v, the integral becomes
infinite, the ae will be within a cone of semi-vertical
angle sin = ~ =; we must therefore only integrate within
this cone, and the equation to determine & is
p eames SIO O, ae ne Beay:
ayy u? * 9 z a u 2?
20 1— 5 sin 0) ce :)
7 v v
oe(1— ia) =
aie oo eae (1-5 — sin "8).
Thus the magnetic force
or
k=
oan 2 zs
u? \2 @ . 3
2
we(1— <) (1- —;sin*8
v v
wo? cana
cos 8 vr? (i- 3 sin’@ )
14 Mr. C. V. Boys on Quartz as an Insulator.
Since sin 8=v/, this expression vanishes unless 0=8,
when it becomes infinite, so that the magnetic force and the
electric displacement seem confined to the surface of a cone
of semi-vertical angle 8, the vertex pointing in the direction
of motion. ;
Trinity College, Cambridge,
April 24, 1889.
II. Quartz asan Insulator. By C.V. Boys, A.R.SAL, FB.S.,
Assistant Professor of Physics at the Normal School of
Science, South Kensington*.
[Plate I.]
my TEN making quartz threads by the bow-and-arrow
process described in the Philosophical Magazine, June
1887, I have sometimes noticed that the thread does not reach
all the way from the arrow to the bow, but that the end
remains suspended in mid air somewhere between. When.
this is the case the last foot about, then very fine, is usually in
the form of an irregular helix. Under these circumstances,
if the hand is brought at all near the end the helix stretches
itself out, and the end of the thread flies to and attaches itself
to the hand. On removing the hand the thread takes its old
form; and this may be repeated several times. :
It did’ not seem possible to account for this in any way
except by supposing the thread to be electrified, though why
it should be electrified is not clear. If this is the case then
the insulating-power of the thread must be very great, for
with the very small quantity of electricity which could remain
on a body of such immeasurably small capacity, all trace of
charge would escape instantly if the thread insulated no better
than glass in the open air.
I therefore thought it would be interesting to see if rods of
fused quartz showed any great superiority over similar rods
of glass under the same circumstances. The plan that I have
followed has been to hang a pair of very narrow gold leaves
from the rod under examination, and observe the rate at
which they closed after being charged. I purposely avoided
all instruments the large capacity of which would increase the
time of discharge, and the leakage of which might be com-
parable with or even exceed that of the rods to be tested.
The arrangement of leaves &c. is shown in fig. 1. A flat brass
hook, A, is fastened to a rod which can slide stiffly through the
* Communicated by the Physical Society: read April 13, 1889.
Mr. C. V. Boys on Quartz as an Insulator. 16D)
centre of the lid of a mahogany box Fig. 1.
lined with tinfoil. From this is
suspended the piece of glass or
quartz, B, bent to the form shown,
so that it can be handled by the
projecting end without touching
the portion that acts as the insu-
lator. On this hangs a piece of
~ bent brass, C, to which the leaves,
D, are attached. A small ring of
wire is soldered to the upper end of
C, which is used when one insulator
is changed for another as follows :—
A stiff wire, E, passes through one
side of the instrument, and this is
pushed forward through the wire
ring. A isthen depressed until the
lower side of B hangs clear of the
hook C. £ is then drawn back
with C and D suspended from it.
Finally, when B is changed, H is
pushed forward again, and A raised
until the ring on C is just free
from E, which is then withdrawn.
By this means the leaves are always.
left at the same level. The leaves are 905 millim., and
the box, which has a glass front and back, is 285 millim.
high x 130 millim. wide, and 185 millim. from front to back.
The leaves are suspended so that the line of junction of C and
D is 160 millim. above the base of the instrument. The
length of the insulating portion of the quartz and glass hooks
B is 21 millim. and the diameter about 1 millim. The leaves
were observed by fixing the object-glass of a telescope at a
distance of 393 millim., which projected an image of the
leaves on a scale 1940 millim. beyond the lens. Thus the
observed divergences were 4°93 times the true distances
between the ends of the leaves.
The results of the experiments can be seen from fig. 2
(Plate I.). The rate at which the leaves close is the same with
lead-glass in air dried by sulphuric acid, with quartz in air
dried by sulphuric acid, and with quartz in air kept moist by
means of a large flat dish of water. Soda-glass in air dried
by sulphuric acid allowed the electricity to escape about
eleven times as fast. With either kind of glass in moist air
the charge escaped almost at once, but soda-glass was much
worse than lead-glass. The glass had in all cases been boiled
Hi
I
16 Mr. C. V. Boys on Quartz as an Insulator.
in distilled water, a process which Warburg and Ihmori* have
shown is necessary in order to make the glass insulate as well as
possible. There is no appreciable difference between the rate at
which positive and negative electricity escapes from the leaves.
The quartz insulator was then treated in various ways to
see how well it is likely to retain its insulating power. It
was boiled for five minutes in a weak solution of potash and
washed. It was boiled for the same time in a strong solution
of potash and washed. In both cases it insulated as before.
It was dipped for two minutes in melted potash and washed.
In moist air it insulated better than either soda or lead-glass,
but not so well as before treatment with potash. Boiling in
strong hydrochloric acid did not restore the lost power. A
new hook was not affected by boiling in strong hydrochloric
acid, or by heating in a batswing gas-flame.
Perhaps the most surprising result is obtained by dipping
the quartz hook in water or ammonia, and immediately hang-
ing on the leaves while the water is standing upon the hook
in beads. Hven so no difference is observed in its insulating-
power. If it is dipped in a solution of potash this is not the
case ; but of course the insulation is restored by washing.
The perfect equality of the rate at which the charge escapes
when the leaves are suspended from lead-glass in dry air, or
quartz in dry or moist air, makes it probable that this loss
of charge is not due to leakage along the insulator, for it is
very unlikely that, under these different circumstances, the
loss should be exactly alike. It is more probable that the loss
is due mainly to convection through the air. This is made
certain by the following considerations. The same leaves,
when hung by the same hook in another box which was badly
made and rough inside, lost their charge much more quickly,
but, as before, at the same rate in the three cases. On the
other hand the leaves, when suspended in the best instrument
by a quartz fibre about ten times as long and one hundredth
of the diameter of the piece B (that is, by one which would
insulate a thousand times as well if the loss was due to surface
creeping, or a hundred thousand times as well if it were due
to actual conduction), lost their charge practically at the same
rate as before.
Pieces of polished rock-crystal, such as are used as objects
for the polariscope, also insulate well ; but they do not seem
to be quite so free from the influence of moisture as the fused
quartz. The same is true with regard to the natural faces
and the fractured surface of the crystal.
The electromotive forces required to produce different diver-
* Wied, Ann. xxvii. p. 481 (1886).
On the Mercury Umit and the British Association Unit. 17
gences of the gold leaves were determined by an absolute
~ electrometer, and the results are shown in fig. 1 (Plate I.).
It is probable that this valuable property of quartz, that it
insulates perfectly in damp air, may be of use in the con-
struction of electrostatic apparatus. The sulphuric acid now
absolutely necessary in electrometers and instruments of that
class is nothing short of a nuisance. If the instrument is
carried about there is the risk of destruction of the instrument
~ from the spiiling of the acid. If the instrument is not moved
the acid, unless specially treated, may give off nitrous fumes
which will corrode the surfaces of metal; or, if forgotten,
it absorbs water and in time overflows, destroying the whole
apparatus. liven if the air were saturated with moisture, rods
of quartz would insulate as well as the lead-glass at present
used does in air dried by sulphuric acid. The needle should
of course be suspended by a fibre of quartz, which is far
simpler to apply and adjust than the double line of silk, and
superior also in other respects.
In conclusion I must express my obligations to Mr. Briscoe,
a student in the laboratory, whose skill in the manipulation
of gold leaf and whose suggestions from time to time have
been of the greatest service. I have with perfect confidence
asked him to carry out the experiments described in this paper,
and the results show that the confidence was not misplaced.
Ill. A Comparison of the Mercury Unit with the British Asso-
ciation Unit of Resistance. By Cary T, HuTcHINSON and
GILBERT WILKES”.
. object of this research, which was conducted in the
Physical Laboratory of the Johns Hopkins University,
under the supervision of Professor Henry A. Rowland, is the
determination of the ratio of the resistance, at 0° C., of a
column of mercury, 1 metre long and 1 square millimetre in
cross section, to the British Association unit of electrical
resistance.
The method employed in making the observations was, with
slight modifications, the same as that used by Lord Rayleigh,
by Glazebrook and Fitzpatrick, and also in a similar determi-
nation already made at this laboratory.
The resistance at 0° C. of a column of mercury, filling a
fine, accurately calibrated glass tube, is determined in British
Association units; the length L is known; its mean cross
* From the ‘Johns Hopkias University Circular’ for May 1889.
Communicated by the Authors.
Phil. Mag. 8. 5. Vol. 28. No. 170. July 1889. C
18 Messrs. Hutchinson and Wilkes’s Comparison of
section at 0° C. is found by weighing the volume of mercury,
contained at that temperature, and dividing this by L multi-
plied by the density of mercury (p) in grammes per cubic
centimetre.
The resistance of a column of mercury of varying cross
section is calculated as follows (Maxwell’s ‘ Hlectricity and
Magnetism ’) :—
Let s be the cross section of the tube at a distance # from
one end; let A be the length of a short thread of mercury,
when its middle point is distant « from this end ; then, assu-
ming s constant, throughout the length A, we have s=¥,
where C is the constant volume of the thread.
The weight of mercury that fills the tube is
W=p | sde=p03 (2)®, 51: (ee et)
in which n is the number of points, at equal distances along
the tube, where A is measured.
The resistance of the tube full of mercury is
/ rf i OF
R= (= ae= 5 20) Reman cima.
where 7’ is the specific resistance of mercury for unit volume.
Hence, from (1) and (2),
WR=r'pd(a) (ee
n/n?
or
Ee NO AVere: 6
ih pL?z(x)2(;) .
in which 7 is the resistance of a column of mercury 1 metre
long and 1 square millimetre in cross section, at 0° C., ex-
pressed in British Association units.
In this equation put
3003(0
n?
ih
The equation for 7 now becomes
RW
T= Te ° ° ° ° Vigo remne (3)
a
a
*
the Mercury Unit with the British Association Unit. 19.
R, W, 7, p, L have already been defined. IL is measured
~ in centimetres ;
» is the coefficient correcting for conicality of the tube.
Let
Then, volume of thread at eC. = a
Li = length of tube at ¢’°, measured by brass bar at ¢,’° ;
t= ,, thread of mercury filling the tube at 0°,
referred to bar at ¢,’°;
_ 6L= correction to L, for junction of column of mercury
with terminals = ‘82 diameter of tube ;
p = specific gravity of mercury at 0° C. =13°595 ;
y = cubic expansion of mercury per degree =:0001795 ;
o> ” ” glass ” ” = "000025 ;
b = linear Ay bar - iy = LO00019:
t) = temperature of brass bar, to which iengths are re-
duced, =8°°7 C.
W
Mean section of tube at 0°
R
H
Solving for 7,
or
it ca ia
~ p I+ b(t =t)}
ENS Kg Gees,
~ p L{1+b(te! —t) }
educed length of tube at 0°
(LU +8L){14+0(G!—t)}
Ts ann
ence .
pe 107*r ye. (L+8L) {140s —t)} pLi{1+(ts/—t)}-
1+4gt WU+490)
= 1ORW(1 +490’)?
eee Poly ened; 1 tl eo, nn
10*RW(1+49t')?(, 6L
24 — (1 5) {1-20(4/—4)},
10¢°RW éL / /
r=— ore (1 Ja +89t 12M}.
The ends of the tube containing the mercury opened into
the ebonite cups about two thirds filled with mercury. Upon
the assumption that these may be considered infinitely large
C2
20 Messrs. Hutchinson and Wilkes’s Comparison of
in comparison with the diameter of the tube, Lord Rayleigh
has calculated that a correction of °82 diameter, additive to
the true length of the tube, is necessary in order to allow for
the resistance of the terminal connexions. Mascart, Nerville
and Benoit, and also Glazebrook and Fitzpatrick have verified
this result experimentally. This quantity is 6L in the above
formule.
In commencing our experiments in the spring of 1888, our
first object was to determine the best methods that had been
used for the different determinations involved. About two
months were spent in standardizing resistances that were to
be used (the comparisons being made in a constant tempera-
ture vault, using a Fleming bridge) and in testing different
methods of measurement.
An attempt to measure the lengths at 0° C. was made, only
the portion of the tube to be observed by the microscopes
being scraped clear of ice. It was found that this method
presented great difficulties ; and as an error of 10 per cent. in
the assumed expansion of glass, in reducing the length of the
tube from 20° C. to 0° C., would only cause an error of
Tooryo9 in the length, the plan was abandoned.
The measurement of a column of mercury a little less than
the length of the tube, which was covered with ice except at
points over the ends of the column, was tried repeatedly, both
by observing the meniscus and by flattening the ends of the
mercury with hard rubber plugs (as suggested by Lord
Rayleigh) without success. The lenses of the microscopes
would naturally coat rapidly with moisture, and the unoccupied
parts of the bore of the tube become so wet that minute glo-
bules of mercury would be left behind when the column was
run out to be weighed. We endeavoured to obviate this by
plugging the ends with soft wooden plugs; but still the
moisture got in, making the meniscus uncertain, and inter-
fering with the removal of the column.
Plate-glass end-pieces, held in place by elastic bands, were
tried, hoping thus to obtain full tubes at 0°; but, owing to
the grinding of the plates against the mouths of the tubes and
the old trouble with wet mercury, these were given up.
The tubes were at first secured to straight, narrow, well-
seasoned boards, and (the end-cups being in place) were put
in watertight rectangular boxes (lined with waxed duck)
about 5 inches wide and 5 inches deep. Crushed ice was
then packed in over them. Though observations taken ten
or fifteen minutes apart would apparently agree, it was found
that, owing to the proximity of the board, the mercury would
sometimes not have reached its minimum resistance in four
the Mercury Unit with the British Association Unit. 21
or four and a half hours. The boards were therefore replaced
by narrow partition-blocks, scored to allow the tubes to rest
firmly. The tubes were thus raised about three quarters of
an inch from the bottom of the box.
Most observers have measured the length of the column of
mercury, used in determining the cross section of a tube, at
the temperature of the room (between 10° and 20° C.), and
then used a formula which reduces their observations to 0° C.
As the cubical coefficient of expansion of mercury in glass
is ‘00016, an error of little more than six tenths of a degree
will make a difference of one part in ten thousand in the final
result. Since the mercury-column is in a thick-walled glass
tube, simply exposed to the air of the room (generally for a
few hours), the uncertainty of its being at the temperature
shown by thermometers placed alongside the tube may be
readily seen. The tendency of this error will be to give too
high a value for 7. Glazebrook and Fitzpatrick measured the
length of the column at intervals of fifteen minutes ; and when
two consecutive readings coincided, it was assumed that the
mercury was at the temperature shown by the thermometers.
They verified the result in several cases after the mercury had
been blown out into a small capsule, but do not mention how
they measured accurately the temperature of so small a volume
of mercury.
In view of the results of our preliminary observations it
was decided to determine the mean cross sections at zero, by
using the mercury upon which the resistance-measurements
had been made and obtaining a full tube as follows :—
When through with the resistance-measurements, one end-
plece was removed and the tube stopped by one finger, over
which was a tight, elastic, pure gum-band. The other end of
the trough was then raised to an angle of about 20° without
disturbing the tube in the ice, the end-piece quickly slipped off,
the end of the mercury-column flattened off with a similarly
covered finger, and any globules wiped away. The angle of
the box being reversed, the mercury was allowed to flow out
into a watch-glass, being afterwards dried over pumice-stone
soaked with strong sulphuric acid.
Supposing that the exposed ends (about 6 centim. in all)
rose to an average of 3° C., which they could hardly do in the
few minutes necessary to empty the tube, as they were in such
close proximity to the ice, and the original temperature less
than 0°°3 C., the error due to this cause would make the result
three parts in one hundred thousand too low.
Determination of w.—The tubes were furnished by Eimer
and Amend, of New York, and out of a very large number
22 . Messrs. Hutchinson and Wilkes’s Comparison of
about fifteen were selected on account of uniformity of bore,
being tested by moving a small mercury column along in
them and measuring its length with a scale. These were
then more carefully tested and the best seven selected, which
were cut as nearly as possible to represent exact multiples of
a B.A. unit in resistance—one tube was cut for one half B.A.
unit. The ends were ground convex, using a fine file and
camphor in turpentine. After this the tubes were carefully
cleaned, using distilled water, nitric acid, distilled water,
ammonia, distilled water, alcohol, distilled water. Before
using these liquids, a small piece of wet cotton-wool was
drawn through the tubes (always in the same direction) in
order to remove any solid particles that might accidentally be
present. This was accomplished by first drawing through a
silk thread by means of an air-pump, and then tying on the
cotton and pulling it through several times in the same direc-
tion. This was always done in cleaning the tubes before
filling. The tubes were dried by warm dry air, which had
passed through calcium chloride and cotton-wool, the flow
being kept up by a pneumatic pump.
The values of w for the different tubes were obtained by two
independent determinations, using different lengths of the
thread of mercury. The lengths of the thread were read on
a dividing-engine.
TABLE [.— Values of p.
iene cas Length of Length of
Tube. Ee pL. thread, in pe thread, in || Mean p.
resistance. . :
centimetres. centimetres.
I. 4 ohm. 1:00056 5 1:00050 39 1-00053
II. Dans 100039 3 1-00043 38 1-00041
p 1-00080 4-0 :
II. 2, 100088} 4:8 | i Bote 35 1-00089
IV. LOG, 1:06132 38 1-00133 4°8 1:00133
We LB sais 100133 46 1-00122 4:0 1-00127
; i 1:00063 34 :
VI. raha 1:00055| 4-7 { | 1000682) 38 \ 1-00060
Determination of L.—As all the tubes except one were
longer than a metre we calibrated two metres of a five-metre
bar; but it was found so unwieldy that better results could
be expected from using a metre bar and three microscopes.
Accordingly a comparator was placed on a long marble slab,
and in prolongation with it a third microscope, mounted on a
solid wooden block cemented to the slab, was placed. The
values of the micrometer-divisions were respectively ‘0025
millim., ‘0022 millim., -0045 millim.
-
the Mercury Unit with the British Association Unit. 23
Hbonite plugs were inserted in the ends, and readings were
taken in at least four positions, by revolving the tube, in each
measurement.
The temperatures of the tube under observation and bar
were given by two thermometers lying against each. Mea-
surements were made by both observers.
a TABLE I{.—Lengths of Tubes, in terms of brass Metre (by
Bartels and Diederichs, Gottingen).
Temp. of| Temp. of
Length, in | Length, in
Be tube. bar.
: i Average.
centimetres.|centimetres. 8
if 127-7598 | 127-7610 || 127-761} 19° C. | 195°C.
EY. 129-8690 | 129-8726 || 129-871] 18 18
EY, Broken in |preliminary|) work.
TV: 91-4500 91-4550 || 91-453] 19 18°5
Vv. 181-0100 | 181:0147 || 181-012] 19 20
yrx | 1510951 | 151-1285 || 151.109] 193 18
| 151-1049 151-1034 || 151-104} 24 24
The former value applies to determinations 1 and 2 of this
tube, the latter to Nos. 3 and 4.
The temperature was very constant for the separate
measurements on each tube and, as it never differed more
than two degrees between corresponding observations, the:
average length is taken at the average temperature.
By comparison with the steel Rogers’s standard, whose
length is accurately known, the brass metre bar was found
to equal 100:031 centim. at 24°C.; a result which agrees
perfectly with previous determinations, using ‘000019 as the
coefficient of linear expansion. This would make the bar
correct at 8°°7 C. |
— Weighing.—Schickert weights and balances were used, the
former being compared with the glass standard kilogramme,
which has been compared with the Berlin standard.
In order to avoid errors due to moisture and uncertainty as
to temperature, the standard and weights-compared were left
standing on the scale-pans for several hours before taking the
weighings, which were made without opening the case of the
balances. The temperature was kept constant, barometer
readings taken, and the air was kept dry by calcium chloride.
The brass kilogramme (K) was found to equal 1000-001
erammes in vacuo, which agrees well with former determina-
tions. Specific gravity 8°3.
* One end became nicked and was smoothed off.
———
24 Messrs. Hutchinson and Wilkes’s Comparison of
Resistances.—The resistances used were :-—
1. Warden-Muirhead 10 B.A.U., No. 292. Value, de-
termined by Glazebrook, October 1887, 9°99416 at 16°°5 C.
Temperature-coefficient ‘00292. This coil was our standard.
2. Elliott 10 B.A.U., which has been several times com-
pared at the Cavendish Laboratory. Itis marked as found ©
correct by Rayleigh at 20°-9. By comparison with W. M.
No. 292, we found it correct at 20°38. Temperature-coefficient
0034.
3. Elliott 1 B.A.U. Resistance -99950 at 16°C. Tem-
perature-coefficient :00037.
4, Pratt 1 B.A.U. Resistance 1:02579 at 16°C. Tem-
perature-coefficient -00030.
5. A circular comparator (designed by Professor Rowland),
containing ten 10 B.A.U. coils wound together on a copper
cylinder, which contained water. The coils are protected by
an outer cylinder which leaves a large air-space. Contacts
are made by means of mercury cups, arranged circularly
in an ebonite top. This comparator was used in standardizing
the one-ohm coils and asa shunt. The coils were always kept
standing in water for several hours before being used, and the
temperature of this water was kept perfectly constant through-
out the day by having in each vessel a coiled lead pipe, which
was connected by rubber tubing with the pipes of the ey
water-supply.
All resistances were compared both before starting and
after completing this portion of the work, and the two sets of
results agreed.
The resistance of the rods used to connect the end terminals
to the bridge was calculated for temperature of room, 18°C.,
"001257. By observation :—temperature of the room 21°5
001258. As this temperature never varied much from 22°,
°00127 was used as the correction in all cases.
A Fleming bridge was used, and the value of a division of
the bridge-wire by two distinct determinations gave agreeing
results. The resistances were so combined (except in the case
of the first measurements made) as to require the use of as
small a portion of the wire as possible.
Tube I. was balanced against coils H 18B.A.u. and P1B.A.v.
in parallel, shunted by coils 1, 2, 8, 5 of comparator in series.
In 1st observation, shunt=coils 1+ 2.
Tube II., against H 1 8.4.u.4+ P18B.A.v. in series, shunted by
coils 2, 8, 4, 5,6 in series. In Ist observation, shunt=coil 1.
Tube III., broken in preliminary work.
Tube LV., against W.M. 10 B.a.v.
ez
the Mercury Unit with the British Association Unit. 25
Tube V., against W.M. 108.4.v. and H108.a.v. in parallel.
Tube VI., against H18.A.v.
When coils were connected in parallel, their terminals
rested solidly on copper disks, about # inch in diameter, well
amaleamated and covered with mercury, in boxwood cups.
The rods connecting these cups to the bridge were short, stout
copper rods, whose calculated resistance was ‘000156 at 16° C.
This is, of course, always taken into account.
After cleaning the tube as described above, each end was
thrust through a perforated cork, which was then fitted into
an end-piece similar to those used by Lord Rayleigh, and
the outer surfaces of the corks were covered with melted
paraffin. The mercury used was new and was distilled in a
vacuum, the temperature of distillation being low. Before
filling the tube, the mercury was gently warmed and was
then poured into one of the end-pieces, the other end being
raised, in order to allow the column to flow in slowly. If
any specks or small bubbles were noticed on the sides of the
bore of the tube, the filling was discontinued and the tube
again cleaned. ‘The terminal cups were about two thirds full
of mercury. These were corked, the tube laid in the notched
Scale ¥.
A. Copper connecting Rod.
B. Ice cup.
C. Hard rubber terminal.
D. Hard rubber.
T. Tube.
partitions in the trough and well covered and surrounded
with crushed ice. About four hours afterwards, the cups
on the connecting rods (see figure) having been previously
filled with ice, in order to have them cooled down before
placing them in position, the resistance measurements were
commenced and usually occupied about twenty minutes.
The galvanometer used was an Elliott, having a resistance
of 1} ohms. A difference on the bridge-wire, amounting to
one part in 100,000 of the resistance, being measured gave
readable deflexions on either side of the “‘ balance”’ position.
Three complete sets of observations were always taken
26
Messrs. Hutchinson and Wilkes’s Comparison of
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060
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190
OI
OFIE9+1
TGV
GGG
18009:
“oye qd.
‘IA | 06
NIE HF Jit
| nove ONC Hise ke FNM ANOS ANH
mn of Hid OH = DOO aN
rf 1
|
"ON | oqny,
the Mercury Unit with the British Association Unit. 27
and the current reversed, in order to eliminate any small
thermal current.
Benoit has determined that the resistance of mercury is
decreased by the diffusion of copper amalgam from the ends
of copper connecting rods. Similar experiments, performed
at this laboratory, have demonstrated the fact that, by leaving
the rods dipping in the mercury in the end-pieces for twenty-
four hours, the resistance was decreased one part in twenty-
four hundred. Therefore, the decrease due to this cause in
our investigations must be inappreciable.
In the cases of nine fillings, a small thermometer was
placed in the mercury cups immediately after removing the
rods. In no case was the temperature thus obtained greater
than 1°C., and the average of the nine sets of observations
was 0°5C. Supposing that 6 centim. of the tube were at
this temperature, in the worst case the error would be -00003
high ; while, in the other cases, it would be about 00002 high.
Table III. (p. 26) gives our final results.
Owing to the tubes being entirely unprotected, great care
was necessary in handling them. Tube III. was broken in
our preliminary work, in trying to remove the end-pieces,
which were then fitted with perforated rubber stoppers.
These were after this replaced by common corks.
Tube I., whose bore was 1°76 millim. in diameter, allowed
the soft rubber thimbles to sink into it and thus cause the
column of mercury weighed to be smaller than it should have
been. A correction should be applied on this account and
might have been obtained by jacketing the tube with a water-
jacket and then taking a number of alternating observations,
using the thimbles and then glass plates. Unfortunately, this
tube was broken after all the other observations had been
completed. Its average—manifestly low—is not included in
the final result.
Only one observation is neglected in the remaining tubes—
17., IV., V., VI. An error of one part in a thousand is
apparent in observation No. 1 of tube LV., which is the case
referred to.
In the final result there are, therefore, on
Tube I1., 7 observations.
NS E
9) Ales o >)
>) niles us 9?
Metal Se++5 LG
28 Messrs. Hutchinson and Wilkes’s Comparison of
Giving the tubes equal weights in the final average, we
have :—
Eobe Wee es 205.0. RRS rae ee
eee EV etcsetis Opiate 5 Sa rte
Sa) Pee IE ea ek
oe NA a ee. ie
Mean ~) 20.) “Some
Arranging the tubes in the order of ratio of length to
diameter, we have
TABLE LV.
Tube. Diameter. oy of length r.
o diameter.
rail
I. 1-763 724 *95255
VI. 1-352 1120 ‘95317
II. "985 1320 95320
V. 670 2650 *95349
IV. °334 2730 95343
This table shows the effect of the sinking-in of the fingers,
in taking the tubes full of mercury, for if we take tubes IV.
and V., in which this ratio is roughly the same, the variations
in r may be due to other causes. So too, tubes II. and VL.,
in which this ratio is roughly the same, agree.
Observations were taken, as suggested above, to determine
the correction for tube VI. The quantity obtained is a
difference and, therefore, difficult to determine accurately.
The results are given below :—
TaBLeE V.—Correction necessary in case of Tube VI., to
reduce for sinking-in of fingers in taking full tube.
Correction in
Number of observation. .
tooo of 1 per cent.
a + 44
2 + 23
3 + 15
4 + 28
Average = + 27-5 = + 00026
ia
the Mercury Unit with the British Association Unit. 29
Average obtained from Tube VI.=°95517
Comceon. . a... s = 00026
Corrected result from Tube VI. =:95343
Taking the mean of tubes IV. and V., the variations of the
other tubes are very nearly inversely proportional to the
squares of these ratios.
Combining the results of tubes II., IV., V., VI., in this
way, the final result would be °95341.
Combining the tubes with weights proportional to their
resistances, that is proportional to —, the final result would
be “95341. e
Applying corrections, as given by Table V., we would have
*95346.
We therefore give, as our value of the resistance of a
column of mercury one metre long, one square millimetre in
cross section, at 0°C.,
95341.
| Taste VI.—Results obtained by different Experimenters.
Value of 1
metre of
Observers. Date. References, Mercury in
B.A.U.
Lord Rayleigh & Mrs. Sidg-| 1883 | Phil. Trans. 1883. 95412
BME peck Sak, os ass occbicolese ss
Mascart, Nerville & Benoit | 1884 | Journal de Physique, 1884. "95374
| Oe Igegaly) Wicdemeunis, Saal (|, | onde
vol, xxv. 1885.
POR OIGZ 5 a cinis'ny'n sais 3 90/0000 1885 | Same. 95388
Toit ae eee 1887 ners ieee ad 95349
Abhandl. der K. Bae,
Akad. der Wissenschat- ’
onIrauseh' ..ci.c.2c..s0s000- 1887 Fema We @laane rok aa 95331
Abth. ITI.
Glazebrook & Fitzpatrick...) 1888 | Phil. Trans. 1888. ‘95352
Hutchinson & Wilkes ...... 1888 "95341
Poe
IV. Electrolytic Dissociation versus Hydration.
By Svante ARRHENIUS”.
Tee distinguished Russian chemist Mendelejeff has lately,
in the Journal of the Russian Physico-chemical Society,
dealt in an adverse manner with the theory of electrolytic —
dissociation. In that paper he expresses an opinion that his
assumption of the existence of hydrates in solutions can be
used to explain all the facts which hitherto have served as the
foundation of the electrolytic-dissociation theory. As many
English chemists (Armstrong, Crompton, Pickering) have in
recent publications accepted and defended Mendelejeff’s views,
I take this opportunity of offering a few observations in an
Hinglish scientific journal on Mendelejeff’s paper.
In his paper the Russian savant makes use only of the data
contained in the first memoir of van’t Hoff (at the time of
publishing which the latter was not acquainted with the theory
of dissociation), and pays no attention to the later develop-
ments of the subject. Only in this way can Prof. Mendelejeft’s
concluding advice be explained, that before going further we
must investigate whether the isotonic coefficients (2) of van’t
Hoff and de Vries are whole numbers or vary with the tem-
perature and concentration. I have proved more than a year
ago (Zeitschr. fiir physikal. Chemie, i. p. 491) that the latter
alternative is correct; e.g. for oxalic acid the values of 7
corresponding to the concentrations ‘06 and °66 gram-
molecules per litre are 1°62 and 1°37 respectively. This can
also be deduced from the electric conductivities of the solu-
tions. Moreover I know of no one who has refused to accept
this alternative. JI refer, for example, to the more recent
papers in the Zetschr. fir phystkal. Chemie of de Vries and van’t
Hoff, both of whom at first held the other view. ‘The state-
ment that the isotonic coefficient of MgSO, at all concentra-
tions 1s unity must also be corrected in the same sense ; as I
have found that this coefficient has the values 1°37,. 1°22, and
1:04 for the concentrations :06, °16, and ‘66 gram-molecules
per litre. Thus the question, ‘ how is it that in this case 7
for an electrolyte is unity ?”’ is answered. Hvidently by this
neglect of a great part of what has been accomplished by the
theory of dissociation Prof. Mendelejeff has come to the belief
that the whole matter may easily be explained in another way.
I therefore give an enumeration of the principal branches of
physical science which have received an explanation from the
_ hypotheses of osmotic pressure and of electrolytic dissociation.
* Communicated by the Author.
Electrolytic Dissociation versus Hydration. 31
Group A.—(1) Osmotic pressure. (2) Lowering of
freezing-point. (3) Lowering of vapour-pressure. (4) Raising
of boiling-point. (5) Hlectromotive force of concentration-
currents in solutions.
Grour B.—(6) Electric conductivity of electrolytes.
Group C.—(7) Diffusion of electrolytic solutions.
Grove D.—(8) Change of the degree of dissociation of
weak acids with dilution. (9) Conductivity of mixed solu-
tions. (10) Change of the strength of weak bases and acids
by the addition of neutral salts. (11) Distribution of. bases
amongst different acids (Thomsen’s “avidity ’’).
Group H.—(12) Velocity of reactions of various chemical
processes caused by the presence of acids or bases.
Group I'.—Additive properties of electrolytic solutions,
such as (13) specific volume and specific gravity. (14) Heat
of neutralization. (15) Compressibility. (16) Internal fric-
tion. (17) Colour, rotatory power, and index of refraction.
It is by means of the two hypotheses named above that for
the first time it has been made possible to calculate the nume-
rical values of several thousand observations in these seventeen
widely different fields ; and with such success that no con-
siderable contradiction between theory and experiment has
arisen. Are we to assume that the view that hydrates exist
in solutions can render such service? So far as I am aware
not a single numerical datum has hitherto been deduced from
this hypothesis. |
I may be permitted to discuss this last question in a few
words. In the first place it may be considered indubitable
that it is impossible to determine whether a salt occurs in
solution as hydrate or not by any of the methods for deter-
mining the properties enumerated in group A (except perhaps
No. 5). Here we perfectly agree with Prof. Mendelejeff ;
his remarks besides are to be found almost word for word in
a memoir of Raoult (Ann. de Chim, et Phys. [6] viii. p. 291).
From this it follows that the conclusions, drawn by Riidorff
and Wiillner, from the lowering of the freezing-point and
vapour-pressure of solutions, in favour of the existence of
hydrates in them, are unfounded, as Tammann and others have
already shown. ‘hese inadmissible conclusions of Riidorff
and Willner were formerly, however, considered as the chief
proof of the existence of hydrates in salt solutions.
On the other hand, there are other phenomena belonging
to the groups B, C, and F which are opposed to this assump-
tion. If, for instance, an electric current is passed through a
solution of KCl, of which we assume that it exists as the hy-
drate KCl.mH,0O, then the ions of this salt are K .nH,O, and
32 Svante Arrhenius on Electrolytic
Cl(m—n)H,O (G. Wiedemann’s hypothesis). Now it appears
from Ostwald’s researches that the velocity of an ion is the
smaller the more atoms it contains. Thus the velocity
(which may be easily determined from the conductivity) for
the potassium ion of a solution of KCl, viz. K.nH,0, must
be smaller the greater is the value of n. But Kohlrausch has
shown that the ion K .nH,0O travels at the same rate in solu-
tions of all the potassium salts, therefore the ion K must be
combined with the same quantity of water in all salts. This
holds for all other ions. As soon therefore as both the ions
ot a salt solution are given, then the hydrate is also known ;
and the composition of this hydrate does not alter with the
concentration, which certainly does not agree with Mendele-
jeff’s views. There are, besides, other circumstances (Ostwald,
Zeitschr. fir physikal. Chemie, ii. p. 840) which make it very
probable that in the ions I.nH,O, nis extremely small ;
and this, again, according to Mendelejeff is not the case in
dilute solutions. But as we have no ground for attributing
any particular value to n, and as it is besides probable that
many salts (e. g. most of those of potassium) exist only in the
anhydrous state, the simplest and likeliest assumption is that
the ions of the salts, and consequently the salts themselves,
exist in solution without water of hydration. In ananalogous
way we come to precisely the same conclusion from consider-
ing diffusion and the additive properties of salt solutions.
The theory of dissociation (contrary to Mendelejeft’s asser-
tion) is therefore decidedly unfavourable to the assumption of
the existence in dilute solutions of hydrates with large quan-
tities of water.
It is well known that for a very long time chemists have
been striving to find hydrates in solutions from a considera-
tion of the properties of the solutions. Graham some forty
years ago lent his support to such a view. The mode of
procedure was very simple. Any property, e. g. internal
friction (Graham), was taken and tabulated as ordinates
against the percentage of substance in solution as abscisse.
In the curves thus obtained are some singular points, e. g.
maxima, minima, points of inflexion, angular points. In
this way Graham found that the internal friction of solu-
tions of alcohol in water had a maximum near 36 per cent.
alcohol, and concluded therefrom that possibly this compo-
sition corresponded to a definite and highly viscous hydrate
(perhaps C,H;O0H.5H,O). This conclusion is evidently
devoid of any theoretical foundation, and is in fact simply a
random shot. Consequently when it was found that the
maximum varies with the temperature, this attempt at ex-
INssociation versus Hydration. 30
plaining the facts was abandoned. Similar attempts have
been made frequently of late, as may be seen by looking into
almost any book on thermochemistry, where we find such
eurves for thermal data. It is obvious that in any not too
simple curve singular points will occur. The conclusion is
that if we look in this way in such a curve for evidence of the
existence of hydrates we shall certainly find it, for every pro-
perty can be represented by acurve which is usually not very
simple (and were it by chance simple, wide conclusions might
yet be drawn from it). The peculiar character of such con-
clusions is that no premisses are required for them.
Prof. Mendelejeff has been very unhappy in his choice of a
property to prove the existence of hydrates. The reasons
which Ostwald has given, that “specific gravity cannot well
be used for setting forth stochiometric laws,” must be con-
sidered correct. From the curves which represent the first
derived functions of the specific gravity as a function of the
percentage composition by weight, Prof. Mendelejeff seeks to
deduce the existence and composition of hydrates. This curve
for solutions of sulphuric acid, which is given as being par-
ticularly instructive, has been twice plotted by Mendelejeff.
Below we reproduce the first form it assumes (Ber. deut. chem.
Ges. 1886, p. 386).
10 20 Sie aU 50 60 70 80 100 p.c. H,SO,4
In this figure the empirically obtained numbers are repre-
sented. In the second curve (see fig. 2) which is influenced
by theory (Zetschr. fir physikal. Chemie, i. p. 275) the same
numbers are represented in a totally different manner.
Who would be likely to discover that these two curves are
identical? Who could recognize the first curve in the straight
Phil. Mag. 8. 5. Vol. 28. No. 170. July 1889. D
34 Svante Arrhenius on Electrolytic
lines of the second? And these straight lines have to serve
alone as the support of the hydration theory! “ Non dantur
saltus in natura” is a proposition which is rightly taken as a
motto in every science capable of mathematical treatment.
Fig. 2.
as = 250 Ho» 504 “7 Hy 0
dp
0
72> \50 : ee 2
When, exceptionally, a sudden break occurs in a series of
phenomena, it must be verified with the greatest care both
theoretically and practically before its existence is finally
accepted. ‘The first curve therefore must be looked upon as
the correct one, because it contains none of those extraordi-
narily improbable breaks, until the contrary is proved by a
thorough investigation such as does not at present exist. We
must therefore reject the idea that the existence of the five
straight lines of the second curve is proved. Even, however,
if this form were correct, still the conclusions which Prof.
Mendelejeff draws would be extremely bold ones. For it
might be that the straight lines change their position at
higher temperatures (as is the case with internal friction),
and thus the singular points where they terminate would
indicate the existence of quite other hydrates. This, accord-
ing to a note (Ber. deut. chem. Gres. 1586, p. 387), actually’
occurs with the point of greatest contraction :—‘ The greatest
contraction g in 100 parts by weight at 0° corresponds approxi-
mately to m=3, but suffers a considerable displacement with
rise of temperature, being at 100° near m=2.” In addition,
attention must be drawn to the extreme difficulty of finding
the exact positions of these singular points. The experimental
material used by Prof. Mendelejeff in his two German publi-
cations must be looked upon as insufficient for such purposes.
ds
Strictly speaking, what does the fact that the values of ip
Dissociation versus Hydration. 35
are represented by five straight lines signify? Nothing more
than that the values of s as a function of p can be represented
by five interpolation-formule of the second degree with fifteen
arbitrary constants, of which Mendelejeff uses only ten. From
the mathematical side, this presents nothing more astonishing
than that really this number of constants is necessary. There
is, we should think, scarcely an example to be found in expe-
rimental physics where such an analytical representation has
been considered satisfactory. The only conclusion to draw
from it is that a much better representation could probably be
found with a little trouble. All our modern experience goes
to show that we obtain much better results when, instead of
percentage composition, we take the number of gram-
molecules per litre as abscissze ; and therefore the latter mode
of representation is the more scientific. Were this much
more justifiable method of plotting adopted the straight lines
in the second figure would change into curves, and so the
whole foundation of the theory of hydrates would collapse.
Mendelejeff proposes, instead of the dissociation of the
electrolytes (M X for example) into ions, a dissociation of
MX. (n+1)H,O into either MX .nH,O and H,0, or into
MOH .mH,O and HX .(n—m)H,0 (base and acid) to ex-
plain the quantity 7(>1). As he himself states, however, the
splitting-off of water would not give a sufficient explanation
of this fact. We must therefore take the other alternative,
that the electrolytes are partially decomposed into acid and
base. This decomposition is not conceivable for those electro-
lytes which are themselves acids or bases, for they could not
possibly be decomposed by the action of water. Yet HCl
and NaOH have values of z greater than unity. For salts,
however, it is at least conceivable. But then we should have
to assume that KCl in normal solution had decomposed to the
extent of 75 per cent. into KOH and HCl. Now HCl dif-
fuses considerably faster than KOH ; so that if KCl solution
were brought into contact with water the latter would become
acid from HCl, and the solution alkaline from the KOH
remaining behind, just as happens with FeCl,. This is, how-
ever, in direct contradiction to all experience, as is every
assumption of dissociation (such as Planck has proposed)
where the parts with greater velocity do not exercise a strong
attraction on those with less, as is the case with electrically
charged ions. The view of electrolytic dissociation, on the
- other hand, is so far from being in contradiction to the facts
of diffusion, that the values of the constants of diffusion can
be actually deduced from it (cf. Nernst, Zetschr. fir physckal.
Chemie, 1. p. 627). It is surely a strange notion that the pro-
D2
36 Svante Arrhenius on Electrolytic
bability of electrolytic dissociation could be in any degree
lessened by the possibility of the phenomena which it explains
being in the future deducible from other data (e. g. the exist-
ence of known hydrates). If this were actually to occur, then,
conversely, the existence of the hydrates could be deduced from
these phenomena, and thus indirectly from the theory of dis-
sociation, so that new territory would be added to the exten-
sive domain already commanded by this hypothesis.
A striking example of this is found in the hypothesis itself.
From his powerful generalization of Avogadro’s law, van’t
Hoff had deduced the conditions of equilibrium for several
electrolytes in one solvent, and I had done the same from a
consideration of the electric conductivity by means of a hypo-
thesis which may be characterized as the imperfectly developed
dissociation hypothesis. Immediately after the appearance of
this paper by van’t Hoff the fusion of the two partially over-
lapping theories took place, and it cannot be denied that the
fruitful period of both was reached only after their union, and
was conditioned by this. Although, therefore, the supporters
of the dissociation hypothesis cannot homologate the mode of
deduction of the views of the great Russian chemist, they
have every reason to wish him the best success in his efforts to
explain the above-mentioned phenomena. |
Leipzig, May 25, 1889.
-Norzt.—In the last numbers of the ‘ Chemical News,’ and
of the ‘ Abstracts of the Proceedings of the Chemical Society,’
are reports of a paper by Mr. 8. U. Pickering which confirms
in the most decisive manner the views I have expressed above.
Mr. Pickering (Chemical News, May 27, 1889, p. 278) says
that ‘on plotting out the first differential of his density-
results, he was surprised to find that it formed an irregularly
curved figure, and not the rectilineal figure given by Men-
delejeff ; and he was still more surprised that, on plotting out
the values used by Mendelejeff himself, the figure obtained was.
curvilinear like his own, and not rectilinear like Mendele-
FELIS. te ele ent Mendelejeff’s statement, therefore, that he had
proved the hydrate theory by showing that the densities dif-
ferentiated into straight lines meeting at points corresponding
to definite hydrates is erroneous.” He then proceeded to a
second differentiation, but “ owing to the magnitude of the
experimental error” did not take the values of ds/dp obtained
directly from his observed results, but instead took “the
smoothed first differential curve” as his point of departure
(Proc. Chem. Soc. May 16, 1889, p. 89).
In this way Mr. Pickering found that the second derived
a ee
ng
Dissociation versus Hydration. 37
function (d*s/dp?) consisted of straight lines. Mathematically
interpreted, this means that in the ds/dp curve angular points
or sudden changes of curvature occur. If Mr. Pickering had
“smoothed”? his curve properly he would evidently have
removed these angular points or sudden changes of curvature,
for a very small fraction of the “experimental error”? would
suffice for this purpose. The result can scarcely be gratifying
to the supporters of the theory of hydration. Mr. Pickering
finds that d?s/dp” is made up of no less than 17 straight lines
corresponding to 16 hydrates. In other words, the specific
gravity can be represented in the form of 17 equations of the
third degree with 68 arbitrary constants, besides the 16 arbi-
trarily chosen points where the curves begin and end !
This really has very much the look of a reductzo ad absurdum.
The mode of representation entirely lacks experimental founda-
tion, as Mr. Pickering himself tacitly admits in the words
“owing to the magnitude of the experimental error.” It is
characteristic also that Mr. Pickering ‘‘agrees with Mr.
Crompton’s conclusion that they (the d?k/dp” curves ; k=con-
ductivity, p = per cent. by weight of sulphuric acid) give a
rectilineal figure, but he differs from him in some of the
details as to where the breaks occur” (p. 88). But the
points ‘‘ where the breaks occur” should correspond to definite
hydrates. The fact is that Mr. Pickering with his multitu-
dinous arbitrary constants can fix the points ‘where the
breaks occur” just where he chooses, and so we need not
wonder that the curve for d*k/dp* can be drawn in such a
manner “that these breaks agree very closely with those
shown by his own density-results”’ (p. 88).
I will quote in addition a very instructive statement of
Mr. Crompton’s (Proc. Chem. Soc. Dec. 1888, p.127) :—“ Mr.
Crompton, replying to Dr. Morley’s objection that there did
not seem to be any reason why a limit should be put to the
differentiation when that had been performed twice, and that
it would be just as reasonable to proceed with a third or
fourth differentiation and so on, said that a limit to the dif-
ferentiation would necessarily have to be made according to
the nature of the case under investigation and the discretion
exercised by the investigator. In the present instance the limit
of differentiation is clearly indicated by the agreement of the
results obtained with those previously arrived at by Mendelejeff
by discussing a totally different physical property.”” But now
that Prof. Mendelejeff’s results are proved to be “ erroneous,”
we should perhaps expect that the differentiation ought to be
earried a little further. This, however, is not necessary, as
most of the physical properties can only be determined with
|
:
|
i
|
|
38 Messrs. Gladstone and Hibbert on the Molecular
such exactness that the second derived function may be repre-
sented, within the errors of observation, by a not too small
number of straight lines with practically arbitrary termina-
tions. The proof of this is furnished by the fact that Mr.
Pickering has deduced from the specific gravity quite different
hydrates (singular points) from Mendelejeft, and from the
electric conductivity quite different hydrates from Crompton.
Mr. Pickering closes as follows: “The conclusion is the
absolute rejection of any other than the hydrate theory”
(p. 89). Looked at from the mathematical point of view the
conclusion might well be the “absolute rejection” of the
so-called theory of hydrates, at least in the form defended by
Mr. Pickering.
V. On the Molecular Weight of Caoutchouc and other Colloid
Bodies. By J. WH. Guavstoneg, Ph.D., F.RS., and WALTER
hameert, 1.C.7
URING the last meeting of the British Association at
Bath, we gave a preliminary account of some attempts
to determine the molecular weights of caoutchoue and a few
other substances by Raoult’s method. We have since re-
peated most of the experiments and largely extended the
inquiry, and it seems to us that the results have a certain
physical as well as chemical interest.
‘It is evident that this method is the only one that offers
much hope of success in dealing with such substances as
caoutchoue, but it is open to question how far the method itself
is to be trusted for giving the correct molecular weight of
compounds of this description. Our confidence in it, how-
ever, was strengthened by the following experiments, made
on substances of the same ultimate composition (nC4)Hj¢),
but of known molecular weight in the gaseous condition.
We also made experiments on one or two closely allied
bodies containing oxygen.
The compounds were dissolved in benzene which had a
freezing-point of 5°25 C., and the experiment was conducted
in the usual manner. Hach degree of the thermometer
scale was divided into twentieths, and it was not difficult to
estimate to the hundredth of a degree. Successive observa-
tions of a freezing-point nearly always agreed to less than
0°-02.
The following table gives:—in col. II. the recognized
molecular formula, in col. III. the strength of solution, in
* Communicated by the Physical Society: read May 25, 1889.
Weight of Caoutchouc and other Colloid Bodies. 39
col. IV. the amount of depression, and in col. V. the mole-
cular weight calculated by Raoult’s formula M= where T is
the molecular depression constant (in this case=49), and A is
the depression given by 1 gram of the substance in 100
grams of solvent. These figures may be compared with col.
VI., which gives the molecular weight deduced from the
formula in col. II.
Substance. Col. II. | Col. III. | Col. IV.| Col. V. | Col. VI.
per cent. | °
Oil of Turpentine...... Canale 4°56 1:59 140°5 136
Oil of Lemon............ 5 6:04 2:17 136-4 136
a ee 5 3°06 112 133°8 .
