of the
verification telescope. It is very narrow, in order to intercept the less
light.
Figs. 11, 12 and 13. are explained in the text.
W. WEBER.
587
ARTICLE XIX.
An extract from Remarks on the Term-Observations for 1839,
of the German Magnetic Association. By W1iLHELM WEBER.
(With a Plate.)
[From the Resultate aus den Beobachtungen des magnetischen Vereins im
Jahre 1839. |
In concluding this notice, I wish to call attention to the ob-
servations made in the high northern latitudes m 1838 and
1839, for which we are indebted to the zeal and perseverance of
the French savans, MM. Lottin, Bravais and Martin, and of
the Swedish naval officers, Lieutenants Siljestrom and Silje-
hook, who joined the French expedition to Spitzbergen and
Finmarken: we may derive instruction from these observa-
tions in regard to the arrangement of future researches of the
same nature in those regions. In looking at the Plate, XXVI.,
it is obvious at the first glance, that the beautiful accordance
in the variations of the magnetic elements, which had been hi-
therto invariably observed, from Catania, Rome, Milan, &c., to
Upsala in the north, ceases when we proceed still further north ;
so that in comparing the curves of Upsala and Alten (in Fin-
_marken, lat. 69° 58!) they would scarcely be recognized as be-
_ longing to the same term. There is no doubt as to the correct-
ness of the observations, as the voyagers undertook the addi-
tional trouble of occasionally observing Gambey’s needle simul-
taneously with the magnetometer, and the movements of both
were found to be in accord. If therefore these observations suffi-
ciently assure us of the great difference between the magnetic
changes in those more northern districts and in Upsala, the im-
portant conclusion follows, that future term-observations in these
very high latitudes will only be rendered truly valuable by the
establishment of intervening stations, which may show the gra-
dual passage of the one system of changes into the other ; or by
having a group of several stations around Alten and its vicinity,
which will afford a sufficient interest by their mutual comparison
independently of others, as it is to be expected that great differ-
ences should there manifest themselves at small distances. Such
observations would be available for inquiries, for which those
588 WEBER ON THE TERM-OBSERVATIONS AT ALTEN.
made elsewhere are little or not at all adapted; in particular we
might, by their means, determine most securely whether the forces
which cause the variations have their seat above or below the sur-
face of the earth. Without this multiplication of stations in its
vicinity, observations of the variations at Alten will have a much
inferior value, as they differ so greatly from those at the nearest
present station, Upsala, of which we may convince ourselves by
inspection of the curves of declination and horizontal intensity
on the 23rd of February, 1839, shown in Plate XXVI. The
three declination curves represent the variations of that element
from noon to 10 p.m., Gottingen mean time, at Alten, Upsala,
and Gottingen, and are all on the same scale. The two curves
of the horizontal intensity are for the same period, and repre-
sent the changes at Alten and at Gottingen, which was the
next most northern station at which the intensity was observed
during that term. We cannot perceive in the two latter curves
even that trace of resemblance which is visible in those of the
declination. W. WEBER.
589
ARTICLE XX.
Results of the Daily Observations of Magnetic Declination
during six years at Gottingen. By Dr. B. Gotpscumipr.
[From the Resultate aus den Beobachtungen des magnetischen Vereins im
Jahre 1839. ]
IN the volume of the Resultate for 1836, M. Gauss com-
municated the results of the observations of the magnetic de-
clination, made daily in the magnetic observatory at Gottingen,
from the 17th March, 1834, to the 31st of March, 1837, and
combined them in various ways for the purpose of determining
the march of the declination*. Since that period these obser-
vations have been continued uninterruptedly by me according
to the same plan, and we have now before us the determina-
tions of six years, which I propose to consider in this treatise.
To the mean values of the declination for the several months
of the three first years, published as above, we have now to add
the following :—
1837 to 1838, 1838 to 1839. 1839 to 1840.
Month. > _ 3 LE | a io inn | a
8 A.M. 1 P.M. 8 A.M. 1 P.M. 8 A.M. 1 P.M.
*) i “l ‘ “ 4 “ 4 “
April......... 21 59:1 | 40 42-2 8 08:9 35 56°7 || 14 43-8 | 28 43:5
May ......... 23 17°3 | 38 35-2 i 439 | 35 46-1 || 15 16-7 | 28 15-0
June ......... 22 46:2 | 38 24:8 7 40°77 | 35 06-2 || 13 54:1 | 27 15-5
Oa 21 33:3 | 36 55-4 8 47-6 | 33 48-2 || 14 27-6 | 28 16-6
August ...... 24 22-2 | 37 51-9 i 43:9 | 34 59-4 || 13 40:9 | 30 07-0
September...|} 25 02-5 | 37 19-1 8 17:1 | 33 17-5 || 13 41:8 | 27 26-5
October...... 25 50:0 | 37 00-2 19 58°7 | 30 48-3 || 14 47-4] 25 53-0
November...|| 25 47-5 | 33 12-7 a 06:6 | 28 14-4 || 16 01:3 | 23 08-9
December ...|| 25 51-4 | 31 14:5 1 34-3 | 26 19-0 |} 16 54:5 | 21 02-6
January...... 25 25°3 | 33 36-2 1 01-6 | 27 35-1 || 15 41:5 | 20 48-6
| February ...|} 23 55-3 | 33 37:8 20 01-0 | 27 29-8 |} 13 53-1 | 22 15-9
| March ...... ¥ : 18 09°6 | 29 52-4 || 11 14:4] 23 42-4
The number of degrees is throughout 18.
We will now proceed to combine these numbers in the same
manner as was done with the observations of the first three
years, beginning with the deduction of the differences between
the forenoon and afternoon declinations. These differences, the
* Translated in the Scientific Memoirs, vol. ii. Part V. pp- 54 to 65.
590 DR. GOLDSCHMIDT ON THE OBSERVATIONS
monthly mean values of which have all the same sign, are exhi-
bited in the following table :—
1837 to 1838, 1838 to 1839. 1839 to 1840.
é “ “se 4 “se
Alpril) scysia.st2se.<. 18 50-1 17 47:8 13 59:7
May. osssd.c-c0steoeds 15 17-9 17 02-2 12 58:3
JUBE\ oscccscncesstes’ 15 38°6 17 25:5 13 21-4
Dl yivccescsvessnsencd 15 22-1 15 00-6 13 49-0
PUD IICi a abeerssarees 13 29-7 16 15:5 16 26-1
September 12 176 15 00-4 13 44:7
October _