EPUTENE «....2..000000ce0 CFs Oe 3°89 1:00 190°8 204
ly See ee ip afi 1-20 1923 i
PECUO esos Jcsceee. Gels 3°30 2°25 71:9 68
ae ¥ 2°20 1°52 709 »
Caoutchene ............ C,,Hi¢ 5:38 201 131-1 136
AEWCCHIC......c0c00-cnces- pebies 12:00 2°32 275 272
Matt tdocstives ens i 9°37 1°85 248 i
PRS. Siialn cura sasids oi 95 7°68 1°53 246 55
amphor .-:...........- C7 H.0 4-69 1:59 1445 152
50) ¢7, HO 321 0:93 169°1 156
- Ae Bs 4-93 1°31 1844 Be
Bea isc dv as 8s ; 3°75 107 ibrar 33
AELWOL «..jaj00d--. 0005 © pH .0 371 1-29 141-0 148
This table shows not merely that the method is applicable
in the case of bodies of this description, but that the mole-
cular weights of the liquids in solution have the same relative.
values as in the gaseous condition.
We then made experiments on caoutchouc, whose empirical
formula as usually given (C,)Hj,) would indicate a molecular
weight of 136, and we found that this was very far below
that deduced from our results, as shown in the following
table:—
Weight in 100 : Molecular
Substance. grame of Solvent. Depression. Weight.
Cautchouc (a) ... 31 Scarcely observable. | Extremely high.
» (0) «. 88 :
55 (B) es 146 0-11 6504
The caoutchouc used in solution (a) had been prepared
from Penang rubber, by the process described in our previous
fa. CSREES Ee es ee Te
eee
Se SS
SSS
SaaS
40 — Messrs. Gladstone and Hibbert on the Molecular
paper (Chem. Soe. Journ., July 1888, p.679). That in solution
(6) was obtained from Para rubber, by dissolving it in ether,
and precipitating the etherial solution with alcohol. Solution
(c) was prepared from (6) by evaporation in a current of
hydrogen. The greater depression observed can hardly be
ascribed solely to the greater strength of the solution, since
that would only give a proportionate effect. We are inclined ©
to think it possible that there wasa lowering of the molecular
weight during a three days’ gentle heating which was
incidentally necessary. The observation, in fact, seems in
harmony with other alterations in physical properties which
we have sometimes noticed.
This very high molecular weight for caoutchouc strengthens
a previous impression of ours that caoutchouc belongs to the
class of substances known as colloids. The impression arose
from the fact that caoutchouc is a substance showing not the
least tendency to crystallize, which cannot be distilled with-
out decomposition, which is subject to great alteration of
properties by the action of heat, which is converted into an
insoluble modification by small quantities of certain reagents,
and which dissolves in its solvents in an extremely sluggish
manner.
Graham, in his classic memoir on the subject* of Colloids,
observed that “the equivalent of a colloid appears to he
always high;” and he also suggested that the colloid molecule
may be “ constituted by the grouping together of a number
of crystalloid molecules.”
It seemed worth while therefore to examine bodies com-
monly regarded as colloidal by Raoult’s method. The follow-
ing table gives the results obtained with aqueous solutions of
organic colloids, the molecular weights being reckoned for
the ordinary value for T given by Raoult in the case of
water :—
Substance. Bee oon Depression. ee
Gum arabie ...... 31-6 De 2001
Ditto purified ... 14:0 0-165 1612
Caramel.;....:6...- 8°76 0-105 1585
SP icanns svt 22'5 0-245 1745
Albumen ......... 20 Scarcely observable. | Extremely high.
* Phil. Trans. 1861, pp. 183-224.
t
Weight of Caoutchoue and other Colloid Bodies. 41
The molecular weight of these known colloids, as determined
by Raoult’s method, is very high and confirms the generaliza-
tion of Graham.
Experiments have already been made upon the so-called
carbohydrates by this process by Messrs. H. T. Brown and
G. H. Morris*. They found that the sugars had a mole-
cular weight agreeing with the received formula, but the
noncrystallizable bodies like soluble starch &c. gave them
results suggestive of specially high molecular weight.
We may also note that in some recent investigations by
C. Liideking, he found that the addition of colloids to water
makes no practical difference to the boiling-point, and in
every case lowers the vapour-pressure very slightlyf. These
results all indicate the same general conclusion.
Our experiments were extended by making an examination.
of solutions of the colloidal hydrates of aluminium and iron.
They were prepared by dialysing solutions of the basic
chlorides, but, as is well known, a small proportion of the
salt must be retained in order to prevent coagulation. The
iron solutions contained almost exactly one molecule of
chloride to fifteen molecules of the hydrate. The first
aluminium solution contained one molecule of the chloride to
five or six of the hydrate, the second one of chloride to nearly
ten of the hydrate.
Weight in 100 . Molecular Weight.
Substance. erams of Solvent, Depression. .—47. 8
Ferric Hydrate ...... 1:16 About 0°01 5452
if 2°60 0-025 4888
Aluminic Hydrate... 0°523 0-060 409°6
nf 1:37 0-06 10730
The figures here given for the molecular weights of the
hydrates are calculated as if the whole depression were due
to the hydrate in solution, but the chloride present must have
exercised a considerable influence, especially in the first
aluminium solution. If allowance be made for this, the
molecular weights found would be higher than those given in
* Chem. Soc. Journ. 1888.
+ Ann. Phys. Chem. [2] xxxv. pp. 552-557.
Se ne ee A EP ae eee Ca er {eS S ASE re a FE SR FIC Se ee
SS SE
=
ey eS
=
ad
SSeS SSeS
SSS Se
42 Mr. G. Fuller on a Water-spray Influence-machine.
the table, and would point to the soluble colloidal hydrates
of iron and aluminium being many multiples of Fe,H,O,,
or Al,H,O., which would give a molecular weight of only
214 and 157 respectively. ‘The molecular weights of ferric
and aluminic chlorides, as determined by Raoult’s method
(T being 47), are about 114 and 106 respectively.
All our experiments, therefore, while affording additional
illustrations of the value of Raoult’s method, confirm the
belief that the molecule of a colloidal substance is an aggre-
gate of a very great number of atoms”.
VI. Water-spray Influence- Machine.
By Greorce FuLuErR ft.
1: machine is for obtaining directly from a fall of water
a supply of electricity of a high potential. It consists
of four similar parts arranged symmetrically round a cen-
tral vertical support, and each division has the following
members.
A nozzle, A, in connexion.
with a head of water by means
of a pipe, a.
A ring, B, of brass or copper
wire placed vertically below A,
and through which the water
descends when the machine is
in action.
A vessel, C, placed below B
to receive the water that has
passed through the ring.
A brass tube, H F, between
the ends of which the vessel C
ean turn about a horizontal
axis.
An insulating glass rod, D,
to the top of which the tube
E F is attached, and with the
lower end fixed in a part of the
frame of the machine, G.
* Since this paper was read we have found that Paterné and Nasini
have arrived at the same conclusion from experiments on albumen and
gelatine (Lincet, April 7, 1889, p. 476).
+ Communicated by the Physical Society: read May 25, 1889,
~ Sa
-as it was found that the water was
Mr. G. Fuller on a Water-spray Influence-machine. 43
A sectional plan on mn shows the connexion between the
four divisions, which are numbered I., II., IIL, IV. The
wire ring of section I. is in elec-
trical connexion with the receiver
of sectionIV. Similarly thering & nt
of II. is connected with I., the
ring of III. with IV., and that of Ox
TV. with I.
K is a central column for sup-
porting four arms of the machine 1 IV
to which are fixed the insula-
tors D.
The discharge of electricity is taken between conductors in
connexion with II. and III.
The nozzle is a flanged brass box, the bottom of which is
perforated with small holes through which the water descends.
It is fixed by a number of small bolts and nuts through its
flange to a brass plate fixed to the
supply-pipe, a a, and the joint is made
watertight by a vulcanized india-
rubber ring. A piece of fine linen
covers the top of the box to strain the
water before it reaches the small holes,
either stopped or diverted by small
particles unless this precaution was
taken. The holes, which are circular,
have a diameter of ~}9; as it was
found that when holes jo/9/’ were
used the water was so much dispersed
by the working of the machine that a great part of the water
ceased to fall into the receivers. This great dispersion also
injured the insulation, and besides this it was extremely diffi-
cult to keep these holes free.
With regard to the number of holes. In the nozzles of
sections I. and IV. there are six arranged in a circle of 121”
diameter. For those of sections II. and III, either a pair
with twelve holes each in a circle of 14” diameter, or with
eighteen holes in a circle of 13” diameter.
The rings are made of brass or copper wire of about 1”
diameter. The inside diameter of the rings used with the
nozzles with six and twelve holes is 23’, and with the eighteen
holes 22”.
The wire of each ring is continued and fixed to a clip of
split brass tube, C, which slides upon the brass tube E or F.
a Le ee
~. — a ee aa
44 Mr. G. Fuller on a Water-spray Influence-machine.
This enables the depth of the ring below the nozzle to be
adjusted, which is of importance, as the greater the head of
water employed the greater must be the distance between the
two, as the ring should be fixed at the point where the small
streams of water break up into spray. The receiving vessel,
C, may be of glass or metal, as the former material, from its
constant state of moisture whilst the machine is working,
seems to conduct the electricity as effectually as the latter.
In the author’s model they were at first of glass, but one of
them having been broken they were replaced by receivers of
zine. The receivers are supported by pins, p, p, which are
soldered to them at one end, whilst their free ends rest in
holes drilled in E and F. To make the receiver self-acting
they are hung so that when a leaden weight, w, is fixed, as
shown in sketch, the vessels being empty, they would turn in
the direction of the arrow if they were not prevented by stops
Mr. G. Fuller on a Water-spray Influence-machine. 45
soldered to them which press against E and F; but when
the receivers are nearly full of water, their balance is such
that they turn in the opposite direction and so empty them-
selves. The four receivers are made to turn towards the axis
of the machine and to deliver the water into a metal bath,
which for continuous action should be connected with a drain.
The following are some of the dimensions of the author’s
model :—
Zine receivers 8” diameter at the top.
Brass tube H and F 2” diameter.
Glass rod D 2” diameter, with an insulation of 4”.
From the rim of C to the lower surface of A, 93”.
From the rim of C to the underside of stand, 1/ 1”.
From centre to centre of insulators D across the centre line
of instrument, 1’ 1”.
46 Mr. G. Fuller on a Water-spray Influence-machine.
The Electrical Action of the Machine.
An instrument made of only sections I. and IV., with their
rings connected with their receivers, as shown above, will
charge itself; and the difference of potential of the two re-
ceivers may be such that sparks $ inch long may occasionally
pass between them, though more usually 2 inch is the longest
that can be obtained with a head of water of about 23 feet.
With this arrangement, after every discharge the potential of
the rings is nearly equalized ; whereas in the machine with
four sections, I. and [V. keep up the difference of potential
of the rings of II. and III.
With respect to the action of the machine, the author,
whilst giving the considerations from which it was constructed,
must leave to the electrician to determine whether they have
anything to do with the true explanation of the phenomena.
The water, at the point where it is divided into drops by the
resistance of the air, is electrified by induction from the rings;
the former being in connexion with the earth through the
unbroken water of the stream, and the action seems similar
to that employed in Sir W. Thomson and Professor Silvanus
Thompson’s water-dropping accumulators. That such is the
case appears to follow from the fact that, if the rings are either
placed much above or much below the level where the water
breaks into spray, the machine ceases to work. When the
rings are at their proper level there is an additional action ;
for the particles that are inductively electrified are split up
into numberless minute particles, some of which are so fine
that they float about in the air and do not fall into the re-
ceiver. And it is this breaking up of the water into minute
particles that the author thinks may account in part for the
effect produced ; for when a number of spheres that have been
electrified unite into a mass of less surface, their potential in
the latter state is higher than in the former.
Another point which the author thinks must be taken into
consideration is the speed with which the particles move
through the ring, as it was only when he experimented with
a fall of some feet instead of inches that he obtained a poten-
tial high enough to produce sparks. With a very slow speed
the attraction of the ring is too strong for the water, so that
it at last, as in Sir William Thomson’s apparatus, bends
against it. That the division of the drops into minute spray
plays a part in the action of the machine seems to be shown
by the fact that sparks of the same length, in the same state
of the atmosphere, have been obtained from it when the ve-
locity of the water has been very much diminished. The
sparks, as a rule, have not been so numerous per minute, but
Mr. G. Fuller on a Water-spray Influence-machine. 47
the water has been divided into finer spray. At times, even
with half the delivery of water, the same length of spark has
been obtained.
One experiment the author has made in which the spray
was not obtained by the action of gravity, but by a steam
“ atomiser,” as it is called. The water and steam passed
through a copper wire ring 14” diameter, connected with one
of the receivers of an apparatus made up of sections I. and [V.,
as above. The nozzle was 3” from the ring and 52” from the
receiver. Sparks + in length were taken freely from the
receiver, which is a better result than has been obtained with
a fall of water of some 23 feet. What was very observable
in this case was the very small amount of water used, a small
teacup-full being passed over in some five or six minutes ; and
the author has recorded in his notes that the experiment was
made on a very wet day.
Adding to the number of jets does not seem to increase the
power of the machine, either in quantity or potential, at all in
proportion to the number added ; though the action of an
electrical machine is so eccentric that it is difficult to be cer-
tain of this, for at times the nozzle with eighteen jets has given
much better results than the one with twelve jets.
It has been stated that, in the machine as made, the rings
are 1” larger in diameter than the circle of the jets, and it is
found that they give a better result than when larger rings
are used ; but in some experiments with a small flow of water
a ring 34” diameter gave as large a spark as one of 14. In
the dark, electricity is often seen to fly off from the rings, the
water on them being made into pointed-shaped drops.
The machine in its present form is by no means powerful,
as with a small Leyden jar attached to it the longest spark
has hitherto been 14, the head of water being about 23 feet.
The state of the atmosphere has very great influence on the
working of this machine; for though in all states of the
weather electricity will be generated, it requires a fairly dry
atmosphere to give 1” sparks.
It may be mentioned that the machine has only been tried
in a small bath-room, which is a very unfavourable place for
electrical experiments ; and it perhaps is worth mentioning,
that on one occasion sparks were only obtained when window
and door were open and the machine was in a thorough
draught.
To what extent the power of the machine may be increased
it is difficult to predict ; but the author thinks that the expe-
riment with the atomiser points to high velocity in the water,
combined with minute subdivision, as the direction in which
any future attempts should be made.
1 aes |
VIL. On Electric Radiation and its Concentration by Lenses.
_ By Prof. Oxtver J. Lover, D.Se., FAS. and JAMES
L. Howarp, D.Sc.*
Introduction by Dr. Lodge.
re making exact optical experiments on electric radiation
it is necessary to be able to converge it and throw a beam
of it in any desired direction. Todo this by means of mirrors
is possible, but not always very convenient. Prof. Fitzgerald
and Mr. Trouton{ have related the difficulty they at first
found in making concave mirrors work ; and we experienced
the same difficulty, intensified probably in our case by the
fact that we tried to work with everything on an extra small
scale—half the linear dimensions of Hertz.
It is much easier to work with a large oscillator than
a small one, because the same extraordinary suddenness
in starting the oscillations is not then essential ; only with
large waves, mirrors and everything have to be heroic to
match, and our laboratory was not big enough for optical
experiments on gigantic waves. Electrical experiments on
such waves I have made in large numbers, obtaining them
originally by means of discharging Leyden jars, but recently
sometimes by a gigantic Hertz oscillator consisting of a pair
of copper plates, each consisting of a couple of commercial
sheets soldered together and rimmed round with wire, con-
nected by a length of No. 0 copper wire interrupted in the
middle by a couple of large knobs. The plates and con-
necting-rod are hung from a high gallery, so that everything
occupies one plane, their distance and dimensions being here
shown.
Fig. 1.--Large Oscillator used for violent and distant effects. Scale 2,
Plates 120 centim. square. Knobs 3:2 centim. diameter.
Each rod 230 centim. long and 8 millim. diameter.
Spark-gap about 1:5 centim.
* Communicated by the Physical Society : read May 11, 1889,
+ ‘Nature,’ vol. xxxix. p. 391.
Dr. O. Lodge on Electric Radiation. 49
Static capacity, = =25 centim.
Self-induction, a =8320 ,,
KB
Characteristic factor, log = = //-3)
Rate of vibration, 10 million per second.
Wave-length, 29 metres.
Dissipation-resistance, 22,500 ohms.
Initial stock of energy, about 300,000 ergs.
Power of initial radiation, 128 horse-power.
Number of vibrations before energy would be at this rate
dissipated, about 3.
The electrical surgings obtained while the Hertz oscillator
is working are of just the same character as are noticed when
a Leyden jar is discharging round an extensive circuit ; but
whereas from a closed circuit the intensity of the radiation
will vary as the inverse cube of the distance as soon as the
circuit subtends a small angle, the radiation from a linear or
axial oscillator varies in its equatorial plane only as the
inverse distance, as Hertz showed.
Hence, for obtaining distant effects the linear oscillator is
vastly superior. . Its emission of plane-polarized, instead of
circularly-polarized, radiation is also convenient.
_ (I may mention that a thundercloud and earth joined by a
lightning-rod or by a disruptive path constitute a linear
oscillator ; and hence radiation-effects and induced surgings
may be expected to occur at very considerable distances from
a lightning-flash. )
Hxciting this oscillator by a very large induction-coil,
extraordinary surgings are experienced in all parts of the
building, and sparks can be drawn from any hotwater-pipe or
other long conductor, whether insulated or otherwise, and from
most of the gas-brackets and water-taps in the building, by
simply holding a penknife or other point close tothem. From
conductors anywhere near the source of disturbance the
knuckle easily draws sparks.
Out of doors some wire feneing gave off sparks, and an
iron-roofed shed experienced disturbances which were easily
detected when a telephone-terminal was joined to it, the other
terminal being lightly earthed. [Sometimes I utilized the
wire fencing as one of the plates of the oscillator, and thus
got still bigger and further spreading waves. |
The waves thus excited are from 30 to 100 yards long, and
optical experiments with them would be as difficult and vague
as are experiments on sound-waves of corresponding length.
Small oscillators can, however, easily be employed which shall
Phil. Mag. 8. 5. Vol. 28. No. 170. July 1889. aD
50 Dr. O. Lodge on Electric Radiation.
give waves from a foot toa yard in length ; and after reading
Hertz’s experiment of the pitch prism*, I made preparations
for casting some great lenses that should give, I hoped, easy
concentration of such waves.
Paraffin was a natural substance to use; but it is rather
expensive, and has not a very high index, After consider-
ing many substances—beeswax, sulphur,
try resin, and laid in a stock of that ties Meanwhile,
to gain experience in casting, and finding that a common
class of pitch :could be obtained at an absurdly low price,
I procured several casks of the commonest pitch also. I
did not contemplate using this substance at first because
I feared it would be an imperfect insulator, and there seemed
no use in permitting any dissipation of energy whatever, so
long as one could get perfectly transparent substances.
On casting a specimen of the pitch, however, it was found
so strongly insulating as nearly to fling off the leaves of a
gold-leaf electroscope it was brought near. It seems, there-
fore, an excellent cheap stuff for electrophorus and such like
use, wherever it.is not expected to be strictly solid ; and it
can har dly help being transparent except to very little waves.
Meanwhile we had calculated that to receive rays from one
point and convey them to another without aberration, a pair
of plano-hyperbolic lenses were very suitable; a parallel
beam being transmitted from one lens to the other. The
lenses would naturally be made cylindrical, instead of sphe-
rical, to suit the linear form of radiator.
The optical calculation of a lens free from aberration for
Fig. 2.
one special point, 8, from which it is to receive rays and emit
* Wied. Ann. xxxvi. p. 769 (1889); translated in Phil. Mag. April
1889.
Dr. O. Lodge on Electric Radiation. 51
them parallel, is as follows :—From fig. 2,
esi) petly te
helsing y=(e+/) tan 0; dg CP:
Solving these equations, and making @ and a vanish
together, we get, as the curve of the lens,
r= (a+/f)sec0
pe ae ee
pcos O—]’
or
a hyperbola with one focus as origin, with eccentricity p,
semi-latus rectum /(«“—1), and semi-axis major ies
Taking « as 1°7 for pitch (according to the measurement
of Hertz with a prism), and calling the semi-axis major unity,
the focal length of the lens is 2°7, the semi-latus rectum
1°89, and half the angle between the asymptotes, being
cos—! ai is 54°,
Using these data, and taking six inches as unit of length,a
curve was drawn as shown in fig. 3, where F, the focus of the
hyperbola, is to be also the principal! focus of the lens ; its
distance from the lens is 41 centim.
Fig. 3.
Mh
This curve was given to the laboratory assistant, Mr. Davies,
who cut out a pair of wooden templates to the pattern,
nailed sheet zinc to them so as to make a mould, propped it up
in an outhouse, and proceeded to cast it full of pitch—the
upper fluid surface constituting the plane surface of the lens.
All went well till the mould was nearly filled, when the
2
52 Dr. O. Lodge on Electric Radiation.
weight of the pitch ripped the zinc from its fastenings, and a
horrid collapse was the result. |
A couple more moulds were made of the same pattern, only
stronger, and a bed of sawdust and mould was made to
sustain the weight. A double partition of thin wood was
introduced across the middle of the mould, so as to enable
each lens to be split into two halves if it should happen to be
too immovable in one piece.
After a time two satisfactory lenses were obtained, each
nearly a metre square. Nothing could be done with them
during term, because of want of space; but in the Haster
holidays I requested my demonstrator, Dr. Howard, to make
experiments in one of the College corridors. There exists a
large open room or iron shed, which I should have preferred
to use; but unfortunately dry rot had set in in its flooring,
and it was in the hands of the carpenters all vacation. We
are therefore somewhat troubled by neighbouring walls and
by hotwater-piping.
Under more favourable circumstances, the distance between
the lenses might no doubt have been much greater ; in fact,
no attempt was made to place the lenses far apart. They
were set up with their flat faces parallel at the opposite ends
of a table, about 6 feet apart, and not afterwards moved,
being, indeed, rather unwieldy ; the oscillator was placed in
the principal focus of one lens, viz. at a distance of from 41
to’ 51 centim. from its curved surface. The focal length,
calculated on the assumption that w=1°7, was 41 centim., but
experimentally 51 centim. seemed to do better.
After the few experiments here recorded were done, one of
the lenses took advantage of Haster week to assert its essential
fluidity, and so much bulged and curved over as to be almost
unserviceable ; since then it has completed its ruin by
breaking its prop and tumbling over into fragments. The
other lens stands remarkably well, and seems as good as
ever. There is evidently an important difference in the
quality of the pitch, though it is not a difference recognized
by the invoice. Qn the whole I think paraffin would have
been the best substance to use.
The particular form of receiver is a comparatively unim-
portant matter, but I prefer linear ones to circular or nearly
closed circuits as being more sensitive at great distances,
for much the same reason as has been stated for oscillators.
Hxact timing of the receiver is unessential. If resonance
occurred to any extent, so that the combined influences of a
large number of vibrations were really accumulated, the effects
might doubtless be great ; but hitherto I have seen no evi-
Dr. O. Lodge on Electric Radiation. 53
dence of this with linear oscillators ; the reason being, I sup-
pose, that the damping out of the vibrations is so vigorous that
all oscillations after the first one or two are comparatively
insignificant; and very bad adjustment, or no adjustment at
all, will give you the benefit of all the resonance you can get
from such rapidly decaying amplitudes. The main reason of
the rapid damping is loss of energy by radiation. The “ power”
of the radiation while it lasts is enormous, and the stock of
energy in a linear oscillator is but small.
Leyden-jar discharges in closed circuits die away more
slowly, and for them some approach to exact timing is essen-
tial, if a neighbouring circuit is to respond easily.
In working with small oscillators it is essential that the
spark-knobs shall be in a state of high polish, else the sparks
will not be sufficiently sudden to give the necessary impetus
to the electrification of the conductors.
Any hesitation or delay about the spark permits the potentials
of the knobs to be equalized by a gradual subsidence which is
followed by ne recoil, just as a tilted beer-barrel may be let
down gently without stirring up the sediment by waves. The
period of a natural vibration is comparable to the time taken by
light to travel a small multiple of the length of the oscillator,
and hence not a trace of delay is permissible in the discharge
of a small conductor if any oscillations are to be excited by
means of it. Thus if an electrostatic charge on a conducting
sphere be disturbed in any sudden way, it can oscillate to and
fro in the time taken by light to travel 1°4 times the diameter
of the sphere, as calculated by Prof. J. J. Thomson; and
hence it is by no means easy to disturb a charge on a sphere
of moderate size except in what it is able to treat as a very
leisurely manner. iven on large spheres the oscillations
cannot be considered slow: thus an electrostatic charge on
the whole earth would surge to and fro 17 times a second.
On the sun an electric swing lasts 64 seconds. Such a swing
as this would emit waves 19 x 10° kilometres or twelve hundred
thousand miles long, which, travelling with the velocity of
light, could easily disturb magnetic needles* and produce
auroral effects, just as smaller waves produce sparks in gilt
wall-paper, or as the still smaller waves of Hertz produce sparks
in his little resonators, or, once more, as the waves emitted
by electrostatically charged vibrating atoms excite corre-
sponding vibrations in our retina. It may be worth while to
suspend at Kew a compass-needle with a natural period of
swing of 6°6 seconds, and see whether it resounds to solar
* Cf. Mr. Oliver Heaviside, Phil. Mag. February, 1888, p. 152.
54 Dr. O. Lodge on Electric Radiation.
impulses. Another, but almost microscopic, recording needle
with a period of j= second might also be suspended.
The charge on the oscillator used in the present set of
experiments vibrates 300 million times a second, which, though
slower than the electric quiverings on, say, a three-inch ball,
is yet quick enough to demand care and attention.
~ With very large oscillators, such as that described at the
beginning of this paper, no such minute precautions need be
taken.
Fig. 4,—Small Oscillator used for optical experiments. Scale .
O-—@
Plates 8 centim. diameter.
Knobs 2 centim. diameter.
Each rod 6 centim. long and 1 centim. diameter.
Spark-gap about 8 millim.
Static capacity, ie = 1-4 centim.
F : L
Self-induction, —=190 ,,
pe
Characteristic factor, log = =4°5.
Rate of vibration, 800 million per second.
Wave-length, 1 metre.
Dissipation-resistance, 7250 ohms.
Initial stock of energy, about 5400 ergs.
Power of initial radiation, 128 horse-power.
Number of vibrations before energy would be at this rate
dissipated, about 13.
My oscillator is a good deal dumpier, and its ends have
-more capacity, than those of corresponding wave-length used
by Hertz ; the reason being that I prefer to make the electro-
static capacity bear a fair relation to the electromagnetic
inertia, so as to gain a reasonable supply of initial energy
for radiation. ‘The store of energy is proportional to the
capacity ; the rate at which it is radiated per second is
independent of it. Large terminal capacity helps to preserve
a high potential longer, and so prolongs the duration of the
discharge.
The wave-length of the emitted radiation is easily calculated
approximately from the expression
n=O, / (2. 2);
no a
Dr. O. Lodge on Electric Radiation. 55
where 2 = 2 log 1 being the length of the entire rod
portion of the oscillator, and d its diameter*. The measure-
ment of / is the most unsatisfactory part. It is best to
include the knobs and spark-gap as part of the whole length ;
the constriction at the spark will increase that part of the
self-induction, but the expanse of the knobs will diminish
another part. A trifle extra length should be allowed for
the currents in the disks or balls at the end; but to measure
1 from centre to centre is rather too much allowance. From
centre of one to nearest point of the other isa fair compromise.
As to 8, it will be practically half the static capacity of the
sphere or plate at either end of the oscillator, especially if
these are pretty big compared with the size of the rod.
Strictly speaking they are not isolated, even when far from
other conductors, because they are in presence of each other,
hut the correction is usually small. . For instance, for two
yppositely charged spheres of radius 7, at a considerable dis-
ance l from centre to centre, the capacity is about
Llp eNO A
2 =k 2
ee =1r(1+7),
Hence the ordinary value of the capacity, as recorded for
convenience below, is always a minimum Ta circumstances
may increase but hardly diminish.
Values of > for Isolated Bodies.
For a globe, ~ > iis Tacs.
For a thin circular de, * times its radius.
For a thin square disk, 1:13 times inscribed circular disk,
"+s . or 786 times a side of the square.
For a thin oblong disk, a trifle greater than a square of the
same area.
Intensity of the Radiation—Hertz has shown{ that the
amount of energy lost per half swing, by a radiator of length
1 charged with quantities + Q and —Q at its ends respectively,
1S | mQ20
, 3K(GA)"
* See Addendum at end.
+ Half, because the two spheres are technically “in series.” See
Addendum at end of paper.
{ Wied. Ann. January 1889; or Nature, vol. xxix. p. 452. -
56 Dr. O. Lodge Gn Hleetrae Padiocians
He omits the dielectric constant K, because he supposes Q
expressed in electrostatic units, but it is better to make ex-
pressions independent of arbitrary conventions.
So the loss of energy per second, being = times the above,
is f
_ 167°(Ql)?o |
HS SK Xa
and this therefore is the radiation power.
For a given electric moment, @/, the radiation intensity
varies therefore as the fourth power of the frequency, 7. e.
inversely as the fourth power of the linear dimensions of the
oscillator, as Fitzgerald some time ago pointed out.
But inasmuch as different oscillators will not naturally be
charged to the same electric moment, but will rather be
charged to something like the same initial difference of
potential, as fixed by the sparking interval between their
knobs, it will be better to write Q=SV, and to insert the
full expression for A.
Doing so, we get for the radiation activity at any instant
when the maximum difference of potentials at the terminals
is V,
He TS? V2? Va
ee WG a0) POE eT
37° KS*L?v aKyt'(2 ee i
V?Kv VY?
x 12 (log =) 12 ye (log a |
an expression roughly almost independent of the size of the
oscillator. Quite independent of it if the length and thick-
ness of its rod portion are increased proportionately.
(The factor wv may always be interpreted as 30 ohms
whenever convenient.)
Thus all oscillators, large and small, started at the same
potential, radiate energy at approximately the same rate ;
short stout ones a little the fastest.
But the initial energy of small oscillators being small, of
course a much greater proportional effect is produced in
them, and the radiation ceases almost instantaneously, their
energy being dissipated in a very few vibrations. On the
other hand, oscillators of considerable capacity keep on much
longer ; and with very large ends, as in Leyden jars, the loss
}
yt 7
;
Dr. QO. Lodge on Electric Radiation. 57
of energy by radiation is often but a small fraction of that
turned into heat by the frictional resistance of the circuit.
The expression for the radiating power may be compared
either with the form 4SV? or with the form and the loss
Vy?
pee
of energy may be said to be like a static capacity of
30 earth quadrants 5556 microfarads
2 ol dm eA iio
6 (log (log =|
charged to the potential V, being discharged once a second ;
or like the heat produced per second in a resistance of
360 (Jog =) ohms, having a difference of potential V_be-
tween its ends. The duration of the discharge must there-
fore be exactly comparable to the time a wire of this resistance
would take to equalize the potential of the oscillator-ends
initially charged to the same difference of potential.
For the small oscillator used in the optical experiments
here recorded, the value of log By approximately 44; hence
the equivalent resistance 1s 7250 ohms. And, since the
initial difference of potential is, say, 26,400 volts, the power
of the initial radiation is 96,000 watts or 128 horse-power.
At this rate the whole original stock of energy (5400 ergs)
would be gone in the two-hundred millionth of a second, 7. e.
in the time of 14 vibration ; but of course the energy really
decays logarithmically. The difference of potential at any
instant being given by
d(48V?) _ is
pears
t
a that is, V=V,e 88>
where R is the above 7250 ohms plus the resistance of the
spark and of the oscillator itself to these currents. The
resistance of the spark is probably but a dozen, or perhaps a
hundred, ohms; that of the small oscillator is about v (Ir)
ohms, where 7 is its ordinary resistance to steady currents
expressed in ohms, and / is its length in centimetres. This,
therefore, is utterly negligible; practically the whole of its
energy goes in radiation. For the big oscillator the resist-
ance is about (slr); and so for a linear oscillator in
general the dissipation resistance may be considered as simply
R= 360(log >) ohms.
a es ie ae
< es:
58 Dr. Howard on Electric Radiation.
Nothing approaching continuous radiation can be main-
tained at this enormous intensity without the expenditure of
great power, a hundred and thirty horse-power if my calcula-
tion is right. Under ordinary circumstances of excitation
the intervals of darkness are enormous; if they could be
dispensed with, some singular effects must occur. To try
and make the radiation more continuous a large induction-coil
excited by an alternating machine of very high frequency,
or by a shrill spring-break, might be tried. But even if
sparks were made to succeed one another at the rate of 1000
per second, the effect of each would have died out long before
the next one came. It would be something like plucking a
wooden spring which, after making 3 or 4 vibrations, ‘should
come to rest in about two seconds, and repeating’ the operation
of plucking regularly once every two days.
Statement of Results by Dr. Howarp.
The apparatus used consisted of (1) an oscillator, or trans-
mitter, with exciting coil ; (2) a resonator or receiver, and
(3) two lenses of pitch. We shall describe these in order.
The Oscillator or Source of Radiatton—This was made in
two similar halves, each constructed by soldering to one end
of a brass rod, 6 centim. long and °95 centim. diameter, a thin
| circular copper disk of 4 centim. radius. To the other end
was soldered a spherical brass knob of 1 centim. radius,
| highly polished. A small hole was drilled in each rod at a
| distance of 1°3 centim. from the knob to allow of the insertion
of connecting wires to the Ruhmkorff coil by which it was
excited. The two disks were cemented to two small wooden
blocks which could be clamped in any position on a vertical
glass rod. By this means the distance between the knobs
could be easily adjusted, and the apparatus could be inclined
when wished.
The induction-coil was of the usual pattern with hammer-
break. With the current used (supplied by 6 accumulator-
cells) it gave a continuous stream of sparks between two
points 2°5 centim. apart connected to the secondary terminals.
The knobs of the oscillator were usually separated by a space
of from *7 to 1-Ocentim. They required cleaning about every
20 minutes owing to burning produced by the spark. This
burning was always greater at one knob than -the other ;
greatest apparently at “the one that mattered least, for if the
primary current was reversed after the oscillator had been
- working some time the intensity of its radiations immediately
decreased perceptibly.
The length of a complete wave emitted by the oscillator,
Dr. Howard on Electric Radiation. 59
calculated from its dimensions after the manner of Hertz,
is 100 centim. And this is a sufficient amount longer than
the conductor itself for the calculation to be not very inexact.
It cannot pretend to accuracy.
The Resonator, or receiver and detector of radiation (the
electric eye, as Sir W. Thomson calls it), was of the simplest
possible construction. Two pieces of copper wire (No. 13
B. W. G.) were cut each to a length of 25 centim. One end of
each was rounded off, and to the other end was attached a small
rectangular brass scrap or plate at right angles to the wire.
These little plates each carried a point ; one of these points
was fixed, and the other adjustable by a screw, by means of
which the distance between them could be varied. The reso-
nator was fastened to a piece of wood a little longer than
itself. Its total length, including points and strips, was 53
centim., 2. e. about half the calculated wave-length of the
oscillator. A better mode of expressing it is to say that each
half of the resonator is approximately a quarter wave-length,
and corresponds to a closed organ-pipe, or to a resonant
column of air in a glass jar.
The lenses were made of common mineral pitch, which was
found to insulate quite well enough for the purpose. They
were cast in the form of hyperbolic cylinders, bounded by a
plane perpendicular to the axes of the principal hyperbolic
sections; the eccentricity of the latter was equal to 1°7, and
was taken as a fair approximation to the refractive index of
pitch for infinitely long waves. A lens of this form should
converge a bundle of parallel rays falling normally on its
plane surface to a line of foci coinciding with the outer foci of
its principal hyperbolic sections ; and, vice versd, rays pro-
ceeding from this focal line and falling on the curved ‘surface
should emerge from the lens as a bundle of parallel rays.
Hence, if the oscillator be placed along the focal line of one
lens, the electric rays from it will be sensibly parallel after
traversing the lens, and after falling normally on the plane
surface of the second lens should converge and meet at its
focal line. The lenses were almost equalin size. Their plane
surfaces were nearly square, being 85 centim. high and about
90 centim. broad. The greatest thickness (from vertex of
hyperbola to plane surface of lens) is 21 centim. The lenses
are each separated into an upper and lower half by means of
a thin wooden partition inserted during the casting. It was
intended to divide this partition by a saw-cut, and thus allow
the lenses (each of which weighs more than 3 ewt.) to be
more easily carried about. So far, however, this has not been
done.
60 Dr. Howard on Electrie Radiation.
In making the experiments the lenses were placed one at
each end of a wooden table 24 metres long, with their plane
surfaces turned towards each other, and as nearly as
possible parallel. The distance between them was 180 centim.,
and remained the same throughout the experiments. On
one side of the table close to the edges of the lenses was a
brick wall about 40 centim. thick ; and on the other side was
a residue of gangway 54 centim. wide between the lens and a
laboratory-apparatus cupboard, which has had to be set up in.
the corridor for want of space elsewhere. The oscillator
stood, together with its exciting coil, on a small table whose
height was adjustable; the plane of its disks was parallel to
the flat surfaces of the lenses in all cases. It was intended to
be placed in the focal line of the first lens ; but apparently
the index of refraction had been assumed too high, and a
position 51 centim. from the vertex of the lens seemed to do
best. We shall speak of the vertical plane through the focal
lines of the two lenses as the “ aaval plane.” It contains the
axes of the lenses and of the oscillator. Waves seem to be
emitted more powerfully in this plane normal to the disks of
the oscillator than in the plane containing them.
The direct effect from the oscillator could be perceived by
the resonator at a distance of 120 centim. in the axial plane
in the most favourable case ; that is to say, in a very dark
room and just after cleaning the knobs of the oscillator.
Under similar circumstances resonance was only just obtain-
able at the vertical edge of the first lens, viz. 85 centim. from
the oscillator in a direction making an angle of about 30° with
the axial plane. To geta rough measure of the intensity of the
radiation at any point, the resonator was placed there, and its
spark-gap arranged so as to just give a continuous stream of
sparks ; it was then brought to the line joining the oscillator
and the edge of the first lens (line of reference), and the dis-
tance from the oscillator observed at which the sparks ceased
to be continuous. When the intensity of the radiation was
very small, however, the converse of this method was adopted;
the resonator was adjusted at the line of reference and then
taken to the point at which the intensity was to be observed.
The following are the phenomena observed in the space
between the two lenses when the oscillator coincides with the
focal line of the first one. The resonator gives brilliant
sparks in the axial plane near the first lens so long as it
is held parallel to the oscillator. On rotating it in a plane
perpendicular to the axial plane the sparks decrease: -in
brilliancy and length, and become entirely obliterated when
the resonator and oscillator are at right angles. If the rota-
Dr. Howard on Electric Radiation. 61
tion is continued the sparks reappear and regain their former
brilliancy, when the resonator again reaches its first position.
If the resonator be placed in the axial plane and then moved
parallel to itself towards the edge of the lens, the intensity of
the sparking gradually decreases as we get nearer the edge,
and on the side nearest the wall the sparks cease altogether
at the edge of the lens. On the other side, however, they
are visible right up to the edge of the lens, and then very
abruptly cease, when the direct effect alone is obtained. The
beginning of the sparking, as soon as the resonator enters the
shadow of the lens, is very noticeable. ‘The same appearances
are observed at all distances from the first lens, but the
intensity of the radiation is, of course, smaller as we get
further from the oscillator. The radiations are always a little
more feeble on the side nearest the wall than on the other
side. The cause of this has not yet been definitely ascer-
tained, but it appears to be produced by some action of the
wallitself. Slightly altering the position of the oscillator did
not get rid of the effect ; so it cannot be due to the oscillator
being out of focus. ‘There was apparently no defect in the
lens itself which could account for it. The concentration of
the radiations by the lens is very well marked. Just after
passing through the first lens in the axial plane they are
almost as intense as when they first impinge on its curved
surface; that is to say, they do not lose appreciably in intensity
by traversing the 21 centim. of pitch. But this concentra-
tion is even more clearly shown by the fact that in the axial
plane, at the surface of the second lens (250 centim. from the
oscillator), the sparks are quite as intense as the direct effect
would be at 100 centim. in the same plane if the first lens
were removed ; or, again, the resonator will give sparks
easily at the surface of the second lens, and when brought to
the line of reference will not give sparks at a greater distance
than 70 centim. At the surface of the second lens the
irregularity mentioned above is a little greater than at the
surface of the first one.
Beyond the second lens the rays are converged, as we
expected, and there is a fairly well defined point in which
they meet ; but the intensity of the sparking at the focus of
the second lens is not appreciably greater than at its surface.
Probably this is due to the fact that the rays from the edge
of the lens, having travelled a much longer distance in air
than those in the axial plane, have thereby lost much of their
intensity ; and the differences between the intensities at
different points could only be detected by a resonator with
more delicate adjustments. The cone of rays between the
ee a
62 Dr. Howard on Electric Radiation.
second lens and its focal line is of almost uniform intensity in
the neighbourhood of the axial plane. At the edge of the
cone the intensity falls off very rapidly ; and if the resonator
be moved parallel to itself in a plane perpendicular to the
axial plane, it shows sharply, by the commencement and
stoppage of its sparking, where the boundaries of the cone
le. The cone is a little unsymmetrical on account of dis-
turbance at the side nearest the wall, but the convergence
of the rays to a focus is placed beyond a doubt.
The following observations were made on the rays after
they had passed the focus of the second lens. The resonator,
after having been set to spark at a distance of 80 centim.
from the oscillator in the line of reference, was taken to the
focus of the second lens, and there gave sparks of fair
intensity. Beyond the focus there were traces of a divergence
of the cone of rays, which became more evident when the
oscillator knobs were quite clean ; but in order to make sure
of the existence of this divergence a more sensitive resonator
would be necessary. In the axial plane itself the resonator
used by us gave an effect when the conditions were most
favourable, at a distance of 120 centim. beyond the focus of
the second lens ; and it would possibly have given an effect
still further away, had there not been an iron hot-water pipe
9-centim. in diameter running from floor to ceiling of the
passage near this point. The furthest point at which any
traces of sparking could be found was in one case 450 centim.
from the oscillator, while without the lenses it was only
120 centim. This statement has to be taken along with the
fact that the lenses were only 180 centim. apart, and that no
attempt was made to elongate the parallel portion of the beam
by increasing their distance.
In order to determine experimentally the wave-length of
the oscillations, a sheet of tin-plate was set up against the flat
(inner) surface of the second lens. The rays reflected from
this plate were thus made to interfere with those incident on
it so as to give stationary waves, as in some experiments of
Hertz. The result was that close to the plate there were
no traces of sparking. On taking the resonator further
away, however, the sparks appeared, reached a maximum,
and then disappeared again at a distance of 50 centim. from
the plate. The point of disappearance was very definite.
The sparks appeared again when the resonator was still
further withdrawn, and as long as it was kept parallel to the
oscillator no further disappearance of the sparks could be
observed. By rotating it, however, in the axial plane, a
7
Messrs. Lodge and Howard on Electric Radiation. 63
_ point was found at which the amount of rotation required to
make the sparks disappear was a minimum. In this position
the centre of the resonator was 101 centim. from the reflect-
ing plate. The observations agree with the previously calcu-
lated value of the wave-length, viz. 100 centim.
In the above experiments the oscillator was always placed
in the focal line of the first lens, that is, vertically. Some
observations were made later, after turning the oscillator
through an angle so as to leave its centre in the axial plane,
but its direction inclined to this plane. The effects were
always of the same nature as those already described, even
when both oscillator and receiver had been turned through a
right angle, but the intensity of the radiation was not so
great beyond the first lens. The focussing of the rays by
the second lens could not be observed in this case, even when
they were rotated only ten or twenty degrees, as the intensity
was too small.
The above results all go to confirm the identity of elec-
trical radiation and light; and are merely a slight extension
of the famous researches of Hertz.
University College, Liverpool,
May 1889
ADDENDUM dated June 20.
An expression for the self-induction of a straight copper
rod, of length J and thickness d, we do not see how to calcu-
late on Maxwellian principles without some sort of a return .
circuit somewhere. On action-at-a-distance principles it can
be done thus :—
Consider two parallel filaments or thin straight wires at a
distance ¢ apart ; call an element of one, at a distance a from
some plane of reference, da, and an element of the other, at a
distance b from the same plane, db. The mutual induction or
potential of two elements on each other is
da db cos €
ae ae ge me,
r
where ¢ is the angle, and r the distance, between them. Hence
the mutual induction of the two parallel filaments, each of
length J, is
da db
LS
“\\recirer
64 Messrs. Lodge and Howard on Electric Radiation.
Integrating with regard to a, this becomes
1 Hep yo nee sie
w= (ag MCRD FEE C=D)
J (6? +6?) —b
where numerator and denominator are of the same form if the
limits for the numerator portion have / subtracted from them
both. Performing the integration of the two parts separately,
and simplifying, we get
P+c?)+l
M=2logVEFOF 94 (P+) —et.
It may be worth while to write down the form this assume
when ¢ is moderately small compared with J, viz.
Zea Didier
214 lon(= +m) (hag +5) }-
If we now put for ¢ the geometric mean distance of the
points in a cross section of a rod of thickness d, we shall have
the mutual induction of the parts of all the filaments in that
rod upon each other, z. e. the self-induction coefficient of the
rod. And unless the rod is very short and thick, it will be
permissible to neglect the c// terms.
Now the geometric mean distance of the points in a circular
section varies from $d, when they are concentrated into its
circumference, to e~#d, or *3894d, when they are spread
uniformly all over it. The first case corresponds to our
rapidly periodic currents, and gives, as the self-induction of a
rod in which currents keep to the periphery,
L=21(log = —1);
whereas if the currents penetrate all through its section, by
reason of being of slowly changing strength,
The difference is not marked : at least for the case supposed,
of non-magnetic material.
Hertz employed this last formula, quoting it apparently
from Neumann ; but he says that in Maxwell’s theory the 3
turns into. We do not know how he makes this out, but
suppose he is somehow right ; and it is this uncertainty which
has caused us to refrain from going into minutiz on the sub-
ject, and to be satisfied with using merely log = instead of
Messrs. Lodge and Howard on Electric Radiation. 65
(log 5 — something), for what we have called the character-
istic factor. It is easy to subtract 1 from it if that is the
proper thing to do, as our calculation indicates itis. But the
violent constriction at the spark, in the case cf an oscillator,
must cause a considerable increase of self-induction.
It may be interesting just to quote in similar form the self-
induction of the same rod bent into a circle, viz.
21 (log —=—2— logs);
if the currents keep to its periphery. When they penetrate
its section uniformly the 4 becomes 5:14, and that is all the
change unless it is made of magnetic material.
It thus approaches the same value as the straight rod for
infinite length, but is always distinctly less.
There is one point on which we find ourselves differing
from Hertz. We regret to say that our calculation of
radiation-intensity comes out four times as great as his. We
get the same formula as he does, so there is no slip in the
working there ; but, in the application, a 2 or a ./2 comes in
wrongly in one or other of our calculations. His using
half-wave lengths is a natural source of confusion, but we
have avoided all that; and it must be that it is owing to a
different calculation of the effective capacity concerned in an
oscillator that the discrepancy arises. If an oscillator has
spheres 30 centim. diameter at either end, Hertz calls its
capacity 15 centim.; we call it 74. We feel bound to call
it 74 according to any method of calculation; although the
radius of either sphere is the natural thing to write down at
first thought. The charge which surges into either sphere
has had to come from the other, not from the earth or any-
thing of infinite capacity. The two spheres are therefore like
two condensers in series. Hence our wave-lengths are
1/./2 of Hertz’s wave-lengths (or rather ./2 times what he
ealls his wave-length) ; and since) occurs to the fourth power
in radiation intensity, it makes our radiation 4 times as strong
for a given oscillator as that which he would calculate.
This discrepancy we by no means view lightly, and it is not
without many qualms that we find ourselves differing, even
about a 2, with a man so splendidly careful in his work as
Hertz has shown himself, It is more than probable that he
is right after all, so we explain what will then turn out to be
our error in this note.
Phil. Mag. 8. 5. Vol. 28. No. 170. July 1889. F
pda 5h
VIII. Notices respecting New Books.
Stellar Evolution and its Relations to Geological Time. By J AMES
Crott, LL.D., F.RS., author of ‘Climate and Time, ge.
Loudon: Stanford.
N this little volume Dr. Croll continues and expands his now
classic researches into the relations of Time and Geological
Evolution. His investigations and speculations he now boldly
carries to the utmost boundaries of time—if time is finite, and to
the morning of creation, not only of the Earth and the solar
system, but of the entire stellar universe. Beyond the point to
which Dr. Croll ventures by his scientific imagination to pierce,
Science certainly is not entitled to travel; but there is little doubt
that long ere opinion finally settles itself into fixed belief as to that
remote point and the cycle of events by which the starry hosts have
come to be what they now appear, there will be many speculations
to be hazarded, and many suggestions offered. Meantime we can
only say that Dr. Croll has made a brave plunge into the unex-
plored; and if he has not finally settled the theory of creation, he
has at least made a most substantial contribution towards the dis-
cussion of the great problem in physics which yet remains for
philosophers of the foremost rank to settle.
The germ of the theory expounded in ‘Steller Evolution’ ap-
peared in the pages of the Philosophical Magazine so long ago as
May 1868. It was further expanded in ‘Climate and Time,’ and
in the more recent work ‘Climate and Cosmology.’ Through an
inquiry into the possible origin and age of the sun’s heat, Dr. Croll
is led to adopt and support the theory that the whole visible uni-
verse is the result of the collision of vast dark masses which have
travelled through limitless space at various velocities and in inde-
pendent paths. Thus with matter and motion in their most
elementary condition the phenomena of creation began; and the
progressive series of changes which we call Evolution only came
into play when in boundless time and space two of these mighty
dark masses clashed together, and by the partial or complete
stoppage of their motion begat that energy of condition which
manifested itself by the expansion of the solid masses into a gaseous
nebula of enormous extent, heat, tenuity, and, from dissociation,
of uniform chemical character. A nebula so created possesses a
store of heat measured by the mass of the colliding bodies and
the rate at which they were travelling at the period of collision.
There is indeed no necessary limit to the store of energy which
might in this way be vested in a nebulous mass. Dealing with
gravitational energy alone, on the other hand, the amount available
in any system is strictly limited. It has been shown by Helmholtz
and Sir William Thomson that the solar system cannot be older
than from twelve to twenty millions of years if its heat is due to
gravitation alone. That amount of time Dr. Croll goes on to show
is utterly inadequate for the evolution of terrestrial phenomena,
aud a considerable portion of his work is occupied in marshalling
Geological Society. 67
a striking series of geological facts which demonstrate the much
greater age of the solar system. A quarter of a century ago Dr.
Croll first pointed out the important evidence afforded by sub-aerial
denudation as to the antiquity of the Earth. By that scale and by
other concurrent sources of testimony he concludes that the Earth
must have existed in a condition not greatly different from what
now prevails for at least seventy millions of years. That being so,
we are bound to seek a source of vastly greater heat than can. be
derived from simple shrinkage of a nebula. Such a source Dr. Croll
finds in his “‘ Impact ” theory of solar genesis, and he supports his
theory by many ingenious arguments. Sir William. Thomson
regards it as enormously less probable than the gravitation theory,
on account of the necessary assumption of exact aiming of the col-
liding bodies ; but the probability of the collision of dark masses is
a question of their numbers, distribution, and of time; and against
the gravitation theory there is the fact that the actual motion
observable in many stars cannot have been derived from that source.
Further, it may be said that the “‘ Impact” theory appears to get
remarkable support from the recent important researches of Dr.
Huggins regarding the constitution of nebule, the results of which
he communicated to the Royal Society during the past session.
Cosmic Evolution, being Speculations on the Origin of our Environ-
ment, By HK. A. Ripspare. London: Lewis.
Mr. RipspAtz, in his essay, assumes that the universe in its pri-
mordial condition consisted of a uniform gaseous expansion
possessed of an inconceivably high temperature. Chemical com-
bination became possible only as temperature of this attenuated
matter decreased; and with each successive combination there was,
in accordance with well-known laws, a shrinkage in volume.
Chemical activity was at first violently energetic; but as inorganic
evoiution proceeded, elements differentiated and compounds in-
creased, more stable couditions arose, and the chemically inert
survived to form a basis favourable for the production and main-
tenance of life and organic compounds. Mr. Ridsdale develops
his thesis in a rather Inconsequent manner; and although in their
general bearings his speculations may be accepted as satisfactory,
he trenches on subjects which are too profound and vast to be fairly
within the grasp of his limited knowledge and experience.
IX. Proceedings of Learned Societies.
GEOLOGICAL SOCIETY.
{Continued from vol. xxvii. p. 435. ]
April 17, 1889.—W. T. Blanford, LL.D., F.R.S., President,
in the Chair.
HE following communications were read :—
1. “On the Production of Secondary Minerals at Shear-zones in
the Crystalline Rocks of the Malvern Hills.” By Charles Callaway,
Esq., M.A., D.Sc., F.G.S.
In a previous communication the author had contended that
————— a ee ee ee ee
68 Geological Society :-—
many of the schists of the Malvern Hills were of igneous origin.
Thus, mica-gneiss had been formed from granite, hornblende-gneiss
from diorite, mica-schist from felsite, and injection-schists from
veined complexes which had been subjected to compression. As a
further instalment towards the elucidation of the genesis of the
Malvern schists, it was now proposed to discuss the changes which
the respective minerals of the massive rocks had undergone in the
process of schist-making.
The schistosity was usually in zones, striking obliquely across
the ridge, varying in breadth from a few inches to many yards, and
separated from each other by very irregular intervals. Within the
zones bands of maximum schistosity alternated with seams in
which the original structure had been less completely obliterated.
The new structure was connected with a shearing movement, by
which the rigid mass was often sliced into countless parallel
lamine or flakes. Ina more advanced stage of alteration, the planes
of movement were obliterated, and a sound clear gneiss or schist
was formed. These foliated bands were called “ shear-zones.”
The most important shear-zones were those in which diorite was
interlaced with granite-veins. The following changes were noticed
in tracing the massive rocks into the zones. The hornblende might
suffer excessive corrosion, or it might become “ reedy” and break
up along the cleavages into numerous fragments, which were drawn
away from each other in the direction of foliation, or it might pass
into chlorite, or chlorite and epidote. The chlorite thus formed
often passes into biotite, and sometimes the biotite was changed to
white mica. Where shearing was excessive, chlorite sometimes
passed directly into white mica.
Soda-lime felspar was altered to epidote or zoisite, and often to
calcite. A more important result was the production of muscovite
in the plagioclase. Much of this felspar was reconstructed in small
clear crystals or granules. Quartz also was abundantly produced.
Diorite might thus be converted either into a gneiss with two micas,
or into a gneissoid quartzite. The granite of the veins passed
through the usual changes into muscovite-gneiss.
Other secondary minerals were actinolite (from augite), sphene
(from ilmenite), and garnet.
It was contended that the granite-veins were exogenous, because
they appeared as apophyses from large masses ; they had the same
coarse texture in different varieties of diorite, and they produced
contact-effects similar to those of intrusive veins, including the
phenomena of aggregation and enlargement in the minerals of the
encasing rock.
Foreign minerals were often introduced by infiltration. Thus,
the hornblende of a diorite was decomposed into chlorite and iron-
oxide, which passed for a considerable distance along the shear-
planes of an adjacent granite, giving rise to a chlorite-gneiss, and
the chlorite was partially changed to biotite. Epidote might be
introduced in the same way.
Both the diorite and the granite of shear-zones tended by loss of
bases to become progressively silicified. Most of the liberated bases
BS a
The Northern Slopes of Cader Idris. 69
could be accounted for. Analyses showed that there was an inter-
change of alkaline bases, soda going to the granite, and potash to
the diorite. Thus, some of the latter contained almost twice as
much potash as soda.
. The evidence collected seemed to prove that the schist-makine
had taken place subsequently to consolidation; but it was clear,
especially where the rock was heavily sheared, that the con-
stituents had been redissolved and reconstructed. Thus, as we
followed a diorite into the core of a shear-zone, we could see the
gradual disappearance of shear-planes and other mechanical effects,
as well as the progressive results of chemical synthesis.
The secondary origin of the micas and of part of the felspar was
proved by the fact that they were moulded on decomposition-pro-
ducts, suvh as chlorite and epidote, and upon fragments of horn-
blende crystals, which had been crushed during the shearing, and
carried away from each other. The mineral changes here described
resulted from contact-action plus mechanical force.
2. “The Northern Slopes of Cader Idris.” By Grenville A. J.
Cole, Esq., F.G.8., and A. V. Jennings, Esq., F.L.S.
From the publication of Mr. Aikin’s paper in the Transactions
of the Geological Society in 1829 to the second edition of the Survey
Memoir on North Wales, the relations of the geological and physical
features of Cader Idris have been pointed out in some detail. The
present paper dealt with the nature of the eruptions that took place
in this area and the characters of their products at successive
stratigraphical horizons. The best exposures occur, as is well
known, upon the northern slopes.
The lowest evidence of contemporaneous volcanic activity is to be
found at the Penrhyn-gwyn slate-quarry, where a somewhat coarse
bed of tuff, with slate-fragments and abundant felspar-crystals,
occurs above an andesitic sheet. Similar slate-tuffs are repeated up
to the base of the great cliff of Cader Idris, with intervening layers
of normal clayey sediment. On the whole, the tuffs and ashes
become more highly silicated as the upper levels are reached, and
-_ they terminate on the southern slopes in beds with fragments of
perlitic and devitrified obsidian, such as are found under Craig-y-
Llam. On Mynydd-y-Gader the intrusive dolerites have altered the
ashes into hornstones; in places, moreover, they have become
jointed into distinct cclumns. Fragments of andesitic glass as well
as trachyte are recorded.
The “pisolitic iron-ore” of the Arenig beds appears to have
resulted from the metamorphism of an oolitic limestone, as in the
ease of the Cleveland ore described by Mr. Sorby, and that of
Northampton described by Prof. Judd. The grains still give
evidence under crossed nicols of their having been built up of
successively deposited concentric layers. The calcite so freely
developed in the hollows of the underlying rocks may have been
largely derived, during metamorphic action, from the destruction of
similar thin limestone-seams. No true lava-flows occur among
70 Geological Society.
these tuffs and sediments, a fact that implies comparative remoteness
from the volcanic centre; and the important masses of intrusive
matter represented upon the maps are themselves largely composed
of the products of explosive action. The numerous sheets of ophitic
dolerite, aphanite, and altered andesite, that lie, seemingly inter-
bedded, on the northern slopes, were probably intruded when the
associated rocks were already weighed down by much superincum-
bent sediment. .A common character of these basic sheets is the
development of small colourless crystals of epidote.
The most striking mass upon the mountain is the main “ felstone ”
(eurite) of the wall, which proves to be minutely ‘“ granophyric,”
and of very uniform grain throughout. An analysis by Mr. T. H.
Holland shows 73 per cent. of silica. This vast intrusive sheet is
regarded as perhaps of no later date than the Llandeilo lavas of
Craig-y-Llam, and as a forerunner of the voleanic conditions that
prevailed in Bala times throughout North Wales.
The stratigraphical horizons, as shown on published sections,
would throw a great part of the tuffs and ashes described into the
Tremadoc beds, or even lower, in contradiction to the generally
accepted statement that volcanic activity began in the Arenig times.
While this point can only be settled by detailed mapping on the
basis of the new six-inch survey, the authors incline to the belief
that the eruptions in this area broke out in the Cambrian rather
than the Ordovician period.
May 8.—W. T. Blanford, LL.D., F.R.S., President,
in the Chair.
The following communications were read :—
1. “The Rocks of Alderney and the Casquets.” By the Rey.
Edwin Hill, M.A., F.G.S8.
The author in this paper described Alderney, Burhou, with its
surrounding reefs, and the remoter cluster of the Casquets, all in-
cluded within an area about 10 miles long.
Alderney itself consists in most part of crystalline igneous rocks,
hornblendic granites of varying constitution which resemble some
Guernsey rocks, but seem more nearly connected with those of
Herm and Sark. ‘These are pierced by various dykes, and among
them by an intrusion containing olivine, which may be placed with
the group of picrites. There is also in the island a dyke of mica-
trap.
The eastern part only of Alderney, but the whole of Burhou, the
Casquets and their neighbouring reefs, consist of stratified rocks.
These contain rare beds of fine mudstone, but are generally false-
bedded sandstones, and grits, sometimes with pebbles, often rather
coarse and angular, occasionally becoming typical arkoses. At a
point on the southern cliffs of Alderney they may be seen to rest on
the crystalline igneous mass. A series identical in constitution and
aspect occurs at Omonville, on the mainland, a few miles east of Cap
La Hague (as had also been noticed a few months earlier by
Intelligence and Miscellaneous Articles. it
M. Bigot). These have been correlated with others near Cher-
bourg, and described as underlying the “grés Armoricain.” The
Alderney grits, therefore, form part of a series which can be traced
over 30 miles, and which belongs to the Upper Cambrian (of Lap-
worth).
Remarks were made on the Jersey conglomerates (Ansted’s con-
jectural identification of these with the Alderney grits being ap-
proved), on the resulting evidence that the Jersey rhyolites are not
Permian, but Cambrian at the latest, on the still earlier age of the
Guernsey syenites and diorites, and on the antiquity of the
Guernsey gneisses.
2. “On the Ashprington Volcanic Series of South Devon.” By
the late Arthur Champernowne, Esq., M.A., F.G.S.
The author described the general characters of the volcanic rocks
that occupy a considerable area of the country around Ashprington,
near Totnes. ‘They comprise tuffs and lavas, the latter being some-
times amygdaloidal and sometimes flaggy and aphanitic. The
aphanitic rocks approach in character the porphyritic ‘‘ schalsteins ”
of Nassau. Some of the rocks are much altered; the felspars are
blurred, as if changing to saussurite, like the felspars in the Lizard
gabbros. In other cases greenish aphanitic rocks have, by the de-
composition of magnetite or ilmenite, become raddled and earthy in
appearance, so as to resemble tuffs. The beds are clearly inter-
calated in the Devonian group of rocks, and the term Ashprington
Series is applied to them by the author. Although this series pro-
bably contains some detrital beds, there are no true grits in it.
Stratigraphically the series appears to come between the Great
Devon Limestone and the Cockington Beds, the evidence not being
discussed by the author, however, so fully as he had intended, as
the paper was not completed.
X. Intelligence and Miscellaneous Articles.
ON A POSSIBLE GEOLOGICAL ORIGIN OF TERRESTRIAL MAGNE-
TISM. BY PROFESSOR EDWARD HULL, M.A., LL.D., F.R.S.,
DIRECTOR OF THE GEOLOGICAL SURVEY OF IRELAND.*
HE author commenced by pointing out that the origin and cause
of terrestrial magnetism were still subjects of controversy
amongst physicists ; and this paper was intended to show that the
earth itself contains within its crust a source to which these
phenomena may be traced, as hinted at by Gilburt, Biot, and
others; though, owing to the want of evidence regarding the
physical structure of our globe in the time of these observers,
they were unable to identify the earth’s supposed internal
magnet.
The author then proceeded to show cause for believing that
there exists beneath the crust an outer and inner envelope or
* Communicated by the Author, being an Abstract of a paper commu-
nicated to the Royal Society, 16 May, 1889.
72 Intelligence and Miscellaneous Articles.
‘“‘magma ”—the former less dense and highly silicated, the latter
basic and rich in magnetic iron-ore. This view was in accordance
with those of Durocher, Prestwich, Fisher, and many other geolo-
gists. The composition of this inner magma, and the condition in
which the magnetic iron-ore exists were then discussed, and it was
shown that it probably exists under the form of numerous small
crystals with a polar arrangement. Lach little crystal being itself
a magnet and. having crystallized out from the magma while this
latter was in a viscous condition, the crystalline grains would
necessarily assume a polar arrangement which would be one of
equilibrium. Basalt might be taken as the typical rock of this
magma.
The thickness and depth of the magnetic magma beneath the
surface of the globe were then discussed, and while admitting that
it was impossible to come to any close determination on these points
owing to our ignorance of the relative effects of increasing tempera-
ture and pressure, it was assumed tentatively that the outer
surface of the effective magnetic magma might be at an average
depth of about 100 miles, and the thickness about 25 or 30 miles.
The proportion of magnetic iron-ore in basaltic rocks was then
considered, and it was shown that an average of 10 to 15 per cent.
would express these proportions ; and assuming similar proportions
to exist in the earth’s magnetic magma, we should then have an
effective terrestrial magnet of from 24 to 3 miles in thickness.
The thickness is, however, probably much greater.
Instances of polarity in basaltic masses at various localities were
adduced in order to illustrate the possibility of polarity in the
internal mass.
The subject of the polarity of the globe was then discussed, and
it was pointed out how the position of the so-called “ magnetic
poles ” leads to the inference that they are in some way dependent
upon the position of the terrestrial poles.
The author regarded the double so-called “ poles ” as merely foci
due to protuberances of the magnetic magma into the exterior non-
magnetic magma, and that there was really only a single magnetic
pole in each hemispheré, embracing the whole region round the
terrestrial pole and the stronger and weaker magnetic foci, and
roughly included within the latitude of 70° within the northern
hemisphere.
It was pointed out that the poles of a bar-magnet embrace a
comparatively large area of its surface, and hence a natural terres-
trial magnet of the size here hypothecated may be inferred to
embrace a proportionably large tract for its poles.
In reference to the question why the magnetic poles are situated
near those of the earth itself, this phenomenon seemed to be con-
nected with the original consolidation of the crust of the globe, and
the formation of its internal magmas.
It was pointed out that, in the case of the magnetic magma the
process of crystallization and the polar arrangement of the particles
of magnetic iron-ore would proceed in a radial direction. The
Intelligence and Miscellaneous Articles. 73
manner in which the phenomena of magnetic intensity, and of the
dip of the needle at different latitudes could be explained on the
hypothesis of an earth’s internal magnetic shell, such as here de-
scribed, was then pointed out; and the analogy of such a magnetic
shell with a magnetic bar passing through the centre of the earth
was illustrated.
The author then proceeded to account on geo-dynamical principles
for the secular variation of the magnetic needle, and also to show
how the objections that might be raised to the views here advanced,
on the grounds of the high temperature which must be assumed to
exist at the depth beneath the surface of the magnetic magma,
could be met by considerations of pressure, and on this subject read
a letter which he had received from Sir William Thomson, F.R.S.
In conclusion, the author stated it was impossible in a short
abstract to go into the details of the subjects here discussed, and
for further information the reader must be referred to the paper
itself.
NOTES ON METALLIC SPECTRA. BY C. C. HUTCHINS.
_ In the work herein described an attempt has been made to deter-
mine the wave-length of several metallic lines with something of
the precision with which wave-lengths of solar lines are known and
tabulated.
It has been repeatedly pointed out that wave-lengths of metallic
lines from the determinations of the best observers are liable to
errors of one part in 3000 or 4000; while Rowland has given us
the position of a long list of solar lines correct to one part in
500,000. 1t is too often forgotten that Thalén used a single bisul-
phide-of-carbon prism in his researches, and that consequently his
places can in no sense be considered standards of precision for the
more powerful instruments of the present time.
The spectroscope employed in the present work has a large flat
grating with ruled space 5 by 8 centim. Upon the margin of this
grating Professor Rowland has written: ‘“ Definitions exquisite.”
The collimator and view-telescope are combined in a single lens, an
excellent objective by Wray, 6 inches in diameter, 8} feet focus.
The radius of curvature of the back surface of this lens equals its
focal length, so that the ray reflected from this surface passes back
to the slit, and any objectionable illumination of the field is avoided.
All parts of the instrument are so contrived that it is operated
without the necessity of the observer leaving his seat at the eye-
piece. A heliostat and achromatic lens of 5-feet focus form an
image of the sun upon theslit. Thus arranged, the instrument
easily performs all tests of spectroscopic excellence with which the
writer is familiar. To produce the metallic spectra an 8-inch
spark, condensed by a number of jars having about six square feet
of coated surface, has been employed. ‘The spark is produced
immediately before the slit, the jaws of which open equally. The
coil is operated sometimes by a dynamo, and sometimes by the
Phil. Mag. 8. 5. Vol. 28. No. 170. July 1889. G
14 Intelligence and Widsetlianzos Articles.
current from a storage-battery. A review of all the spark spec-
trum-lines has been made with the arc, and a few lines added to
those that the spark gave. A steam-jet* was employed to increase
the luminosity of the spark. The work has been confined to the
lower portion of the spectrum, where it still appears that eye-
observations have advantages of the photographs.
The position of a metallic line is determined by bringing the
crosswire of the micrometer upon it, letting in the sunlight, and
moving the crosswire to one of the standard lines of Rowland’s
tables. The true wave-length of the metallic line can then be
computed from a previously determined micrometer-constant. As
a check to the result so obtained the metallic line has been inter-
polated, with the micrometer, between two of the standard lines
in the same field of view, and the whole process has been repeated
on different days until it became assured that positions of the me-
tallic lines were as precise as those of the standard lines themselves.
Copper Spectrum.
The subjoined table gives the results as obtained for the spectrum
of copper. The first two columns contain respectively the wave-
lengths and intensities as given by Thalén; the third, the wave-
lengths as determined in the present work.
Copper Spectrum.
Thalén X. Corrected X. | Remarks.
6379-7 | 2 | 6380°899 | Surrounded by continuous spectrum. Reversed in sun.
O2US SMD Wee on. No line seen.
5781°3 | 2 | 5782°285 | Reversed in are. Reversed in sun.
5700-4 | 1 | 5700-442 | Reversed in are. Reversed in sun.
553564 | Reversed in sun. Seen only in the arc.
5555:119 | Seen only in the are.
5292:0 | 2 | 5292°68 Reversed in sun.
52171 | 1 | 5218308 | Reversed in are. Reversed in sun.
5152°6 | 1 | 5153°345 | Reversed in arc. Reversed in sun.
51049 | 1 | 5105-663 | Reversed in sun.
HOLU:4 | 47). niece. ee No line seen.
5016°86 | Seen only in the are.
AK yea Neos aeonne de No line seen.
4932°5 | 3 | 4933°181 | Reversed in sun.
Zine Spectruin.
The examination of the zinc spectrum is here limited to five
lines; many of the remaining lines being mere dots close to the
poles of the metal, others very broad and nebulous, and in general
too ill defined to admit of measurement with the apparatus em-
ployed. In strong contrast to the remaining lines these five are
very bright and sharp, and may be called the representative lines
of the metal within those limits.
* Silliman’s American Journal, Feb. 1889; Phil. Mag. Feb. 1889.
asf
Qs
Intelligence and Miscellaneous Ariicies,
Zine Spectrum.
Phalén X. Corrected X. Remarks,
6362°5 | 1 | 6362°566 | Reversed in sun.
6204°708 | Faint but very sharp. Reversed in sun.
5893°5 | 2 | 5894-454
4809:7 | 1 | 4810°671 | Very bright. Keversed in sun.
4721-4 | 1 | 4722:306 | Very bright. Reversed in sun,
Results of comparison with Solar Spectrum.—It will be seen by
inspection of the tabulated results that nine out of the eleven lines
ef copper are reversed in the sun, and four out of the five of zine.
The conclusion reached in each of these cases was after repeated
examination, when the conditions were such as to show a clear
space between the components of the EK line. The latest available
authority * gives copper among the doubtful elements in a list of
those found in the sun, and on the same list zinc does not appear
at all. The present investigation makes it quite probable that zinc,
and almost completely demonstrates that copper, exists in the solar
atmosphere,—Silliman’s American Journal of Science, June 1889.
ON THE INFLUENCE OF SOLAR RADIATION ON THE ELECTRICAL
PHENOMENA IN THE ATMOSPHERE OF THE EARTH. BY SV.
ARRHENIUS.
In earlier researches (Wied. Ann. vol. xxxii. p. 546, and xxxiil.
p. 638) the author has concluded from a series of investigations that
the air, when irradiated by ultra-violet light, conducts like an elec-
trolyte. Starting from Peltier’s hypothesis of a negative charge of
the earth, the author makes use of this point of view to represent
the electrical phenomena of the atmosphere as consequences of
solar radiation. The earth’s charge, according to the author, is
neither imparted to the molecules of the air as shown by the expe-
riments of Nahrwold, nor does the aqueous vapour ascending from
the earth carry electricity with it, for which the experiments of
Kalischer, Magrini, and Blake speak. ‘The carriers of the elec-
tricity in the atmosphere are the solid and liquid particles suspended
in it (dust, fog-vesicles) ; and they obtain their charge from the
earth by conduction, when the air becomes a conductor in conse-
quence of the influence of the sun’s rays. There is then a very
feeble electrical current in the air. The author considers that a
proof of this is met with in the formation cf ozone in the atmo-
sphere, for which, according to Wurster, sunshine and liquid
deposits are necessary.
It is in accordance with the assumption of a negative charge of
the suspended particles, that on cloudy days the fall of potential
is much lower than on bright ones; that deposits, especially hail,
are for the most part negative, while snow is occasionally positive,
because it occurs at the time at which the sun’s action is weakest ;
in like manner he considers that the positive fall of potential observed
* Young’s ‘General Astronomy.’
76 Intelligence and Miscellaneous Articles.
in the morning fog is due to the sun not having as yet acted on
the fog. The author adduces a table of Quetelet, which shows as
the result of many years’ observations that the monthly mean of
the strength of atmospheric electricity is the less, the greater is
the monthly mean of the solar radiations measured with the actino-
meter. ;
The author explains in the well-known manner the formation of
the high tensions observed in storms. As the first condition in the
original charge of the drops is the solar radiation, thunderstorms
are in causal connexion with this, and are most frequent in hot
countries in summer, and in the afternoon. That the maximum
daily occurrence of thunderstorms is somewhat behind that of the
solar radiation is ascribed by the author to the time required for
the charge and for the coalescence of the individual drops. The
other meteorological phenomena which accompany the storms are
considered by the author to be secondary. The more infrequent
whirlwind storms, which, in contradistinction to the heat-storms,
eccur mostly in winter, and at night, and which cannot be explained
on the above principles, were supposed to be brought from more
southern regions.
The author finds a further support for his theory in the course
of the yearly and of the daily periods of atmospheric electricity.
The yearly period, with its winter maximum and summer mini-
mum, would directly correspond to the influence mentioned. The
daily period is more complicated, for it exhibits two maxima
and two minima. But this may also be explained, if to the influ-
ence of the solar radiation the influence be added which must be
exerted by the ascending motion of the negative clouds at daytime
and the descent at night-time. The author observes that Exner’s
theory, according to which aqueous vapour is the carrier of nega-
tive electricity, is quite in disaccordance with the facts of the daily
period of atmospheric electricity.
In conclusion the author develops the result that, since the
greater part of the active solar radiation is absorbed in the upper
regions, these must conduct far better than the lower layers of air.
Now since these upper layers of air are moving strongly from west
to east round the earth, a conductor would be obtained under the
influence of the sun’s rays, which rotated about a magnet (the
earth); by unipolar induction electromotive forces must be set up
which would drive the electricity in the higher atmosphere from
the equator to the pole. The aurore boreales and the daily varia-
tions of terrestrial magnetism would be referred to these phe-
nomena. The author observes that Schuster and Balfour Stewart
had already assumed an increase of the electrical conducting power
of the air with the sun’s rays; they, however, had sought for the
eause in a heating of the layers of air, an hypothesis the improba-
bility of which had already been demonstrated by Hann.— Meteor.
Zeitschrift, vol. v. p. 297 (1888); Beiblatter der Physik, vol. xiii.
p. 328.
THE
LONDON, EDINBURGH, ann DUBLIN
PHILOSOPHICAL MAGAZINE
AND
JOURNAL OF SCIENCE.
[FIFTH SERIBS.]
AUGUST 1889.
XI. On Achromatic Interference-Bands. By Lord RAayieiceu,
Sec. R.S., Professor of Natural Philosophy in the Royal
Institution*.
Introduction.
| HEN there is interference of light, the width of the
resulting bands, measured for example from darkness
to darkness, is usually a function of the colour of the light
employed. ‘Thus, in the case of Fresnel’s well-known inter-
ference-experiment, in which light reflected from two slightly
inclined mirrors illuminates a screen, the width of the bands
is proportional to the wave-length of the light. In order that
a considerable number of bands may be visible, it is necessary
that the light be highly homogeneous ; otherwise it is impos-
sible that the various band-systems can fit one another over the
necessary range. If the light could be supposed to be abso-
lutely homogeneous, there would be no limit to the number
of observable bands: and, what is especially to be remarked,
there would be nothing by which one band could be distin-
guished from another,—in particular there could be no central
band recognizable. When, on the other hand, the light is
white, there may be a central band at which all the maxima
of brightness coincide ; and this band, being white, may be
called the achromatic band. But the system of bands is not
usually achromatic. Thus, in Fresnel’s experiment the centre
of symmetry fixes the position of the central achromatic band,
* Communicated by the Author.
Pita. Sol 23) Now t7 1s August 1889. HF
18 Lord Rayleigh on Achromatic
but the system is far from achromatic. Theoretically there is
not even a single place of darkness, for there is no point where
there is complete discordance of phase for all kinds of light.
In consequence, however, of the fact that the range of sensi-
tiveness of the eye is limited to less than an “octave,” the
centre of the first dark band on either side is sensibly black ;
but the existence of even one band is due to selection, and the
formation of several visible bands is favoured by the capa-
bility of the retina to make chromatic distinctions within the —
range of vision. After two or three alternations the bands
become highly coloured*; and, as the overlapping of the
various elementary systems increases, the colours fade away,
and the field of view assumes a uniform appearance.
There are, however, cases where it is possible to have
systems of achromatic bands. For this purpose it is neces-
sary, not merely that the maxima of illumination should
coincide at some one place, but also that the widths of the
bands should be the same for the various colours. The inde-
pendence of colour, as we shall see, may be absolute ; but it
will probably be more convenient not to limit the use of the
term so closely. The focal length of the ordinary achromatic
object-glass is not entirely independent of colour. A similar
use of the term would justify us in calling a system of bands
achromatic, when the width of the elementary systems is a
maximum or a minimum, for some ray very near the middle
of the spectrum, or, which comes to the same, has equal values
for two rays of finitely different refrangibility. The out-
standing deviation from complete achromatism, according to
the same analogy, may be called the secondary colour.
The existence of achromatic systems was known to Newtonf,
and was insisted upon with special emphasis by Fox Talbott;
but singularly little attention appears to have been bestowed
upon the subject in recent times. In the article ‘“ Wave
Theory” (Hncyc. Brit. 1838) I have discussed a few cases,
but with too great brevity. It may be of interest to resume
the consideration of these remarkable phenomena, and to
detail some observations which I have made, in part since the
publication of the ‘ Hncyclopeedia’ article. A recent paper
by M. Mascart § will also be referred to.
* The series of colours thus arising are calculated, and exhibited in the
form of a curve upon the colour diagram, in a paper ‘‘On the Colours of
Thin Plates,” Edinb. Trans. 1887.
Tt ‘Optics,’ Book ii.
t Phil. Mag. [3] ix. p. 401 (1836).
§ “On the Achromatism of Interference,” Comptes Rendus, March
1889; Phil. Mag. [5] xxvii. p. 519.
Interference-Bands. 79
Fresnel’s Bands.
In this experiment the two sources of light which are
regarded as interfering with one another must not be inde-
pendent ; otherwise there could be no fixed phase-relation.
According to Fresnel’s original arrangement the sources Q,,
O, are virtual images of a single source, obtained by reflexion
in two mirrors. The mirrors may be replaced by a bi-prism.
Or, as in Lloyd’s form of the experiment, the second source
may be obtained from the first by reflexion from a mirror
placed at a high degree of obliquity. The screen upon which
the bands are conceived to be thrown is parallel to O,O,, at
distance D. If A be the point of the screen equidistant from
O,, O2, and P a neighbouring point, then approximately
O,P—0,P= v {D?4+ (w+ 40)? —V {D?4+ (u—4b)?} =ub/D,
where
O,0;=6,-AP=u.
Thus, if % be the wave-length, the places where the phases
are accordant are determined by
We DID, Maaergeh tant eienclyptany iG le)
n being an integer representing the order of the band. The
linear width of the bands (from bright to bright, or from dark
_to dark) is thus
A=nD/b. SED A TOS) 2)
The degree of homogeneity necessary for the approximate
perfection of the nth band may be found at once from (1) and
(2). For, if du be the change in uw corresponding to the
change dA, then
ON dN | Ne we oe sa me, ALCS)
Now clearly du must be a small fraction of A, so that dr/r
must be many times smaller than 1/n, if the darkest places
are to be sensibly black. But the phenomenon will be tole-
rably well marked, if the proportional range of wave-length
do not exceed 1/(2n), provided, that is, that the distribution
of illumination over this range be not concentrated towards
the extreme parts.
So far we have supposed the sources at O,, O, to be mathe-
matically small. In practice the source is an elongated slit,
whose direction requires to be carefully adjusted to parallelism
with the reflecting surface, or surfaces. By this means an
important advantage is obtained in respect of brightness with-
out loss of definition, as the various parts of the aperture give
rise to coincident systems of bands.
The question of the admissible width of the slit requires -
2
80 Lord Rayleigh on Achromatic
careful consideration. We will suppose in the first place that
the lights issuing from the various parts of the aperture are
without permanent phase-relation, as when the slit is backed
immediately by a flame, or by the incandescent carbon of an
electric lamp. Regular interference can then only take place
between lights coming from corresponding parts of the two
images ; and a distinction must be drawn between the two
ways in which the images may be situated relatively to one
another. In Fresnel’s experiment, whether carried out with
mirrors or with bi-prism, the corresponding parts of the
images are on the same side; that is, the right of one corre-
sponds to the right of the other, and the left of one to the left
of the other. On the other hand, in Lloyd’s arrangement the
reflected image is reversed relatively to the original source :
the two outer edges corresponding, as also the two inner.
Thus, in the first arrangement the bands due to various parts
of the slit differ merely by a lateral shift, and the condition of
distinctness is simply that the width of the slit be a small
proportion of the width of the bands. From this it follows as
a corollary that the limiting width is independent of the order
of the bands under examination. It is otherwise in Lloyd’s
method. In this case the centres of the systems of bands are
the. same, whatever part of the slit be supposed to be opera-
tive, and it is the distance apart of the images (0) that varies.
The bands corresponding to the various parts of the slit are
thus, upon different scales, and the resulting confusion must
increase with the order of the bands. [rom (1) the corre-
sponding changes in u and 0 are given by
du=—nXD db/d” ;
so that
duj/ N=>—n dbj> Ws 2) nes
If db represents twice the width of the slit, (4) gives a measure
of the resulting confusion in the bands. The important point
is that the slit must be made narrower as 7 increases, if the
bands are to retain the same degree of distinctness.
If the various parts of the width of the slit do not act as
independent sources of light, a different treatment would be
required. To illustrate the extreme case, we may suppose
that the waves issuing from the various elements of the width
are all in the same phase, as if the ultimate source were a star
situated.a long distance behind. It would then be a matter of
indifference whether the images of the slit, acting as proxi-
mate sources of interfering light, were reversed relatively to
one another, or not. It is, however, unnecessary to dwell
upon this question, inasmuch as the conditions supposed are
Interference-Bands. 81
unfavourable to brightness, and therefore to be avoided in
practice. The better to understand this, let us suppose that
the slit is backed by the sun, and is so narrow that, in spite
of the sun’s angular magnitude, the luminous vibration is
sensibly the same at all parts of the width. For this purpose
the width must not exceed 5 millim.* By hypothesis, the
appearance presented to an eye close to the slit and looking
backwards towards the sun will be the same as if the source
of light were reduced to a point coincident with the sun’s
centre. The meaning of this is that, on account of the
narrowness of the aperture, a point would appear dilated by
diffraction until its apparent diameter became a large mul-
tiple of that of the sun. Now it is evident that in such a case
the brightness may be enhanced by increasing the sun’s appa-
rent diameter, as can always be done by optical appliances.
Or, which would probably be more convenient in practice, we
may obtain an equivalent result by so designing the experi-
ment that the slit does not require to be narrowed to the
point at which the sun’s image begins to be sensibly dilated
by diffraction. The available brightness is then at its limit,
and would be no greater, even were the solar diameter in-
creased. The practical rule is that, when brightness is an
object, slits backed by the sun should not be narrowed to
~ much less than half a millimetre.
Lloyd’s Bands.
Lloyd’s experiment deserves to be more generally known,
as it may be performed with great facility and without special
apparatus. Sunlight is admitted horizontally into a darkened
room through a slit situated in the window-shutter, and at
a distance of 15 or 20 feet is received at nearly grazing
incidence upon a vertical slab of plate glass. The length of
the slab in the direction of the light should not be less than 2
or 3 inches, and for some special observations may advan-
tageously be much increased. The bands are observed on a
plane through the hinder vertical edge of the slab by means
of a hand magnifying-glass of from 1 to 2 inch focus. The
obliquity of the reflector is of course to be adjusted according
to the fineness of the bands required.
From the manner of their formation 1t might appear that
under no circumstances could more than half the system be
visible. But, according to Airy’s principle ft, the bands may
be displaced if examined through a prism. In practice all
* Verdet’s Lecons d’ Optique physique, t. i. p. 106.
+ See below.
82 Lord Rayleigh on Achromatic
that is necessary is to hold the magnifyer somewhat excentri-
cally. The bands may then be observed gradually to detach
themselves from the mirror, until at last the complete system
is seen, as in Fresnel’s form of the experiment.
If we wish to observe interference under high relative
retardation, we must either limit the light passing the first
slit to be approximately homogeneous, or (after Fizeau and
Foucault) transmit a narrow width of the band-system itself
through a second slit, and subsequently analyse the light into
a spectrum. In the latter arrangement, which is usually the
more convenient when the original light is white, the bands
seen are of a rather artificial kind. If, apart from the hetero-
geneity of the light, the original bands are well formed, and
if the second slit be narrow enough, the spectrum will be
marked out into bands; the bright places corresponding to
the kinds of light for which the original bands would be
bright, and the black places to the kinds of light for which
the original bands would be black. The condition limiting
the width of the second slit is obviously that it be but a
moderate fraction of the width of a band (A).
If it be desired to pass along the entire series of bands up
to those of a high order by merely traversing the second slit
in a direction perpendicular to that of the light, a very long
mirror is necessary. But when the second slit is in the region
of the bands of highest order (that is, near the external limit
of the field illuminated by both pencils), only the more distant
part of the mirror is really operative ; and thus, even though
the mirror be small, bands of high order may be observed, if
the second slit be carried backwards, keeping it of course all
the time in the narrow doubly-illuminated field. In one
experiment the distance from the first slit to the (38-inch)
reflector was 27 feet, while the second slit was situated behind
at a further distance of 4 feet. The distance (>) between the
first slit and its image in the reflector (measured at the
window) was about 13 inches.
As regards the spectroscope it was found convenient to use
an arrangement with detached parts. ‘The slit and collimating
lens were rigidly connected, and stood upon a long and rigid
box, which carried also the mirror. The narrowness of the
bands in which this slit is placed renders it imperative to
avoid the slightest relative unsteadiness or vibration of these
parts. The prisms, equivalent to about four of 60°, and the
observing telescope were upon another stand ata little distance
behind the box which supported the rest of the apparatus.
Under these conditions it was easy to observe bands in the
spectrum whose width (from dark to dark) could be made as
Interference-Bands. 83
small as the interval between the D lines ; but for this purpose
the first slit had to be rather narrow, and the direction of its
length accurately adjusted, so as to give the greatest distinct-
ness. ote the wave-lengths of the two D lines differ by
about tooo part, spectral bands of this degree of closeness
imply interference with a-retardation of 1000 periods.
Much further than this it was not easy to go. When the
bands were rather more than twice as close, the necessary
narrowing of the slits began to entail a failing of the light,
indicating that further progress would be attained with
difficulty.
Indeed, the finiteness of the illumination behind the first
slit imposes of necessity a somewhat sudden limit to the
observable retardation. In this respect it is a matter of
indifference at what angle the reflector be placed. If the
angle be made small, so that the reflexion is very nearly
grazing, the bands are upon a larger scale, and the width of
the second slit may be increased, but in a proportional degree
the width of the first slit must be reduced.
The relation of the width of the second slit to the angle of
the mirror may be conveniently expressed in terms of the
appearance presented to an eye placed close behind the
former. The smallest angular distance which the slit, con-
sidered as an aperture, can resolve, is expressed by the ratio
of the wave-length of light (A) to the width (w,) of the slit.
Now, in order that this slit may perform its part tolerably
well, 2, must be less than $A; so that, by (2),
Dias eb Mae he) DOT) sal eR)
The width must therefore be less than the half of that which
would just allow the resolution of the two images (subtending
the angle b/D) as seen by an eye behind. In setting up the
apparatus this property may be turned to account as a test.
The existence of a limit to n, dependent upon the intrinsic
brightness of the sun, may be placed in a clearer light by a
rough estimate of the illumination in the resulting spectrum ;
and such an estimate is the more interesting on account of
the large part here played by diffraction. In most calcu-
lations of brightness it is tacitly assumed that the ordinary
rules of geometrical optics are obeyed.
Limit to Illumination.
The narrowness of the second slit would not in itself be an
obstacle to the attainment of full spectrum brightness, were
we at liberty to make what arrangements we pleased behind
84 Lord Rayleigh on Achromatic
it. In illustration of this, two extreme cases may be con-
sidered of a slit illuminated by ordinary sunshine. First, let
the width w, be great enough not sensibly to dilate the solar
image; that is, let w, be much greater than X/s, where s denotes
in circular measure the sun’s apparent diameter (about 30
minutes). In this case the light streams through the slit
according to the ordinary law of shadows, and the pupil (of
diameter p) will be filled with light if situated at a distance
exceeding d*, where
: pid=s. se)
At this distance the apparent width of the slit is w./d, or was/p;
and the question arises whether it lies above or below the
ocular limit A/p, that is, the smallest angular distance that
can be resolved by an aperture p. The answer is in the
affirmative, because we have already supposed that w.s exceeds
r. The slit has thus a visible width, and it is seen backed by
undiffracted sunshine. If a spectrum be now formed by the
use of dispersion sufficient to give a prescribed degree of
purity, itis as bright as is possible with the sun as ultimate
source, and would be no brighter even were the solar diameter
increased, as it could in effect be by the use of a burning-
glass throwing a solar image upon the slit. The employment
of a telescope in the formation of the spectrum gives no
means of escape from this conclusion. The precise definition —
of the brightness of any part of the resulting spectrum would
give opportunity for a good deal of discussion; but for the
present purpose it may suffice to suppose that, if the spectrum
is to be divided into n distinguishable parts, so that its angular
width is 7 times the angular width of the slit, the apparent
brightness is of order 1/n as compared with that of the sun.
Under the conditions above supposed the angular width
of the slit is in excess of the ocular limit, and the distance
might be increased beyond d without prejudice to the brilliancy
of the spectrum. As the angular width decreases, so does the
angular dispersion necessary to attain a given degree of
purity. But this process must not be continued to the point
where w,/d approaches the ocalar limit. Beyond that limit
it is evident that no accession of purity would attend an in-
crease in d under given dispersion. Accordingly the dis-
persion could not be reduced, if the purity is to be maintained ;
and the brightness necessarily suffers. It must always be a
condition of full brightness that the angular width of the slit
exceed the ocular limit.
Let us now suppose, on the other hand, that wy is so small
* About 30 inches.
Interference- Bands. 85
that the image of the sun is dilated to many times s, or that
w, is much less than A/s. The divergence of the light is now
not s, but A/w,; and, if the pupil be just immersed,
pld=n/ wo.
The angular width of the slit w,/d is thus equal to X/p, that
is, it coincides with the ocular limit. The resulting spectrum
necessarily falls short of full brightness, for it is evident that
further brightness would attend an augmentation of the solar
diameter, up to the point at which the dilatation due to
diffraction is no longer a sensible fraction of the whole. In
comparison with full brightness the actual brightness is of
order wys/X; or, if the purity required is represented by n,
we may consider the brightness of the spectrum relatively to
that of the sun to be of order ws/(nd).
In the application of these considerations to Lioyd’s bands
we have to regard the narrow slit w, as illuminated, not by
the sun of diameter s, but by the much narrower source
allowed by the first slit, whose angular width is w,/D. On
this account the reduction of brightness is at least w,/(sD).
If w, be so narrowas itself to dilate the solar image, a further
reduction would ensue; but this could always be avoided,
either by increase of D, or by the use of a burning-glass
focusing the sun upon the first slit. The brightness of the
spectrum of purity n from the second slit is thus of order
Wy WS WW
sDe nh nXD-
We have now to introduce the limitations upon ww, and wy.
By (4) w,; must not exceed b/(4n); and by (2) w. must not
exceed XD/(2b). Hence the brightness is of order
Ops) Meer llr ounee tare eC)
independent of s, and of the linear quantities. The fact that
the brightness is inversely as the square of the number of
bands to be rendered visible explains the somewhat sudden
failure observed in experiment. If n=2000, the original
brightness of the sun is reduced in the spectrum some 30
million times, beyond which point the illumination could
hardly be expected to remain sufficient for vision of difficult
objects such as narrow bands.
In Fresnel’s arrangement, where the light is reflected per-
pendicularly from two slightly inclined mirrors, interference
of high order is obtained by the movement of one of the
mirrors parallel to its plane. The increase of n does not then
entail a narrowing of w,; and bands of order n may be
86 Lord Rayleigh on Achromatic
observed in the spectrum of light transmitted through wa,
whose brightness is proportional to n—', instead of, as before,
Lom.
Achromatic Interference- Bands.
We have already seen from (3) that in the ordinary arrange-
ment, where the source is of white light entering through a
narrow slit, the heterogeneity of the light forbids the visibility
of more than a few bands. The scale of the various band-
systems is proportional to A. But this condition of things,
as we recognize from (2), depends upon the constancy of 0,
that is, upon the supposition that the various kinds of light all
come from the same place. Now there is no reason why such
a limitation should be imposed. If we regard 0 as variable,
we recognize that we have only to take b proportional to X,
in order to render the band-interval (A) independent of the
colour. In such a case the system of bands is achromatic, and
the heterogeneity of the light is no obstacle to the formation
of visible bands of high order.
These requirements are very easily met by the use of
Lloyd’s mirror, and of a diffraction-grating, with which to
form a spectrum. White light enters the dark room through
a slit in the window-shutter, and falls in succession upon a
grating, and upon an achromatic lens, so as to form a real
diffraction-spectrum, or rather series of such, in the focal
plane. The central image, and all the lateral coloured images
except one, are intercepted by a screen. The spectrum
which is allowed to pass is the proximate source of light in
the interference experiment ; and since the deviation of any
colour from the central white image is proportional to X, it is
only necessary so to arrange the mirror that its plane passes
through the white image in order to realize the conditions for
the formation of achromatic bands.
There is no difficulty in carrying out the experiment practi-
cally. I have used the spectrum of the second order, as given
by a photographed grating of 6000 lines in an inch, and a
photographic portrait lens of about 6 inches focus. Ata
distance of about 7 feet from the spectrum the light fell
upon a vertical slab of thick plate-glass 3 feet in length and
a few inches high. ‘The observer upon the further side of the
slab examines the bands through a Coddington lens of some-
what high power, as they are formed upon the plane passing
through the end of the slab. It is interesting to watch the
appearance of the bands as dependent upon the degree in
which the condition of achromatism is fulfilled. A com-
paratively rough adjustment of the slab in azimuth is sufficient
Interference-Bands. 87
to render achromatic, and therefore distinct, the first 20 or
30 bands. As the adjustment improves, a continually larger
number become visible, until at last the whole of the doubly
illuminated field is covered with fine lines.
In these experiments the light 1s white, or at least becomes
coloured only towards the outer edge of the field. By means
of a fine slit in the plane of the spectrum we may isolate any
kind of light, and verity that the band-systems corresponding
to various wave-lengths are truly superposed.
When the whole spectrum was allowed to pass, the white
and black bands presented so much the appearance of a grating
under the microscope that I was led to attempt to photograph
them, with the view of thus forming a diffraction-grating.
Gelatine plates are too coarse in their texture to be very
suitable for this purpose ; but I obtained impressions capable
of giving spectra. Comparison with spectra from standard
gratings showed that the lines were at the rate of 1200 to the
inch. A width of about half an inch (corresponding to
600 lines) was covered, but the definition deteriorated in the
outer half. A similar deterioration was evident on direct
inspection of the bands, and was due to some imperfection in
the conditions—perhaps to imperfect straightness of the slab.
On one occasion the bands were seen to lose their sharpness
towards the middle of the field, and to recover in the outer
portion. :
With respect to this construction of a grating by photo-
graphy of interference-bands, a question may be raised as to
whether we are not virtually copying the lines of the original
grating used to form the spectrum. More may be said in
favour of such a suggestion than may at first appear. or it
would seem that the case would not be essentially altered
if we replaced the real spectrum by a virtual one, abolishing
the focusing lens, and bringing Lloyd’s mirror into the
neighbourhood of the grating. But then the mirror would be
unnecessary, since the symmetrical spectrum upon the other
side would answer the purpose as well as a reflexion of the
first spectrum. Indeed, there is no escape from the conclusion
that a grating capable of giving on the two sides similar
spectra of any one order, without spectra of other orders
or central image, must produce behind it, without other
appliances and at all distances, a system of achromatic inter-
ference-fringes, which could not fail to impress themselves
upon a sensitive photographic plate. But a grating so
obtained would naturally be regarded as merely a copy of
the first.
Another apparent anomaly may be noticed. It is found in
88 Lord Rayleigh on Achromatic
practice that, to reproduce a grating by photography, it is
necessary that the sensitive plate be brought into close contact
with the original ; whereas, according to the argument just
advanced, no such limitation would be required.
These discrepancies will be explained if, starting from the
general theory, we take into account the actual constitution of
the gratings with which we can experiment. If plane waves
of homogeneous light (X) impinge perpendicularly upon a
plane (¢=0) grating, whose constitution is periodic with
respect to # in the interval o, the waves behind have the
general expression
A, cos (kat —kz) + A; cos (pe+f,) cos (kat— p42)
+ B, cos (pa +g,) sin (kat — pz)
+ A, cos (2px +f5) cos (kat— poz) +...3 « (8)
where
p=2tj/aq, je 2a
a pyH=hP—p?, py=h—Ap’, We.,
the series being continued as long as w isreal*. Features in
the wave-form for which mw is imaginary are rapidly elimi-
nated. For the present purpose we may limit our attention
to the first three terms of the series, which represent the
central image and the two lateral spectra of the first order.
When the first term occurs, as usually happens, the phe-
nomena are complicated by the interaction of this term with
the following ones, and the effect varies with < in a manner
dependent upon >. This is the ordinary case of photographic
reproduction, considered in the paper referred to. If Ao
vanish, there is no central image; but various cases may still
be distinguished according to the mutual relations of the other
constants. If only A,, or only B,, occur, we have interference-
fringes. The intensity of light is (in the first case)
A,’ cos? (pep) 2: a ee
petfa\(ntl)r
and these fringes may be regarded as arising from the inter-
ference of the two lateral spectra of the first order,
4A, cos (kat—me+pet+f,),
4A, cos (kat —py2—pa—f,).
vanishing when
As an example of only one spectrum, we may suppose
By=Ay, m=fi—27,
* Phil. Mag. March 1881; Ene. Brit. Wave Theory, p. 440.
ae
Interference-Bands. 89
= A, cos (kat—pmz—pa—fi). . . . . (10)
A photographic plate exposed to this would yield no impres-
slon, since the intensity is constant.
In order, then, that a grating may be capable of giving rise
to the ideal system of interference-fringes, and thus impress
itself upon a sensitive plate at any distance behind, the
vibration due to it must be of the form
A cos (pe+f) cos (kat—pyz). . 2. . (11)
It does not appear how any actual grating could effect this.
Supposing z=0, we see that the amplitude of the vibration
immediately behind the grating must be a harmonic function
of x, while the phase is independent of 2, except as regards
the reversals implied in the variable sign of the amplitude.
Gratings may act partly by opacity and partly by retardation,
but the two effects would usually be connected ; whereas the
requirement here is that at two points the transmission shall
be the same while the phase is reversed.
We can thus hardly regard the interference-bands obtained
from a grating ard Lloyd’s mirror as a mere reproduction of
the original ruling. As will be seen in the following para-
graphs, much the same result may be got from a prism, in
place of a grating; and if the light be sufficiently homogeneous
to begin with, both these appliances may be dispensed with
altogether.
Prism instead of Grating.
If we are content with a less perfect fulfilment of the
achromatic condition, the diffraction- spectrum may be
replaced by a prismatic one, so arranged that d(A/b) =0
for the most luminous rays. The bands are then achromatic
in the same sense that the ordinary telescope is so. In this
case there is no objection to a merely virtual spectrum, and
the experiment may be very simply executed with Lloyd’s
mirror and a prism of (say) 20° held just in front of it.
The number of black and white bands to be observed is not
so great as might perhaps have been expected. The lack of
contrast which soon supervenes can only be due to imperfect
superposition of the various component systems. That the
fact is so is at once proved by observation according to the
method of Fizeau; for the spectrum from a slit at a very
moderate distance out is seen to be traversed by bands. If
the adjustment has been properly made, a certain region in
the yellow-green is uninterrupted, while the closeness of the
bands increases towards either end of the spectrum. So far
90 Lord Rayleigh on ono ie
as regards the red and blue rays, the original bands may be
considered to be already obliterated, but so far as regards the
central rays, to be still fairly defined. Under these circum-
stances it is remarkable that so little colour should be apparent
on direct inspection of the bands. It would seem that the eye
is but little sensitive to colours thus presented, perhaps on
account of its own want of achromatism.
It is interesting to observe the effect of coloured glasses
upon the distinctness of the bands. If the achromatism be in
the green, a red or orange glass, so far from acting as an aid
to distinctness, obliterates all the bands after the first few. On
the other hand, a green glass, absorbing rays for which the
bands are already confused, confers additional sharpness. With
the aid of a red glass a large number of bands are seen
distinctly, if the adjustment be made for this part of the
spectrum.
A still better procedure is to isolate a limited part of the
spectrum by interposed screens. For this purpose a real
spectrum must be formed, as in the case of the grating above
considered. 7
We will now inquire to what degree of approximation
d/b may be made independent of > with the aid of a prism,
taking Cauchy’s law of dispersion as a basis. According to it
the value of 6 for any ray may be regarded as made up of two
parts—one constant, and one varying inversely as \*. We >
therefore write
Xu Ne
5 ep (12)
where A is to be so chosen that A/b is stationary when dX has
a prescribed value, Ap. This condition gives
Ady =8B3. c.7 000 eel)
so that
A/b Mee Soe
ify 13 Vee.
As an example, let us suppose that the disposition is achro-
matic for the immediate neighbourhood of the line D, so that
Ny=Ap, and inquire into the proportional variation of d/b,
when we consider the ray C. Assuming
Ay = 08890, XN, — 69018;
we obtain from (14)
r/b
Xo/bo
The meaning of this result will be best understood if we
inquire for what order (n) the bands of the C-system are
: ee
Interference-Bands. 91
shifted relatively to those of the D-system through half the
band-interval. From (1)
du = nDJ{r/b—No/bo}
— $ryD/bo
by hypothesis ; so that
2No/ bo
O95 HB. /ce es el)
Thus, in the case supposed, n=32. After 32 periods the
black places of the C-system will coincide with the bright
places of the D-system, and conversely. If no prism had
been employed (6 constant), a similar condition of things
would have arisen when
Lr»
fo oe ee
n= ie 4°2.
If (A—X,) or, as we may call it, 6’ be small,
d/ b—NXo/ Dy
A/S
is of the second order in 6A. An analytical expression is
readily obtained from (14). We have
A/b 14+ 86A/Ay + B(S2/Ay)? + (5A/Ao)*
No/bo 1+ 36A/A,+ 3 (6A/Ap)?
shai §(OA/No)” + (8A/Ao)®
| £4 860/04 8(6A/A5)?
= 1+ §(6A/Ao)* —§ (OA/Ay)®,
approximately ; so that, by (15),
oe Cane ; Ov } ;
n=4(<2) {14+$5c+. ee ees cic)
This gives the order of the band at which complete dis-
erepance first occurs for A, and Ay» + 6A, the adjustment being
made for A». It is, of course, inversely proportional to the
square of OX, when 6” is small.
The corresponding value of n, if no prism be used, so that
6 is constant, is
SA
ea ee
The effect of the prism is thus to increase the number
of bands in the ratio
(=
bole
ZING tee OX.
[To be continued. ]
age]
XII. Note on some Photographs of Lightning and of “ Black”
Electric Sparks. By A.W. CLaYDEN™.
AG) eae the thunderstorm on the night of June 6 I ex-
posed several plates in the hope of securing photographs
of lightning. ‘Three of these gave results.
One was exposed to two flashes, not counting such as did
not cross the field of view. ‘These two flashes show compli-
cated and beautiful structure. One of them is a multiple flash,
distinctly seen as double by both my wife and myself. An
enlargement of this shows curious flame-lke appendages
pointing upwards from every angle. The other flash is a
broad ribbon. The images of the masonry in the left-hand
corner (which are necessarily slightly out of focus) show
three positions of the camera. ‘They are sharp, hence the
camera did not move during the existence of a flash ; and the
directions of those movements which did occur do not in any
way correspond to the movements (if such there were) which
would have been required to produee the ribbon-like effect
from a linear flash.
A second plate shows four flashes, and the camera moved
much more than in the first case. None of these flashes are
ribbons. Development showed the plate to be overexposed.
The third was exposed to six flashes ; that is to say, I .
judged that six of them crossed the field of view. There
were many others between times, which were either in the
clouds or occurred in other parts of the sky. One flash, I
remarked at the time, must be “ right down the middle of the
plate.’ Development showed this plate to be very much
overexposed, and the image required careful nursing. I was
much surprised to see nothing but one triple flash in the
corner. I supposed that I must have mistaken the plate, and
was about to throw it away, but on carefully searching for
the above-mentioned vertical flash, I found its image was
reversed, printing as a black flash with a white core. Sub-
sequent observation showed other dark flashes; and the enlarge-
ment of part of the. plate shows that there are indications of
white cores to each of them. ,
Now the connexion between this reversal and overexposure
was very striking. Hence it occurred to me that the black
flashes might be due to a sort of cumulative action. Not to
the excessive brightness of the individual flashes, but rather
to the excessive action produced by the superposition of the
* Communicated by the Physical Society: read June 22, 1889.
j ————— oo
Photographs of Lightning and “Black” Electrie Sparks. 93
glare from an illuminated white cloud upon the normal image
of the flash.
To test this I endeavoured to obtain the same effect with
the sparks from a small Wimshurst machine ; but, under the
conditions in which I worked, I could not get a longer spark
than one inch.
I first photographed a series of brilliant sparks, using two
large Leyden jars. These gave normal images, very dense,
and shaded off at the margins, although the focus, as shown
by the knobs of the machine, was good.
Next I tried less brilliant sparks from the machine with its
ordinary small jars. These gave similar images, but less dense.
Then I repeated both experiments, and before developing
the plates exposed them to the diffused light from a gas-flame.
The brilliant sparks then yielded images which may either be
called normal with a reversed margin, or reversed with a
normal core. The fainter sparks were completely reversed.
One plate of bright sparks was exposed to the gas-light, so
that different parts were acted upon for different times. The
reversal seems to spread inwards as the exposure to diffused
light is increased.
One plate of faint sparks was only half of it exposed to
diffused light. The result is that on that part the sparks are
reversed, while on the other they are normal.
Finally I photographed a number of sparks in a series
across the plate, and placed a sheet of white cardboard behind
them to do duty for the white background of cloud. Some
of the first sparks impressed on the plate show reversed
images.
Coupling these experiments with the observations as to the
overexposure of the “dark-flash”’ plate, and with the fact
that all dark-flash plates I have seen show symptoms of con-
siderable exposure, I submit that there is at least a good case
for this theory of cumulative or repeated action producing
the reversal. The partial reversal of the bright sparks seems
to correspond with the bright core to some dark flashes; and
the complete reversal of the less brilliant sparks to the absence
of any such core from the less conspicuous portions of a dark
flash.
There is certainly one difficulty yet to be got over, and that
is the crossing of a dark flash by a bright one. However, I
have some experiments* in view which I hope may throw some
* Since writing the above communication I have made a number of
further experiments, which I hope to describe in detail at some future
time. But perhaps I may be allowed to say at once that I have suc-
ceeded in imitating the phenomenon of a bright image crossing a dark
Phil. Afag. 8. 5. Vol. 28. No. 171. August 1889. I
94 Mr. J. T. Bottomley on Expansion with Rise of
light upon this also. In my own negative the point of
crossing seems to be extra bright.
Meanwhile I must apologize to the Society for bringing
forward these notes in such an immature and hastily con-
structed condition. My excuse must be that the photographs
of electric sparks were only taken the day before yesterday,
and today’s meeting is the last of the session.
XIII. Hzpansion with Rise of Temperature of Wires under
Pulling Stress. By J. VT. Borrominy, Aly eee
LLCS
[Plate IX.]
{' is probably well known to the members of the Physical
Society that, at the instance of the British Association
and with the assistance of a money grant from that body,
very interesting secular experiments on the elasticity and
ductility of wires were commenced some years ago in
Glasgow. In the tower of the Glasgow University buildings
certain wires are hung in pairs for comparison. One of each
pair carries a heavy load about half the breaking weight of
the wire ; the other carries about one tenth of the breaking
weight. Certain marks are put on the wires; and the object
of the experiment is to find whether the heavily loaded wire
seems, on comparison with the lightly loaded wire, to go on
running down incessantly, or whether it comes asymptotically
to a fixed length for a given temperature, ceasing to ex-
perience further permanent elongation.
The observations of the last few years show that the
elongation due to further pulling out has, to say the least,
become exceedingly small, so small that it is extremely
difficult to observe it; and at the Aberdeen meeting of the
British Association I pointed out that a great difficulty is
introduced into the making of deductions from these observa-
one. The experiments point to the conclusion that diffused light acting
upon a plate can reverse previously impressed images of electric sparks,
but is powerless to affect any such impressions which may be made after-
wards. Similar results are obtained whether the source of the diffused
light is a gas-flame, a lamp, or a series of sparks. I do not at present
offer any theoretical explanation of these facts, but they are in themselves
sufficient from a meteorological point of view. ‘‘ Dark” flashes of light-
ning have no existence in nature, but are caused by the exposure of the
plate to an illuminated sky after the passage of the flash. This illumi-
nation may be due to subsequent flashes, the more recent of which will
give normal images possibly crossing the reversed ones.
* Communicated by the Physical Society: read June 22, 1889.
Temperature of Wires under Pulling Stress. 99
tions through the impossibility of controlling the temperature
of the tube in which the wires are placed. If, for example,
there is any difference as to expansion with temperature of
the same wire when lightly and when heavily loaded, a cause
of disturbance would be introduced which it would be ex-
cessively difficult to allow for. It seemed therefore absolutely
essential to make direct experiments on this point. The
object of the present communication is to give an account of
some experiments of this kind. A preliminary account of
these experiments was communicated to the British Associa-
tion at the Manchester meeting (1887), and was printed in
the Philosophical Magazine for October of that year.
The wires hung up in the tower of the Glasgow University
building are two of platinum, two of gold, and two of palla-
dium, these wires being chosen on account of their small
lability to oxidation. The wires on which I have experi-
mented up to the present time have, however, been of copper
and platinoid. The latter metal is an alloy* of nearly the
same composition as German silver, but containing a small
quantity of tungsten and made in a peculiar way.
The figures show the arrangements for experimenting. A
long tube of tin-plate about 24 inches in diameter was set up
vertically, fixed by means of brackets at two or three places.
This tube has inlets and outlets for steam, of which I have a
plentiful supply in the laboratory from boilers connected
with the University apparatus for heating and ventilation.
It has also openings for thermometers. The length of the
tube was 174 feet in the experiment with copper wire, and
somewhat shorter in the platinoid experiment.
A piece of excellent copper wire was taken, and its break-
ing weight was found to be 750 grammes. Its diameter was
0-22 millim. Two portions of this wire were hung side by
side in the centre of the tube. In order to suspend them
their ends were passed into two small trumpeted holes in a
stout brass plate and soldered to the back of the plate. The
plate was screwed up to a strong beam in the ceiling of the
laboratory. This forms by far the best mode of supporting a
wire for experiments on elasticity. One of the wires carried
75 grammes, the other 375 grammes.
A few preliminary experiments as to heating and cooling
revealed a difficulty the magnitude of which I was unprepared
for. When the steam was admitted into the tube the wires
of course expanded, the heavily loaded wire going down
far more than the other; and when the steam had been
stopped and the tube allowed to cool, they contracted again
* Invented and patented by F. W. Martino of Sheffield.
2
96 Mr. J. T. Bottomley on Hapansion with Rise of
but not to the same extent; and neither came back to its
original length. This was of course to be expected. But
it turned out, on repeating the heating and cooling, that the
same thing occurred again and again; and it was not till
after about 150 heatings and coolings that the heavily loaded
wire assumed a permanent state, expanding and contracting
by equal amounts with the heating and cooling*. ‘The lightly
loaded wire took its permanent condition much sooner.
This itself was a valuable result, applying directly to the early
observations on the secular wires in the University tower.
Fig. 1, Pl. [X., shows the arrangement for these preliminary
experiments. Behind the wire a half-millimetre scale was put
up; and each wire carried a pointer moving over the scale. The
readings at hot and cold temperatures were taken with the well-
known Quincke microscope-kathetometer ; and the process and
observations were carried on, as has been said, till each
pointer gave unvarying readings at the hot and cold tempe-
ratures. It was then considered that the wires had assumed
a permanent condition.
The pointers and scale were now removed and two hooks,
of peculiar construction, figs. 2 and 3, were attached to the
ends of the wire, the wires being passed into holes made for
the purpose and soldered in. These hooks carried and formed
part of the stretching weights. The upper parts of the hooks
are turned over to form two horizontal plates, and the vertical
parts of the hooks press very lightly against each other and
form almost frictionless guides one for the other. In one of
the vertical faces a vertical V-groove is cut, while the
remainder of the face is plane and well-polished. Two little
feet on the vertical face of the other hook move in the
V-groove of the first, and a third foot rests against the smooth
vertical face. A relative geometrical guide is thus provided
for the hooks, and the shape of the hooks is such that the
gravity of the whole, including the weights, gives the requisite
slight pressure of the one against the other. The horizontal
parts of the hooks just mentioned carry what is practically
a small three-legged table, of which two legs rest on one
platform and the third on the other. ‘To be more precise, one
of the platforms carries on its top a little plate with a
V-groove cut init; and a knife-edge, cut away at the central
parts and thus leaving two feet at the extremities, attached
* I must not fail to express here my indebtedness to Mr. Thomas A. B.
Carver, assistant, and Mr. W. S. Cook, student in the Physical Laboratory,
who carried out these experiments in the winter sessions 1887-8 and
1888-9 respectively. Without their patient labour the work would have
been impossible to me.
. ——_e—_
Temperature of Wires under Pulling Stress. 97
to the table, rests in the V. A third foot, rounded, rests on
the other platform, which is plane and polished. On the top
of this little table, which is a square of about 14 centimetre
in the side, there is fastened a perfectly plane parallel Stein-
heil mirror; and a telescope with cross wires, looking down
very nearly vertically on the mirror, views, reflected in the
mirror, a half-millimetre scale suitably placed.
It will be seen at once that if the two wires were to elon-
gate equally with rise of temperature, their extremities would
go down together and almost the only effect (not absolutely
of course) on the scale-reading would be to alter somewhat
the focus. But if one wire elongates more than the other the
mirror is tilted, and the change in the scale-reading readil
gives the amount of relative displacement of the ends of
the wire. ;
The arrangement works in the most satisfactory way, and
it now only remains for me to state the results. J must
remark, however, that it was exceedingly difficult to make an
exact estimate of the temperature of the tube, even when the
steam was running strongly through it. Thermometers in-
serted by means of corks in holes provided for the purpose
showed that differences of 2° or 8° (I think not so much as
5°, however) existed at different parts of the tube.
This being understood, | may say that the range of tem-
perature in the various experiments was from 15° ©. or 16° C.
(cold) to 98° or 99° (hot), or about 83°C. The length of
copper wire experimented on was 530 centimetres. The
difference of expansions observed was 0°14 millim. or 0°014
centimetre, the heavily loaded wire going down most. This
gives a relative expansion of 26 x 10-6 per centimetre for a
change of temperature of 83° ; or 0:314 x 10~° per centimetre
per degree.
I find the linear expansion of copper per degree stated at
about 17°2 x 10~®, and thus the ratio of this extra expansion to
the total expansion is 3°14/172, or about =k.
With regard to platinoid wire—after more than three
months of daily heating and cooling, the wires (0°35 millim.
in diameter) came toa thoroughly permanent condition. Ona
length of 490 centimetres a relative extra extension of 0°111
millim. or 0°011 centim. was observed for a change of
temperature of 83°, and as with copper the heavily loaded
Wire experienced most elongation. These numbers give
22-4 x 10-° as the extra expansion per centimetre, or
0°27 x 10~° per centimetre per degree Centigrade.
The linear expansion of platinoid was unknown, though it
might be supposed to be something not very different from that
98 Messrs. Duncan, Wilkes, and Hutchinson on the Value
of German silver. Accordingly a series of experiments were
carried out on this question, with the result that the linear
expansion of the specimen used was found to be -0000154 per
degree Centigrade.
The relative extra expansion of platinoid wire is therefore
2°7
15a? or =.
XIV. A Determination of the Value of the B.A. Unit of
Resistance in. Absolute Measure, by the Method of Lorenz.
By Dr. Louis Duncan, Ginpert WiLkss, and Cary T.
HUTCHINSON*.
faa work was done at the Physical Laboratory of Johns
Hopkins University during the spring of 1888. lord
Rayleigh’s modification of Lorenz’s original method was used.
In this, as is well known, a measured part of the current
flowing through the inducing coils is balanced by the current
induced by the rotation of the disk.
The apparatus employed is that designed by Prof. Rowland
for his determination of the ohm undertaken for the United
States Government. A detailed description of it is contained
in his forthcoming report, so only a few words will be given
to it here. The induction-coils, four in number, were wound
in square channels cut in heavy flanges, which were cast on
the exterior of a hollow brass cylinder open at both ends.
The coils were respectively 30°171, 9°786, 10°545, and 30°775
centim. from the mean plane of the disk, itself placed as
nearly as possible midway between the ends. The cylinder is
about 66 centim. long, 100 centim. in diameter, and 1 centim.
thick. It is thus the longest ever used in work of this kind.
The flanges and cylinder were cast in one piece, and the
tooling was all done without removing the casting from the
lathe. The walls of the channels were left very thick to
prevent spreading during the winding of the coils. The
radius of the disk was so chosen that an error in its value
should enter as slightly as possible in the value of the co-
efficient of induction.
The disk was brass, 21°5 centim. radius and °5 centim.
thick. It was fixed to a brass axle, 3 centim. diameter, turn-
ing in bearing-boxes carried by suitable framework fixed
inside the cylinder. There was a cone of grooved pulleys
toward one end of the axle, used for getting different speeds
of the disk. The motor for running the disk was in the
* Communicated by the Authors.
of the B.A. Unit of Resistance in Absolute Measure. 99
adjoining room, about 10 metres from the disk. The speed
obtained varied from 26 to 47 revolutions per second, higher
than has usually been used.
The current was taken from the edge of the disk by three
brushes which bore on it at angular distances of 120°; each
brush was made of three or four brass strips of different lengths
soldered together at one end; each strip in every brush
touched the disk, one brush occupying a length of 2 centim.
or more on the edge. ‘The strips were made of various
lengths in order to avoid systematic vibrations. For the
contact at the centre, a conical counterboring was made in
one end of the axle and a brass point was pressed into it con-
stantly by a stiff spring. The counterboring in the axle, the
point, the brushes, and the edge of the disk were all carefully
amalgamated before each observation; particular care was
given to this. The insulation resistance of the coils was found
to be from six to ten megohms.
The arrangement for getting the speed differed from that
generally employed. As the quantity desired is the average
speed during the time of an observation, it seemed that a
chronograph, if sufficiently accurate, would give this better
than any other means, besides furnishing at a glance the
history of the systematic variations of the speed, while the
galvanometer showed the abrupt changes. The spot of light
of the galvanometer was usually very steady, showing that
there were no sudden changes. Every hundredth revolution
of the disk was recorded on the chronograph. To accomplish
this, one end of the axle was connected to an ordinary speed-
counter, consisting of a worm wheel and endless screw,
whieh rested on a board fixed to receive it. The worm
wheel carried a small brass pin, which made contact every
revolution with a brass strip fixed near it, thus closing the
chronograph circuit. The strip was adjustable and the con-
tact was always made as slight as possible consistent with
certainty. The duration of this contact was about J, sec.,
while the clock-break was nearly twice this.
The connexion of the axle with the endless screw was
made in this way:—A small hard rubber screw with square
head was fitted in the end of the axle and was joined to the
screw of the speed-counter by drawing over both a piece of
pure rubber tubing with thick walls, about 2 centim. long,
This connexion is easily made, permits no slipping, and absorbs
vibrations so completely that even for comparatively high
speeds no fastening is required to hold the counter down to
the board; but for the very high speeds we used it was
necessary to secure it to the rubber bed on which it lay by
100 Messrs. Duncan, Wilkes, and Hutchinson on the Value
rubber bands, in order to ensure perfectly uniform contact
between the pin and the spring.
The chronograph was a large and excellent instrument by
Fauth ; the drum was about 18 centim. diam., and in this
work revolved in 30 seconds ; the length of a second was thus
nearly 2 centim. ; the sheet could be read with rough means
to 4 millim. (= 7,5 sec.); and was actually read much closer.
As each observation lasted five minutes, even this gave an
estimation of the mean speed to gaoz-
The galvanometer was a low resistance one of the Thomson
reflecting type ; a small piece of wire which dipped in a light
oil was hung from the needle and acted as a damper: with
this the needle was found to be sufficiently sensitive, and to
come nearly to rest in about twelve seconds after reversing
the current throughit. The resistance a in the figure through
aoe ta galy
which the main current flows is a large 1-ohm coil of German
silver wound about a skeleton cylinder of glass rods, and is
about 30 centim. high and 15 centim. in diameter. The ends
of the coil are soldered to copper blocks which form the bot-
toms of mercury-cups. It is placed in an earthenware jar
filled with special light oil known to be a good insulator, and
is provided with a stirring-paddle. Resistance 6 is a l-ohm
coil, by Hlliot, of the usual form ; this is put in a large glass
jar and surrounded with water. Jesistance ¢ is taken from
specially made “ comparators ;”’ each consists of ten coils of
the same nominal value wound together on a copper cylinder
6 centim. diameter ; they are properly insulated &c., and pro-
tected by a larger concentric cylinder. The terminals are
soldered to the copper bottoms of mercury-cups arranged in
two circles around the hard rubber ring which closes the
annular space between the inner and outer copper cylinders.
The inner cylinder is filled with water. The connexions of
the ten coils can be varied at pleasure ; they can all be thrown
in series, in parallel, or in any intermediate arrangement.
There were two comparators used, with the coils 100 and 10
ohms respectively.
of the B.A. Unit of Resistance in Absolute Measure. 101
To keep the temperature constant, spirals of lead pipe were
placed round the Elliot coil and in the inner cylinders of the
comparators, through which there was a constant flow of
water from the city supply. This answered its purpose ad-
mirably : the temperature varied only a degree or so even
from day to day. The water was of course allowed to flow
some hours before beginning observations.
The terminals of all resistances were brought to large
mercury-cups, m,m, each having an amalgamated copper
disk lying on the bottom. The main current did not flow
through any part of the circuit of the induced current; a
short bridging-piece, d, is used, as Lord Rayleigh found
necessary.
The resistances used were all compared several times by
different observers with the standard: this was a Warden
Muirhead 10-ohm coil, whose value was determined at the
Cavendish Laboratory in 1887 ; it was 9:99416 B.A. units at
16°5, with temperature-coefficient of ‘000292 per ohm per
degree.
In taking the observations, the aim was to adjust the resist-
ances first so that there should be only a small deflexion.
After a number of galvanometer-readings for this ‘“ balanced ”
arrangement had been taken, the resistance c was changed so
as to give a deflexion of ten divisions (say) ; readings were
taken for this “unbalanced” arrangement; the original
‘“‘ balanced ” was then restored and readings taken. If
nothing had changed sensibly since the beginning of the ex-
periment the average deflexions for the two “balanced ”’
would agree: of course this condition was only approximated
to. The “unbalanced” set gives the data for correcting for
the small deflexion of the ‘‘ balanced.”
Each experiment then consists of the galvanometer-, speed-,
temperature-, &c. readings pertaining to the three arrange-
ments of resistances: these three arrangements are called A,
B, and A’, in the order taken, irrespective of the magnitude
of the defiexions. In general R, and R,; (subscripts 1, 2, 3
refer to A, B, A’ respectively ; R is the “ effective” resist-
ance) are the same, and the corresponding deflexions are small;
B is in this case used to correct both R, and Rs, and the mean
of the corrected values is used. When, however, the deflexion
for A happens to be undesirably large after beginning the
experiment, B is made to give a small deflexion, and A’ made
as nearly as may be the same as A. We have in this case to
apply the mean of two corrections to R,, one from A and the
other from A’,
In each arrangement, as A, the current is reversed four
102 Messrs. Duncan, Wilkes, and Hutchinson on the Value
times; it is kept in the same direction for one minute at a
time, and five galvanometer-readings at equal intervals of
time are taken each minute: this gives, then, twenty-five
galvanometer-readings and occupies five minutes. The set B
is begun as quickly as possible after A. The chronograph-
record is started by dropping the pen on the revolving drum
only a few seconds before the first galvanometer-reading, and
an effort is made to use that portion of the record beginning
exactly with the readings ; the record is stopped at the instant
of the last reading by lifting the pen. Temperature-readings
are taken before, ‘after, and often during the set. The resist-
ance carrying the main current is constantly stirred, and the
others frequently. After A’ the temperature of the ona
and disk is noted.
Variety was given to the different experiments by using
different pairs of induction-coils, inner or outer, and by vary-
ing the speed and direction of rotation. Sometimes, too, an
experiment was repeated with everything the same, except
that the resistance ¢ would be made up of different coils.
The coefficient of mutual induction for the two pairs of coils
as used by Prof. Rowland are :—
Coils 1+4, M=)60292°5;
5» 2+8, M=102030-2:
Diameter of disk . =43°1334 at 17°.
Before beginning these experiments, the disk was slightly
turned off in order to smooth the edge; the diameter was
measured by two observers, and was found to be
43°1201 at 17° C.
The formule expressing the effect on M of small changes in
the quantities entering in its expression are,
aM dA da me
: aM _ dA da ]
where A = mean radius of the coil,
a = radius of disk,
6 = distances of mean planes of disk and coil.
of the B.A. Unit of Resistance in Absolute Measure. 103
The corrections, calculated by these formulz, due to the
change in a give
for 1+4, M= 60257 at 17° C.,
fon Zoo. M= 101964. ee
Let p = ratio of the B.A. unit to the ohm,
ieee
se sae
N= number of revolutions per second,
R
“ effective” resistance,
D= Ds— Dy = difference of mean deflexions,
for the two positions 8 and N of the reversing-key ; 7. e. D
would be the mean deflexion for either direction of current,
if no irreversible effects existed.
Then will
ieee ( oy, Ma ;
ee MN.) me M.3p,—D,, Us as ()
and ‘
a) ceo (2)
5 MN, ) Nad, Se. Sees ee
(1) is used when D, < D,; (2) is used when 1D, > Dg.
The double subscripts, as Rj, 3, means that the two quantities
R, and R; are to be used in turn ; that is to say, each formula
above is really double: first we use the subscript 1’s, and
then the subscript 3’s._ It was found more convenient to cal-
culate the values of p; and p3 this way and average them than
to apply an average correction. Indeed, when the speeds N,
and N; are different, this is the only way.
The following table gives the data and results of these
experiments ; the (+) direction of rotation is zenith, north,
nadir, south. 2
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106 Dr. H. H. Hoffert on
Experiments Nos. 1, 2, 8,6, 14A’,17A, and 22 were in-
terrupted by divers accidents and never completed; in
No. 19 there is confusion in the notes, making the sign of
the deflexion doubtful ; Nos. 21, 23, and 24 give values of
p from 2 per cent. to 10 per cent. out, due to some error in
the record of resistances used. This accounts for all the
experiments begun.
The average of all the above is °98622; without No. 27
which differs about twice as much from the mean as any other
observation, the average is °98634. The great divergence of
No. 27 is in itself reason enough for giving it less weight ;
but in addition, the chronograph sheet shows that the speed
here was very irregular, increasing, decreasing, and increasing
again; this is the only occurrence of such irregularity.
Therefore, giving it about one third weight, we find as the
most probable value
1 B.A. Unit = °9863 ohm.
A determination of the “Mercury Unit” was recently —
made by Messrs. Hutchinson and Wilkes (Johns Hopkins
University Circulars, May 1889; Phil. Mag. July 1889)
who found the value to be °95341. Taking this with the
above number for the B.A. unit, we have as the length of the
mercury column corresponding to the ohm,
106°34 centims.
XV. Intermittent Lightning-Flashes. By EH. H. Horrzrr,
D.Sc., ARS.M., Demonstrator of Physics at the Normal
School of Science and Royal School of Mines*.
[Plate IV.]
\HE storm which passed over London on the evening of
June 6th afforded an unusually favourable opportunity
for observations, both with and without the aid of the camera,
on the character of lightning-flashes, and for determining
the causes of some of the curious effects noticed by previous
observers.
While watching the storm from my house in Haling I
could in several instances distinctly perceive a flickering
appearance in a discharge, and in one particular case the repe-
titions were at least 5 or 6 in number, just sufficiently slow
for the eye to detect the variations in brightness without re-
moving the impression of one single flash. Other observers
* Communicated by the Physical Society : read June 8, 1889.
Intermittent Lightning-Flashes. 107
with whom I have since spoken have informed me that they
had observed a similar effect, and that in some instances
flashes, following as nearly as could be seen in the same path,
were separated by an appreciable interval, often of several
seconds duration. Photographs of lightning have frequently
been obtained showing banded, ribbon, or double flashes;
but, so far as I am aware, these have not been of so decided
a nature as to remove doubts whether the appearances could
not be ascribed to the etfects of halation by reflexion from
the back of the negative, or to blurring from the photograph
having been taken through the glass of a window, or to some
other similar cause. I was therefore anxious to obtain some
decisive evidence of the repetition of the flashes, and as my
friend Mr. G. J. Snelus was at my suggestion attempting to
obtain some photographs of the lightning, I joined him, and
he kindly placed his camera and some plates at my disposal.
The rain having ceased for the moment, I was able to go
out on to a balcony and thus get a good view of the storm,
which had now approached quite close and seemed to surround
us. The camera was held in the hand and pointed towards
the north-east, where, about half a mile away, numerous
brillant flashes were occurring. The cap of the camera was
taken off, and then the camera was moved in a horizontal
_ plane about the lens as a centre at the rate of about once to
and fro in three quarters of a second, untila flash was observed
in the direction in which it was pointed, when the cap was
at once replaced. The duration of the exposure of the plate
was about half a minute. The camera was of quarter-plate
size, the plates were Ilford rapid, and the lens, which was a
rapid rectilinear, was used with full aperture (7/8).
I hoped, by having the camera moving, to be able to separate
the successive components of the flashes, and in this I was
fortunately successful. In fig. 1 (Pl. LV.) is a reproduction of
one of the photographs obtained, and on it can be seen two
triple flashes (I., [1., LI1., and IV., V., VI.), and one double
flash (VII. and VIII.).
During the interval that the plate was exposed the illumina-
tion of the sky from flashes out of the line of view, or behind
clouds, produced the glare seen in the centre and upper part
of the photograph, and some faint flashes which were noticed
ere probably the cause of the streaks seen in fig. 2 at 0, p,
and 7.
A careful examination of the photograph reveals many
interesting features. The three successive flashes I., II., IL.
are identical in form. If the negative be placed over a print
so that either of the three lines on the negative lies over
108 : Dr, Be H. Hoffert on
either of those on the print, the coincidence is seen to be
exact even to the smallest irregularities. Nevertheless, of all
the branch-flashes which spread out from I. only a small trace
exists at m in II.,and none whatever in III. Sweeping across
the photograph and connecting corresponding points in the
successive flashes are streaks of light, showing that a very
considerable residual illumination remains between the dis-
charges. These streaks are especially well marked between the
components of the double flash VII., VIII., and are also very
bright along the path of the head of flash I. They are not
always present; for in another photograph obtained upon a
moving plate by Mr. Snelus, in which a flash is reduplicated,
there is no trace of them, the flashes being quite sharp and
distinct. The streaks commence abruptly with one discharge
and end abruptly with another. Their extension to the left
of I. was probably due to the camera not having quite reached
the end of its swing. Where they are brightest there is in
all cases a swelling at the part of the flash where they start. .
At the upper left-hand corner there is a curious dark flash
with bright edges and short luminous streaks. The form of
this dark flash is exactly reproduced in the two bright flashes
V.and VI. Dark flashes are frequently met with in photo-
graphs of lightning, and have been usually ascribed to
reversal of the image by overexposure; but I do not think
this explanation applies in the present case, both on account
of the appearance which the dark flash presents, and also
because as far as I can recollect the brilliant downward
flash I. appeared to the eye much the brightest of those that
occurred while the plate was exposed. ‘There is a similar but
less distinct dark gap to the left of VI. ; and to the right of
II. are three or four faint bands parallel to it and following
its sinuosities. These all seem to be due to variations in
brightness in the luminous streaks, which are thus shown to
be electrical and not phosphorescent in character.
When carefully compared, the forms and positions of the
flashes I. to VIII. are found to present such agreement as to
show that they must have formed a system of discharges
closely connected together. If V. be placed over LV. so as
to coincide with its left-hand border, the portion d exactly
coincides in form and position with the portion a of L, and
both a and d terminate in a curious bifurcated enlargement
which, when examined with a lens, shows a beaded appearance,
roughly sketched in fig. 3. This coincidence of form and
position would be difficult to account for if I. and LV. were
independent flashes not occurring eat the same time. It is
Intermittent Lightning-Flashes. 109
evident, however, that the series I, II., III. cannot have
occurred during the same sweep of the plate as IV., V., VI.,
since the curve joining a, 0, ¢ is concave upwards, while that
joining a, d, e is concave downwards. The flashes VII., VIII.
seem also to have formed part of the same system of dis-
charges, for the part of VII. from / to just above h is coin-
cident with the upper portion of I., while the luminous streaks
extending between VII. and VIII. agree in their directions
with the curves joining a, b, ¢ and a, d, e, those at g being
parallel to the line joining d and e, and those at & following
nearly but not exactly the line of a,b,c. There is thus
afforded some clue to the determination of the order of
the discharges, and I think the order was probably as
follows:—VII., VIII. VI, V., IV., L, LL, ILL, the first
two occurring during one sweep of the camera; VI., V., LV.
during the backward sweep; and I., IIL., III. in the next
onward sweep. There must thus have been an interval of
a little over a second between the first and last discharge, for
the motion of the camera was at about the rate of three
quarters of a second for a complete swing to and fro. The
interval between the successive discharges was, therefore, be-
tween the fifth and tenth of a second. Had it been much
longer the flash would have presented to the eye a flickering
appearance.
Whatever be the explanation of some of the effects noticed
above, it is evident that a lightning flash has not the simple
instantaneous character formerly supposed; but that it con-
sists of a varying number of successive discharges following
one another in the same path at intervals which may in some
cases be comparatively long.
Note.—Since the above was written I have had an oppor-
tunity of inspecting the photographs of banded, ribbon, and
curtain lightning collected by the Royal Meteorological
Society. There is, I think, no doubt that the explanation of
these is afforded by the multiple flashes and luminous streaks
noticed above. It is noteworthy that they were always ob-
tained with a camera held either in the hand or in such a way
as to render motion probable.
Science Schools, S. Kensington.
Phil. Mag. 8. 5. Vol. 28. No. 171. August 1889. K
Fad BO. |
XVI. On the Reflexion and Refraction of Light at the Surface
of a Crystal on the Quasi-labile Atther Theory. By hk.
T. Guazeprook, W.A., £.A.S.*
N his comparison of the Electric Theory of Light and the
theory of a Quasi-labile A‘%ther, in the Philosophical
Magazine for March 1889, Prof. Willard Gibbs has shown
that the conditions to be satisfied at the common surface of
two media, whether crystalline or not, are the same for the
Hlectromagnetic Theory of Light and for the new Labile
Aither theory of Sir William Thomson. The formule which
give the intensities and azimuths of the planes of polarization
for the new theory may therefore be deduced from those
for the electromagnetic theory; they may, however, be
obtained in a fairly simple manner from the new theory itself,
and it seems desirable to have them expressed and so to
bring out more clearly the connexion between the two
theoriest.
The pressural wave in the new theory disappears from the
equations of motion within the medium ; it has, however, its
effect in the conditions at the surface. Let us call u,, vp the
components of the displacement in this wave, and let the
axis of « be normal to the surface, and the axis of z the in-
tersection of the surface and the plane of the waves. Then
fh A d d
for an isotropic medium uy= 7) Y= = , where
a = C sin = (fv + imoy— Vit).
Also, if V, /, m, are the corresponding quantities for the
transverse wave, we have the relations
V/A = Vo/Ao, m/A¥ = mMo/Aq;
. 297 § lok
ae y=Osin fe vtmy—Ve \, sll Seas sauna elle)
Now Sir William Thomson has shown that when A=0O, and
therefore V)>=0, we must have C=0, but at the same time
Ay is zero. Thus, if we put 27Cl,= Dry, we have
* Communicated by the Author.
+ Since much of the above was written, a paper on somewhat the same
subject has been read before the Mathematical Society by Mr. A. B.
Basset. Some of the results of his paper, which is not yet printed, have
been communicated to me in a letter from Mr. Basset, and agree with
those of the present investigation.—June 18, 1889.
On the ane and Refraction of Light. Me
ga Ww cos a ea -vi} |
DrAym Arf hr mtd)
——— en ae ya tmy — Ve}
xn ie J)
Also
du dv 27m 2c
O22 0 Wit giecee es SA eves ee
eee = D Wan is Wee veh, (3)
while vy vanishes compared with wp when A, is zero; and in
this case we have merely a surface wave of normal displace-
ment given by wu, travelling over the boundary.
Let us suppose the same to be the case at the common sur-
face of an isotropic medium and a crystal; we know that
the normal wave has no effect in the interior, we shall find
shortly that all the surface conditions are satisfied by the
hypothesis of a normal displacement over the surface of the
same form as at the boundary of two isotropic media.
Let S be the amplitude of the optical disturbance in the
incident wave so that the disturbance is
S cos = (In+my—Vi),
a, 8, y the angles it makes with the axes, /, m,n the direction
cosines of the wave-normal. Let 81, «1, @1, 91, l1, 11, m refer
to the reflected wave ; 8’, a’, &. to one refracted wave; 8",
a to the other. Let y! and y" be the angles between the
rays and the wave-normals.
The conditions at the surface are that u, v, w, Ni, T., Ts
are all continuous. The last three taken in order give, since
we suppose the rigidity the same in all media, and since
u, v, w are not functions of z,
dv du . dv d dw
dy’ dy Pe” ae
continuous. The first of these three is already satisfied by the
continuity of v; and we have thus five equations to find the
amplitudes of the two refracted waves, the amplitude and the
azimuth of the plane of polarization of the reflected wave, and
the amplitude of the surface effect.
These five ee may be written, if we introduce the
values of wp, - &e., and divide by the periodic factor, as
follows :—
Ke?
112 Mr. R. T. Glazebrook on the Reflexion and
S cosa +8,cosa,+D=S8' cose’ + S"cosa’! + D!' . . (4)
S cosB +8,cos®; =S8'cos6! + 8" cos Bl = eh hattea)
Scosy +8, cosy, =N'cosy + 8" cosy" 5) 3 ht)
mcos a + 1 cosB my, cos a, +1, cos By 2mD
< Sas %, Sy + x
m cos a! +1 cos 6! m cos a!’ + 1" cos Bl" 2m!
= =o, a S! + - [a Se tu Ss" + r! D! (7)
Slcosy , Si4, cosy, — Sll’cosy’ . S"Z!" cos gy!
unr
with the conditions
and on eliminating D—D! from (4) and (7) we find
[cos B—m cos & qui l, cos et COS a S,
1
l' cos B'— m1! cos a! l" cos B"—m' cos al!
This equation, together with (5) (6) and (8), will determine
all our unknown quantities. It remains to express them in
terms of the angles of incidence and refraction and of the
directions of vibration. ig IL
Let ¢, ¢', 6” be the angles of incidence and refraction.
Let 0, 0,, 6’, &" be the angles between Oz and the directions
of vibration, and let 6’, 6" be the angles between Oz and the
projections on the wave fronts of the directions of vibration
(fig. 1).
Refraction of Light at the Surface of a Crystal. 113
Let ON be the wave-normal, OP the direction of vibration
in the incident wave, and let this wave cut the plane z=0
in OQ.
Then clearly
cos a= —sin > sin 0
cosB= cos¢sin 0 (10)
cos y= cos 0
cos 8, =—cos®¢ sin 0,
COS = cos 8,
cos 4;= —sin @ sin at an
[— ¢os o, m =sintd
4,=—cos d, m=sin d (12)
“= cos @!, m’=sin ¢’
Again, for the refracted wave, S! is equivalent to S! cos x’
in the wave-front, and 8! sin y’ along the wave-normal.
S' cos x’ is equivalent to S! cos y! cos 6 along Oz, and
S! cos y’/ sin 6’ along the intersection of the wave and the
plane xy, and this last is equivalent to S! cos x! sin 6 cos d!
along Oy, and —S! cos y’ sin 6’ sin d! along Ox. Again, the
component 8! sin x’ along the wave-normal gives §! sin y'cos ¢!
along Oz, and 8! sin y’ sin ¢! along Oy.
Hence
cos «'= —cos x’ sin 6 sin ¢’+sin x! cos ¢'
cosB'= cosy’ sin @ cosd!+siny’ sing’ 7. - - (18)
cosy/= cos yx! cos 6!
On substituting these values in equations (6), (8), (9), and
(5) respectively we obtain
S cos + 8; cos 6,=8/ cos y! cos 6'+ terms in 8" &e. . (14)
(S cos 0—§, cos 0,) cot 6=8' cos x! cos & cot d'+ terms in 8!
15)
(S sin 0+, sin 6;) cosec 6=_
S! cos x! sin 6! cosec ¢'+ terms in 8"... (16)
(S sin @—§, sin 0,) cos =
S! cos x! (sin @' cos d! + sin d! tan y') + terms in S".. (17)
The corresponding equations on the electromagnetic theory
are given in the same form in a paper by myself in the ‘ Pro-
ceedings of the Cambridge Philosophical Society’ (vol. iv.
p- 165, equations 24-27). If we suppose the magnetic per-
meability the same in the two media, and write > for the
114 Mr. R. T. Glazebrook on the Reflexion and |
amplitude of the electric displacement, then the two sets of
equations are identical, provided S cosy is proportional to
V’>, V being the velocity of light and y the angle between
the ray and the wave-normal; that is to say, provided that
the electric displacement is proportional to the component in
the wave-front of the actual displacement, and inversely pro-
portional to the square of the velocity of light. It must be
remembered that 6’ does not determine the direction of vibra-
tion in the refracted wave, but the projection of that direction
on the wave-front. Fie. 2.
Again, let Y’ be the angle between the plane through Oz
and the direction of vibration and the plane of the refracted
wave; then we have, if OP! (fig. 2) be the direction of vibra-
tion, OP’ its projection on the wave-front,
io gible gl PPS,
PzeP=y', yeP'=¢!, yD'=B',
“. Pey=d'—p;
and we readily find that
cos B'=sin & cos (¢'—wW’'),
cos 6'=cos 6 cos y’,
sin 0! cos x’ =sin 6! cos W’.
So that the last two equations (16) and (17) become
(S sin @+8, sin 4;) cosec 6=
N/ sin 6! cos wy cosec $'+ terms in 8’, . (18)
(S sin @—8§, sin 6,) cos 6=
S’sin 6! cos W! cos (f'—1") + terms in 8", . (19)
forms which may sometimes be useful.
ae
Refraction of Light at the Surface of a Crystal. 115
If we take the case in which only one wave traverses the
erystal we find the following relations by eliminating the
ratios 8/8, and 8/S!:—
sin 7¢! tan x’
= ! neabivgps 8 _ Sm ep tan y _
pee PEO) + cos G' sin (6+ ¢') y+ + (20)
tan 6, = —tan pcos (PtH) 2 sin 2¢ sin *¢! tan x!
cos (6—$) * sin2(¢—@!) sin(d+¢!) cos”
cY. Sinenerar ess
The first of these equations was tested by me experimen-
tally, the second medium being Iceland spar (see Phil. Trans.
1582, Part Il.). There was fair agreement between the
theory and experiment; but the errors of the experiment were
larger than they need have been, in consequence of some
want of annealing in one of the lenses of the telescope used
in the observations, which was not discovered till too late
(Proc. R. 8. vol. xxxiv. p. 233). Hquations the same as (20)
and (21) have been obtained by Neumann, MacCullagh,
Kirchhoff, and others.
Fiquation (4) gives us a value for D/—D. We find
D— D’= sin ¢(S sin @+8, sin 4,)
—$' cos x’ (sin 6’ sin ¢! — tan x! cos ¢’)— terms in 9!"
=! cos y’ sin 6! cosec ¢! (sin 26 —sin 2d’)
+8! sin x’ cos d'+terms in 8" &e.
=§' cos x! cosec $! {sin (6+¢') sin (6—@’) sin @!
+tan y! cos d! sin d!} + terms in 8" &. . (22)
Thus the problem of reflexion and refraction at a crystal
on the Labile Atther theory is fully solved, and some of the
results exhibited in a form which can be tested by experiment,
though the experimental results will not discriminate between
it and the electric theory.
It will be noticed that the terms in D and D’ arising from
the surface action have no place in the electric problem.
Hquation (26) of my paper in the C. P. 8. Proceedings,
already referred to, which is the same as equation (16) above,
expresses the conditions either that the electric displacement
along the normal, or that the magnetic force along the axis of z
is the same in the two media. So long as we suppose the surface
to remain unelectrified, these conditions lead to the same
equations. On the Labile Alther theory the two conditions
116 = On the Reflexion and Refraction of Light.
of equality of normal displacement and of surface traction
parallel to Oz cannot be satisfied without some surface action.
The elimination of the terms expressing this surface-action
from these two equations of condition gives us our equation
(16). On the Hlectric theory, if we suppose a surface dis-
tribution of variable density possible, terms would come into
the two surface conditions already mentioned, depending
on this distribution; we should thus have two equations
corresponding to our (4) and (7), and the elimination of
the surface-density from these would give us an equation
equivalent to (16).
It is perhaps worth while to remark that equation (9) or
(16) holds, even though the constant A be not zero. For
since wu is continuous across the surface, so is also — 3; and
dy
since ie + oe is continuous, we see that dp ny is also con-
dx dy dz dy
; dvg dug s :
tinuous. But we have Tae PD ; and hence, in the expression
isa)
for the continuity of coy
sural wave will not occur, and this condition will give us
equation (9) at once. But if A is not zero, (5) will be
modified, and becomes
the terms involving the pres-
DAgn _ a ire Sie i
Xl, =’ cos 6’ +8” cos 8’ + Vie 3
while the continuity of N, leads, if we assume A to be the
same in both media, to
(2 dv dv ‘du! dv!
/ du!’
ieee =A(— + ene . (24)
Scos8+8, cos 8,+
ew dv .
which since v, and therefore 7,’ 13 continuous, reduces to
J
du dw
We also require the equation of motion for the pressural wave
and the problem is much more complicated ; it has been
solved for two isotropic media in Sir W. Thomson’s paper
and the solution in the present case must proceed along the
same lines.
Dyin!
perry
XVII. On the Propagation of Electric Waves through Wires.
By Prof. H. Hertz*.
[ a constant electric current flows in a cylindrical wire, its
intensity is the same in all parts of the section of the wire.
But if the current is variable, self-induction causes a deviation
from this most simple distribution. or, since the inner parts
of the wire are in the mean less distant from all the rest than
are those on the circumference, induction opposes alterations
of the current in the interior of the wire more strongly than at
the circumference ; and in consequence of this the flow is con-
fined to the exterior of the wire. If the current alters its
direction a few hundred times per second the deviation from
the normal distribution is no longer imperceptible; this
deviation increases rapidly with the rate of alternation, and
when the current alternates many millions of times per second,
according to theory almost the whole interior of the wire must
appear free from current, and the flow must be confined to
the immediate neighbourhood of the circumference. In such
very extreme cases the hitherto accepted theory of the pheno-
menon is plainly not without physical difficulties ; and pre-
ference must be given to another view of the subject, which
was indeed first put forward by Messrs. Heaviside t and
Poynting { as the true interpretation of the equations of
Maxwell as applied to this case. According to this view, the
electric force which determines the current is in no wise pro-
pagated in the wire itself, but under all circumstances enters
the wire from without and spreads itself in the metal compara-
tively slowly, and according to similar laws as changes of
temperature in a conductor of heat. If the forces in the
neighbourhood of the wire are continually altering in direc-
tion, the effect of these forces will only enter to a small depth
into the metal ; the more slowly the changes take place, so
much deeper will the effect penetrate ; and if, finally, the
changes follow one another infinitely slowly, the force has time
to fill the whole interior of the wire with uniform intensity.
In whatever way we wish to regard the results of the theory,
an important question is, whether it agrees with fact. Since,
in the experiments which I carried out on the propagation of
electric force, I made use of electric waves in wires which
* Translated from Wied. Ann. xxxvil. p. 395 (July 1889), by Dr. J. L.
Howard, Demonstrator of Physics in University College, Liverpool.
Tt Heaviside, Electrician, Jan. 1885; Phil. Mag, [5] xxv. p. 153 (1888).
{ Poynting, Phil. Trans. 11. p. 277 (1885).
118 Prof. H. Hertz on the Propagation
were of extraordinarily short period, it was convenient to
prove by means of these the accuracy of the inferences drawn.
In fact, the theory was proved by the experiments which will
now be described ; and it will be found that these few expe-
riments suffice to confirm in the highest degree the view of
Messrs. Heaviside and Poynting. ‘Analogous experiments,
with similar results, but with quite different apparatus, have
already been made by Dr. O. J. Lodge*, chiefly in the
interest of the theory of lightning-conductors. Up to what
point the conclusions are just which were drawn by Dr. Lodge
in this direction from his experiments, must depend in the first
place on the velocity with which the alterations of the elec-
trical conditions really follow each other in the case of
lightning.
The apparatus and methods which are here mentioned are
those which I have described in full in previous memoirs f.
The waves used were such as had in wires a distance of nearly
3 metres between the nodes.
1. If a primary conductor acts through space upon a
secondary conductor, it cannot be doubted that the effect
penetrates the latter from without. For itcan be regarded as
established that the effect is propagated in space from point to
point, therefore it will be forced to meet first of all the outer
boundary of the body before it can act upon the interior of it.
But now a closed metallic envelope is shown to be quite opaque
to this effect. If we place the secondary conductor in sucha
favourable position near the primary one that we obtain sparks
5 to 6mm. long, and surround it now with a closed box made
of zinc plate, the smallest trace of sparking can no longer be
perceived. ‘The sparks similarly vanish if we entirely surround
the primary conductor with a metallic box. It is well known
that, with relatively slow variations of current, the integral
force of induction is in no way altered by a metallic screen.
This is, at the first glance, contradictory to the present expe-
riments. However, the contradiction is only an apparent one,
and is explained by considering the duration of the effects. In
a similar manner, a screen which conducts heat badly protects
its interior completely from rapid changes of the outside tem-
perature, less from slow changes, and not at all from a con-
tinuous raising or lowering of the temperature. ‘The thinner
the screen is the more rapid are the variations of the outside
temperature which can be felt in its interior. In our case also
the electrical action must plainly penetrate into the interior, if
* Lodge, Journ. Soc. Arts, May 1888 ; Phil. Mag. [5 ]xxvi. p. 217 (1888).
t+ Hertz, Wied. Ann. xxxiv. p. 551 (1888).
of Electric Waves through Wires. i}
we only diminish sufficiently the thickness of the metal. But
I did not succeed in attaining the necessary thinness in a
simple manner; a box covered with tinfoil protected com-
pletely, and even a box of gilt paper, if care was taken that
the edges of the separate pieces of paper were in metallic
contact. In this case the thickness of the conducting-metal
was estimated to be barely 45 mm. I now fitted the pro-
tecting envelope as closely as possible round the secondary
conductor. For this purpose its spark-gap was widened to
about 20 mm., and in order to detect electrical disturbances
in it an auxiliary spark-gap was added exactly opposite the
one ordinarily used. The sparks in this latter were not so
long as in the ordinary spark-gap, since the effect of resonance
was now wanting, but they were still very brilliant. After
this preparation the conductor was completely enclosed in a
tubular conducting envelope as thin as possible, which did not
touch it, but was as near it as possible ; and in the neighbour-
hood of the auxiliary spark-gap (in order to be able to use it)
the envelope contained a wire-gauze window. Between the
poles of this envelope brilliant sparks were produced, just as
previously in the secondary conductor itself; but in the
enclosed conductor not the slightest electrical movement could
be recognized. The result of the experiment is not affected
if the envelope touches the conductor at a few points; the
insulation of the two from each other is not necessary in order
to make the experiment succeed, but only to give it the force
of a proof. Clearly we can imagine the envelope to be drawn
more closely round the conductor than is possible in the expe-
riment ; indeed, we can make it coincide with the outermost
layer of the conductor. Although, then, the electrical dis-
turbances on the surface of our conductor are so powerful that
they give sparks 5 to 6 mm. long, yet at 55 mm. beneath the
surface there exists such perfect freedom from disturbance that
it is not possible to obtain the smallest sparks. We are brought,
therefore, to the conclusion that what we call an induced
current in the secondary conductor is a phenomenon which is
manifested in its neighbourhood but to which its interior
scarcely contributes.
2. One might grant that this is the state of affairs when the
electric disturbance is conveyed through a dielectric, but
maintain that it is another thing if the disturbance, as one
usually says, has been propagated in a conductor. Let us
place near one of the end plates of our primary conductor a
conducting-plate, and fasten to it a long straight wire ; we
have already seen in the previous experiments how the effect
of the primary oscillation can be conveyed to great distances
120 Prof. H. Hertz on the Propagation
by the help of this wire. ‘The usual theory is that a wave
travels along the wire in this case. But we shall try to show
that all the alterations are confined to the space outside and
the surface of the wire, and that its interior knows nothing of
the wave passing over it. J arranged experiments first of all
in the following manner. A piéée about. 4 metres long was
removed from the wire conductor and replaced by two strips
of zine plate 4 metres long and 10 cm. broad, which were laid
flat one above the other, with their ends permanently connected
together. Between the strips along their middle line, and
therefore almost entirely surrounded by their metal, was laid
along the whole 4 metres length a copper wire covered with
gutta-percha. It was immaterial for the experiments whether
the outer ends of this wire were in metallic connexion with,
or insulated from, the strips ; however, the ends were mostly
soldered to the zinc strips. The copper wire was cut through
in the middle, and its ends were carried, twisted round each
other, outside the space between the strips to a fine spark-gap,
which permitted the detection of any electrical disturbance
taking place inthe wire. When waves of the greatest possible
intensity were sent through the whole arrangement, there was
nevertheless not the slightest effect observable in the spark-
gap. But if the copper wire was then displaced anywhere a
few decimetres from its position, so that it projected just a
little beyond the space between the strips, sparks immediately
began to pass. ‘The sparks were the more intense according
to the length of copper wire extending beyond the edge of the
zine strips and the distance it projected. ‘The unfavourable
relation of the resistances was therefore not the cause of the
previcus absence of sparking, for this relation has not been
changed ; but the wire being in the interior of the conducting
mass, was at first deprived of the influence coming from
without. Moreover, it is only necessary for us to surround
the projecting part of the wire with a little tinfoil in metallic
communication with the zine strips, in order to immediately
stop the sparking again. By this means we have brought the
copper wire back again into the interior of the conductor. If -
we bend another wire into a fairly large are round the pro-
jecting portion of the gutta-percha wire, the sparks will be
likewise weakened ; the second wire takes off from the first a
certain amount of the effect due to the outer medium. Indeed,
it may be said that the edge of the zinc strip itself takes away
the induction from the middle of the strip in a similar manner.
_ For if we now remove one of the strips, and leave the insulated
wire simply resting on the other one, we certainly obtain
sparks continuously in the wire ; but they are extremely weak
EI, PID th
of Electric Waves through Wires. 121
if the wire lies along the middle of the strip, and much stronger
when near its edge. Just as in the case of distribution under
electrostatic influence the electricity would prefer to collect on
the sharp edge of the strip, so also here the current tends to
move along the edge. Here, as there, it may be said that the
outermost parts screen the iffterior from outside influence.
The following experiments are somewhat neater and equally
convincing. I inserted into the conductor transmitting the
waves a very thick copper wire, 1°5 metre long, whose ends
carried two circular metallic disks of 15 cm. diameter. The
wire passed through the centres of the disks; the planes of
the disks were at right angles to the wire ; each of them had
on its rim 24 holes, at equal distances apart. A spark-gap
was inserted in the wire. When the waves traversed the wire
they gave rise to sparks as much as 6 mm. long. A thin
copper wire was then stretched across between two corre-
sponding holes of the disks. On doing this, the length of the
sparks sank to 3°2 mm. There was no further alteration if a
thick copper wire was put in the place of the thin one, or if,
instead of the single thin wire, twenty-four of them were
taken, provided they were placed near each other through the
same two holes. But it was otherwise if the wires were dis-
tributed over the rim of the disks. If a second wire was
inserted opposite the first one, the spark-length fell to 1:2 mm.
When two more wires were added midway between the first
two, the length of the spark sank to 0°5 mm.; the insertion of
four more wires still in the mean positions left sparks of scarcely
0:1 mm. long ; and after inserting all the twenty-four wires at
equal distances apart, not a trace of sparking was perceptible
in the interior. The resistance of the inner wire was never-
theless much smaller than that of all the outside wires taken
together ; we havealso a still further proof that the effect does
not depend upon this resistance. If we place by the side of the
partial tube of wires, and in parallel circuit with them, a con-
ductor in all respects similar to that in the interior of the tube,
we have in the former brilliant sparks, but none whatever in
the latter. The former is unprotected, the latter is screened
by the tube of wires. We have in this an electrodynamic
analogue of the electrostatic experiment known as the electric
birdeage. I again altered the experiment, in the manner
depicted in fig.1, p. 122. The two disks were placed so near
together that they formed, with the wires inserted between them,
a cage (A) just large enough for the reception of the spark-
micrometer. One of the disks, «, remained metallically con-
nected with the central wire ; the other, 8, was insulated from
the wire by means of a circular hole through its centre,
122 Prof. H. Hertz on the Propagation
at which it was connected to a conducting-tube, y, which,
insulated from the central wire, surrounded it completely for
Fig. 1.
a A hd
a length of 1:5 metre. The free end of the tube, 6, was then
connected with the central wire. The wire, together with its
spark-gap, is once more situated in a metallically protected
space ; and it was only to be expected, from the previous
experiments, that not the slightest electrical disturbance would
be detected in the wire in whichever direction waves were sent
through the apparatus. So far, then, this arrangement pro-
mises nothing new, but it has the advantage over the previous
one that we can replace the protecting metallic tube, y,
by tubes of smaller and smaller thickness of wall, in order to
investigate what thickness is still sufficient to screen off the
outside influence. Very thin brass tubes, tubes of tinfoil and
Dutch metal proved to be perfect screens. I now took glass
tubes which had been silvered by a chemical method, and it
was then perfectly easy to insert tubes of such thinness that,
in spite of their protecting power, brilliant sparks occurred in
the central wire. But sparks were only observed when the
silver film was no longer quite opaque to light and was cer-
tainly thinner than =}, mm. In imagination, although not
in reality, we can conceive the film drawn closer and closer
round the wire, and finally coinciding with its surface ; we
should be quite certain that nothing would be radically altered
thereby. However actively, then, the real waves play round
the wire, its interior remains completely at rest; and the
effect of the waves hardly penetrates any more deeply into the
interior of the wire than does the light which is reflected from
its surface. Tor the real seat of these waves we ought not to
look, therefore, in the wire, but rather to assume that they take
place in its neighbourhood ; and instead of asserting that our
waves are propagated in the wire, we should be more accurate
in saying that they glide along on the wire.
Instead of placing the apparatus just described in the cir-
cuit in which we produced waves indirectly, we can insert it in
one branch of the primary conductor itself. In such experi-
ments I obtained results similar to the previous ones. Our
primary oscillation, therefore, takes place without any partici-
pation of the conductor in which it is excited, except at its
of Electric Waves through Wires. 123
bounding surface ; and we ought not to look for its existence
in the interior of the conductor™.
To what has been said above about waves in wires we wish
to add just one remark concerning the method of carrying out
the experiments. If our waves have their seat in the neigh-
bourhood of the wire, the wave progressing along a single
isolated wire will not be propagated through the air alone ;
but since its effect extends to a great distance it will partly be
transmitted by the walls, the ground, &c., and will thus give
rise to a complicated phenomenon. But if we place opposite
each pole of our primary conductor in exactly the same way
two auxiliary plates, and attach a wire to each of them,
carrying the wires straight and parallel to each other to equal
distances, the effect of the waves makes itself felt only in the
region of space between the two wires. The wave progresses
solely in the space between the wires. We can thus take
precautions to propagate the effect through the air alone or
through another insulator, and the experiments will be more
convenient and free from error by this arrangement. Tor
the rest, the lengths of the waves are nearly the same in this
case as in isolated wires, so that with the latter the effect of
the disturbing causes is apparently not considerable.
3. We can conclude from the above results that rapid
electric oscillations are quite unable to penetrate metallic
sheets of any thickness, and that it is, therefore, impossible
by any means to excite sparks by the aid of such oscillations
in the interior of closed metallic screens. If, then, we see
sparks produced by such oscillations in the interior of metallic
conductors, which are nearly, but not quite, closed, we shall
be obliged to conclude that the electric disturbance has forced
itself in through the existing openings. This view is also
correct, but it contradicts the usual theory in some cases so
completely that one is only induced by special experiments
to give up the old theory in favour of the new one. We shall
choose a prominent case of this kind, and by assuring our-
selves of the truth of our theory in this case, we shall demon-
strate its probability in all other cases. We again take
the arrangement which we have described in the previous
section and drawn in fig. 1 ; only we now leave the protect-
ing tube insulated from the central wire at 6. Let us now
send a series of waves through the apparatus in the direction
* The calculation of the self-induction of such conductors on the
assumption of uniform density of current in their interior must therefore
lead to quite erroneous results. It is to be wondered at that the results
obtained with such wrong assumptions should still appear to approximately
coincide with truth.
124. Prof. H. Hertz on the Propagation
from A towards 6. We thus obtain brilliant sparks at A ;
they are of similar intensity to those obtained when the wire
was inserted without any screen. ‘The sparks do not become
materially smaller, if, without making any other alteration,
we lengthen the tube y considerably, even to 4 metres.
According to the usual theory it would be said that the wave
arriving at A penetrates easily the thin, good-conducting
metal disk a, then it leaps across the spark-gap at A, and
travels on in the central wire. According to our view, on
the contrary, we must explain the phenomenon in the follow-
ing manner. ‘The wave arriving at A is quite unable to
penetrate the metallic disk ; it therefore glides along the disk
over the outside of the apparatus and travels as far as the
point 6, 4 metres away. Here it divides: one part, which
does not concern us at present, travels on immediately along
the straight wire, another bends into the interior of the tube
and then runs back in the space between the tube and the
central wire to the spark-gap at A, where it now gives rise
to the sparking. That our view, although more complicated,
is still the correct one, is proved by the following experiments.
Firstly, every trace of sparking at A disappears as soon as
we close the opening at 6, even if it be only by a stopper of
tinfoil. Our waves have only a wave-length of 3 metres;
before their effect has reached the point 6 the effect at A has
passed through zero and changed sign. What influence then |
could the closing of the distant end 6 have upon the spark at
A, if the latter really happened immediately after the passage
of the wave through the metallic wall? Secondly, the sparks
disappear if we make the central wire terminate inside the
tube y, or at the opening 6 itself; but they reappear when we
allow the end of the wire to project even 20 to 30 centim. only
beyond the opening. What influence could this insignificant
lengthening of the wire have upon the sparks in A, unless the
projecting end were just the means by which a part of the
wave breaks off and penetrates through the opening 6 back
into the interior? Thirdly, we insert in the central wire
between A and 6 a second spark-gap B, which we also com-
pletely cover with a gauze cage like that at A. If we make
the distance of the terminals at B so great that sparks can no
longer pass across, it is also no longer possible to obtain
visible sparks at A. But if we hinder in like manner the
passage of the spark at A, this has scarcely any influence on
the sparks in B. Therefore, the passage of the spark at B
determines that at A, but the passage of a spark at A does not
determine that at B. The direction of propagation in the
interior is therefore from B towards A, not from A to B.
of Electric Waves through Wires. 125
We can moreover give further proofs, which are more con-
vincing. We may prevent the wave returning from 6 to A
from dissipating its energy in sparks, by making the spark-
gap either vanishingly small or very great. In this case the
wave will be reflected at A, and will now return again from
A towards 6. In doing so, it must meet the direct waves
from 6 to A and combine with them to form stationary waves,
thus giving rise to nodes and ventral segments. If we suc-
ceed in proving their existence, there will be no longer any
doubt as to the truth of our theory. For this proof we must
give somewhat different dimensions to our apparatus in order
to be able to introduce electric resonators into its interior. I
_ therefore led the central wire through the axis of a cylindrical
tube 5 metres long and 30 centim. diameter. It was not con-
structed of solid metal, but of 24 wires arranged parallel to
each other along the generating surface, and resting on seven
equidistant and circular rings of strong wire, as shown in
fiz. 2. I made the requisite resonator in the following
manner :—A closely-wound spiral of 1 centim. diameter was
Fig. 2.
formed from copper wire of 1 millim. thickness; about 125
turns of this spiral were taken, drawn out a little, and bent
into a circle of 12 centim. diameter; between the free ends
an adjustable spark-gap was inserted. Previous experiments
had shown that this circle responded to waves 3 metres long
in the wire, and yet it was small enough in size to admit of its
insertion between the central wire and the surface of the tube.
If now both ends of the tube were open, and the resonator
was then held in the interior in such a way that its plane
included the central wire, and its spark-gap was not directed
exactly inwards or outwards, but was turned towards one end
or the other of the tube, brilliant sparks of $ to 1 millim.
length were observed. On now closing both ends of the tube
by four wires arranged crosswise and connected with the cen-
tral conductor, not the slightest sparking remained in the
interior, a proof that the network of the tube is a sufficiently
good screen for our experiments. The end of the tube on the
side £, that, namely, which was furthest away from the origin
of the waves, was now removed. In the immediate neigh-
bourhood of the closed end, that is at the point « which corre-
sponds to the spark-gap A of our previous experiments, there
were now no sparks observable in the resonator. But on
Phil. Mag. 8. 5. Vol. 28. No. 171. August 1889. — L
126 On the Propagation of Electric Waves through Wires.
moving away from this position towards 8, sparks appeared,
became very brilliant at a distance of 1:5 metre from a, then
decreased again in intensity, they almost entirely vanished at
3 metres distance from #, and increased again until the end
of the tube was reached. We thus find our theory borne out
by fact. That we obtain a node at the closed end is clear, for
at the metallic contact between the central wire and the sur-
face of the tube the electric force between the two must
necessarily vanish. It is different when we cut the central
conductor at this point just near the end, and insert a gap of
several centimetres length. In this ease the wave will be
reflected in a phase opposite to that of the previous case, and
we should expect a ventral segment ata. As a matter of fact
we find brilliant sparks in the resonator in this case; and they
rapidly decrease in strength if we move from a towards §,
they almost entirely vanish at a distance of 1°5 metre, and
become brilliant again at a distance of 3 metres ; moreover
they give a second well-marked node at 4°5 metres distance,
that is 0°5 metre from the open end. The nodes and loops
which we have described are situated at fixed distances fronr
the closed end, and alter only with this distance ;- they are,
however, quite independent of the occurrences outside the
tube, for example, of the nodes and loops formedthere. The
phenomena occur in exactly the same way if we allow the
wave to travel through the apparatus in the direction from
the open to the closed end ; their interest is, however, smaller,
since the mode of transmission of the wave deviates from that
usually conceived, less in this case than in the one which has
just been under our consideration. If both ends of the tube
are left open with the central wire undivided, and stationary
waves with nodes and loops are now set up in the whole
system, there is always found, for every node outside the tube,
a corresponding node in the interior ; which proves that the
propagation takes place inside and outside with, at any rate
approximately, the same velocity.
On looking over the experiments which we have described,
and the interpretation put upon them, as well as the explana-
tions of the physicists ’referred to in the introduction, a differ-
ence will be noticed between the views here put forward and
the usual theory. According to the latter, conductors are
represented as those bodies which alone take part in the pro-
pagation of electric disturbances ; non-conductors are the
bodies which oppose this propagation. According to our
view, on the contrary, all transmission of electrical disturb-
ances is brought about by non-conductors : conductors oppose
a great resistance to any rapid changes in this transmission.
One might almost be inclined to maintain that conductors
Apparatus Illustrating Crystal Forms. 127
and non-conductors should, on this theory, have their names
interchanged. However, such a paradox only arises because
one does not specify the kind of conduction or non-conduction
considered. Undoubtedly metals are non-conductors of elec-
tric force, and just for this reason they compel it under certain
circumstances to remain concentrated instead of becoming
dissipated, and thus they become conductors of the apparent
source of these forces, electricity, to which the usual termi-
nology has reference.
Karlsruhe, March 1889,
XVIII. An Apparatus Illustrating Crystal Forms. By
R. J. ANDERSON, M.A., M.D., Professor of Natural History
in Queen’s College, Galway".
[Plate II.]
‘| ae apparatus by which I propose to illustrate crystal
forms consist of frameworks and cords and weights.
The first piece of apparatus is figured in Plate II. fig. 1, and
consists of a frame made of wood. This is divided into two
compartments. One of these has, above, a slit half an inch
wide that runs from end to end; in this slit a slide moves to
aN fro, and can be fixed by means of a binding-screw at any
place.
A slide of a similar kind moves in a slit in the lower part of
the framework ; this can be fixed by binding-screws in any
position. Pulleys are fixed at the ends of this compartment.
Slips of wood run from end to end at the sides and carry
riding-slides. These slides have -binding-screws and pulleys
whose sheaves revolve on a vertical axis fitted to them.
A figure is easily constructed by carrying cords over the
pulleys. Single cords only are shown in the figure. This is
for the sake of distinctness.
Starting from e’, which marks a ring connected with the
weight p, a single cord runs through § (ring), 7 (ring),
6’, through ring «’, through 7’, to be fixed to a weight.
A second cord starting from y/ runs through 2’, é’, 7,
throngh ring 9, and then across to ée through this ring to
hook up a weight p’. A third cord is fixed to & and runs
through ¢’, 8’, >, through & and £’ to loop up another weight.
The actual tension-weights are fixed to the small rings, which
act as pulleys.
Kach rhombus has in this way a cord to itself, and the size
of the rhombus depends on the weights attached. The smaller
the rhombus the more cord is to spare.
The figure shown is the regular octahedron if the axes he
* Communicated by the Physical Society: read April 13, 1889.
L 2
128 Prof. R. J. Anderson on an Apparatus
equal. This condition is easily produced by adjusting the
weights.
The octahedron of the second dimetric system, or pyramidal
system, is produced by increasing the weights above and below.
The octahedron of the third system may be easily formed
by increasing a pair of the horizontal weights.
The octahedral figures may be easily formed by leaving out
the diagonals and running the cords from the rings at one
extremity of the rhombuses through two rings, and then
through the opposite ring, to be there fixed to a weight.
The tension-weights, as shown in the figure, will then corre-
spond to the apices of the rhombuses.
For the oblique systems further changes are necessary.
The upper slide is moved to the right and the lower to the
left, or vice versd. This is attended with elongation of the
vertical axes, and the cords passing through the pulleys above
and below and at the ends are increased, and the slack below
is pulled in toa less extent. ‘The other sides of the octahedron
are less affected.
In the first place, the lateral rider-slides are allowed to
remain in a position such that the line joining them is per-
pendicular to the central vertical longitudinal plane. This
gives the Monoclinic System.
Secondly, the rider-slides are moved one to the right, the
other to the left, and in this way the Anorthie or Triclinic
System is produced.
In each case it is desirable to have the slack for each
rhombus at different angles of the octahedron.
All the possible varieties of the fifth system eannot be pro-
duced in this way. So it is necessary to arrange for the
elevation and depression to the rider-slides in extreme cases.
This is accomplished by means of a large ring which carries
a pulley.
I have chosen the octahedron as the simplest figure.
The cube is formed by the introduction of two horizontal
hoops, one above and one below the level of the horizontal
bars. These by a simple mechanism are made movable ; and
if eight pulleys be fixed opposite the eight edges of the octahe-
dron, and the edges of the octahedron be drawn out by rings
running on these cords, it will be necessary, then, only to
run cords through rings above and below, and to relax the
horizontal and apical weights in order to produce the cube.
The modifications caused by truncating or bevelling the
edges or faces can be produced by increasing the number of
the hoops or rings. For the simplest figures, however, vertical
hoops answer best. The sliding-rings that are carried by the
a OT —_—
Illustrating Crystal Forms. 129
cords may with their transverse cords be lowered to the level
of the bar again, and the octahedron again produced.
The cube and the corresponding forms of the pyramidal
and prisiuatic systems may be easily constructed by running
the cords as follows :—
Take the cube as sieht ae dew b
AO ag |
where the first row represents the upper face, and the second
the lower, as in fig. 2. |
The cords will have the following course :—
b’ g h’ fe: b’ a! b! g! hi! a!
Cys 2b bef! ie se ERROR ig EO
tf a! a’ g’ fi ¢ d ] el fi ! ( af
hi Roaeur: el HASTEN Fh!
eC ame ee sg!
The faces of the cube corresponding to the angle of the octa-
hedron.
Now by drawing out the cords opposite the middle of the
faces (that is, the diagonals of the faces) a 24-sided figure is
produced which can be reduced in the limit to a 12-sided
figure, namely the rhombic dodecahedron.
If the sides be connected by cords with pulleys and drawn
out, and at the same time cords connecting the centres of
the sides with the centres of the faces be drawn out, then the
trapezohedron is produced.
Cause the two lateral pulleys of the cube to approach
above and the longitudinal pair to approach below, and the
tetrahedron is produced. A prism surmounted by pyramids is
produced by drawing out the diagonals of the terminal faces ;
from this the corresponding octahedron may be obtained by a
simple method.
The other part of the framework is shown in the drawing
(fig. 1, left-hand) as containing the double hexagonal pyramid.
Sliding-pulleys, as in the part already described, are fitted
above and below. Rider-pulleys are attached to the bars at
the sides. Two are shown on each side.
The cords are attached in this way :—A bundle of six are
fastened together above to a cord, and drawn by this cord
through a ring. ‘The cord passes over two pulleys and reaches
a weight outside the framework. ‘The six cords pass through
the rings marked £, y, 6, &, @, and e in the figure, then down
to be attached to a cord below, which goes through a pulley-
sheaf. The rings marked by the Greek letters are seen at-
tached by cords to weights, through each of these a cord
passes. This cord is carried through one of the rings and
130 Prof. R. J. Anderson on an Apparatus
kept there by means of a small weight. The ratio of the
vertical to the horizontal axes may be easily altered by means
of the weights. The approximation of the lateral pulley gives
rise to the octahedron. The number of the sides may be
increased by increasing the cords and pulleys.
In order to show other figures two hoops are fitted to the
framework, above and below. The cords of the pyramids
are hooked out, and the cords connected with the hooks
pass over pulleys and are attached to weights. A cord is
made to go through the rings (hook-rings) above and below.
By running down the rings and unhooking the weights above
and below, the hexagonal prism is produced.
Prisms with more sides can be produced by increasing the
number of the cords, which correspond to the edges. The
pyramids surmounting the prism are produced by drawing
out the cords at the extremities of the prism. Figures with
fewer sides are produced by causing the pulleys to approach.
Forms the result of bevelling and truncation are produced by
pulling out the cords of the terminal pyramids and running
other cords through the rings. The original double six-sided
prisms are produced by causing the hoops to approach one
another.
The ikosahedron is produced by forming the five-faced
equilateral pyramid above and below, and approaching the
hoops towards one another, so that the distance between the —
hoops is equal to the perpendicular of one of the triangles.
Then it is only necessary to rotate the lower hoop though 36°,
and to connect the obtuse angles of the rhombus. In this
way the figure ean be produced.
The relations of the hexagonal to the rhombohedral division
of the sixth system may be shown in this way. Take the
double pyramid, hook up each alternate horizontal angle, and
hook down the others. Adjust suitably the superior and in-
ferior angles, and the rhombohedron is produced. ‘The cords
in reality follow the course of the lines in the glass models.
This method is very interesting in this way, that by a little
dodging the rhombohedron can be converted into the cube,
so that the relations between the sixth and other systems are
rendered more distinctly apparent.
The rhombohedron may be easily changed into the hexa-
hedron by unhooking the weights and pulling in the cord.
The hoops are shown in the lower part of fig. 3, Pl. I., with
the rhombohedron attached. The hexagonal prism is figured
separately for the sake of distinctness.
The ikosahedron may be produced by hooking up and
down the horizontal cords of the decahedral pyramids. If
~ te ee
a
Illustrating Crystal Forms. 131
we begin with the double octahedral pyramids, the rhombic
dodecahedron can be easily produced by hooking up the cor-
responding alternate edges above and below, and running cords
through the hooks looped up and those rings still stationary.
In order to show the effects of uniting and separating forces
the form shown at fig. 2 is useful. The instrument consists of
a frame in which hoops revolve, some on vertical and others
on horizontal axes. ‘The hoops carry sliding-pulleys as shown
on the plate. The cube is easily constructed by running cords
over eight pulleys fixed on two rings revolving on a vertical
axis. Cords are carried through small rings above and
below (fig. 2, a’ ld de fg! l’).
Without going into details, it will be easily seen that one
orthogonal hexahedron can be easily changed into another,
and into the corresponding octahedron. The octahedron of
the first system, abcde, if constructed by running cord
over the pulley B, and the pulley attached to the same ring
below, may be changed into the octahedron of the dimetric
or trimetric system, or of either of the oblique. The latter is
accomplished by causing the hoop to revolve, and for the
triclinic the vertical hoops come into action. Adjustment
of the weights leads to an alteration in the axes, and the
relations of the weights for a special form may be studied.
It is evident that the dodecahedron and trapezohedron may
be produced in this instrument as in the first, and that the
forms due to truncating or bevelling of the sides are obtained
very readily.
The following are the advantages of the apparatus :—First,
it shows clearly the effect of changes of force in producing
changes of form. The weights can be approximated or sepa-
rated, and thus the relations of allied forms may be studied.
The number of weights may be increased, and the change of
form by grouping may in this way be well shown.
If we take an india-rubber tissue ball inflated with air as
an example of an infinite number of forces acting from a
centre, and a piece of stretched cord with a weight attached
as the other extreme limit, many of the intermediate conditions
where strings are made to form the edges of figures may be
easily understood from the arrangements I have described.
It is true that such methods as are here suggested are open
to the objection that mathematical principles of a very 1m-
portant kind are involved. I think the same objection may
be made to any mechanical contrivance; but so far from
getting rid of a difficulty without explaining it, I hold that
the apparatus, whilst it will produce a better conception of
crystal forms, and the actual work in the crystals themselves,
132 Mr. E. W. Smith on
in the minds of those students who know very little about
mathematics, viz., almost all students of chemistry and mine-
ralogy, and a still larger number of geological students, the
apparatus will prove useful to mathematical students inas-
much as the arithmetical processes are tedious and complex
for even those forms in which the mathematical relations are
comparatively simple. For the forms with oblique axes the
advantages of a simple method of noting the weights neces-
sary to maintain equilibrium far outweigh the disadvantages.
Note.—Professor Wiltshire informs me that many years
ago, Mr. Mitchell, at the Royal Institution, showed a model
by which the derivation of the crystalline systems from the
octahedron was explained.
EXPLANATION OF Puare II.
Fig. 1.—e', 8’, y', 8’, €, 7, octahedron.
Dp, p, weights.
a, 8, y, 8, €, G 7, 8, double hexagonal pyramid.
Fig. 2.-—a, 6, c, d, e, f, octahedron.
a',v',c',d, e, f',g', h', cube.
A, B, C, D, EH, F, weights.
Fig. 3.—The upper figure shows the hexagonal prism surmounted by
hexagonal pyramids. The lower shows the rings with the rhombo-
~ hedron formed.
XIX. A Shunt-Transformer. By Mr. B. W. Suitx*.
OUCH this experiment has already been described
by Professors Ayrton and Perry in a paper at the Insti-
tution of Hlectrical Engineers, it was thought to be worth
while occupying this Socicty’s time in showing it here, as it
forms a good lecture-experiment, if nothing more, to illustrate
acceleration and lag of alternating currents.
The experiment consists as follows :—Between two leads a
Fig. 1.
certain alternating potential difference, V,is maintained. We
have two resistances, A and B (fig. 1), in series, through
# Communicated by the Physical Society: read June 8, 1889.
a Shunt-Transformer. ° 133
which part of the current flows. If the“impedance of A is
equal to that of B, then P.D. at terminals of A, V,, and P.D.
at terminals of B, Vs, are equal. If A and B are alike in
resistance and self-induction, then V, and V; would be in the
same phase and each equal to $V. If curve 0000 (fig. 2)
Fig. 2.
represents V, then curve 1111 represents $V. But if A
has large resistance and B much self-induction, then, although
V, may be still equal to V,, V, will be lagged and V, accele-
rated. Then curve 3338 will represent V,, and 4444 V,.
We have also two similar sets of lamps, L, and L, (fig. 1)
in series between the two main leads. Under ordinary cir-
cumstances they would each have a P.D. of $V (curve 1111
fig. 2) at their terminals. But if we connect the junctions of
the two sets of lamps with the junction of the two resistances
then lamp L, will have P.D. V,, and lamp L,a P.D. Vy; and
therefore both lamps will become brighter. If the lamps take
an appreciable current, then, when the junctions of the different
circuits are joined, the current in the inductive resistance as
well as in the lamps becomes greater, but that in the main
circuit becomes smaller, as may be seen by a dynamometer.
The resistance A may of course consist of lamps, and B
may be a choking coil, which absorbs very little energy.
Prof. Ayrton has given this inductive part of the circuit the
name of a “ Shunt-Transformer.”
I have made a similar experiment with one of Mr. Mordey’s
transformers wound with three coils, each having the same
number of turns. Using one of these as a primary and the
other two as two independent secondaries, then, by having
one circuit comparatively non-inductive and the other in.
ductive, one gets the arithmetic sum of the amplitudes of the
secondary currents greater than that of the primary current,
although of course the vector sum must be less. For instance
take one particular experiment. The primary was on a Gir
cuit having a P.D. of 128 volts. One secondary, A, was
composed of lamps, and the other, B, was a Tesla motor.
134 Mr. A. W. Ward on the Use of the Biquartz in
Volts in primary, 128
5 secondary A, 119
5, secondary B, 119°5
Connecting up the secondaries of transformers A and B in
parallel, the volts at the terminals of the primary being the
same as before, and the secondary circuit being lamps.
Current in primary, 14-2
. secondary A, oh 162
: secondary B, 82
Volts in primary, 128 | Current in primary, 17°4
Be secondary, - 120 ‘5 secondary, 16°3
Here we have to give 17:4 amperes to the primary instead of
14-2 to get same current in secondary, and the volts in
secondary are practically the same as before.
If we were being supplied with electricity, what should the
meter measure? Surely the amount of energy we use. But
ordinary meters only measure ampere-hours, and so cannot
but give records in favour of consumer or supplier. The
sooner the public understand this, the sooner we shall have a
scientific meter in our houses.
XX. On the Use of the Biquartz in determining the position
of the Plane of Polarization. By A.W. Warv*.
HE biquartz has been so often used, especially on the
‘Continent, by investigators on the rotation of the plane
of polarization of light, and with such extremely varying
degrees of accuracy, that it seems of interest to account for
these results mathematically. Verdet and H. Becquerel ob-
tained results which varied by less than 4’; while Wertheim,
Matteucci, Edlund, Liidtge, and Villari obtained results vary-
ing by as much as 2°. Liidtge has in one case obtained a
rotation of 4° where, on his own showing, the light was circu-
larly polarized. Verdet’s and Becquerel’s accurate results
were obtained when rotation was looked for in liquids and
isotropic substances ; and the inaccurate results of Wertheim
&c. were obtained when seeking for a rotation in doubly-
refracting substances. In the former case the light remained
plane-polarized, in the latter it became elliptically-polarized,
and the position of the plane of polarization was really that of
one of the axes of the ellipse. In the present investigation
we shall then determine with what degree of accuracy the
biquartz can be used to determine the position of the axes in
elliptically-polarized light.
Let us suppose that the elements of the elliptically-polarized
* Communicated by the Physical Society: read June 8, 1889.
determining the position of the Plane of Polarization. 135
light are given by the displacements along the axes of the
ellipse, and by the inclination of an axis of the ellipse to some
direction fixed in space. let the displacements & and 7 be
parallel to the axes of the ellipse, and let the axes of x and y
be fixed in space, z being the axis along which the light
travels; and let w be the angle between the axes of a and &.
If then c* be the intensity of the light, tan y the ratio of the
axes of the ellipse, the vibrations of the light are given by the
equations
E=c cosy cos 7 (wt—2),
: . 297
n=csiny sin (vt— 2).
The angles y and » are known whenever we know the
history of the light ; how it became converted from plane-
polarized into elliptically-polarized. If, for instance, the
change took place in passing through a doubly refractive
medium whose axes are those of x and y, then
tan 2@= tan 2 cos B, }
sin 2y = sin 2a sin B,
- (2)
_ where £ 1s the total angular retardation, and « the inclination
of the initial plane of vibrations to that of az. In these equa-
tions @ is a function of d, viz. = (4,—M2)2, where mp, and ps
are the indices of refraction along the axes of x and y respect-
ively. If issmall, variations in w due to Xare not important;
but if a is large this is no longer the case, as we shall even-
tually see.
Let us now pass the light (1) through a biquartz which is
such that the plane of polarization of light, of wave-length A,
is turned through an angle ¢. This rotation will simply turn
the ellipse as a whole, and not affect the ratio of the axes.
Hence for upper half of the biquartz w becomes w + ¢, and for
lower half o—¢.
Let the light be now ana-
lysed by a Nicol whose plane
of vibrations makes an angle 0
with the plane of #z. Ifthen
i? be intensity of light passing
through the upper half of bi-
quartz, and k* that of light
passing through the lower half,
we have, as usual,
136 © Mr. A. W. Ward on the Use of the Biquarte in 3
h? =c’ cos*y cos? w +¢,— 9 ac |
(3)
k? =¢? cos’ y cos? o —d — 6 +c’ sin? y sin? a—gd—8O;
or
2
}?7= ie cos 2y cos 2(@+h6—8)},
r (4)
v= 5 {1+ cos 2y cos 2(w—f—8A)}.
We have now to determine what value of 6 makes ?=k*
for all values of X.
Hquating h? to k’, we get
cos 2ysin2¢sin2a—A0=0. . . . . (9)
This equation is satisfied whenever
cos 2y=—0, 9 6s i rer
or
sin 2@=0,' 3...) er
or
sin 2{@—0)=—0.,... .) 2) cee)
The first of these solutions occurs when y= = z. €. when the
elliptically-polarized light is really circularly polarized. In
this case the phrase plane of polarization has no meaning at
all, and so it need not be discussed.
The second solution (7) gives $= = This can only be the
case for one particular wave-length, and depends simply on
the thickness of the biquartz. A biquartz is usually made of
such a thickness that ¢ is = for the yellow light from: the
brightest part of the spectrum. We shall suppose this to be
the case here.
The third solution gives
w=.
If, then, this solution does not hold for all values of X, then,
however the analysing Nicol be turned, both halves of the
biquartz can never be made of the same uniform tint.
Now, considering the equation
tan 2w= tan 2a cos B,
we seo that w=a always if 8=0, that is, if the incident plane-
polarized light always remains so. If§ is not equal to 0, then
oy eae 0, then
still o=« for all values of A, if a=0 or 1
determining the position of the Plane of Polarization. 137
y=0, and the light is plane-polarized as before. The case we
have to discuss, then, is «= By
A
ae = and also for any particular value of A, B=z, then
light of that colour is circularly-polarized. Hence, however we
alter 0, no change in the intensity of that light will take place.
If this circularly-polarized light comes from a prominent part
of the spectrum, it will be impossible to note small change in
the tint of passage due to the varying presence of other
colours. The difficulty experienced will be precisely similar
to that of fixing the position of the plane of polarization by
means of the yellow tint of passage instead of the violet tint.
If 6 is never so great as = then, when both halves of the
biquartz are of the same uniform tint, the position of the ana-
lyser determines the position of the ellipse; but the uniform
tint will not be that due to excluding the yellow light of the
spectrum, but will contain lights of every colour, but not in
that proportion which constitutes white light. The tint may
be rosy or yellow. 5
If « is neither 0 nor 2
possibly satisfy the solution for all values of 6. In this case,
then, both halves of the biquartz can never be made of the
same tint. As this is the general case, we conclude that the
biquartz is not a suitable instrument to use when, instead of
plane-polarized light, we have elliptically-polarized.
The following table gives the values of w due to variations
in « and 2» when the light has passed through a quarter undu-
lation-plate of quartz. The values have been calculated from
Rudberg’s table of indices, quoted on p. 317 of Glazebrook’s
‘Optics.’ The capital letters refer to the lines of the spectrum.
then varies with A, and cannot
0. D. E. G.
s. | soe. | 90°. | 100°. | 1260.
Spa oe datos wlehie wap uh 60 |
a—20°. w 4° O a a == 1/8
phan f 39° 0 —39° | —43°
The above is simply given as an illustration of the magni-
tude of the quantities involved in a particular case where it is
easy to make the calculations. I have tried the experiment
138 , Notices respecting New Books.
by passing light the reverse way through an elliptic analyser
t. e. a Nicol prism and quarter undulation-plate), then
through the biquartz, and finally through an analyser. It is
found quite impossible to get any match between the two
halves of the biquartz when a is large. The actual dispersion
of the axes depends upon the variations of 8 with d, and this
is very much greater in quartz than in such a doubly refract-
ing substance as compressed glass. But in most cases there
will always be sufficient variation to make the use of the
biquartz a very unsuitable method, and this does, I think,
account for the two classes of results mentioned at the begin-
ning of this paper.
In conclusion, I have only to express my gratitude to Mr.
Glazebrook for many valuable suggestions, and to Professor
Thomson for the use of the Cavendish Laboratory.
XXI. Notices respecting New Books.
A Treatise on Spherical Trigonometry, and its application to Geodesy
and Astronomy; with numerous examples. By Dr. J. Casey,
F.R.S. (Longmans: 1889.)
JT )R. CASEY has “struck oil” as a writer of Mathematical
Text-books. It is not so many years since he began this
career with his useful and excellent ‘Sequel to Euclid, which has
now reached a fifth edition, and since that time he has produced
other text-books of like good quality. Having given us an “ele-
mentary” and a more advanced Plane Trigonometry, he now -
completes this special corner of mathematical literature with the
work before us. The student will find here all, or nearly all, he
wants in a text-book on the subject, illustrated by much matter
selected from foreign periodicals, with variety of proofs. Follow-
ing @ practice which has come much into vogue of late years, many
results are ticketed with the names of the earliest publishers of
them: for instance, two formule which frequently occur in the
solution of triangles are called the first and second Staudtans of a
triangle. Recent points and lines which occur in Plane Geometry,
and which have analogues in Spherics, have the like names here:
some, as the Lemoine point and the Symmedian point, which are
identical in plane, do not coincide in Solids. The specially noteworthy
chapters, as might be expected from Dr. Casey’s original work in
this field, are, in our opinion, those upon the small Circles on the
Sphere and on Inversions. There is a large collection of exercises,
and, after the author’s previous manner, the more noteworthy
results are numbered ; of these, 495 are given. In addition to a
handy and compact account of the purely Trigonometrical details,
there is a final chapter on the applications to Geodesy and Astro-
nomy. ‘The text is accompanied by a short index.
eacces
XXII. Proceedings of Learned Societies.
GEOLOGICAL SOCIETY.
[Continued from p. 71.]
May 22, 1889.—W. T. Blanford, LL.D., F.R.S., President,
in the Chair:
a following communications were read :—
1. “Notes on the Hornblende Schists and Banded Crystalline
Rocks of the Lizard.” By Major-Gen. C. A. M*Mahon, F.G.S.
The Lizard district has been visited by the author on three occa-
sions during the years 1887—8-9, and the specimens of the rocks
collected were subjected to microscopic examination. After sum-
marizing the work of previous writers, the author proceeded to
consider the hornblende schists. He described these rocks and
gave a table showing their constituent minerals. He noted the
absence of quartz, the presence of pyroxene, and the fact that the
minerals present are those commonly met with in volcanic rocks
either as original minerals or as secondary products, and he con-
siders that the microscopic study of the schists confirms the
opinion of some previous writers that the schists had a volcanic
origin and consisted principally of ash-beds. The absence of free
quartz militates strongly against the supposition that they were
originally sedimentary rocks of an ordinary character, whilst
the fact of their being bedded shows that they are not plutonic.
The author has found no evidence that the foliation of these rocks
is due to dynamic deformation, and gives reasons for supposing that
such was not the case. The rock seems to have been originally
homogeneous, and its banding produced at a later stage by the
segregation of the hornblende in planes parallel to the bedding.
The rocks furnish abundant evidence of the action of water, as
shown by the presence of calcite, chlorite, steatite, and other pro-
ducts of aqueous action, as well as by channels fringed with magne-
tite, ferrite, or limonite. The action of water in converting augite
into hornblende may be distinctly traced when the slices still contain
pyroxene. The production of periodical currents of water through
the water-bearing strata adjoining the roots of a voleano was com-
mented on, and the author suggested that the banding of the horn-
blende schists was produced by such water leeching out unstable
minerals, such as pyroxene, from the spaces between the planes of
lamination, and the formation of comparatively stable minerals,
such as hornblende, along those planes. The Lizard rocks contain
good examples of the formation of hornblende in the wet way, that
mineral having been deposited in cracks in such a way as to join
together the ends of hornblende crystals severed by these cracks.
"The « granulitic” group, of which the author gave a table
showing the constituent minerals, was then described. Judged by
ES oe EE Se Sd tS eae tee aie
waite NAME Chee os
140 Geological Society :—
their mineralogical contents the dark bands consist of diorite and
the white bands of granite.
The author considers that portions of this group consist, like the
hornblende schists, of converted ash-beds, but that other portions
are composed of intrusive diorites of later date, the quasi-bedded
appearance of both being due to the injection of granite. He
pointed out that the quasi-banding is very irregular in its cha-
racter, that the bands inosculate, bifurcate, and entangle them-
selves in complicated meshes inconsistent with the idea of regular
banding, and that they are deflected by the blocks of serpentine
imbedded in the dioritic portions of the granulitic rocks as well
as by the porphyritic crystals of felspar contained in the latter. In
certain places, as on the foreshore at Kennack Cove, the intrusive
character of the granitic veins is undoubted, as they cut through
the diorite in all directions, but they graduate into bands of normal
character. The author considers that the process of injection
was aided by the plasticity of the ‘ granulitic” beds induced
by the neighbourhood of igneous masses; also in the case of sub-
marine ash-beds by the planes of sedimentation, and in the case of
intruded sheets of diorite by the foliation parallel to the bedding,
the intrusion of the granite being subsequent to that of the diorite.
At Pen Voose a foliated granite, the author pointed out, occurs in
association with a non-foliated gabbro and diorite, a fact indicating
in his opinion that the foliation of the granite was produced before
its perfect consolidation. The granite was the last to appear in the
order of time, and had the foliation of the granite been produced by
pressure after cooling, the gabbro and diorite would also have been
foliated.
2. “The Upper Jurassic Clays of Lincolnshire.” By Thomas
Roberts, Esq., M.A., F.G.S.
In Lincolnshire it has generally been considered that the Oxford
and Kimeridge Clays come in direct sequence, and that the Corallian
eroup of rocksis not represented. The author, however, endeavoured
to show that there is between the Oxford and Kimeridge a zone of
clay which is of Corallian age.
Six palzontological zones were recognized in the Oxford Clay.
The clays which come between the Oxford and Upper Kimeridge
the author divided into the following zones :—
(1) Black selenitiferous clays.
(2) Dark clays crowded with Ostrea deltordea.
(3) Clays with Ammonites alternans; and (4) clays in which this
fossil is absent.
The black selenitiferous Clays (1) are regarded as Corallian,
because
(a) They come between the Oxford Clay and the basement bed
of the Kimeridge.
(b) Out of the 23 species of fossils collected from this zone 22 are
Corallian.
Origin of Movements in the Earth’s Crust. 141
(c) Ostrea deltoidea and Gryphea dilatata occur together in
these clays, and also in the Corallian, but in no other forma-
tion.
The zones 2, 3, and 4 are of Lower Kimeridge Clay age. The
lowest zone (2) is very persistent in character, and is met with in
Yorkshire, Cambridgeshire, Oxfordshire, and the south of England.
The remaining zones (3 and 4) are local in their development.
3. “Origin of Movements in the Earth’s Crust.” By James R.
Kilroe, Esq. F
The author is convinced that a very important factor has been
omitted from the usual explanation offered in accounting for the
vast movements which have obtained in the Earth’s crust. His
acknowledgments are due to Mr. Fisher for the extensive use
made of his valuable work. THe also refers frequently to the views
and publications of other writers on terrestrial physics. From a
somewhat conflicting mass of figures he concludes that about 20
miles would remain to represent the amount of radial contraction
due to cooling during the period from Archean to Recent times,
corresponding to a circumferential contraction of 120 miles. This
will have to be distributed over widely separate periods, at each of
‘ which there is abundant evidence of lateral compression.
But he considers that this shrinkage alone will not account for
all the plication or distortion of strata which constitute so im-
portant a factor in mountain-making, and he is disposed to supple-
ment it in the way to which allusion has already been made by
_ Mr. Wynne in a recent Presidential Address, viz. by considering the
effects of the attenuation of strata under superincumbent pressure
from deposition in subsiding areas, which involves the thickening,
puckering, reduplication, and piling up of strata in regions where
pressure has been lessened. It should be noted that, until disturb-
ance of ‘cosmical equilibrium” takes place, mere pressure does not
produce metamorphism. The extent of these lateral movements is
described, and it is asserted that the theories hitherto adopted to
account for plication, &c. are inadequate.
The origin of the horizontal movements is further discussed on
the hypothesis that solids can flow after the manner of liquids,
when they are subjected to sufficient pressure. He considers that
the displacement in N. W. Scotland may have been initiated by the
force due to contraction and accumulating in the crust throughout
the periods marked by the deposition of Torridon Sandstone and
Silurian strata, the elements of movement finding an exit at the
ancient Silurian surface. In this case the pile of Silurian strata
formerly covering the region now occupied by the North Sea and
- part of the Atlantic forced the lowest strata to move laterally, the
protuberances of the underlying pre-Silurian rocks being also
involved in the shearing process. Similar results obtain in other
mountain areas. The strata compressed have been greatly attenuated,
and extended in proportion ; in this way we may account for the
piling up of strata by contortion in certain regions. The connexion
ial, Mag. >. 5. Vol. 238. No: 171. August 18389.. M
142 | Geological Society -—
of this interpretation with Malet’s theory of volcanoes is also
indicated, and the author concludes by applying these views to
other branches of terrestrial physics.
June 5.—Prof. J. W. Judd, F.R.S., Vice-President,
in the Chair.
The following communieations were read :—
1. “Observations on some undescribed Lacustrine deposits at
Saint Cross Southelmham, in Suffolk.” By Charles Candler, Esq.
2. ‘‘On certain Chelonian Remains from the Wealden end Pur-
beck.” By R. Lydekker, Esq., B.A., F.G.S.
3. “On the Relation of the Westleton Beds or Pebbly Sands of
Suffolk to those of Norfolk, and on their Extension inland.” By
Prof. Joseph Prestwich, M.A., D.C.L., F.B.S., F.G.S.
Part I.
The author in this, the first part of his paper, described the
Westleton beds of the East Anglian coast. He commenced with a
review of the work of previous writers, especially Messrs. Wood and
Harmer, and themembers of H.M. Geological Survey, including Messrs.
H.. B. Woodward, Whitaker, and Clement Reid. In discussing this
work, particular attention was paid to the Bure-valley beds, which
were considered as a local fossiliferous condition of the Pebbly Sands ; -
but the term is not so applicable to these sands as that of the
“ Westleton and Mundesley Beds,” which the author proposed im-
1881.
The Westleton beds were carefully described, as seen in coast-
sections in Hast Anglia, proceeding from south to north, and the
following classification was adopted :—
1. Laminated clays, sand, and shingle with plant-re-
mains and freshwater shells (the Arctic forest-bed of
Reid.
2. Sand and quartzose shingle with marine shells (the
Leda nyalis bed of King and Reid).
3. Carbonaceous clay and sands with flint-gravel and
pebbles of clay, driftwood, land and lacustrine shells
\ and seeds (the Upper freshwater bed of Reid).
( 4. A greenish clay, sandy and laminated in places, con-
The Forest-bei taining abundant mammalian remains, and drift-
GE OL EAS wood, with stumps of trees standing on its surface
(the forest- and elephant-bed of authors; the estua-
rine division, in part, of Reid).
5. Ferruginous clay, peat, and freshwater remains and
\ gravel (the Lower freshwater bed of Reid).
The Westleton
and Mundesley
series
(The Mundesley
section of it).
—A~————_-—_
series of Reid :
(exclusive of No.3
of above). |
The Westleton beds were found to rest with discordance on
various underlying beds; in places on the Forest series, elsewhere
on the Chillesford Clay, whilst occasionally the latter had been
LS airy Acai aaa She
a eee
a
eS ee an ye ree Mie
oT a
Tachylyte from Victoria Park, Whiteinch. 14é
partly or entirely eroded before the deposition of the Westleton
beds. In the north, where the present series dies out, they come
in contact with the so-called Weybourn Crag, which the author
supposed to be the equivalent of the Norwich Crag. A similar
discordance has been neted between the Westleton beds and the
everlying glacial beds, so that the former mark a distinct period,
characterized by a definite fauna, and by particular physical con-
ditions. The Westleton beds being marine, and the Mundesley
beds estuarine and freshwater, the author propesed te use the
double term to indicate the two facies, as has been done in the éase
of other deposits. But these facies were found to be local, and the
most persistent feature of the beds is the presence of a shingle of
precisely the same character over a very wide area. By means of
this the Westleton beds can be identified far beyond Hast Anglia,
and where there is no fossil evidence, and they throw considerable
light on important physiographical changes.
The author described the composition of the shingle, which,
unlike the glacial deposits, contained pebbles of southern origin.
The paper concluded with a list of fossils, excluding these of the
Forest-bed (the stumps of which, the author considered, were
frequently in the position of growth). Should the Forest-bed
eventually prove to be newer than the Chillesford beds, it was
maintained that the former must be included in the Westleton
series, and its flora and fauna added to the list, whilst if, on the
contrary, the Forest-bed should be proved synchronous with the
Chillesford beds i6 must be relegated to the Crag.
The second part of this paper will treat of the extension of these
peds inte and beyond the Thames Valley, and on some points con-
nected with the physical history of the Weald.
June 19.— Prof. J. W. Judd, F.R.8., Vice-President,
in the Chair.
The following communications were read :—
1. “ On Tachylyte from Victoria Park, Whiteinch, near Glasgow.”
By Frank Rutley, Esq., F.G.S.
This paper dealt with the microscopic characters of certain thin
tachylytic selvages occurring on the margins of white-whin (basalt)
velns which traverse Carboniferous shales in Victeria Park, and
which have already been described in some detail by Messrs. John
Young and D. Corse Glen, The white-whin veins, which sometimes
are not more than an inch in breadth, are found to become gradually
more vitreous in passing from the middle to the sides of the veins.
Near the margin they become densely spherulitic, the spherulitic
band on either side of the vein being followed by a less spherulitic
and more glassy band, the vitreous matter of which appears nearly
or quite colourless. A sharp but irregular boundary-line follows,
beyond which lies a band of a more or less deen brown or coffee-
coloured glass which the author considers to have resulted from the
i44 Geological Society.
fusion of the shale, two narrow vitreous bands of different origin
being thus developed side by side on each side of the vein, the
colourless bands representing the chilled margins of the vein, the
brown bands the fused surfaces of the walls of shale. The author
only suggested this as a plausible explanation of the microscopic
phenomena. An analysis of portion of one of these whin veins
with its adherent tachylyte, made by Mr. Philip Holland, was
die to the paper.
. “The Descent of Sonninia and of Hammatoceras.” By 8. 8.
Badiman, Esq., F.G.8.
3. “ Notes on the Bagshot Beds and their Stratigraphy.” By H.
G. Lyons, Ksq., R.H., F.G.S.
The author deplored the neeessity of quitting the area which he
had studied before completing his observations, and wished to place
his results at the disposal of other workers.
In a previous paper he had discussed the beds at their southern
outcrop, over a small area, and showed that there the Bagshot and
London Clay strata remained of constant thickness, and dipped
northwards at an angle of about 21°. He had since examined the
country between Aldershot and Ascot over an area of about 1d
miles square, and attempted by contouring the surface of the Middle
Bagshot beds (which showed a nearly constant thickness of 60 feet
ever the area), to give the form into which the beds had been
pushed by the different slight flexures which might occur. After
giving details of the heights at which this surface was found,
he concluded that an anticlinal of which the axis pointed upon
Windsor Castle, appeared to pass through the Swinley and Wel-
lington-College area, and probably to Hazeley Heath ; and that asyn-
clinal started by Minley and Hawley, and ran by the Royal Albert
Asylum, Gordon Boys’ Home, upon Ongar and Row Hills, and
Woburn Hills; and that another anticline ran to St. George’s Hill,
Weybridge.
The author had attempted to map the southern and eastern
limits of the Upper Bagshot beds, and claimed a much greater
extent for these beds in those directions than had been assigned by
the members of the Geological Survey. The outcrop of the beds
was described in some detail, and the occurrence of outliers on
Knaphill Common, by Donkey Town, on Chobham Common, and
on Staples Hill was noted.
4, “Description of some new Species of Carboniferous Gastero-
poda.” By Miss Jane Donald.
5. “ Uystechinus erassus, a new Species from the Radiolarian
Marls of Barbadoes; and the evidence it affords as to the Age and
Origin of those Deposits.” By J. W. Gregory, Esq., F.G.8.
Plt 4
XXIII. Intelligence and Miscellaneous Articles.
ON THE KINETICS OF BODIES IN SOLUTION. BY W. NERNST.
QIN CE Van t’Hoff disclosed the great analogy of the constitution
of dissolved bodies in dilute solution with the gaseous state, it
becomes possible, as the author shows, to explain diffusion on purely
mechanical principles. The most essential difference from gaseous
diffusion lies in the much snaaller velocity of diffusion of solutions,
which justifies the inference that the solvent offers an enormous
resistance to the moving molecules.
The author investigates in the first place the diffusion of non-
electrolytes. Here the dri iving force is solely the alteration of
osmotic pressure p with the locality w. Since p is proportional to
the concentration ¢ (number of g-molecules in 1 cub. centim.), and
thus p=p,¢c, we get for the quantity of substance in g molecules,
which travels through the section g of a cylinder in the time z :—,
K is the force which imparts unit velocity to a molecule in solution.
This law, which is of the same form as the well-known one stated
by Fick, renders it possible to calculate K in absolute measure, as
the author shows by a few examples.
Still more interesting is the calculation of the diffusion for
solutions of electrolytes; for the coefficient of diffusion may here
be calculated in absolute measure, on the basis of the hypothesis of
dissociation propounded by Arrhenius and others. By means of
Ohm’s law, Kohlrausch, as is well known, has calculated from the
galvanic migration of the ions, which is solely due to electrostatic
forces, the force which imparts to a g-ion in aqueous solution unit
velocity of migration. If now, in the diffusion of an electrolyte
the inequality of osmotic pressure were the only driving force, then,
from the different mobility of the positive and the negative ions
(e. g. H and Cl), free electricity would at once form in the solution.
This is prevented by the establishment of an electrostatic force, the
action of which has just the result that the ions in the solution
are present in equivalent ratios. From this condition the magni-
tude of that force may be calculated, and retaining the same nomen-
clature as above, we get for the actual quantity of the anion or
kation diffusing in unit time :—
=H 2Zuv dc
S=— 1-121 .10 z becie SiS. gay,
1* Po utv dx
u and v are the molecular conductivities in mercury units. From
this formula we have for the centimetre, the day, and 18° :—
= Tr 768 . 107.
146 Intelligence and Miscellaneous Articles.
For the sake of comparison with experiment, the influence of
temperature on the coefficient of diffusion is taken into account
on the basis of the theory of dissociation: the coefficients 0-026 for
salts and 0-024 for acids and bases represent the alteration of
conductivity with temperature ; these numbers are found to agree
very well with the observations of de Heen and Schumeister.
The coefficients of diffusion reduced to 18° agree very well with
the observations of various experimentalists, as shown in the table
given; and this agreement is an excellent proof of the validity of
the author’s consideration.
From the same point of view the author treats the diffusion of a
mixture of salts, as well as of electrolytes at greater concentration.
He shows further, how in the same way the difference of electrical
potential between solutions of different concentration may be
calculated. Between two places of a sclution in which the osmotic
W—Y og Ps
UtV smh
Zertschrift fir phys. Chemie [2] vol. 1. p. 613; Berblatter der
Physik, vol. xiii. p. 181.
a
pressure is p, and p,, the difference of potential is p
ON THE MOLECULAR CONDITION OF DISSOLVED IGDINE.
BY MORRIS LOEB.
By means of a determination of the vapour tensions, the author
’ endeavoured to determine whether iodine in its brown solution is in
a different molecular condition to that of its violet solution.
Ether was used asa solvent for the brown, and bisulphide of carbon
for the violet. The measurement of the tension was effected by
means of a Regnault’s apparatus, suitably modified. A trial of its
applicability, by means of solutions of naphthaline &c. in ether and
in bisulphide of carbon, gave satisfactery results, since the molecular
weights 132 and 127°5 were obtained instead of 128. The mode
of calculation is given in the original. For solutions of iedine in
bisulphide of carbon, the median values of the separate series of
experiments varied between 264 and 326-6, the general mean was
found to be 303:25. For molecules of the composition I, the
molecular weight is calculated at 254, and for I, at 381; the
number obtained is about the mean of these.
The solution ef iodine in ether also gave very divergent values
for the individual series of experiments, as they varied between
466-1 and 577:2, while the general average 507-2 agrees almost
entirely with the value 508 required for I,, The existence of the
molecules I, appears therefore probable for the brown moditica-
tion.
Experiments made to determine the question by means of
Raoult’s freezing-point method were unsatisfactory, for within the
limits caused by the difficult solubility of iodine the errors of
8
|
]
|
:
ee
~~ aw a
Intelligence and Miscellaneous Articles. 147
observation are too great.— Zeitschrift fiir phys. Chenve, vol. i.
p- 206; Besblitter der Physik, vol. xiii. p. 134.
SOME OBSERVATIONS ON THE PASSAGE OF ELECTRICITY
THROUGH GASES AND VAPOURS. BY DR. NATTERER.
The experiments were made with the aid of an induction appa-
ratus, and special regard was had to the sparking distance of the
electrical discharges, to their luminosity, and to the extension of
the glow-light which occurs at the negative electrode under dimin-
ished pressure. It appears that these three phenomena, which are
characteristic fer each individual gaseous body, are in relation with
the number of atoms in the molecule, and with the molecular
weight.—Sitzungsberichte der Wiener Akadenve, June 21, 1889.
ON THE ELECTRICAL RESISTANCE OF INSULATORS AT HIGH
TEMPERATURE. BY DR. H. KOLLER.
This is a continuation of a paper by the same author on the
passage of electricity through very bad conductors. It forms two
arts.
; In the first, the author investigates the connexion between the
electrical conductivity of some liquid insulators, and their fluidity
at various temperatures ; it was found that the course of these two
properties is parallel, but not proportional. The conductivity
always increases more rapidly than the fluidity, so that, for instance,
with petroleum ether a twelvefold increase of the conductivity
corresponds to only a threefold increase of the fluidity. The con-
ductivity of those substances exhibits the greatest increase when
their fluidity also increases most strongly with the temperature.
Castor-oil, for jmstance, conducts 350 times better at 132° than
at 20°, while between these two limits its fluidity increases by
only 43 times.
The second part deals with the gradual change which an imper-
fect dielectric experiences in consequence of rise of temperature.
The author concludes, partly from Hopkinson’s and partly from
his own experiments, that the first effect of the increase of an
imperfect dielectric consists in the fact that it begins to form
residues. The formation of the residue is at first of very short
duration, but with increase of temperature extends over a longer
interval of time, and the residues developed adhere in accordance
with this continually more firmly to the dielectric. At still higher
temperatures they are rapidly altered into a form in which a reverse
change with free electricity is only possible with difficulty and with
great loss; and is finally not possible at all.
The experimental result is that in a condenser formed of the
dielectric in question the amount of residue which can be demon-
strated—that is, that which neither takes part in a discharge of
148 Intelligence and Miscellaneous Articles.
short duration, nor is so similar to heat that it cannot change into
dielectric displacement--increases on heating from approximately
zero toa maximum. It decreases after this, and with the occurrence
of perfect conduction it entirely disappears.—ASttzungsberichte der
Wiener Akademie, June 21, 1889. ;
ON THE RESISTANCE TO DISRUPTIVE DISCHARGE OFFERED BY
GASES UNDER HIGH PRESSURES. BY MAX WOLF.
At the instance of Prof. Quincke the author attempted to ascer-
tain what resistance certain gases offered at high pressure to the
passage of the electrical spark. In other words, the difference of
potential of two spherical surfaces was determined at the moment
of the discharge, for different gases and at various pressures
greater than one atmosphere. In this a method was used similar
to that used by Quincke for determining striking distances in insu-
lating liquids. It was to be expected that under higher densities
the irregularities in the discharge occurring under smaller pressures
must be less prominent.
_ The conclusions arrived at are as follows :—
(1) The electrical force which produces the disruptive discharge
in various gases between spherical surfaces of 5 centim. radius and
at a distance of 0-1 centim. increases proportionally to the pressure
for pressures between 1 and 9 atmospheres.
(2) The increase of the electrical force for simpler gases (oxygen,
hydrogen, and air) is inversely proportional to the mean path of
the gas-molecules.
(3). With carbonic acid the product from the increase in the elec-
trical force into the mean path for an increase of pressure for one
atmosphere is considerably smaller (almost one half) that of simple
pases.
(4) One or more discharges are necessary until the resistance of
a gas is attained, and the resistance is at first so much the less than
in the later discharges, the higher is the pressure on the gas.—
Wiedemann’s Annalen, vol. xxxvii. p. 306 (1889).
THE NATURE OF SOLUTIONS. BY S. U. PICKERING.
On pages 36-38 of this Magazine Prof. Arrhenius publishes a
criticism of my paper on this subject. I venture to think that it
is somewhat rash of Prof. Arrhenius to attack a paper which has
not yet been published, and of which only a short abstract, destitute
of all experimental data, has as yet appeared in print. If he will
wait till the paper be published in full (and it may be some months
yet before it is so) he will, I think, find that several of his criti-
cisms are mistaken, and that the others have already been answered.
If otherwise, I shall then be ready to answer him on any point
which he may raise.
July 2, 1889,
EEE
THE
LONDON, EDINBURGH, ann DUBLIN
PHILOSOPHICAL MAGAZINE
AND
JOURNAL OF SCIENCE.
[FIFTH SERIES. |
SEPTEMBER 1889.
XXIV. On the Mechanics of Luminosity.
By H. WIiEDEMANN*.
[Plate IIL.] |
A LTHOUGH we possess numerous measurements of the
positions of lines in the spectrum, and although many
attempts have been made to measure the distribution of lumi-
nosity and energy in the spectrum, and to express the same
by means of formule, yet the experiments are few which have
for their object to obtain an insight into the mechanics of
luminosity. In general, we have contented ourselves with in-
vestigating the intensity of radiation without investigating
the energy of the vibrating particles which emit the light,
upon which it depends.
In what follows we shall attempt to fix the data for in-
vestigating the mechanics of luminosity, to verify particular
conclusions by means of experiment, and to determine the
numerical value of the quantities which occur.
The present research is a continuation of earlier investi-
gations of minef.
* Wied. Ann. xxxvil. p.177. Translated from a separate impression
communicated by the Author.
+ E. Wiedemann, Wied. Ann. v. p. 506 (1878); vi. p. 298 (1879) ;
ix. p. 157 (1880) ; x. p. 202 (1880) ; xviii. p. 508 (1883) ; xx. p. 756 (1883) ;
xxxiv. pp. 446 and 464 (1888). Svtzwngsber. d. Societas physio-medica Er-
langen vom 1 Aug. 1887. Bull. Soc. de phys. génévoise 6 Oct. 1887.
I shall return more at length to numerous obligations to the above-
mentioned works—where no special acknowledgment is made—upon a
future opportunity. The results of this investigation themselves were
communicated to the Physico-Medical Society of Erlangen on Dee. 10,
1888,
Phil. Mag. §. 5. Vol. 28. No. 172. Sept. 1889. N
a = RO ee
P roan’, Fonte
= py a es
Y ones
P BL Pe,
150 Prof. E. Wiedemann on the
General._—Production of Light.
1. According to the newer views of the constitution of
bodies, we assume motions of translation of the molecules”
with their centre of gravity ; further, rotation and oscillation
round the centres of gravity considered as fixed, not only of
the material parts of the molecules but also of their eether-
envelopes. With gases the motions of translation of the
centres of gravity produce only feeble emission of light. Sir
G. G. Stokes* has sought in this the explanation of the feeble
continuous spectrum of sodium seen at the same time as the
line-spectrum. I have myselff endeavoured to show that
the motions of rotation cannot be the cause of the line- and
band-spectra. Consequently we must seek the cause of the
production of light in gases in the intermolecular move-
ments which occur within the molecule—either of their material
particles or of their ether-envelopes. We shall endeavour
to show later on that it can only be the vibrations of the
‘material particles to which the emission of lightisdue. With
sold and liquid bodies the emission of light may be due to
the vibrations of the whole molecule about its position of
equilibrium as well as to the intermolecular motions of the
constituent atoms of the molecule. Upon the first depends
the uniform continuous spectrum of all solid bodies when
heated, and upon the last the differences between the light |
emitted by different bodies.
| 2. The following theoretical considerations rest upon the
| conception of dwminosity introduced by me, and the discrimina-
| tion of totally different phenomena which have generally been
confused.
I designate as light the whole complex of rays between the
infra-red and the extreme ultra-violet. The motions of the
| molecules which produce the luminosity I will call, for the
sake of brevity, /wmcnous motions, in contradistinction to the
vibrations of the emitted waves of light.
I shall always designate as intensity of the light-vibrations
the energy measured in gramme-calories per second which
the vibrations of the light-waves emitted by the molecules of
! the body carry with them ; but as luminous energy the energy
! | of those motions of the molecules or their atoms which pro-
duce the radiated light. The first energy depends upon the
decrease of the second with the time. A chief problem of
| : * See a Research of A. Schuster, Phil. Trans. Lond. 1879, p. 37.
) t+ Wied. Ann. v. p. 507 (1878).
Mechanics of Luminosity. 151
this research is to show how the luminous energy may be
determined from the intensity.
I shall speak of brightness when the intensity is measured
by photometric methods, that is by a physiological method.
d. I take as the basis of my investigations the kinetic
theory of gases. According to this there exists at constant
temperature a perfectly definite relationship between the kinetic
energy of the motion of translation, corresponding to the
temperature, and that of the intermolecular motions, both as
a whole as well as for each kind thereof, and consequently
also between those of the motion of translation and the lumi-
nous motion; otherwise no permanent condition would be
possible. This relationship may be regarded as the normal
one. If, for any reason, the normal relationship is disturbed
in any way, it will in time again become normal.
If, for example, we exalt the luminous motion in a molecule
in comparison with the motion of translation, the first will be
transformed into the latter; if the luminous motion becomes
lowered by radiation the loss will be partly replaced from the
store of energy of the motion of translation by means of the
impacts of the molecules.
Luminescence and Temperature of Luminescence.
4. In special cases, however, the normal relationship be-
tween the motion of translation corresponding to the tempera-
ture and the luminous motion does not exist.
In a former paper I have ventured to employ the term
luminescence for all those phenomena of light which are more
intense than corresponds to the actual temperature.
In all phenomena in which luminescence is manifested the
energy of the luminous motion is higher than that charac-
terized above as corresponding to the relationships determined
by the temperature alone. According to the mode of excita-
tion I distinguish Photo-, Hlectro-, Chemi-, and Tribo-lumi-
nescence. In particular, photo-luminescence, including fluores-
cence and a number of cases of phosphorescence, is defined as
those phenomena in which the incident light excites vibrations
within the molecule of a body which produce directly an
emission of light. I do not include in this those cases in
which the incident light produces primarily chemical pro-
cesses, upon which a production of light is secondarily
dependent. This occurs for example with a large number of
phosphorescent substances, g g. calcium sulphide. These
2
SSS SSS a ee a a ee
152 Prot. E. Wiedemann on the
phenomena apparently belong to photo-luminescence, but
really to chemi-luminescence.
The temperature of luminescence is defined to be the tem-
perature at which a body, heated without decomposition,
would give light of a particular wave-length in each case of
exactly the same brightness as it does in consequence of the
processes of luminescence.
The production of light in the phenomena of luminescence
in gases cannot be explained by assuming that in consequence
of the different velocities of the individual molecules, as
assumed by the kinetic theory of gases, the individual mole-
cules possess a very high temperature, and therefore become
luminous. Tor at the temperature of ignition, defined by the
great velocity of the motion of translation, most substances
would be decomposed. Certainly all organic substances,
fluorescent or phosphorescent, in the gaseous condition.
The like holds good for solid bodies and for liquids, only that
here the limits within which the velocities of the molecules
. are included are much narrower than with gases.
The Temperature of Lumunescence and the Second Law of
the Thermodynamic Theory.
5. Ina number of phenomena we have to take account of
the temperature of luminescence.
In all mathematical developments which are based upon ~
the second law of the thermodynamic theory expressions
d e e e e e
such as dQ occur, involving quantities Q of heat communi-
T
cated to or withdrawn from the body, divided by the absolute
temperature T at which this takes place.
If luminescence occurs in consequence of this addition of
energy, then the temperature corresponding to certain inter-
molecular motions, to be defined later on (39), upon which the
luminescence depends, i. e. the temperature of luminescence,
is much higher than the temperature of the luminescent
body as measured by the thermometer™.
We must therefore divide the changes of energy which
* The assumption upon which deductions from the second law rest,
viz. that heat cannot be conveyed from a body of lower temperature to
one of higher temperature without the expenditure of work, must there-
fore be otherwise conceived in accordance with the above considerations
upon the temperature of luminescence, since when phenomena of lumines-
cence occur such a transference may very well take place, as I shall show
more fully further on.
Mechanics of Luminosity. 153
occur into two parts—the first, which corresponds to the
prevalent mean temperature as defined by the motion of
translation of the molecules; and the second, which is de-
termined by the intermolecular motion. Consequently the
expression fdQ/T must be divided into two parts correspond-
ing to these two processes. If the luminescent light is not
homogeneous, but if it consists of separate bright lines, or if
it yields a continuous spectrum, then for each ray of light
of definite wave-length emitted the temperature of lumi-
nescence and the corresponding quantity of energy must be
determined. Hach member of J dQ/T takes then the form
>.dQ,/T,, where T, represents the temperatures defined by the
motions of translation or by the internal motions, and dQ,
represents the corresponding quantities of heat. We must
further remark that in the integral all the members whose
temperature of luminescence is very high become very small,
whilst according to the usual mode of treatment they have a
considerable value.
6. That such phenomena of luminescence actually occur
may be directly shown in numerous cases, as in gases which
are made luminous by electric discharges without any corre-
sponding elevation of temperature; further, in cases of
chemi-luminescence, and indeed in processes where one would
not have expected it. The experiments of W. von Siemens*
have shown that gases heated far above 1000°C. emit no
light ; and yet an alcohol flame is luminous. It produces |
preeminently ultraviolet rays; in the combination of the
constituents of the alcohol with the oxygen internal motions
arise, for which the corresponding temperature of lumi-
nescence is situated far above the temperature of the flame.
The case is similar with burning carbon disulphide, and
sulphur, and in many other cases; so also with the luminosity
of phosphorus at low temperatures, the emission of light by
arsenious acid upon crystallization attended with rearrange-
ment of its molecules, Xe.
7. In these phenomena of luminescence the occurrence of
internal motions of other temperature than that shown by the
thermometer may be perceived immediately by the eye.
Hence the necessity of dividing the quantities of heat into
two parts is at once apparent. But analogous processes occur
in many other cases, as in most chemical changes, although
they may not be directly perceptible, e.g. when the lumines-
* Wied. Ann. xviii. p. 311 (1888).
154 Prof. EK. Wiedemann on the
cence is restricted to rays of greater or smaller wave-length
than those which the eye can perceive.
Besides these oscillatory internal motions, of other tem-
perature than the mean, which produce this luminescence,
yet others may occur, rotatory and others, which are not of a
nature to produce light-waves in the surrounding ether, as
may be the case in the conduction of electricity through
electrolytes. But of this I make here only a preliminary
mention.
Luminescence and Kirchhoft’s Law.
8. The production of light may therefore occur in conse-
quence of a rise in temperature, as well as in consequence ofa
rise in luminescence. But these two modes must always be
considered separately if we wish to obtain an insight into
the mechanics of luminosity.
For luminosity resulting from a rise of temperature Kirch-
hoff’s Law as to the relationship of emission and absorption
holds good. Upon this rests the well-known reversal of
the lines of the spectrum. The light produced by lumi-
nescence does not obey the same law, as is shown for example
by the behaviour of fluorescent substances, which emit light
of a refrangibility different from that of the incident light.
In trying whether Kirchhoff’s Law holds good or not, we are
often able to distinguish the two phenomena. (See further
on under 30.)
To discover the reasons why in glowing bodies Kirchhoff’
Law of the ratio between emission and absorption holds good,
and why this is not generally the case with luminescent bodies,
let us consider the following circumstances :—
As we have said, there takes place in a gas a constant ex-
change between intermolecular energy and that due to
motions of translation in consequence of the impact of mole-
cules (the luminous energy forming a part of the inter-
molecular energy), so that a mean condition ensues. If any
molecule suffers an increase of intermolecular energy, e. g.
in consequence of the absorption of incident light, this is
given up again in the next impact or so, and if it has a
deficiency in intermolecular energy this is made good.
The emission-coefficient depends upon the ease with which
part of this intermolecular energy produced by the impacts,
corresponding to the luminous energy, is given up again
in the form of light-vibrations, that is upon the friction be-
tween the vibrating molecules of the body and the surround-
ing ether. The absorption depends upon the same quantity,
and thus also upon the structure ofthe molecule. But since,
Mechanics of Luminosity. 155
on the one hand, the coefficient of emission is greater the
greater the friction, and on the other hand the coefficient of
absorption equally increases with this; the coefficients of
absorption and emission must run together; and so for all
bodies in which this reciprocity exists Kirchhoff’s Law must
hold good.
The applicability of Kirchhoff’s Law to the phenomena of
luminosity thus assumes a uniform transmutability of lumi-
nous energy with that of translation, and vice versd, for only in
this case can the ratio between absorbed and emitted energy
be a function of the wave-length. But if the conditions are
such that intermolecular energies produced by the absorp-
tion of incident light &., are not converted back into motions
of translation after a few impacts, then the store of luminous
energy will gradually increase, and a new emission will be
added to that dependent on the temperature—that is to say,
luminescence is produced. That Kirchhoft’s Law no longer
holds good here, and cannot hold good, is clear, since the
structure of the molecule is such that the uniform transforma-
tion of luminous energy into that of motion of translation,
and of that of translation into luminous energy no longer
takes place. Indeed, it would seem as if Kirchhoff’s Law
only held good for an ideal case, viz. only if no increase of
the luminous motions could be produced in the luminous
body by absorption. Hence Kirchhoff’s Law can only hold
good for that part of the luminous motion which does not
consist in luminescence. Moreover, Kirchhoff’s Law has not
been quantitatively proved for luminous gases; but we have
contented ourselves with verifying certain qualitative-quanti-
tative consequences of it.
Dependence of Luminescence on the Mode of Excitation.
9. Luminescent light is in a high degree dependent in
colour and intensity upon the mode of production, so that in
investigating it it is necessary to consider both of these
qualities. In photo-luminescence, and so in fluorescence and
phosphorescence, the colour of the emitted light is dependent
upon that of the incident light. In electro-luminescence,
discharges of various strengths call forth different assemblages
of rays. The borders of the stratifications in discharge-tubes,
as is well known, are of different colours towards the positive
and negative poles. This occurs with hydrogen or air alone,
but, as I have observed, more distinctly if the discharge-tube
contains hydrogen and sodium vapour. Further, the glow-
light and the positive light are, ceteris paribus, differently
coloured.
ae a c+ o
in
156 Prof. E. Wiedemann on the
The sulphur compounds of the metals of the alkaline earths,
glowing in consequence of chemi-luminescence, yield light of
different colours according to difference of temperature.
The order of intensity of emission of light may be com-
pletely reversed by change in the mode of excitation. Thus
if, in electro-luminescence, a body A shines as bright as, or
brighter than, another body B, this will not necessarily be the
case upon ignition or with chemi-luminescence. Mercury and
sodium give us examples of this. The first, introduced in
the gaseous state into the flame, gives scarcely any light,
whilst in a Geissler’s tube it gives an intensely bright light ;
sodium, on the other hand, is very bright in both cases.
10. In many cases luminescence and ignition occur together.
If we wish to arrive at conclusions in such cases we must
endeavour to separate the two phenomena. The following are
probably processes in which both phenomena occur together :—
In flame the production of light depends partly upon chemi-
luminescence and partly upon phenomena of ignition, so soon
~ at least as solid particles are separated.
If electric discharges pass between metal electrodes the
metal is disintegrated and volatilized, and the vapour is heated
to incandescence, at the same time it may be brought to
luminescence by the electric current.
If we pass through a tube filled with hydrogen discharges
of such a strength that the line-spectrum just appears, the
hydrogen is far from being heated to the temperature of
incandescence. If, on the other hand, we employ very strong
discharges, we have, in addition to the original luminosity, a
very great rise in temperature, which produces incandescence.
We can expect to obtain an absorption corresponding to
Kirchhoff’s law only for the rays emitted by the process of
incandescence, but not for the others.
The phenomena of long and short lines observed when an
image of a horizontal flame is thrown upon the vertical slit
of a spectroscope depend, no doubt, in part at least, upon
the different processes of luminescence and incandescence.
Several factors are simultaneously concerned in their pro-
duction. Thus, for example, the short lines appear in the
inner portions, and the long lines both in the inner and outer
portions of the flame. But in the inner portions, according
to the usual arrangement of the experiment, both the tempe-
rature and the quantity of incandescent material are greater
than in the external portion. Experiments are in progress to
separate these different conditions ; this is especially important
in order to decide which lines in the spectrum are produced
by luminescence and which by incandescence; and how these
Mechanics of Luminosity. 157
are arranged, as well as on account of their application to the
Giron) lines of the solar spectrum.
Differences in the Mode of Evolution of Light, and of Emis-
sion of Light. Continuous and Discontinuous Excitation.
Store of Luminous Energy.
11. In all investigations on luminosity two chief classes of
phenomena are sharply to be distinguished: first, those where
it is always the same particles which emit the light; and,
secondly, those where continually new molecules take up the
luminous motions. ;
The first is the case in the usual phenomena of luminosity,
fluorescence, electro-luminescence, &c. ; the second case occurs
when the luminosity is produced by chemical changes, e. g.
combustion, oxidation of phosphorus, of lophine, crystallization
of arsenious acid, and, as I shall show further on, also in the
luminous phenomena of phosphorescent calcium-sulphide
compounds.
In the present treatise only the phenomena of the first class
will be treated at length.
12. In considering the mechanics of luminosity, we must
observe that there are two factors to be considered together.
First, a definite amount of energy must be communicated
to the molecules, which gives rise to the production of the
luminous motions; and, secondly, in consequence of the
radiation of light a continuous diminution of this energy is
brought about. The final condition of the body, as far as the
phenomena of light are concerned, depends on the relation
between these two quantities. A stationary condition ensues
when the supply of energy is equal to the loss of energy.
(a) The addition of energy producing light may either be
continuous, or it may be repeated after longer or shorter
intervals.
A continuous addition occurs when a body is brought to
photo-luminescence by means of incident light. The interrup-
tions observed in the phosphoroscope are of course not to be
taken into account, since In comparison with the vibration-
period of light they are infinitely long. To the same category
probably belong electro- and kathode-luminescence ; since in
the anode light the changes in the dielectric polarization of the
molecules produce vibrations, whilst the kathode-rays are
probably connected with the ultra-violet rays*.
A discontinuous excitation occurs in many other cases, as
in glowing gases. In the contact of two molecules a part of
the energy of translation is converted into luminous energy,
* Wied. Ann, xx, p. 781 (1883).
158 Prof. E. Wiedemann on the
a part of which is lost by external radiation on the free path
between two impacts.
The two cases require separate vonsideranae for the mode
of excitation is essentially different. In incandescence it is
the reciprocal relationships between the impinging molecules,
whether of the same, or of different kinds, which produce the
motions causing light ; while in photo- and electro-lumines-
cence these are due to an external motion affecting the
particles.
(b) The loss in luminous energy may also have various causes.
A loss of energy ensues in consequence of the issuing light-
vibrations ; further, in luminescent bodies in consequence of
the impact of two molecules a part of the energy of the lumi-
nous motions may be converted into energy of translation and
thus produce a rise of temperature. Further, within each
molecule only those atoms associated in a particular way, the
chromogenic, which we will here call lucigenic, may perform
luminous vibrations together. These motions may in part be
- transferred to the neighbouring non-lucigenic atoms, and may
thus suffer diminution. According to the structure of the
molecules, only a particular kind of vibrations will be checked
in any high degree, whilst others will remain undisturbed—a
process to which numerous analogies are well known in
acoustics.
We have appropriate examples amongst the phenomena of |
light in the observations on solutions of fluorescein and
eosin'in gelatine, which I have previously communicated’,
where the gelatine is mixed with solutions of the substances
and allowed to dry. In the fluorescent light yielded by these
substances, observed while illuminated, the spectrum appears
almost continuous from red to green. On the other hand, the
phosphorescent light observed some time after the illumination
has ceased, shows a very dark band in the orange. The phos-
phorescent light was examined in the phosphoroseope de-
scribed by me, the arrangement being such that the phospho-
rescent light was examined from the same side as that on
which the incident light fellf. The absorption of the light
excited before the observation was diminished as much as
possible. We must conclude from these observations that in
these bodies the loss of luminous energy for the complex of
rays in the orange is determined, not only by radiation, but
also by an absorption within the molecule itself.
13. We will now consider the intensity-relationships of the
light emitted by a body, and will investigate the two cases :
* Sitsungsber. d. physikal-med. Soc. Erlangen, July 1887.
+ Wied. Ann, xxxiy. p. 453 (1888).
Mechanics of Lunvinosity. 159
first, that the body is continuously excited ; and, secondly,
that at any time the exciting cause is removed, and then the
body, left to itself, gradually radiates its store of luminous
energy.
A. If the body is continuously excited we may use the
equation
MaNb—bi} dio. ee A)
The change of intensity di which occurs in the element of
time dt is equal to the change of intensity ¢dt produced by
the external cause, diminished by the change of intensity bz dt
in consequence of radiation, where we assume that the decrease
in intensity is proportional to the intensity existing at the
moment”,
b is, as follows from the equation, the reciprocal value of
the time in which the unit of intensity is radiated if the radi-
ating body is maintained at unit brightness. The decrease in
brightness may be produced both by radiation and by internal
absorption.
The function ¢ is essentially different according to the mode
of excitation.
For phenomena of photo-luminescence we may assume that
@=AJ, 7. e. that d is proportional to the intensity J of the
incident light. A is the reciprocal value of the time neces-
sary for unit intensity to be excited by incident intensity 1.
We may also say that A expresses how large a fraction of
the incident intensity is converted into excited intensity in
unit time. Then
di=(AJ —bz)dt.
Hence, if C is a constant,
i= + (AT—Ce-¥)
If 7=0, for t=0, then C=AJ, and
Acid ot
eel aes eye. - 2)
If we make some other assumption for the relationship be-
tween the decrease in intensity dz and the intensity 2, equa-
* This equation holds good in the first instance for the communicated
and radiated intensities; but if we assume that the radiated intensity is
proportional to the luminous energy existing at the moment, it may
further be applied without alteration to the intensities of the luminous
motions.
160 Prof. E. Wiedemann on the
tion (1) and consequently equation (2) will take a different —
form; but since with increasing intensity the quantity
radiated must also increase, we shall have an equation analo-
gous to (2). The further conclusions will therefore not be
essentially affected.
Strictly speaking a separate equation of the form of (1) is
required for rays of each wave-length. For the value of 6
may be very different for the rays of different wave-length
emitted, as the experiments described above with eosin and
fluorescein show ; and, again, the value of A is very differ-
ent for exciting light of different colours, as we learn from
numerous experiments with fluorescent substances.
The intensity ¢y of the fluorescent light, 7. e. the intensity of
the light observed upon continuous illumination, is determined
by the value of i for¢=oo. It is so great that the logs is
equal to the gain ; hence d7/dt=0. Hence it follows that
Ph inpeae |
Up — a hg e ° ° ee e e (3)
From this expression we see that the brightness of the
fluorescent light depends upon two quantities—first, on the
fraction of the incident energy converted into light-vibra-
tions ; and, secondly, on the loss of energy determined by 6.
The first quantity is dependent upon absorption &c.; but the
second upon the strength of the emission and the loss of
energy either in the impact of two molecules or in conse-
quence of mutual attractions of the constituent atoms of a
molecule.
The great increase in intensity of the fluorescent light,
which occurs when solutions of fluorescent substances are
thickened by addition of glycerine, gelatine, &., may be
referred to the decrease in that portion of 6 which corre-
sponds to the loss of energy by mutual impacts, since, in
consequence of the greater friction and consequent less
mobility, the molecules of the same kind impinge much
less frequently.
In other cases we may find in solutions of the same sub-
stance in different media hardly any difference in the
intensity of the absorption, but a displacement of the absorp-
tion-bands, as with saffranine and magdala-red, and at the
samme time a complete disappearance of fluorescence. The
explanation in my opinion is to be sought in the forma-
tion of hydrates &c., and a consequent alteration of ab-
sorption-relationship within each molecule in a way as
yy és
i. rc
i:
- ces
Mechanics of Luminosity. 161
yet unmeasurable. FF. Stenger has published another expla-
nation *.
B. Let us now turn to the second case. Let the luminous
energy be brought by any cause to a constant height, and
then at a time ¢=0 let the radiating body be left to itself,
after the exciting cause has been removed. We will further
assume that the loss of energy takes place by radiation and
not by absorption. Further, the luminous energy contained
in a particle shall not receive any further increase during tlie
radiation, in consequence of processes going on within the
molecule itself, or by the impact of two molecules.
If, then, i is the intensity measured in any units, z.¢. the
energy emitted in the unit time at the time ¢, and 0 the con-
stant introduced above, then during the time dé the radiating
body suffers a loss of luminous energy
di= — bidt.
If we integrate this expression from 0 to © we obtain the
total store of energy of the vibrating particles, for in an
infinitely long time all the energy will be radiated; hence
the total luminous energy present is
L= idt =| ige td = 2
: 0 0
If, then, we know the intensity 7 at the time 0, and the
constant b, we can find the total luminous energy contained
in the luminous body under the above assumptions. The store
of luminous energy is equal to ig, the initial intensity, divided
by b, the constant of loss of energy.
Total and True Coefficient of Emission.
14. We may express the energy emitted by the unit weight
of a body in the unit time contained in the rays lying within
an infinitely small breadth of the spectrum between wave-length
»% and A+dr by sdX3; s, would then denote the energy con-
tained in the region between >A and X+1 if at all points
within the same the same energy is yielded as at the point 2;
we may appropriately call s, the true coefficient of emission
at the point A, referring, of course, to the unit weight. The
radiating layer is supposed to be so thin that the absorption
of the emitted rays within it may be neglected. The energy
is to be measured in calorimetric units. If the region of the
spectrum that we are considering extends from A, to Ay, the
* Wied. Ann. xxxiii. p. 577 (1888).
162 | On the Mechanics of Luminosity.
energy emitted is
Ag
Sa =| sadn.
A
The quantity 8, we will designate as the total coefficient of
emission of the unit weight between the wave-lengths A, and Ay.
It is the energy emitted in the unit time by the unit weight
of the body in question corresponding to all rays between the ~
wave-lengths >, and Ay. The two quantities 8, and s) are
exactly analogous to the total quantity of heat necessary to
heat a body from ¢,° to ¢,° and the true specific heat. The two
quantities S, and s, in the form given above have not been
experimentally determined as yet. _We have above all not
referred the emission to a definite quantity of the radiating
body, but only to the unit of surface of the particular body.
The molecular coefficients of emission are obtained by multi-
plying s, and 8, by the molecular weight of the body under
investigation.
15. In this investigation of spectra two problems may
occur. We determine
(1) The total coefficcent of emission 8), between the wave-
lengths A, and A,» of a body which is maintained in a constant
condition (e.g. of a platinum wire of constant temperature).
Then the total coefficient of emission can be determined for
the whole spectrum from ~=0 to X=, or for particular
parts of it, which may ultimately consist of one or more so-
called spectral lines or bands stretching continuously between
every two waye-lengths. Then 8 assumes the value
5, =| sdr and =| r+ | SAN+ ...
0 A;
A3
It is to be observed that the value of the first integral cannot
be directly determined, since we do not know what the radia-
tion is either for very small wave-lengths or for very great
wave-lengths, but our experiments are limited to a very small
portion of the possible rays. Further, we must observe that
in our experiments as soon as s) relates to rays which are
also given off by surrounding bodies, we determine not the
coefficient itself but s,—a,, where a, denotes the coefficient of
emission of the bodies serving for the measurement of the
wave-length X, also in calorimetric measure.
(2) We determine the true coefficient of emission s, for a
single wave-length if belonging to a definite point of the
spectrum. Here we must observe that line-like portions of
the spectrum are not directly comparable with continuous
* ee
On the Thermoelectric Position of Platinoid. 163
spectra, but account must be taken of dispersion (see further
on).
16. For the experimental determination of the two co-
efficients of emission in the visible spectrum measured in
calorimetric measure, we must determine for a definite
body, best a perfectly black one, the radiation in calorimetric
measure, and compare (by the method to be explained im-
mediately) with its brightness that of the body to be investi-
gated, by making the brightness of the two bodies exactly the
same, since with equal brightness the energies of the rays per-
ceived by the eye in the same regions of the spectrum are
equal. We thus fix the ratio of the energies received by the
apparatus ; these are themselves proportional to the coefficients
of emission of the two sources of light, and are further
dependent upon the distance of the luminous body, the thick-
ness of the radiating layer, &. (see further on). Further,
the dispersion must be taken account of.
(To be continued. }
XXV. Note on the Thermoelectric Position of Platinoid. By
J. T. Bottomury, I.A., F.RS., F.CS., and A. Tana-
KADATE, Ltigakust™.
N carrying out a series of experiments on radiation of heat
by solid bodies, an investigation to which one of the pre-
sent writers has for some time past devoted considerable atten-
tion, it became necessary, for a purpose which need not here
be detailed, to select a thermoelectric pair of metals, of which
one metal was essentially platinum, as it had to pass through
glass. Various pairs were considered, and some trials were
made; and it was finally determined to make use of platinum
and platinoid. The latter metal is an alloy whose electrical
and mechanical properties were investigated some years ago
by one of the present writerst; and since that time it has
assumed considerable importance in the construction of elec-
trical instruments and resistance-coils. Partly on this account,
and partly from present requirements, it became both inter-
esting and necessary to determine the thermoelectric constants
for a specimen of this alloy.
Platinoid is in composition very similar to German silver.
In the manufacture of the alloy, however, phosphide of tung-
sten is employed; and although an exceedingly minute
* Reprinted at the request of the Authors, having been read before the
Royal Society, June 20, 1889.
+ J. T. Bottomley, Roy. Soc. Proc, 1885.
164 Messrs. Bottomley and Tanakadaté on the
quantity of metallic tungsten remains in the alloy, yet the
properties of the substance are in many respects remarkable. ©
The metal is capable of being polished so as to be almost as
beautiful as silver in appearance, having only a slightly darker
and more steel-like colour ; and when it has been polished it
remains absolutely untarnished even in the atmosphere of a
large town, for years at any rate. It has very remarkable
properties as to electric resistance. It possesses a very high —
resistance, while at the same time it has a much lower tempe-
rature-variation of electric resistance than any other known
metal or alloy. It has also, as Sir William Thomson has found,
very excellent elastic qualities.
Although it was not proposed to use the platinoid with any
metal other than platinum in the investigation on thermal
radiation above referred to, it nevertheless seemed advisable,
when these experiments were being undertaken, to determine
its position with respect to some other metals. It was accord-
ingly tried as a pair with platinum, iron, aluminium, and with
two specimens of copper.
A low-resistance Thomson’s reflecting-galvanometer was
specially prepared for the purpose of the experiments. The
mirror was a plane parallel mirror of very excellent quality, by
Steinheil of Munich. Its deflexions were observed by means
of a telescope with cross-wires and scale, instead of with lamp
and scale. To avoid any influence of the suspending fibre
(which even though of single cocoon-silk fibre does with
short fibres give an appreciable torsional resistance) the
mirror was suspended by spider-line. The suspending of a
mirror, weighing with its magnet 0:2 gram, by a single
spider-line is a matter of some nicety and difficulty ; but
when it has been accomplished the result is so thoroughly
satisfactory that it is easily admitted to be well worth a morn-
ing’s labour.
To make the suspension, two small pieces of very thin
bristle or of hard-spun silk fibre or split horsehair are attached
to the ends of a suitable length of spider-line recently spun by a
good large spider*. By means of these attachments, which are
easily seen, the spider-line can be handled. It is then brought
over the galvanometer-mirror ; and great assistance is expe-
rienced in these operations, and in operations with single silk
fibres, by performing them on the top of a piece of looking-
glass laid on the table. The illumination from beneath of the
fibres makes it easy to do with these fine filaments that which
is otherwise scarcely possible. The fibre is attached to the
* The body about as large as a pea.
Thermoelectric Position of Platinoid. 165
galyanometer-mirror with the smallest possible speck of shellac
yarnish, the greatest care being taken not to varnish any part
of the spider-line. When the varnish has dried, the. mirror
ean be lifted up by the spider-line ; caution being used at the
moment of raising the one mirror off the surface of the other,
on account of the vacuum which is liable to be formed at the
moment of separation. The mirror should be allowed to hang
on the fibre inside a glass beaker for twenty-four hours at.
least, as the spider-line stretches considerably for some time
after the weight comes on it. A spider-line which will carry
a galvyanometer-mirror and magnet weighing 0:2 gram may -
have, according to an estimate made by one of the present
writers, about 74, of the torsional rigidity of a single cocoon-
silk fibre.
For the heating of the junctions, a number of glass vessels
were blown, resembling the flasks, with neck and condensing-
tube, used for fractional distillation, but with the condensing-
tube projecting upwards into the air, so that the steam of a
liquid boiling in the flask ran back into the flask on being
condensed. Into the shorter neck of the flask was introduced
a cork, which carried the thermo-junction and a mercurial
thermometer ; the thermo-junction being loosely bound to the
bulb of the thermometer, or, at any rate, kept in close contact
with the middle part of the thermometer-bulb. The cool
junction was bound to the bulb of a second thermometer,
which dipped into a vessel containing water at the tempera-
ture of the laboratory. The water was kept thoroughly
stirred from top to bottom by a properly arranged stirrer.
In the heating-flasks the vapours of the following liquids
were used :—alcohol, water, chlorobenzol, aniline, methyl
salicylate, and bromobenzol*. The liquids were boiled
vigorously, and the temperatures of the vapours were deter-
mined by means of the mercurial thermometer. Both the
mercurial thermometers were compared directly with the air-
thermometer ft. The obtaining of a set of points of tempera-
ture by this means was very satisfactory in every case except
that of the liquid of highest boiling-point—bromobenzol. In
this case a curious phenomenon was observed}. In spite of
the fact. that the vapour of the substance was rushing strongly
into the condensing-tube, and, indeed, out into the open air
at an elevation of two feet above the surface of the liquid, it
was found exceedingly difficult to keep the temperature of the
various parts of the boiling flask anything like uniform. The
* Ramsay and Young, Chem. Soc. Journ. (Trans.), 1885.
1+ J. T. Bottomley, Phil. Mag. August 1888.
_ { Perhaps due to want of purity of the substance.
ive Mag. S. OeVol, 28. No. 172. Sept. 1889. O
166 Messrs. Bottomley and Tanakadaté on the
vapour formed itself into layers of different temperatures, the
parts of the flask nearest the surface of the liquid being the
hottest. Ata height of 24 inches above the surface of the
liquid the temperature was often found to be as much as 8° or
10° C. cooler than it was just above the surface. The diffi--
culty could, to a certain extent, be overcome by putting a
cloak of fine flexible wire gauze all round the upper part of
the flask; but the greatest watchfulness was needed to avoid
mistakes.
In order to reduce the results obtained from the readings
of the galvanometer to absolute electromagnetic measure, a
carefully prepared standard Daniell’s cell was kept with its
current always flowing through a known high resistance : and
from time to time the galvanometer which was being used was
thrown into the circuit, and the value of the galvanometer-
deflexion determined. ‘The electromotive force of the Daniell’s
cell was valued at 1:072 volt.
The results obtained are shown in the accompanying curves
and tables,
7X _ Es |
Seu eeeee) oan
eT ee
eee cea
(oR Ae ees
|
fof
An ae
|
|
|
cS
ie
‘Bree e o cane
BME Cn Traité de U Lléetricité, iv. p. 151.
* Luke Howard, ‘Climate of London,’ cites examples of luminous hail.
> Quoted in Priestley’s ‘History of Electricity.’
® Bertholon, De ? Electricité des Météores, ii. p. 159, This was at one
time a work of considerable authority.
7 Elements of Meteorology, 3rd edition, 1845, i. p. 241.
the Theory of Hail. 171
the French grésil), and does not accompany a thunderstorm, he
classes with the hail, properly so called, that often does do so.
He regards both kinds as electrical phenomena, only the elec-
tricity has more tension in the one case than in the other. But
when a man is on a wrong tack, he is sure to meet with facts
that contradict his hypothesis. In such cases Kamtz’s aphorism
will apply to many an observer :—‘‘ Man glaubt dennoch was
man gern wiinscht ;” but it does not apply to Kamtz himself,
for he honestly states facts that are against him, and waits for
further light. Thus: he has occasionally noticed larger hail-
stones in winter than in summer, although there is more moisture
in the air in the latter season than in the former. Smaller hail
is found on the top of the mountain than in the valley below,
just as if the increase in volume took place during the fall.
The inhabitants of mountain districts speak of Graupel, whilst
those in the valley refer to it as Hagel,
The advocates of the electric theory of hail had no better
method of accounting for the large masses that fell, consisting
often of a number of coatings round a nucleus, than by sup-
posing that a small stone gathered to itself clear and opaque
coatings of ice during its descent. This idea prevailed long
after Volta attempted to explain the formation by a well-
known electrical process. Mrs. Somerville ® adopts this view;
and Prout?’ supposes that there must be formed an icy nucleus
far below the freezing-point, acquiring magnitude as it
descends by condensing on its surface the vapour of the
lower regions of the atmosphere.
As the formation of hail was firmly believed to be an effect
of the sudden disturbance of the electrical equilibrium of the
clouds, it was supposed that if the electric fluid could be
quietly and gradually drawn away hail would be altogether
prevented. Accordingly, soon after the introduction of the
lightning-conductor ( paratonnerre), 1t was proposed in France,
where hail is regarded as a real scourge, to introduce a hail-
conductor (paragréle)**. For this purpose, tall wooden poles
were erected, furnished at the top with a sharp copper point,
and connected by means of a metal wire with the ground. In
some cases the wire was omitted, but as wood is a bad conductor
it is difficult to see the use of the poles (even supposing the
theory that erected them to be valid). It was even contended
that the poles were equally efficacious with or without the
wires ; and this we can readily believe, seeing that a tree ought
to be more efficacious than the pole, in consequence of its
greater elevation and the multitude of points presented by its
5 Physical Geography. ° Bridgewater Treatise.
10 Journal de Physique, 1776.
172 Mr. Charles Tomlinson on
twigs and leaves. Nevertheless, hail was known to be of
frequent occurrence in well-wooded localities, also in towns
where lightning-conductors were common. In spite of this,
vast numbers of poles, with or without metal wires, were
erected at great cost in fields and vineyards in various parts
of Hurope ; and in 1820 an ignorant apothecary recommended
pillars of straw as being excellent paragréles, and they, too,
were extensively adopted. Well may Becquerel denounce the
paragréle as “ cette invention de lignorance dont la science et
le bon sens public ont déja fait justice ” !
Other methods of guarding against hail have been recom-
mended and adopted, such as making fires on the ground on
the approach of a storm, discharging artillery and otherwise
exploding gunpowder ; but these methods must be classed
among the inventions of ignorance, although so good an
observer as Matteucci! refers to a village in Italy where the
peasants, acting under the advice of the Curé, place, at
intervals of about 50 feet, heaps of stones and brushwood, and
set fire to the latter when a storm is seen to be approaching.
The plan had only been adopted three years when Matteucci
made his report, and that is too short a time to base any con-
clusion on ; but it has been suggested that, while hail does
great damage in the outskirts of London, it is less harmful in
the denser part of the metropolis, probably on account of the
vast column of heated air that rises from it altering the local
atmospheric conditions required for the production of large
hail.
The occurrence of hail in hot weather, often at the hottest
part of the day, sometimes in the form of masses of ice of con-
siderable size, apparently from a cloud situate far below the
snow-line, is a problem that has often appealed to the scientific
ingenuity of physicists for solution. As already remarked, the
accompanying electrical displays naturally led to an electrical
theory, of which Muschenbroek” was the original parent.
He was succeeded, amongst others, by Mongez 3. Muncke™,
De Luc”, Lichtenberg", “Lampadius” , and lastly, by Volta®
Now, as the inventor of the pile and of the electrophorus took
higher rank as an electrician than the others just named
(whose hypotheses he doubtless had examined), it will be
11 Avago, Meteorological Essays, Sur la Gréle.
2 Introduction. 2 _ Jour nal de Physique, vil. a 202.
14 Gehler’s Worterbuch, v. p. 54. > Idées, ii. sec. ili. chap. 2
16 Schriften, vill. p. 88. ria Re ol, p. 153.
18 Sopra la Grandine, Opere, i. part 11. p. 353.
the Theory of Hail. 173
suficient for our present purpose to give an outline of his
theory.
This theory has first to account for a reduction of tem-
perature sufficient to freeze water on a hot day, and then to
explain how the hailstones, so formed, can be held suspended
in the air so as to attain a volume often of several inches
in circumference. The cold is supposed to be produced by a
powerful evaporation, due to the action of the sun on the
upper surface of the cloud; and the evaporation is the more
rapid in proportion as the air above the cloud is rarefied and
electric, for it is admitted that electricity greatly favours eva-
poration. Hence one portion of the cloud, in evaporating,
lowers the temperature of the other portion sufficiently to
produce congelation. |
The nuclei of the hailstones being thus formed, they cannot
attain fresh coatings of clear transparent ice, however low in
temperature they may be, in the short time they are falling to
the earth; but it is in the power of electricity so to sustain
them, while they are thus being developed in volume and
weight.
Let us suppose that a cloud, strongly electrified, is suddenly
congealed at its upper surface, in consequence of an energetic
evaporation. The result will be a multitude of small frozen
particles which form the nuclei of the hailstones. These
particles, repelled upwards by the strong electric action of the
cloud, are held suspended at a certain distance, just as a
feather is when an excited glass tube is held under it. In
like manner, if these frozen particles are placed on an insulated
horizontal plane, and this be strongly electrified, they will rise
up into the air and remain there so long as the plane retains
its electricity, or until they lose their electric charge, when
they will fall back by their weight upon the plane, and take a
fresh charge and be again repelled. During these motions
the hailstones increase in volume by condensing the vapour
of water upon their surfaces, and this immediately becomes
solid. A few of the stones increase in size more rapidly than
the others, and these are the first to fall—the avant couriers
of the general shower of hail when the weight of the individual
stones is too great for the electric force to maintain them
suspended. .
But the action above described is more complete by sup-
posing the existence of two or more clouds, one above the
other, in opposite electrical states. In such case the motion of
the frozen particles is much more rapid ; it is like the pith
figures oscillating between two metal plates in opposite elec-
174 _ Mr Charles Tomlinson on
trical states, when the attractions and repulsions are performed
with great celerity, and the hailstones, being equally active,
produce that peculiar noise that precedes a fall of hail ™.
Volta’s theory has frequently been discussed, and objected
to on many grounds. SBecquerel points out the mistaken
notion that vapour in the act of forming becomes negative,
and while being condensed positive. When a dense cloud is
acted on by the sun, vapour arises charged with the same
electricity as that of the cloud; but when, on reaching an
upper and colder region, it becomes condensed, it is said
to assume an opposite kind of electricity. But the clouds are
not electrified after this manner, seeing that electricity is not
set free by change of state, unaccompanied by decomposition.
Moreover, the question arises why the two clouds in opposite
states, connected as they are admitted to be by conducting
particles of vapour, do not immediately neutralize each other.
The oscillations of the hailstones between the two clouds could
only take place if the clouds were solid planes, as in the expe-
riment with the dancing pith figures. Then, again, the snow-
flakes which form the nuclei of the hailstones are said to be
formed at the upper surface of the lower cloud, and hence
must form a portion of it; how, then, can they be driven out
of it without breaking up the whole cloud? Even supposing
them to have reached the upper cloud, they must form an
integral portion of it, and can escape from it only by their
weight, and falling upon the moist surface below must be
detained there, as in the dancing-figures experiment, if,
instead of the lower metal plate, a surface ot water be sub-
stituted, the adhesion between this and the pith figure is so
great that further motion ceases.
It will be remarked that in Volta’s theory the action of the
sun 1n promoting the evaporation of the cloud is all important.
This might be admitted if hailstorms occurred only by day ;
but such storms may occur at any hour of the night as well as
of theday. Kéamtz has collected a long list of nocturnal hail-
19 The sound that precedes the fall of hail is supposed to be due, not
only to the rattling of the stones against one another, but also to the fierce
wind from all quarters that usually accompanies a hailstorm. The sound
has been variously compared to the rushing or roaring of waters, as when
Morier, in Persia, thought that the river had suddenly swollen into
a torrent. Kiamtz likens the sound to the rattling of a large bunch
of keys; Peltier to that of a flock of sheep galloping over a stony road ;
Daniell to the emptying of a bag of walnuts. Others speak of the noise
as crackling, chattering, clashing; and Volta regarded it as one of the
strong proofs of his theory. It should also be stated that the noise has
been attributed to the combination of the individual sounds produced by
each hailstone cutting the air with great swiftness.
the Theory of Hail. 175
storms, dating from the year 1449 to his own time. One
example will suffice for our present purpose. At midnight,
between the 25th and 26th June, 1822, a violent storm of hail
burst over Meissen, and the next morning the farmers had to
mourn the entire loss of their crops of fruit and grain, and
they found hundreds of starlings lying dead in the fields.
Another objection with respect to the sun is that, if it —
promotes evaporation, it also raises the temperature, as was
shown by Bellani®’, who covered the bulbs of two thermo-
meters with wet linen, and exposed one to the sun and the
other to the shade. Evaporation was the more rapid in the
sunshine, but the temperature was higher; whereas, according
to the theory, it ought to have been lower, even to freezing.
The celebrity of Volta’s name gained for his theory much
attention, and with some modifications it was more or less
adopted. Perhaps the most distinguished physicist who
quarrelled with it, and yet put forth a theory very much like
it, was Peltier ”*, who, in announcing it, complacently remarks
that “‘ Volta a placé des suppositions ot je place des faits.”’
Peltier also imagines two clouds in opposite electrical states,
placed one above the other. Their mutual attraction is con-
siderable ; they approach without any notable discharge, but
the electricities are exchanged, and there can be no such
exchange without producing vaporization of the minute drops
or vesicles which compose the clouds. Hence there is a
lowering of temperature, rapid in proportion to the electric
tension of the two clouds. Should the temperature of the
clouds be considerable, no noticeable effect ensues ; but if one
be at or below the freezing-point, some portions of the cloud
that had not been vaporized are converted into flakes of snow,
which act as nuclei to the hailstones. These flakes are quickly
surrounded by condensed water, which freezes into trans-
parent ice. The globules fall by their own weight from the
upper to the lower cloud, where they become recharged and
wetted. They are then attracted by the upper cloud, change
their electricity, and become reduced in temperature by radia-
tion and evaporation, and so acquire a new coating of moisture,
which freezes. They again return to the lower cloud, and thus
by a series of oscillations increase in volume until they become
too heavy for the attractive force of the electricity, and they
fall to the ground.
Many of the objections urged against Volta’s theory apply
also to Peltier’s. But in matters of science the authority of
a great name is so potent that a false theory stamped with it
will retain its vitality long after its funeral obsequies have
°° Brugnatelli’s Giornale, x. p. 369. 21 Météorologie, chap. xvl.
176 Mr. Charles Tomlinson on
been performed. ‘Thus in ‘ Nature,’ for June 13th last, an
account is given of a hailstone that fell at Liverpool on the
2nd of that month at 3.35 p.m., consisting of an opaque
nucleus surrounded by a circle of almost clear ice with fine
circular lines, and that was bounded by a frilled outline of
opaque ice. ‘The writer goes on to say :—‘‘ If a hailstone is
formed during electric oscillation from cloud to cloud, and if
it receives opaque ice from one cloud and clear ice from
another, the alternation of layers would be a natural conse-
quence. The violence of the hail scarcely seemed as great
as their size justified, and this suggested that electrostatic
attraction had upheld them against the force of gravitation
down to a moderate height above the ground.”
Of course it is not meant to deny that in the formation and
fall of hail two or more layers of cloud may exist in opposite
states of electricity. All that modern theory contends for is
that the electricity and the hail are not related as cause and
effect. The hail-clouds do not often, if ever, assume the well-
defined planes described in Volta’s theory. Hail-clouds are
generally very massive, of a peculiar ash-grey colour, very
different from that of other clouds ; the edges are much rent,
and there are swellings and outgrowths on the surface. On
some occasions the hail-cloud is made up of rounded clustered
masses with long processes shooting downwards almost to the
earth, before it discharges its icy load. Péron*” gives an
account of a storm at Sydney, in Australia, in which there
were several layers of cloud. In the morning the weather
was fine and the sea tranquil, but soon after noon the wind
suddenly veered to the N.W. blowing in squalls. An enor-
mous mass of black cloud was driven by the wind from the
summit of the Blue Mountain into the plain below, and it
seemed so dense as to cover the face of the ground. The
heat became overpowering, the thermometer rising suddenly
from 73° to 95°F. The clouds burst open with a fearful
noise, and a dazzling lightning of a bluish colour everywhere
prevailed. The wind blew from all points of the compass,
and its violence increased in proportion as the disorder and
change in direction became more evident. Hach time that a
fall of heavy raindrops occurred, the end of the storm was
looked for, but each time also there fell a copious hail frem a
cloud that was far higher and blacker than alt the others.
M. Le Coq” describes a storm among the mountains of
Auvergne, where the hailstones were mostly of the size of a
22 ‘Voyage, 1. p. 396.
23 Quoted by M. de la Rive in a paper On the Formation of Hail,”
Edinb. New Phil. Journ. xxi. p. 280.
“the Theory of Hail. — ‘177
pullet’s egg, but some as large as a turkey’s. There were
two strata of clouds, one over the other, and two winds from
different quarters, both which conditions he considers necessary
for the production of hail. Harly on the morning of July
28th, 1835, the sky was cloudless, but about 10 a.m. the heat
became intense, and at noon almost intolerable. Thin flakes
of vapour were seen floating at a great distance, the wind.
was N. but feeble. At 1 p.m. it had freshened, and white -
clouds had descended considerably, and soon after covered a
great part of the horizon. They were of a greyish tint,
which became darker and darker till nearly black, and at
2 p.m. they covered the whole of Auvergne. Flashes of
lightning were seen, and a distant low murmuring sound was
heard, when a vast cloud advanced from W. to H., pure white
in some places, chiefly at the edges, and deep grey at the
centre: it seemed to advance rapidly under the impulse of a
violent west wind, and it sailed below all the other clouds ;
its borders were festooned and deeply slashed, and pro-
tuberances in the shape of long nipples were suspended from
the lower portion. At 2.15 the cloud had approached nearer
and the noise became very intense, the edges of the cloud
seemed to be in rapid motion, and hail was apparently within
it. Soon after this whirlwind kind of motion hail fell, and
did much damage, it being propelled by the N. and the W.
wind, it took the mean direction. ‘The hailstones that now
fell succeeded one another very slowly, but all at once there
was an immense downpour. After this the distant rolling
sound entirely ceased, and the cloud, freed from its swelling
appendages, was carried away by the wind, and the storm
was over.
It was from narratives such as the above that meteorologists
began to turn their attention from electricity to the cyclonic
action of the wind, as the efficient cause of the formation of
hail. Thus Kimtz attributed such formation to the low
temperature of the upper atmospheric strata in which the
watery particles solidify, and Muncke to the meeting of cold
and warm winds. Sir John Herschel** also suggested that
the generation of hail seems always to depend on some very
sudden introduction of an extremely cold current of air into
the bosom of a quiescent, nearly saturated mass. So long
ago as 1830 Professor Olmsted” realized this idea by means
of the cyclone, in which a mass of air revolving round an axis
more or less inclined to the earth is more or less highly
rarefied at or about its vortex, and is thus in a condition to
*4 Scientific Essays.
*6 American Journal of Science, xvii. p. 1.
178 Mr. Charles Tomlinson on
draw down cold air from above, or draw up warm moist air
from below, in either case supplying some at least of the con-
ditions for the generation of hail. The diminution of the
temperature of the air with the altitude may be roughly stated
as one degree I’. for every 343 feet of ascent, and the point
of perpetual congelation at and above the equator 14,000 feet ;
at 380° 12,000 feet; at 40° 10,009 feet ; at 50° 8000 feet ;
at 60° 6000 feet; at 70° 4000 feet; at 80° 2000 feet, and
after this the point rapidly approaches the earth.
Prof. Olmsted’s theory has been admirably elaborated by
the officers of the United States Coasts Survey, as will
presently be noted. In the meantime a few cases may be
cited to show how the idea gradually became developed into
the present consistent theory. Thus Mr. J. C. Martin”, of
Pulborough in Sussex, writing in 1840, refers to masses of
ice having fallen five, six, and seven inches in circumference,
and goes on to state that there can be only one way by which
such masses are suspended in the air long enough to grow to
such a size, and that is by the assistance of a nubilar whirl-
wind or waterspout. He states that he once witnessed an
appearance of this sort between a higher and a lower cloud,
that had a strongly electric aspect before they had resolved
themselves into mmbus. It was a bent massive column of
dark vapour in rapid rotatory motion, passing from one cloud
to the other, continuing for some minutes, and gradually
disappearing. The hailstones are described as_ spheres
flattened at the poles, the result of rotatory motion. In a
hail-storm which devastated Dublin on April 18th, 18507’,
some observers state that they saw two strata of oppositely
electrical clouds and discharges passing between them, and
that the hailstones were as large as pigeons’ eggs, and were
formed of a nueleus of snow or sleet, surrounded by transpa-
rent ice; this was succeeded by an opaque white layer,
followed by a second coating of ice, and, in some examples,
five alternations were counted. The storm is described as a
cyclone, but Mr. Piddington, in quoting it, prefers to call ita
tornado. He also remarks on a common entry of the logs of
ships, which have been involved in cyclones, and especially if
near the centre, of “ rain as cold as ice,’ “ sea-water warm,
rain bitterly cold ;”’ also, ‘‘ rain accompanied by sleet.”
In the account of the “ Duke of York’s”’ cyclone, the entry
occurs twice—“ Cold most intense during the hurricane.”
The enormous force with which hail is sometimes projected
almost horizontally indicates a force very different from
26 Quoted in Piddington’s Sailor’s Horn-Book, 1860.
7 Ibid.
the Theory of Hail. — 179
gravitation. In a storm described by Luke Howard 78, that
occurred at Tottenham on the 19th April, 1809, at 5 p.m., the
icy bullets, some of them a full inch in diameter, were dis-
charged almost horizontally, and with such velocity that in
‘many instances a clean round hole was left in the glass they
pierced, and one large pane had two such perforations, dis-
tinctly formed, the glass being otherwise whole. The com-
paratively small width of the hail’s track is also in favour of
the cyclonic theory, although the length may be considerable.
The great storm that began in the south of France early on
the 13th of July, 1788, extended in a few hours over the
whole kingdom, even as far as Holland. It proceeded in two
parallel zones from S.W. to N.H.; one zone was 175 leagues
in length, and the other 200 ; the breadth of the western zone
was four leagues, and of the other only two. The zone between
the two was five leagues wide, but no hail fell there, only
heavy rain. There was also rain on the outer boundary of
the two zones. A thick darkness accompanied the hail, and
spread on both sides. The storm travelled at the rate of
1624 leagues an hour in both zones. Upwards of a thousand
parishes were ravaged by this storm.
Turning now to Mr. William Ferrel’s theory” of the
formation of hail in connexion with a tornado or cyclone, he
calculates in an assumed example that the plane or stratum
of zero temperature is 6428 metres above the base of the
cloud, and in the absence of friction may be supposed to be
brought down to the earth in the centre, where the gyrations
are very rapid. Below this base aqueous vapour is condensed
into cloud and rain, but above it into snow. The rain-drops
below may also be carried up into the snow-region in the ascend-
ing currents, and if kept suspended there fora short time they
may become frozen into small hail. They may then be kept
suspended near the base of the snow-cloud, and increase in
size by the rain, which is carried up into this region, coming
into contact with them before it has had time to freeze. In
this way compact homogeneous hailstones of ordinary size
are formed. At the height of nearly 7000 metres the density
of the air in comparison with that at the earth’s surface is
0-42, and it is calculated in the assumed example that a
velocity of 20 metres per second in the ascending current will
sustain a hailstone one centimetre in diameter at that altitude.
This is no unusual velocity for ascending currents in tornados.
It is not necessary that the hailstones should remain long in
8 Climate of London.
*° United States Coasts Survey. Meteorological Remarks for the
Use of the Coast Pilot, part ii. p. 85. Washington, 1880.
“ae
Ss Tos
Be. te aaah sai
‘ ical ’
s) an
180 Mr. Charles Tomlinson on
the freezing region, or even be stationary. They may be :
carried from the vortex out where the velocity of the ascend-
ing current is small, and dropping down some distance may
then be carried in towards the vortex by the inflowing current
on all sides, and up again rapidly into the freezing region.
The nucleus of large hailstones is generally composed of
compact snow. A small ball of snow saturated with unfrozen
rain, which is carried up into the snow-cloud, is formed in
that region and freezes, and being of less specific gravity
than compact hail is kept where it receives a thick coating
from the rain carried up, as in the case of the small hail, and
afterwards falls to the earth, either at some distance from the
centre, where the ascending currents are weak, or near the
vortex after the rapidity of the ascending currents has become
sufficiently diminished. Asthere may be in the case of cloud-
bursts a great accumulation of rain, and a sudden down-
pouring of it, all in a short time, so in a hail-storm a great
quantity of hail may be collected in the lower part of the
cloud, brought in by inflowing currents on all sides towards
the vortex, after the ascending currents have become too weak
to carry it up and again throw it out above, and are still too
strong to permit it to fall. But soon the interior of the
tornado becomes so overloaded, and the energy of the whole
system so much spent that the hail falls to the earth almost at
once. Hence the large quantities of hail which sometimes fall
in a short time.
-When a hailstone is carried up in or near the vortex, and
carried out above to where the ascending current is too feeble
to sustain it in the air, it gradually drops down, and the inflow-
ing current draws it in towards the vortex, where it is again
carried up, and thus describes a sort of oval orbit. It may
be thrown up very high into the snow-cloud region, or but
little above its base. It may describe a number of such
orbits or revolutions before it falls to the earth. While high
up in the snow-cloud region it receives a coating of snow;
and then, while descending very gently, where the strength
of the currents is not quite sufficient to sustain it, and near
the base of the snow region, where rain yet unfrozen is carried
up, it receives a coating of solid ice, which may be continued
for some time after it falls into the rain-cloud, since the hail-
stone still continues for some time below zero. After a short
time the inflowing current below draws it again into the
vortex, where it is again thrown up into the snow-region to
receive a new coating of snow. It thus receives alternate
coatings of snow and ice, and the number of each sort denotes
the number of revolutions described before it falls to the
the Theory of Hail. | 181
earth. When we consider the enormous amount of water
which is rapidly carried up in a tornado, and that the lower
part of the region of freezing must contain mostly rain not
yet frozen, since the snow there formed is at once carried still
higher, we can readily understand how the hailstone can _re-
ceive a considerable coating of ice ina short time. While
high up in the snow-cloud at its turning point, it of course
remains some time nearly at the same altitude, and it is
reasonable to suppose long enough to receive its coating
of snow®*”.
Hailstones vary greatly in shape as well as in weight.
Some resemble a disk, or very oblate spheroid. If for any
reason the hailstone becomes in the least flattened, the ascend-
ing current which keeps it suspended in the air also keeps its
shortest diameter perpendicular to the current, and hence it
increases most on the edges. Others are of a pyramidal
form.
Enormous masses of ice are reported to have fallen from
the sky from time to time, but these seem to have consisted
of a vast number of hailstones swept into hollows or
cavities by the wind, and united by regelation. Nevertheless,
some of the masses that are known on good authority to have
fallen are sufficiently formidable. Mr. Darwin” refers to
cases in South America of hailstones sufficiently large to kill
deer, and many cases are recorded of hailstones in India
large enough to kill men and cattle**. The hailstones chiefly
occur in the driest months, February, March, and April ;
they are well known in the Delta of the Ganges down to the
sea, in other places 1500 feet above the sea ; in Ceylon the
storms are formed by violent whirlwinds and eddies. Thus
on May 12th, 1853, a storm occurred in the Himalayas,
when the hailstones were very hard, compact and spherical,
3° In a hailstorm at Northampton, Mass., June 20th, 1870, two hail-
stones fell weighing over half a pound. One is described in Silliman’s
Journal 1. p. 405, consisting of thirteen layers, like the coats of an onion.
It must have oscillated as many times between the rain-cloud and the
suow-cloud region; that is, it performed six or seven revolutions with
the lower part of its orbit in the rain-cloud, and the upper part in the
snow-cloud.
$1 On this subject see a paper by Professor Osborne Reynolds on
Raindrops and Hailstones in ‘ Nature,’ Dec. 21st, 1876.
3° Journal of a Naturalist.
33 See a paper by Dr. George Buist, F.R.S., on Hailstorms in India,
read before the British Association in 1885. The writer corrects the
statements of Dr. Purdie Thompson and others that hailstorms are nearly
unknown between the tropics.
Phi Mag.8.0.¥ ol. 28. No. 172. Sept. 1889, ie
182 Mr. Charles Tomlinson on
many of them measuring 33 inches in diameter, or nearly a ‘
foot in circumference ; 84 human beings and about 8000 oxen
were killed. At Nainee Tal, a sanatorium in the Lower
Himalayas, the noise of the approaching storm was as if
thousands of bags of walnuts were being emptied in the air.
The hail that first fell was of the size of pigeon’s eggs, and
at length became of the size of cricket balls. Dr. Buist
describes the largest hailstones that fell in India as from
10 to 18 inches in circumference, and from 9 to 18 ounces in
weight; the average maxima are from 8 to 10 inches in
circumference, and 2 to 4 ounces in weight, but ordinary hail
exceeds filberts in size.
In the accompanying Plate (IV.) I have collected some re-
markable figures of hailstones, a number of which (1 to 8) fell
during a storm which I witnessed at Leipzig on August 27th,
1860. I was proceeding by rail from Cassel to Leipzig ;
the day was hot, and the afternoon sultry, the thermometer
marking 22°R. (813° F.).. About 4 p.m. copper-coloured
clouds appeared in the west, the sky darkened, and about
6.30, when close to Leipzig, a black cloud, streaked with white
bands, rose up like a pillar; there was a flash of lightning,
and as soon as the thunder had ceased, a rattling noise was
heard, which was succeeded by a shower of large hail. Just
before this I had quitted the railway-station in a drosky, the
flexible leathern covering of which was drawn down, and
the windows on each side were up. The carriage had not
quitted the station when a fiercely wailing wind twisted the
leathern covering from its fastenings ; it fell upon my head,
when I felt a succession of rapid blows, and heard the crash-
ing of the window-glass ; the horse was rearing from fright,
but the porters secured it, and brought the vehicle under
cover. I picked up some of the hailstones, placed one on
paper, and drew a pencil round it. It consisted of a nucleus
of clear ice in the form of a flat spheroid, surrounded by
semiopaque ice with lines radiating to near the circum-
ference, as shown in fig. 1. Other stones were more irregular,
as in fig. 2, where the opaque nucleus is surrounded by clear
ice, this by opaque, while the outside layer is clear. TVigs. 3,
4, 5 are from drawings made at the time, and inserted in the
Leipzig illustrated papers. Figs. 6 and 7 represent a stone
with ice crystals on a portion of the surface, while the other
portion is smooth and rounded, as shown in the outline
34 The details of this storm are abridged from a work of mine entitled
“The Rain Cloud,” published in 1876 by the Society for Promoting
Christian Knowledge.
the Theory of Hail. 183
fig. 7. Fig. 8 seems to be a happy example of regelation.
It broke through the studio window of the artist Georgy,
who immediately made a sketch of it. It was of bright
transparent ice, very hard and strong, with a cavity at the
top large enough to admit the little finger. It was described
as a perforated hailstone ; but the nucleus which occupied the
cavity seems to have fallen out before the artist sketched it.
Some of the stones weighed 5 oz., and the damage to trees,
crops, and fruit, glass windows and roofs was considerable ;
curtains and blinds were torn into tatters; the furniture of
rooms, including pictures and mirrors, was also injured, and
in the fields large numbers of hares and rabbits were killed.
A curious example of the force of the icy bullets was shown
in the destruction of the new cane-bottom of a chair. It
would be supposed that so elastic a material would cause the
hailstones to rebound. Zinc water-pipes were shot through,
and in one case a pipe was flattened.
The extent of this hailstorm was about 25 miles in length
by 5 miles in width, and the damage was very unequally
distributed. The whirlwind character of the storm was
noticed by many observers. The hail was preceded by rain-
drops of large size, after which the rain and hail became
mingled in one grey white fog, in which the leaves and twigs
of trees, brought apparently from a distance, were seen whirl-
ing round. Other proofs of this whirling motion were shown
in the unequal action of the storm in different parts of its
comparatively narrow limits, and the various angles at which
hail fell in different parts of Leipzig. ;
The storm of hail was over in about ten minutes, and the
temperature fell from 814° F. to 454° F.
Figs. 9 and 10 represent in front and in section a beautiful
example of the structure, so often referred to in this article,
of alternate coats of opaque and transparent ice round a
nucleus *.
The four figures, 11 to 14, are from drawings made by my
King’s College colleague, Mr. H. Hatcher. The stones fell
during a thunderstorm on the 22nd May, 1865. Fig. 11
shows layers of clear and opaque ice. Fig. 12 is apparently
the end of a stone broken in the fall. Fig. 13 is a smaller
stone of similar structure, and fig. 14 represents a stone show-
ing a mammillated termination. Such was the general struc-
ture, but some of the smallest stones were nearly spherical,
and entirely of clear glass-like ice. The largest stone observed
* ‘These figures are from Buehan’s Meteorology, 2nd edition, 1868.
R2
184 On the Theory of Hail.
was 2 in. long, and $ in. indiameter. All the perfect stones
(except those of clear ice) had a distinctly fibrous structure,
and were more or less pear-shaped, unless broken in their fall.
Some showed only two broad bands, others as many as five
or six.
Figs. 15 and 16 represent two different forms of hailstone,
which fell during a violent storm in Cambridgeshire, on
August 9th, 1843. Some of the stones were so large that
they stuck in a wine-glass°*®.
Vig. 17 represents a hailstone that fell in Georgia on May
27th, 1869. It was picked up, together with others like it,
and drawn at the time by Staatsrath Abich, and described by
him in a letter to Chevalier W. von Haidinger®’. Similar
stones also fell on June 9th at 6 p.m. They were 2% in.
in diameter, spheroidal, of definite crystalline structure, over-
grown along the plane of the major axis by a series of clear
crystals, exhibiting various combinations belonging to the
hexagonal system. The most abundant were combinations
of the scalenohedron with rhombohedral faces, crystals ? in.
in height, and corresponding thickness, prettily grouped, with
combinations of the prism and obtuse rhombohedron. The
terminal plane was also occasionally noticeable. Some which
fell at the beginning of the storm were flat tabular crystalline
masses 14 in. in diameter. The ring surrounding the nucleus
had a milky appearance from the presence of small air-bubbles,
as had the nucleus itself in most instances; many had also a
clear nucleus. In melting down, some of the stones took the
shape of a regular hexagon. The milky ring round the
central point was a sort of fibrous web, composed of the
finest air-cavities, traversed by thread-like pores. Some of
the air-bubbles were pear-shaped or worm-like, running from
centre to circumference. The crystals were attached para-
sitically to the edge of the stone, or else inserted in a kind
of socket, as was noticed when the stones thawed down.
Highgate, N., July 1889.
36 Observations in Meteorology, by the Rev. R. Jenyns, M.A., F.L.S.
37 Journal of the Austrian Meteorological Society, iv. p. 417, translated
into the Annual Report of the Board of Regents of the Smithsonian
Institution for 1869, Professor Henry was kind enough to send me a
copy of this work.
E 185°")
XXVII. On Endless Availability ; and on a Restriction to the
Application of Carnot’s Principle. By Caries Y.
Burton, D.Sc.*
a the following pages some experiments are described
, which appear to be in obvious disagreement with the |
Second Law of Thermodynamics. The first apparatus used
is shown in fig. 1. A piece of glass tube, A, is closed below
by a dialysing membrane, B, tied
over it in the usual manner. It
contains a solution to be dialysed,
and is supported within a beaker, OC,
by wedges of cork, D, H. The
beaker, C, stands on a glass plate,
I’, the whole being covered by a
bell-jar, G H, which is luted with
wax round the edge, K L, so that
evaporation from the solution in
the dialyser is prevented as far as
possible. The beaker, QC, is at first
empty; and when a certain portion
of the solution in A has passed into
it through the membrane B, the process is stopped by taking
the apparatus to pieces and mixing the solutions. A thermo-
meter measures the rise or fall of temperature which ensues.
Experiment I.—A saturated solution of normal sodium
sulphate (Na,SO,, 10H,O) was placed in the dialyser, together
with a crystal of the salt. Contrary to anticipation, 1t was
found after some days that the crystal had entirely disappeared
and about ? of the solution had passed through the dialyser.
When the experiment had lasted 14 days, about 2 of the
solution had passed through, The solutions in A and C were
then mixed, and the temperature rose 1°2 (Centigrade). By
next day some crystals had been deposited from the mixed
solutions; and had this crystallization taken place under
adiabatic conditions, there must have been a further elevation
of temperature. ‘The following are the details of the experi-
ment :-—
1888. Oct. 26; 5.10 p.m. Solution of sodium sulphate
saturated at 15°, together with a crystal of the salt, placed in
dialyser and completely protected from evaporation,
Nov. 9; 4.5P.mM. About 8 of the solution has passed
through ; no crystal remains.
Fig. 1.
* Communicated by the Author.
186 Dr. C. V. Burton on Endless Availability ; and on a
Temp. of thermometer, which has lain
ce)
beside the apparatus for 14 days =14:2
Temp. of solutions in A and in 0 = 142
Temp. of solutions after mixing =15°4
Rise of temperature == 41:2
Nov. 10. Crystals, apparently about equal to the original
crystal in A, have been deposited.
Thus we can perform a complete cycle of changes. Starting
with saturated solution and crystals of sodium sulphate in the
dialyser, at the temperature of surrounding objects, an iso-
thermal change first takes place. Next the separated portions
of the solutions are mixed, and may be maintained under
adiabatic conditions till all possible crystallization has taken
place, evaporation being of course excluded. The result is a
considerable rise of temperature, with corresponding gain of
motivity ; and finally, when the liquid has been cooled down
(with further deposition of crystal) to the initial temperature,
we have come back to precisely the conditions with which we
started—-a saturated solution and crystals of sodium sulphate,
at the temperature of surrounding objects.
Now consider what is the action of the dialysing membrane.
According to the view of Arrhenius, dissociation and recom-
bination are continually occurring amongst the molecules of
the solution, each dissociation being accompanied by an
absorption of heat, and each recombination by an equal evo-
lution of heat. By filtering such a solution through a mem-
brane, the equilibrium of these processes is disturbed. The
various chemical constituents will pass through at different
rates, thus giving rise to chemical separation and (isothermal)
absorption of heat*. The membrane then plays the part of a
sieve ; it does not really cause dissociation ; it only effects a
selective distribution of molecules already dissociated. If
reliance could be placed in the constancy of a dialysing mem-
brane, and if the composition, temperature, and level of the
liquid above the membrane were also maintained constant, an
analysis of the portion which passes through might furnish
‘some conclusions as to the amount of dissociation in the
solution, It would be interesting to compare such results
with the data afforded by measurements of electrolytic con-
ductivity.
Experiment I1—The acid sodium sulphate being more
soluble than the normal sulphate, the more acid liquid which
* The solution remaining in the dialyser is alkaline, and therefore non-
saturated; hence the crystal dissolves.
Restriction to the Application of Carnot’s Principle. 187
passes through the dialyser will be able to dissolve some more
sodium-sulphate crystals. The apparatus (fig. 1) was aecord-
ingly arranged with excess of crystals in the beaker C, as well
as in the dialyser A. The following are the details of the
experiment :—
1888. Nov. 20; 5pm. Dialyser set up with 3 layers of
parchment-paper and excess of crystals (Na,SO,, 10H,O) in
both A and C. Saturated sodium-sulphate solution in A. .
Apparatus completely protected from evaporation.
Dec.5;4pP.m. Temp. of solutions (before mixing) =14°-4,
On pouring both solutions into a stoppered bottle which had
lain some days beside the apparatus, the temp. rose to 152.
Rise of temperature =0°8. :
Bottle now stoppered (one mgrm. sodium-sulphate crystals
added to promote further crystallization).
Dec. 10. Crystals have tormed in the bottle.
Hemp.o solution’. -.. 5. == 14-2
Mass of solution -. .:.- .=26°156 grams
Miassor cnystais: ....,./ = 2446 | ,,
Now [I find the latent heat of solution of crystallized sodium
sulphate to be 64°6, and the specific heat of a saturated solu-
tion at 15° about :97; so that if the mixed solutions had
_ been kept under adiabatic conditions while the crystals were
forming, there would have been a total rise of temperature of
more than 3 degrees (due allowance being made for the
increased solubility at higher temperatures).
The mechanical availability would then be
ee MO —273-- 12-4) d0
J Ci, Cae oa Ale
273+14°4
where M is the mass of the substance, and & its specific heat
at the temperature 0. Putting
ik = constant = -97,
the above expression becomes
‘97 x JM { (290-4—287-4)—287-4 ee
| = about 500,000 M ergs.
That is, after descending under gravity through an average
height of about 2 cm., the solution has increased the motivity
of the system by an amount sufficient to raise itself vertically
through more than 5 metres.
188 Dr. C. V. Burton on Endless Availability.
Eaperiment 111.—The apparatus was arranged as follows:—
A beaker, A (fig. 2), contained saturated solution and crystals
of sodium See in which some Fig. 2
parchment-paper, ©, was partly im- :
mersed, so as to increase the surface
for evaporation; A was placed within
a larger beaker, e. which was closed
by a glass plate, D, luted on with
soft wax so as to be air-tight. The
apparatus was left in a dark corner,
and after a day or two, dew was seen
to have collected on the sides of
the outer beaker, B. After six weeks, about half a gram of
water had collected in the beaker.
Now, undoubtedly the apparatus underwent changes of
temperature ; but these would be essentially very slow, so
that the difference of temperature between one part of the
apparatus and another would be extremely small, and this
must have been especially the case between the surface of the
solution and the adjacent walls of the beaker A, where dew
had also formed and gradually increased in amount.
From the continued distillation it seemed probable that the
vapour-pressure over thoroughly saturated sodium-sulphate
solution is slightly greater than over pure water. It is evident
that the saturated solution has the smaller latent heat of
vaporization, since evaporation is then always accompanied
by . crystallization. Hence a water-molecule expends less
energy in attaining the gaseous state than would be the case
at the surface of pure water.
Here, again, we can perform a complete cycle of operations.
The water which has distilled may be collected, and the
deposited crystal dissolved in it. A fall of temperature will
result, which will render some of the heat of surrounding
objects available for mechanical work. When the resulting
solution has been raised to its previous temperature, it will
just be saturated ; and on pouring it back into the beaker A,
the initial conditions are exactly restored.
A direct measurement was also made of the vapour-pressure
over saturated sodium-sulphate solution (without parchment-
paper). A flask containing a thick paste of sodium-sulphate
solution and powdered crystals was immersed in a bath of
water, and was connected by a rubber tube to a Sprengel
pump "and a barometer-tube. The vapour-pressure at 12°72
was found to be 10°7 mm., which differs from the vapour-
pressure over pure water at the same temperature by only
en!)
> Fle 7
On Achromatic Interference- Bands. 189
about —0°2 mm.; while Wiillner* found for a (non-saturated)
15-per-cent. solution of sodium sulphate at 26°3, a vapour-
pressure 1:2 mm. less than that of pure water. Hence it
seems that, just at the point where the solution becomes fully
saturated, there is a discontinuity in its vapour-pressure.
According to Regnault’s classical researches, a vapour-
pressure of 10°7 mm. over pure water corresponds to a tem-
perature of 12°-40 (instead of 12°72). The influence of the -
parchment-paper wick remains to be determined. But even
should it produce no increase in the vapour-pressure, there
would still be, on the whole, a considerable gain of motivity in
experiment IIT.
In all these experiments the working substance becomes
separated into two portions, which are not identical in che-
mical composition. I would therefore suggest this restric-
tion, that we cannot as yet assume with certainty the truth of
Carnot’s Principle when chenucal separation occurs between two
finite portions of the working substance. Further research
seems necessary before we can say whether or not this is the
only exception to the truth of Carnot’s Principle.
XXVIII. On Achromatic Interference-Bands. By Lorp
Rayueien, Sec. £.S., Professor of Natural Philosophy in
the Royal Institution.
[Concluded from p. 91. ]
Airy’s Theory of the White Centre.
F’ a system of interference-bands be examined through a
prism, the central white band undergoes an abnormal dis-
placement, which has been supposed to be inconsistent with
theory. The explanation has been shown by Airy ft to depend
upon the peculiar manner in which the white band is in
general formed. ‘Thus, “ Any one of the kinds of homoge-
neous light composing the incident heterogeneous light will
produce a series of bright and dark bars, unlimited in number
so far as the mixture of light from the two pencils extends,
and undistinguishable in quality. The consideration, there-
fore, of homogeneous light will never enable us to determine
which is the point that the eye immediately turns to as the
centre of the fringes. What, then, is the physical circumstance
that determines the centre of the fringes ?
“The answer is very easy. For different colours the bars
* Poge. Ann. cill. p. 543.
+ Airy, “Remarks on Mr. Potter’s Experiment on Interference,”
Phil. Mag. ii. p. 161 (1833),
190 Lord Rayleigh on Achromatic
have different breadths. If, then, the bars of all colours coin-
cide at one part of the mixture of light, they wiil not coincide
at any other part ; but at equal distances on both sides from
that place of coincidence they will be equally far from a state
of coincidence. If, then, we can find where the bars of all
colours coincide, that point is the centre of the fringes.
“It appears, then, that the centre of the fringes is not
necessarily the point where the two pencils of light have
described equal paths, but is determined by considerations of
a perfectly different kind. ... The distinction is important
in this and other experiments.”
The effect in question depends upon the dispersive power
of the prism. If v be the linear shifting due to the prism of
the originally central band, v must be regarded as a function
of X. Measured from the original centre, the position of the
nth bar is now
v+tnrD/b.
- The coincidence of the various bright bands occurs when this
quantity is as independent as possible of A; that is, when 7 is
the nearest integer to
b dv
Da: se ene)
i
or, as Airy expresses it, in terms of the width of a band (A),
n=—dvjdA. 2 Oe ae eee)
The apparent displacement of the white band is thus not v
simply, but
w—AdoldA. 2) ss eenente
The signs of dv and dA being opposite, the abnormal displace-
ment is in addition to the normal effect of the prism. But,
since dv/dA, or dv/dX, is not constant, the achromatism of the
white band is less perfect than when no prism is used.
If a grating were substituted for a prism, v would vary as
A, and the displacement (20) would vanish.
More recently the matter has engaged the attention of
Cornu *, who thus formulates the general principle:—“ Dans
un systeme de franges Minterférence produites a Vaide dune
lumiére héterogéne ayant un spectre continu, il existe toujours
une frange achromatique qui joue le réle de frange centrale et
qui se trouve au point de champ ot les radiations les plus in-
tenses présentent une diff érence de phase maximum ou minimum.”
In Fresnel’s experiment, if the retardation of phase due to
an interposed plate, or to any other cause, be F(A), the whole
* Journ. d. Physique, 1. p. 293 (1882).
Interference-Bands. 191
relative retardation of the two pencils at the point u is
C—O) apeevet “t yan} «ff (21)
and the situation of the central, or achromatic, band is de-
termined, not by $=0, but by d¢/dXA=0, or
ew DI CN) Maske ae es (22)
It is scarcely necessary to say that although the nth band -
may be rendered achromatic, the system is no more achromatic
than if the prism had been dispensed with. The width of the
component systems being unaltered, the manner of overlapping
remains as before. The present use of the prism is of course
entirely different from that previously discussed, in which
by a suitable adjustment the system of bands could be
achromatized.
Thin Plates.
The series of tints obtained by nearly perpendicular re-
flexion from thin plates of varying thickness is the same as
that which occurs in Lloyd’s interference experiment, or at
least it would be the same if the material of the plates were
non-dispersive and the reflecting power small. If ¢ be the
thickness, ~ the index, e’ the inclination of the ray within
the plate to the normal, the relative retardation of the two
rays (reckoned as a distance) is 2ut cose’, and is sensibly
independent of 2X.
“This state of things may be greatly departed from
when the thin plate is rarer than its surroundings, and
the incidence is such that e’ is nearly equal to 90°; for
then, in consequence of the powerful dispersion, cos a’ may
vary greatly as we pass from one colour to another. Under
these circumstances the series of colours entirely alters its
character, and the bands (corresponding to a graduated
thickness) may even lose their coloration, becoming sensibly
black and white through many alternationst. The general
explanation of this remarkable phenomenon was suggested by
Newton, but it does not appear to have been followed out in
accordance with the wave theory.
“ Let us suppose that plane waves of white light travelling
in glass are incident at angle a upon a plate of air, which is
bounded again on the other side by glass. If mw be the index
of the glass, « the angle of refraction, then sin a’ =wsin ¢ ;
and the retardation expressed by the equivalent distance in
alr, 18 2t sec a’ —p 2t tan «& sin «=2¢ cos a’ ;
* Ene. Brit. Wave-Theory, vol. xxiv. p. 425.
+ Newton’s Optics, Book 1i.; Fox Talbot, Phil. Mag. ix. p. 401 (1836).
192 Lord Rayleigh on Achromatic
and the retardation in phase is 2¢ cos a'/d, X being as usual
the wave-length in air.
“ The first thing to be noticed is that, when « approaches
the critical angle, cos «’ becomes as small as we please, and
that, consequently, the retardation corresponding to a given
thickness is very much less than at perpendicular incidence.
Hence the glass surfaces need not be so close as usual.
“A second feature is the increased brilliancy of the light.
But the peculiarity which most demands attention is the
lessened influence of a variation in X upon the phase retarda-
tion. A diminution of 2 of itself increases the retardation
of phase, but since waves of shorter wave-length are more
refrangible, this effect may be more or less perfectly com-
pensated by the greater obliquity, and consequent diminution
in the value of cose’. We will investigate the conditions
under which the retardation of phase is stationary in spite of
a variation of 2.
“In order that X-' cos «’ may be stationary, we must have
sin « da’+cos a’ dA=0,
where (a being constant)
cos a da’= sin adp.
Thus
cot? af = — ee ea)
giving e’ when the relation between wu and d is known.
“ According to Cauchy’s formula, which represents the facts
very well throughout most of the visible spectrum,
| pa=At BAT, .. ... 22. eee
2B — 2(w—A)
9) jee
cot’ a = a pe
If we take, as for Chance’s ‘ extra-dense flint,’
B=984 105.
and, as for the soda-lines,
w=165, A=5:89x 10-5,
so that
(25)
we get
Cd 30:
At this angle of refraction, and with this kind of glass, the
retardation of phase is accordingly nearly independent of
wave-length, and therefore the bands formed, as the thick-
ness varies, are approximately achromatic.”
Interference-Bands. 193
Perfect achromatism would be possible only under a law of
dispersion*
fo Nseries oie das: osiria Hs 26 (26)
where A and ¢? are constants, of which the latter denotes the
value of cot? a’.
The above investigation, as given in the Enc. Brit., was
intended to apply to Talbot’s manner of experimenting, and
it affords a satisfactory explanation of the formation of °
achromatic bands. In order to realize the nearly grazing
incidence, the plate of air must be bounded on one side by a
prism (fig. 1). Upon this fall nearly parallel rays from a
Bigs
“radiant point of solar light,” obtained with the aid of a lens
_ of short focus. The bands may be observed upon a piece of
ground glass held behind the prism in the reflected light, or
they may be received directly upon an eyepiece.
These bands undoubtedly correspond to varying thicknesses
of the plate of air, just as do the ordinary Newton’s rings
formed at nearly perpendicular incidence. For theoretical
purposes we have the simplest conditions, if we suppose the
thickness uniform, and that all the rays incident upon the
plate are strictly parallel. Under these suppositions the field
is uniform, the brightness for any kind of light depending
upon the precise thickness in operation. If the thickness be
imagined to increase gradually from zero, we are presented
with a certain sequence of colours. When, however, the
relation (23) is satisfied, the formation of colour is postponed,
and the series commences with a number of alternations of
black and white. In actual experiment it would be difficult
to realize these conditions. If the surfaces bounding the
plate are inclined to one another, the various parts of the
field correspond to different thicknesses; and, at any rate
if the inclination be small, there is presented at one view a
serles of colours, constituting bands, the same as could only
* A mistake is here corrected.
194 Lord Rayleigh on unduiatie
be seen in succession were the parallelism maintained
rigorously.
The achromatism secured by (23) not being absolute, it is
of interest to inquire what number of bands are to be ex-
pected. The relative retardation of phase, with which we
have to deal, is 2¢ cos «’/A, or
Ee ite
a . en)
If this be stationary for extra-dense glass and for the line D,
we have, as already mentioned, e«’ =79° 30’, and corresponding
thereto «=36° 34’. Taking this as a prescribed value of a,
we may compare the values of (27) for the lines OC, D, H,
using the data given by Hopkinson*, viz.:—
C, p=1:644866, rA="6561S5 <0
D, »=1°650388, A=58890% 10
H, »p=65760a, rA=-52690 Gee
We find
for © (27) =3086:9 « 2¢.
D (27) =3094'5 x 2,
E (27) = 2984-3 x 2.
These retardations are reckoned in periods. If we suppose
that the retardation for the C-system is just half a period less
than for the D-system, we have
57:6 xX 2t=4;
so that ¢=54, centim. Thus about 27 periods of the D-bands
correspond to 264 of the C-bands.
If the range of refrangibility contemplated be small, the
calculation may conveniently be conducted algebraically.
According to Cauchy’s law we may replace (27) by
2t J =pPsin?a) (u=A) ag)
/B
Setting w=)+ 6p, we have approximately
(1—? sin? «) (w—A)=(1—y,” sin’ «) (u,—A)
+ du{1—p,? sin? «—2u, sin? a) (u,—A)}
— (du)? {\8u,—A} sin?at....
If « be so chosen that the value of (28) is stationary for p,,
the term of the first order in 64 vanishes, and we obtain
* Proc. Roy. Soc., June 1877.
Interference-Bands. 195
finally as the approximate value of (28)
/B 4pig(Mo—A)? J -
If now the circumstances be such that n periods of the py
system correspond to n—4 of the mw system,
i (e4o— 4) (Op)? |
5 = Diy (fp —A)? ” ° ° e . e (30) é
in which the ratio of (84,—A,) to 2 does not differ much from
unity. In the application to extra-dense flint the simplified
formula
n=(Mp—A)*/(u—wo)?. - - « « (81)
gives very nearly the same result as that previously found.
The number of bands which approximately coincide is
inversely as the square of the range of refrangibility included.
It must not be overlooked that the preceding investigation,
though satisfactory so far as it goes, is somewhat special on
account of the assumption that the angle of incidence (a)
upon the plate of air is the same for the various colours. If
the rays are parallel before they fall upon the prism, they
cannot remain parallel unless the incidence upon the first
surface be perpendicular. There is no reason why this should
not be the case ; but it is tantamount to a restriction upon
the angle of the prism, since « is determined by the achro-
matic condition. If the angle of the prism be other than
a, the required condition will be influenced by the separation
of the colours upon first entering the glass. Although the
general character of the phenomenon is not chan ged, 1t may
be well to give the calculation applicable to all angles of
prism, as was first done by M. Mascart.
Denoting, as before, by a, «’ the angles of incidence and
refraction upon the plate of air, let 6’, 8 be the angles of
incidence and refraction at the first surface of the prism
(fig. 2), whose angle is A. ‘Then, if A, equal to nd, be the
retardation,
A=nv=2i cose) 6. i... (32)
as before ; while the relations among the angular quantities
are:—
Baga eS, rs sgh ede, (BB)
ae it cel atin syle ona) st (34)
SUL |v TSU Chas We amennenmeae 159)
196 Lord Rayleigh on Achromatic
Fig, 2.
We have now to inquire under what conditions A/A, or n,
will be stationary, in spite of a variation of A, if 6’ be con-
tant. Thus
Seber aus sin a! de’ +cos a'dr=0,
while cos a'da’ =dp sin a+ cos ada,
da+dB=0,
O=dpu sin8+pmcos dp.
Accordingly,
cot adr ; ;
eo COs =dp sin a+ pcos ada
=du sina—pcosa dB
=dyusina+cos a tan du
= sin Adpz/cos B;
so that
cot? a! = — Mite i IOS eo)
pdr sinacos 8
is the condition that n should be stationary. In the more
particular case considered above, 6'=0, B=0, «=A.
These bands, which I should have been inclined to desig-
nate after Talbot, were it not that his name is already con-
nected with another very remarkable system of bands, are
readily observed. For the “radiant point of solar light”
we may substitute, if more convenient, that of the electric
arc. A small hole in a piece of metal held close to the are
allows sufficient light to pass if the bands are observed with-
out the intervention of a diffusing-screen. Ata distance of
say 20 feet the nearly parallel rays fall upon the prism*™ and
* A right-angled isosceles prism (A =45°) answers very well. The plate
should be blackened at the hind surface; or it may be replaced by a
second prisin.
Interference-Bands 197
plate, which should be mounted in such a fashion that the
pressure may be varied, and that the whole may be readily
turned in azimuth. The coloured bands are best seen when
the surfaces are nearly parallel and pretty close. It is best
to commence observations under these conditions. When
the achromatic azimuth has been found, the interval may be
increased. If it is desired to see a large number of bands,
a strip of paper may be interposed between the surfaces along
one edge, so as to form a plate of graduated thickness.
Talbot speaks of from 100 to 200 achromatic bands ; but I
do not think any such large number can be even approximately
achromatic. The composition of the light may be studied
with the aid of a pocket spectroscope, and the appearances
correspond with what has been already described under the
head of interference-bands formed from a prismatic spectrum
in place of the usual line of undecomposed light. As has
been already remarked, the colours of fine bands are difficult
to appreciate ; and indistinctness is liable to be attributed to
other causes when really due to insufficient achromatism.
The use of a wedge-shaped layer of air is convenient in
order to obtain a simultaneous view of a large number of
bands; but it must not be overlooked that it involves some
departure from theoretical simplicity. The proper develop-
ment of the light due to any thickness requires repeated
reflexions to and fro within the layer, and at a high degree of
obliquity this process occupies a considerable width. If the
band-interval be too small, complications necessarily ensue,
which are probably connected with the fact that the appearance
of the bands changes somewhat according to the distance from
the reflecting combination at which they are observed.
Herschel’s Bands.
In the system of bands above discussed, substantially identical
(I believe) with those observed by Talbot, all the rays of a
given colour are refracted under constant angles, the variable
element being the thickness of the plate of air. A system
in many respects quite distinct was described by W. Herschel,
and has recently been discussed by M. Mascart*. In this case
the combination of prism and plate remains as before, but the
thickness of the film of air is considered to be constant, the
alternations constituting the bands being dependent upon the
varying angles at which the light (even though of given
colour) is refracted. In order to see these bands all that is
necessary 1s to view a source of light presenting a large angle,
such as the sky, by reflexion in the layer of air. They are
* Loc. cit.; also Traité d’ Optique, tom. i. Paris, 1889.
Phil. Mag. 8. 5. Vol. 28. No. 172. Sept. 1889. Q
198 Lord Rayleigh on Achromatic
formed a little beyond the limit of total reflexion. They are
broad and richly coloured if the layer of air be thin, but as
the thickness increases they become finer, and the colour is
less evident.
The theoretical condition of constant thickness is better
satisfied if (after Mascart) we place the layer of air in the
focus of a small radiant point (e.g. the electric arc) as formed '
by an achromatic lens of wide angle. In this case the
area concerned may be made so small that the thickness in
operation can scarcely vary, and the ideal Herschel’s bands
are seen depicted upon a screen held in the path of the re-
flected light. It will of course be understood that bands
may be observed of an intermediate character in the formation
of -which both thickness and incidence vary. Herschel’s
observations relate to one particular case—that of constant
thickness; Talbot’s to the other especially simple case of
constant angle of incidence. :
From our present point of view there is, however, one very
important distinction between the two systems of bands. The
one system is achromatic, and the other is not. In order to
understand this, it is necessary to follow in greater detail the
theory of Herschel’s bands. :
We will commence by supposing that the light is homo-
geneous (A constant), and inquire into the law of formation of
the bands, ¢ being given. The same equations, (82) c.,
apply as before, and also fig. 2, if we suppose the course of
the rays reversed, so that the direction of the emergent ray is
determined by @’. The question to be investigated is the
relation of 6’ to n, and to the other data of the experiment.
The band of zero order (n=0) occurs when «’ =90°, that is
at the limit of total reflexion. The corresponding values of
a, 8, and 6’ may be determined in succession from (83), (84),
(35). The value of «’ for the nth band is given immediately
by (82). For the width of the band, corresponding to the
change of n into n+1, we have
A= —2¢ sin ede’,
and from the other equations,
cos a’ del = wu cosada,
da+d8 = 0,
cos 2! dé! = w cos BdB ;
so that the apparent width of the nth band is given by
pe tee cos B
ae AT cos B' cos a sine’) | ee (37)
In the neighbourhood of the limit of total reflexion sin «’
Interference-Bands. 199
is nearly equal to unity, and the factors cos 8, cos 8’, cos
vary but slowly with the order of the band and also with the
wave-length. Hence the width of the nth band is approxi-
mately proportional to the order, to the square of the wave-
length, and to the inverse square of the thickness.
This series of bands, commencing at the limit of total
reflexion, and gradually increasing in width, are easily
observed with Herschel’s apparatus by the aid of a soda-
flame. In order to increase the field of view, the flame may
be focussed upon the layer of air by a wide-angled lens. The
eye should be adjusted for distant objects, and the thickness of
the layer should be as uniform as possible. For the latter
purpose the glass surfaces may be pressed against two strips
of rather thin paper, interposed along two opposite edges.
We have now to consider what happens when the source of
light is white. According to Airy’s principle the centre of
the system is to be found where there is coincidence of bands
of order n, in spite of a variation of X. This is precisely the
question already dealt with in connexion with the other
system of bands, and the answer is embodied in (86). About
the achromatic centre thus determined will the visible bands
be grouped.
And now the question arises, Are these bands achromatic ?
Certainly not. M. Mascart, to whom is due equation (87),
appears to me to misinterpret it when he concludes that the
bands are approximately achromatic*. At the central band
n is the same for the various colours. Consequently the
widths of the various systems at this place are approximately
proportional to »*. It will be seen that, so far from the
system being achromatic, it is much less so than the ordinary
system of interference-bands, or of Newton’s rings, in which
the width is proportional to the first power of X. And this
theoretical conclusion appears to me to be in harmony with
observation.
At first sight it may appear strange that an achromatic
centre should be possible with bands proportional to 7. The
explanation depends upon the fact that the limit of total
reflexion, where the bands commence, is itself a function of 2.
The apparent width of the visible bands depends upon ¢, but
is not, as might erroneously be supposed, proportional to ¢-%.
For this purpose 7 in (37) must be regarded as a function of ¢.
In fact, by (82), if a’ be given, n varies as ¢/A; so that, in
estimating the influence of ¢, other circumstances remaining
* Traité d Optique, t. i. p. 451. “On s’explique ainsi que la largeur
apparente des franges voisines de la frange achromatique soit 4 peu prés
indépendante de la longueur d’onde dans une ouverture angulaire notable
et qu’on en distingue un grand nombre.”
Q 2
200 Lord Rayleigh on Achromatic
unaltered, the width is proportional to ¢—!. Hence, as the
interval between the surfaces increases, the bands become
finer, but the centre does not shift, nor is there any change in
their number as limited by the advent of chromatic confusion.
Effect of a Prism upon Newton’s Rings.
If Newton’s rings are examined through a prism, some very
remarkable phenomena are exhibited, described in his 24th
observation*.
‘When the two object-glasses were laid upon one another,
soas to make the rings of the colours appear, though with my
naked eye I could not discern above 8 or 9 of these rings, yet
by viewing them through a prism I have seen a far greater
multitude, insomuch that I could number more than 40, besides
many others which were so very small and close together that
I could not keep my eye steady on them severally so as to
number them, but by their extent I have sometimes estimated
them to be more than a hundred. And I believe the experi-
ment may be improved to the discovery of far greater
numbers ; for they seem to be really unlimited, though visible
only so far as they can be separated by the refraction, as
I shall hereafter explain.
“But it was but one side of these rings—namely, that
towards which the refraction was made—which by that
refraction was rendered distinct ; and the other side became
more confused than when viewed by the naked eye, insomuch
that there I could not discern above 1 or 2, and sometimes
none of those rings, of which I could discern 8 or 9 with my
naked eye. And their segments or ares, which on the other
side appeared so numerous, for the most
part exceeded not the third part of a
circle. If the refraction was very great,
or the prism very distant from the
object-glasses, the middle part of those
ares became also confused, so as to dis-
appear and constitute an even white-
ness, while on either side their ends,
as also the whole arcs furthest from the
centre, became distincter than before,
appearing in the form as you see them
designed in the fifth figure [ fig. 3].”
“The ares, where they seemed distinctest, were only black
and white successively, without any other colours intermixed.
But in other places there appeared colours, whose order was
* Opticks. See also Place, Pogg. Amn. exiv. p. 504 (1861).
Interference-Bands. 201
inverted by the refraction in such manner that if I first held
the prism very near the object-glasses, and then gradually
removed it further off towards my eye, the colours of the 2nd,
drd, 4th, and following rings shrunk towards the white that
emerged between them, until they wholly vanished into it at
the middle of the are, and afterwards emerged again in a con-
trary order. But at the ends of the arcs they retained their
order unchanged.”
“T have sometimes so laid one object-glass upon the other,
that to the naked eye they have all over seemed uniformly
white, without the least appearance of any of the coloured
rings; and yet, by viewing them through a prism, great
multitudes of these rings have discovered themselves. And
in like manner, plates of Muscovy glass, and bubbles of glass
blown at a lamp-furnace, which were not so thin as to exhibit
any colours to the naked eye, have through the prism exhibited
a great variety of them ranged irregularly up and down in the
form of waves. And so bubbles of water, before they began
to exhibit their colours to the naked eye of a bystander, have
appeared through a prism, girded about with many parallel
and horizontal rings ; to produce which effect it was necessary
to hold the prism parallel, or very nearly parallel, to the
horizon, and to dispose it so that the rays might be refracted
upwards.”
Newton was evidently much struck with these “so odd
circumstances,” and he explains the occurrence of the rings
at unusual thicknesses as due to the dispersing power of the
prism. The blue system being more refracted than the red,
it is possible, under certain conditions, that the nth blue ring
may be so much displaced relatively to the corresponding red
ring as at one part of the circumference to compensate for the
different diameters. White and black stripes may thus be
formed in a situation where, without the prism, the mixture of
colours would be complete, so far as could be judged by the eye.
The simplest case that can be considered is when the “ thin
plate’ is bounded by plane surfaces inclined to one another
at a small angle. Without the prism, the various systems
coincide at the bar of zero order. The width of the bands is
constant for each system, and in passing from one system to
another is proportional to». Regarded through a prism of
small angle whose refracting edge is parallel to the intersection
of the bounding surfaces of the plate, the various systems no
longer coincide for zero order; but by drawing back the
prism, it will always be possible so to adjust the effective dis-
persing power as to bring the nth bars to coincidence for any
two assigned colours, and therefore approximately for the
202 Lord Rayleigh on Achromatic
entire spectrum. The formation of the achromatic band,
or rather central black bar, depends indeed upon precisely
the same principles as the fictitious shifting of the centre of a
system of Fresnel’s bands when viewed through a prism.
In this example the formation of visible rings at unusual
thicknesses is easily understood ; but it gives no explanation
of the increased numbers observed by Newton. The width of ©
the bands for any colour is proportional to A, as well after the
displacement by the prism as before. The manner of over-
lapping of two systems whose nth bars have been brought
to coincidence is unaltered ; so that the succession of colours
in white light, and the number of perceptible bands, is much
as usual.
In order that there may be an achromatic system of bands,
it is necessary that the width of the bands near the centre be
the same for the various colours. As we have seen, this con-
dition cannot be satisfied when the plate is a true wedge; for
- then the width for each colour is proportional to x. If, how-
ever, the surfaces bounding the plate be curved, the width for
each colour varies at different parts of the plate, and it is
possible that the blue bands from one part, when seen through
the prism, may fit the red bands from another part of the
plate. Of course, when no prism is used, the sequence of
colours is the same whether the boundaries of the plate be
straight or curved.
For simplicity we will first suppose that the surfaces are
still cylindrical, so that the thickness is a function of but one
coordinate «, measured in the direction of refraction. If we
choose the point of nearest approach as the origin of a, the
thickness may be taken to be
“tS @+be, «eS Se
a being thus the least distance between the surfaces. The
black of the nth order for wave-length X occurs when
S7N = A102" 5...) 5 eee)
so that the width (6x) of the band at this place (x) is given by
NX = 2be bx,
2 Se Nfdbe oe
Substituting for « from (88), we obtain, as the width of the
band of nth order for any colour,
r
47d. oJ (dak —a)' eae
It will be seen that, while at a given part of the plate the
62 =
Interference-Bands. 203
width is proportional to X, the width for the nth order is
a different function dependent upon a. It is with the latter
that we are concerned when, by means of the prism, the
nth bars have been brought to coincidence.
If the glasses be in contact, as is usually supposed in the
theory of Newton’s rings, a=0; and therefore, by (41),
Sa oc d?, or the width of oie band of the zxth Rniee varies as
the square root of the wave-length, instead of as the first
power. Even in this case the overlapping and subsequent
obliteration of the bands is much retarded by the use of the
prism ; but the full development of the phenomenon demands
that a should be finite. Let us inquire what is the condition
in order that the width of the band of the nth order may be
stationary, as X varies. By (41) it is necessary that the
variation of \?/(4nA—a) should vanish. Hence
2r(4nri—a) —hnd = 0,
pri nN WEL SSL TERIOR (42)
The thickness of the plate where the nth band for 2 is
formed being 3nd, equation (42) may be taken as signifying
that the thickness must be half due to curvature and half to
imperfect contact at the place of nearest approach. If this
condition be satisfied, the achromatism of the nth band,
effected by the prism, carries with it the achromatism of a
large number of neighbouring bands*.
We will return presently to the consideration of the
spherically curved glasses used by Newton, and to the
explanation of some of the phenomena which he observed ;
but in the meantime it will be convenient to state the theory
of straight bands in a more analytical form.
or
Analytical Statement.
If the coordinate & represent the situation of the nth band,
of wave-length 2, then, in any case of straight bands, may
be regarded as a function of n and 4, or, conversely, n (not
necessarily integral) may be regarded as a function of &
and x. If we write
WON) een. os. (43)
and expand by Taylor’s oe
n—ny = SE 28+ nah ts [yt
dE dX
+45 (any. see 6) {olicua)
* Ene. Brit., Wave-Theory, p. 428 (1888).
d€ On
204 Lord Rayleigh on Achromatic
s |
wee nw = (£o, No) e . e e e 6 (45)
The condition for an achromatic band at &, Xo 18
ap _
—_ = Meee
eee eo)
and, further, the condition for an achromatic system at this
place is
WOR) |
= wg a LE Se a
ac en Ce
If these conditions are both satisfied, n becomes very
approximately a function of only throughout the region in
question.
In several cases considered in the present paper, the func-
tional relation is such that
wees), o. 2 ee
_ar(A) denoting a function of X only. The expansion may
then be written
— Ny =E{ Wr (Ao) +’ (Ap)bA+ 4’ (Ay) (SA)? +...}- (49)
The line €=0 is here of necessity perfectly achromatic. If
there be an achromatic system,
W'Ac) = 93
and when this condition is satisfied, the whole field is achro-
matic, so long as (6X)? can be neglected.
If the width of the bands be a function of » only, n is of
the form n= &. ap (A) + (A), reer 5 0)
more general than that just considered (48), though of course
less general than (48). The condition for an achromatic
line is
dn
R= EV O)tXO)=0, - . » OD
and for an achromatic system,
dn
fae a Miners unt ci (2) |
so that, for an achromatic system, y’ and y’ must both
vanish.
Curved Interference-Bands.
If the bands are not straight, n must be regarded as a
function of a second coordinate 7, as well as of & and 2X.
In the equation
N= PCE, 9, A);) 2 oe ees
Interference- Bands. 205
if we ascribe a constant value to X, we have the relation
between £,7 corresponding to any prescribed values of n—
that is, the forms of the interference-bands in homogeneous
light. If the light be white, the bands are in general con-
fused ; but those points are achromatic for which
dn
pe eeL Wi gtw in eaters <4)
This is a relation between & and 7 defining a curve, which we
may call the achromatic curve, corresponding in some respects
to the achromatic line of former investigations, where n is
independent of 7. ‘There is, however, a distinction of some
importance. When n is a function of &€ and 2 only, the
achromatic line is also an achromatic band; that is, n remains
constant as we proceed along it. But under the present less
restricted conditions n is not constant along (54). The
achromatic curve is not an achromatic band ; and, indeed,
achromatic bands do not exist in the same development as
before. They must be regarded as infinitely short, following
the lines n=constant, but existent only at the intersection of
these with (54). Practically a small strip surrounding (54)
may be regarded as an achromatic region in which are visible
short achromatic bands, crossing the strip at an angle de-
pendent upon the precise circumstances of the case.
The application of this theory to the observations of Newton
presents no difficulty. The thickness of the layer of air at the
point x,y, measured from the place of closest approach, is
ROO Ye ich rae aha s (5D)
and since t=4ndA, the relation of n to w, y, and X is
aie Oa ON ee) cae a mer, 2 (00)
This equation defines the system of bands when the com-
bination is viewed directly. The achromatic curve determined
by (54) is
at+b(a’+y") = 0,
and is wholly imaginary if a and 6 are both positive and
finite. Only when a=0, that is when the glasses touch,
is there an achromatic point =0, y=0.
When a prism is brought into operation, we may suppose
that each homogeneous system is shifted as a whole parallel
to « by an amount variable from one homogeneous system to
another. If the apparent coordinates be &,7, we may write
2 == S70) ag en ne ee OY)
Using these in (56), we obtain as the characteristic equation
206 On Achromatic Intenference-Bands.
of the rings viewed through a prism,
2 2
ny = SEO FOOT? eee)
The equation of the achromatic curve is then, by (54),
LE+S Ad) od (Ao) fF 7° = Do" J" (Ao) fF? — a/b, - (99)
which represents a circle, whose centre is situated upon the
axis of &.
If the glasses are in contact (a=0), the locus is certainly
real, and passes through the point
E+f(Ao) =0, 7=0;
that is, the image with rays of wave-length Xy of the point of
contact (e=0, y=0). The radius of the circle is Ap f’(Ap),
and increases with the dispersive power of the prism. The
other point where the circle meets the axis,
@ = 2Xof"(), y=9,
marks the place where the bands, being parallel to the achro-
matic curve, attain a special development. It is that which we
should have found by an investigation in which the curvature
of the band-systems is ignored.
If a be supposed to increase from zero, other conditions
remaining unaltered, the radius of the achromatic circle
decreases, while the centre maintains its position. The two
places where the circle crosses the axis are thus upon the
same side of the image of z=0, y=0. When a is such that
aJb = Ao’ 4 f"(Ao)}*, o cs ° ° e (60)
the circle shrinks into a point, whose situation is defined by
= E+fQ) = mofo), y=r=0. . . El)
Since there are two coincident achromatic points upon the
axis, the condition is satisfied for an achromatic system. By
(60), (61), eee
- go that
t= a+ ba? = 2a. . 2 2 ee ee)
This is the same result as was found before (42) by the
simpler treatment of the question in which points along the
axis were alone considered.
If a exceed the value specified in (60), the achromatic
curve becomes wholly imaginary*.
* Compare Mascart, ZTraité d’ Optique, t. i. p. 485.
Re 2e7
XXIX. The Thermal Effect due to Reversals of Magnetization
in Soft Iron. By A. Tanakapate, Regakusi*.
[Plates VI.-VIII. | .
a following experiment on the measurement of the heat
due to the reversals of magnetization in soft iron wire
was carried out in the Physical Laboratory of the Glasgow
University during the summer months of 1888. The method
pursued is due to Sir William Thomson, in accordance with
whose instructions the work was undertaken.
Cotton-covered soft iron wire, of °115 centim. diameter, was
coiled upon a specially prepared wooden groove. The ends of
the wire were insulated from each other ; and the bundle was
tied at several places with fine silk thread to keep its shape,
and when the wooden frame was removed the coil of the
wire was left in shape of an anchor-ring. The object of thus
building the ring with insulated wire instead of solid mass
was to reduce the Foucault current in the substance of iron
when an alternating current is passed in the magnetizing coil.
The ring thus formed was now wound uniformly over with
No. 16 silk-covered copper wire in two layers, a thermoelec-
tric junction consisting of platinoid and copper being placed
upon the outer surface of the ring before winding. The
principal dimensions of the ring were as follows :—
Diameter of the soft iron wire . . . . 0°115 centim.
Number of turns of the soft iron wire in
per Oma ial fla Han bony sitodecteciren fe yn. 2LBO
Total number of turns of copper wire in
the magnetizing solenoid . ... . 177
Internal diameter of the ring . . . . . 6 centim.
Hxternal diameter of the ring . 4 eee es
Mean. 8
1)
Mean strength of magnetizing field due to 1 ampere through
the coil 177
=A Bar x 10 = 880 C.G:8.
A wooden ring, of very nearly the same size and shape as
that of the iron wire, was turned and wound similarly with
the same silk-covered copper wire, total number of turns,
however, being 174. The other junction of the same thermo-
electric couple was laid on the surface of this wooden ring in
the same way as the other junction was disposed with regard
to the iron ring, so that the platinoid wire stretched between
the two rings, and copper wire from the two rings led to
terminals of a mirror-galvyanometer, as in the diagram.
The magnetizing coils of the two rings were joined in series,
* Communicated by Sir William Thomson.
208 A. Tanakadaté on the Thermal Effect due
and led to an alternating-commutator through an idiostatic
galvanometer. The alternator was driven by a clockwork.
TrvonRin
Gatlr ~~ Y
Saag b ee 7
— ¢
E=Ery 3 K
e :
x : ; Mirror
is | On Pe, ses
a ar
Counter WaedenRing
It had forty teeth on each side, so that one revolution of it
made forty complete reversals of magnetization in the iron
ring inside the core. The current was supplied from secondary
batteries, and its strength was adjusted by means of resistances,
which were in most cases Edison lamps joined in multiple are.
The thermoelectric constant of the junctions was determined
by heating the iron ring in a specially prepared sand-bath,
while the wooden ring was kept at the temperature of the
room. The sand-bath was first heated by a gas-flame up to
about 60° C., and left to cool slowly. Several simultaneous
readings of the galvanometer-deflexion and temperature-
difference of the junctions were taken, and the value of the
difference of temperature corresponding to one division of the
galvanometer-deflexion was deduced as follows :—
Determination of Thermoelectric Constant (April 5, 1888).
Difference of
temperature
Temp. of | Difference |@ 1. nometer- (Corresponding
: Temp. of oLe
Time. . : wooden | of tempe- . to one division
eee ring. rature. Senesie, of galvano-
meter-deflex-
ion.
hm ° ° fe) °
12 0 53°6 C. 14:4 C. 39'2 OC. 489 0802 C.
1 5 42:4 15:2 272 343 ‘0794
1 27 38'8 LA a dlecous, 297 0798
ay 1) 29°6 15:7 13°9 Les 0785
6 0 20°8 14:3 6°5 81 0801
From the time-rate of the fall of temperature of the iron
ring we may judge of the uniformity of temperature inside
the sand-bath. The constant was assumed to remain the same
till the 20th of the same month, when a sudden change, due
to changes in the arrangement of magnets in the laboratory,
was observed. ‘The constant was redetermined as follows :—
hf
to Reversals of Magnetization in Soft Iron. 209
Determination of Thermoelectric Constant (April 20, 1888).
Difference of
temperature
Temp. of | Difference _|corresponding
Time. Temp. of wooden | of tempe- eee to one division
Se ring. rature. ie sare of galvano-
meter-defiex-
ion.
hm ° fo) ° °
3 16 534 C. 16:2 C. 3720. 458 0:0811
3 47 47-9 16°5 314 3874 0-0811
4 15 42:9 16-4 26°5 326 0:0814
Br 2 36°3 163 20:0 245 0:0816
Meant 21%: 0:0813
Hereafter the constant was tested every day by comparing
the deflexion of the galvanometer caused by a permanent bar-
magnet placed at a definite place.
The experiment consisted in making three different deter-
minations, 7. e.:—(1) the strength of the alternating current
from which the magnetizing field is calculated ; (2) the rate
of alternation per second of time ; (8) the rise of temperature
of the junction at the iron ring above that at the wooden ring.
_ The alternating current was measured by a deci-ampere
balance for small current, and by Siemens’s dynamometer for
large current. The dynamometer was carefully compared
with the ampere-balance, and its constant was ‘878 ampere per
division. The rate of alternation was determined by means of
a counter connected to the commutator, and it varied between
28 and 400 complete reversals per second. The difference of
temperature was observed by the mirror-galvanometer in the
thermoelectric circuit. In most cases several observations
were made during one experiment, so that the rise of tempera-
ture of the iron ring above that of the wooden ring can be
graphically represented. Sometimes only the final readings
were taken, omitting the intermediate points: these are dis-
tinguished from others by simply connecting the final point
to the origin by a dotted line. The figures from 1 to 19
represent the experiment.
From the foregoing description of the method of measuring
the difference of temperature, it appears that if the thermal
qualities of the two rings are exactly the same, there will be
no difference of temperature between the two junctions so long
as heat is supplied from the current only, and hence the dif-
ference of temperature between the two junctions will indicate
the heat due to the reversals of magnetization; in other words,
Joule’s effect will be entirely eliminated.
210 A. Tanakadaté on the Thermal Effect due
It was found, however, in the course of experiment that
when a continuous current was passed through both the rings,
the tendency of the temperature of the thermo-junction at the
wooden ring was to rise above that at the iron ring, principally
due to the difference of thermal diffusivity. But when the
current was made to alternate, this was entirely overmasked
by the heat arising from reversals of magnetization.
Thus, in order to find how much heat is due to the reversals
of magnetization, a proper amount of allowance must be made
for the heat diffused and radiated. A satisfactory way of
arriving at the rate at which heat is generated in the substance
of iron would be to solve the general equation of the conduction
of heat when part of the conducting medium is generating
heat. Such an equation will be
Ce ae
Em *KV et g/e,
with proper boundary conditions as to time and space: v being
the temperature, ¢ time, « diffusivity, g the rate of genera-
tion of heat per unit volume per unit time, c thermal capacity
per unit volume.
Now when gq is constant and the sole source of heat,
i=0, o=0;
and therefore ai) a aie
ay ae
that is, the time-rate with which the temperature begins to
rise is the true measure of the rate of generation of heat in
the substance. As soon, however, as the elevation of tempe-
rature becomes sensible, heat will be diffused inside the body
and radiated into the outside space. But whatever be the way
in which heat is conducted in the body, when we consider the
time-variation of temperature at a definite point in the body,
the law of diffusion of heat will be expressed by
Ca nae
Ge SS Of) >
where h is a mixed coefficient depending upon conduction and
emission, as the generating body is in contact with other
conducting body as well as being exposed to the air. This
mixed coefficient might be called dissipativity, as it measures
the rate at which heat is taken away from the generating
body irrespective of how it is done.
Putting the single letter g for q/c for convenience, the above
equation with the initial condition t=0, v=0, gives
j= i (1—e-*),
This will be strictly applicable to the rise of temperature in
to Reversals of Magnetization in Soft Iron. eA h
an infinitely thin wire through which current is made.
Curves in fig. 21 give the rise of temperature thermoelectri-
eally determined plotted against time, when a continuous
current was sent through the copper coil of only one of the
rings; the other being kept at the temperature of the room.
They show how far the equation thus calculated is realized in
experiment.
Expanding v in powers of ¢, thus
a ae he
v= F(A 1c he a)
ht? = hh
iinet B co
we see that the time-rate of the rise of temperature at the
beginning gives the rate of generation of heat independent of
the dissipativity h, as was indicated by the general equa-
tion ; and, therefore, whatever the diffusivities of the wooden
and iron rings may be, the heating-effect due to current alone
would have been eliminated in the beginning, if only the rate
of generation of heat had been the same in both rings; in other
words, the curve of temperature growth would have begun
tangent to the time-axis, when the same continuous current
was sent through both the rings. Experiment revealed, how-
ever, that this was not the case; the curve of difference of
temperature growth began with definite rate (see fig. 22), so
that there must have been a difference in the rate of supply of
heat in the two rings. This is very likely due to the difference in
the resistance of wire used in winding the rings, or irregulari-
ties in the rate of winding in the neighbourhoods of junctions.
Assume, therefore,
v,=g/h(l1—e-) for the wooden ring,
mag/il(l—e*) ,, iron ring;
taking their difference, we have
V=U1— Vo,
which is observed in the thermoelectric current. From this
we have ;
te de
which shows that at the beginning the temperature rises at
the rate g—q' per unit of time ; and, further, the difference of
temperature, v, is maximum when
t=log (4) (a1);
and, therefore, there is or is not a maximum according as
g and h are greater or less than g' and h’ correspondingly or
212 A. Tanakadaté on the Thermal Effect due
not. In the present case g>q’, hence we infer that h>h’ from
the existence of a maximum. ‘The point of inflexion in the
temperature-curve is given by
t=log (4) | (h—W),
which shows that when there is a maximum the point of in-
flexion takes place at a later period than the maximum.
The ultimate temperature when the current is kept run-
ning for a very long time is given by
v=g/h—d lh’ ;
and, therefore, we see that the curve does or does not
cross the zero-line of temperature according as the ratio
g/his< or > q’/h’. See fig. 20, where the temperature of
iron ring above that of wooden ring is taken positively.
So much for continuous current, that is, when the supply
of heat is derived solely from the magnetizing solenoid, which
forms a kind of anchor-ring shell. Now, when an alternating
current is passed, the whole mass of the iron ring becomes a
source of heat, which is the subject of the study. The dissi-
pativity h’ will no longer be the same as before; for the whole
mass of iron, instead of conducting away heat from the surface
shell, becomes a source of heat, and therefore, when its rate
of generating heat is greater than that due to the current it
gives heat to the outer shell.
Put Q for the heat produced per unit time by reversals of
magnetization, and H the dissipativity at the point where the
thermoelectric junction is placed, then
ff
i= ae (1—e-#*) for the iron ring,
v= q/h (1—e-™) » wooden ring.
Expanding v, and v, and subtracting,
t?
V9 — ty =v=(Q+¢q'—-9q) POs 7 ee ae ieee
But g and q’ will have a constant ratio, as they are both pro-
portional to the square of current, so that we may put
qI—-P=ne’,
and this is what is approximately true, as found by experi-
ment (see fig. 22).
Also ash and H are constants, and H, -9 H,0.
Temperatur Pe on oe r Dee Vee.
Sera aly Seconds (é). i 20° (p) 1000° =| Water at 20°=1.
al 867 32-48 28-16 1-21
29:7 157-5 32:48 24-60 1:06
39-4 658 32 48 21:37 ‘921
57°38 528°5 32-48 17-16 ‘740
49:4 578 32:53 18:80 ‘810
67:3 47] 32:59 15:35 662
82:5 403 32-60 13-14 “566
Taste VII.—Solution Il. 93°8 C,H,O2, 6-2 HO.
Pressure.
Time. ; pxt Viscosity.
Tompersbt®-| Secouds (2)./\ oe key i 1000' | Water at 20°=1,
20 1497°5 29-61 44.36 1-91
| 29:9 1207°5 29°61 35°76 1-54
: 39:4 1009 29-57 29 82 1-28
| 49-5 8435 29:57 94-93 1-07
| 58-1 735 29:57 21°73 ‘O15
69:5 622°5 29-60 18-43 794.
82:2 531-5 29-60 15°73 678
|
| Taste VIII.—Solution HI. 88°24 C,H,O,, 11°76 H,0.
| Time eResenne. pxt Viscosity
nate. t US
| Temperature. | 9. oonds (2). ee ee 1000 Water at 20°=1.
| 20:1 1938 28°79 55-81 241
: 29:85 1518 28:86 43:8 1-89
| 39:5 1299 28-88 353 1-52
| 49-9 995°5 28:88 28°75 1-24
| 59:5 841:5 28-91 24-33 1-05
76-2 682'5 28:37 18:84 812
| 65°7 766 28:87 22-19 953
Viscosity of Solutions.
227
Taste 1X.-—Solution IV. 83°33 C,H,O,, 16°67 H,O.
Temperature.
[e}
22:7
30°2
40:3
50:1
59°8
71:9
79
TABLE X.—NSolution V.
Temperature.
TABLE XI.—Solution VI.
Temperature.
fo}
20:2
29'9
39°5
49-7
59°4
67-7
78:3
Time.
Seconds (7).
1706
1617
1273
1043
877
720
648
Time.
Seconds (7).
Time.
Seconds (f).
1836
1421
1131°5
917
771
671°5
570
Pressure. i
Cm. of water DERG
32°67 nar
28°79 46°55
28°78 36°64
28°78 30°01
28°78 25:24
28°87 20°79
28°87 LSet
Pressure.
Cm. of water PAG
at 20° (p). 1000
33°13 61:08
33°12 46-92
33°24 37-01
33°26 31:03
39°26 24°66
33°26 20°62
33°16 18:90
Taste XII.—Solution VII.
Temperature
MH SOSS So!
OO G> Cn PB dD
OWA AGH ae
Time.
Seconds (7).
1848°5 —
1436
1120
921
766°5
649°5
545
Pressure. A
Cm. of water Sas
at 20° (p). 1000
33°12 60°81
33°13 47°08
33:14 ay iy
30°15 30°40
33°16 25°57
83°16 22-26
33°16 18°90
Viscosity.
Water at 20°=1.
2°40
2°01
1°58
1:29
1:09
894
‘807
81:08 O,H,O., 18°92 H,0.
Viscosity.
Water at 20°=1.
2°63
202
1:59
1°34
1-06
"889
"815
78:95 CyH,O>, 21:05 H,0.
Viscosity.
Water at 20°=1.
76:92 C,H,0,,
Pressure. Kt
Cm. of water O00"
at 20° (p).
32°87 60°77
32°86 47°19
32°86 36 81
32°86 30°27
32°86 25°19
32°86 21:34
32°86 17°91
23°08 HO.
Viscosity.
Water at 20°=1.
2°62
2°03
1:59
131
1:09
"92
7172
228 Mr. R. F. D’Arcy on the
Taste XIII.—Solution VIII. 75 C,H,O,, 25 H,0.
Time. Pressure. | px? Viscosity.
Temperature. | Seconds (¢). | Cm.ofwater’| 1000 | Water at 20°=1.
“at 20° (p).
20-7 1813 32/89 59°64 257
303 1403-5 32:89 A617 1-99
39-4 1130 32:89 37-17 1:60
498 909 32 89 . 29:90 1-29
57°8 783 32:89 O5°75 Ll
68 659 32:89 21-68 934
84 519 32°89 17:07 736
|
TasLE XIV.—Solution IX. 73°17 C,H,O,, 26°83 H,O.
Time. Pressure. pxt Viscosity.
Temperature. | Seconds (¢). | Cm. of water 1000 Water at 20°=1.
at 20° (p).
ie)
19°8 1845 32 78 60:47 2°61
299 1408 32°78 46°13 1:99
40 1 1106 32°78 36°24 1:56
49-3 914 32°76 29°93 1:29
58°5 772 32°74 25°27 1:09
68°4 655 32°71 21-41 925
81-7 536 32 68 17°52 a8
TABLE XV.—Solution x. 68°19 C,H,0,, 31°81 3:
|
; Time. Pressure. pxt | Viscosity.
Temperature. | Seconds (2). | Cm. of water 1000 Water at 20°=1,
at 20° (p).
(e}
196 1813'5 32°91 56:69 2°57
29°5 1395 32°91 45°93 1:98
40 1084°5 32 91 35°72 1°54
50:2 881 32°88 28:97 1:25
99 TAT 32°88 24:57 1-06
701 621 32°88 20°42 88
84:9 502 32°88 1o:ol “G11
TaBLE XVI.—Solution XI. 62°5 C,H,O,, 37°5 H,O.
: Pressure me ade
Time. ee pxt Viscosity.
Pembersiure! | Seconds (2). owas. 1000° Water at 20°=1.
2)
WS 1697-5 32°82 55°73 2°40
30°5 12755 32°82 41-89 181
40 1022 32°82 33°55 1:45
50°5 823°5 32°85 27:06 apn 7g
57:6 7185 32°88 23°62 1:02
68°6 598°5 32°88 19°68 848
78:7 «617 32°88 17:00 ‘733
Viscosity of Solutions. 229
Taste XVIT.— Water.
Time. Pressure. pxt Viscosity.
Temperature. | Seconds (¢), | Cm. of water 1000 Water at 2U°=1.
at 20° (p).
note Ls peers SE tea a
21-4 687 32°62 29°42, | 966
30°3 568°5 32-61 18:54 799
40-7 467-5 32°58 15°24 656
53°3 3845 32-58 12:53 540
60°1 353°5 32-62 11°53 -497
73-6 304 32-62 9-92 -427
78:3 290 32°62 9-46 ‘408
Arrhenius has recently (Phil. Mag. July 1889) made some
remarks on Graham’s paper above referred to. He appears
to think the explanations given by Graham to be quite anti-
quated. [Graham’s work is not forty years old yet, by the
way, since it was published in 1861.] He cites, in particular,
the example of alcohol, and inaccurately states that the vis-
cosity is a maximum for a solution having the composition
C,H;O0H .5H,0 instead of C,H;OH.3H,O; the proportions,
in fact, for which, as Mendelejeff has shown, the greatest con-
traction occurs on mixing. He states that the fact that a
maximum of viscosity occurs on dilution cannot be used as
evidence of a combination of the liquids. Now the strange
thing is, if this be so, that in a series of experiments such as
Graham’s these maxima should occur in every case when the
number of molecules of water and the number of molecules
of the other liquid are in some simple ratio; that in the case
of sulphuric acid the hydrate can be obtained in the solid
state; that in other cases the solution of maximum viscosity
is that for which the greatest contraction occurs.
Again, Arrhenius states that the reason the hydrate expla-
nation has been “abandoned” is because it was found that
the maximum varies with the temperature. The solutions
used in the acetic-acid experiments, above described, were
specially chosen to test this; no such change occurs within
the limits of experimental accuracy in the case of this acid
below 60° at any rate.
In cases where the maximum does vary, I do not think the
hydrate theory need be abandoned; since, if such a solution
be considered as a dissociating system, the mixture containing
the largest percentage of hydrate at any temperature need not
necessarily be that in which the components are mixed in the
proportions in which they combine, but there will be for each
acid &. at any particular temperature a certain mixture (the
case being analogous to that of a gas mixture) which will
230 Mr. R. F. D’Arcy on the
contain a maximum percentage of hydrate, and this will be
the solution having maximum viscosity.
Experiments on Chrome-Alum Solutions. .
It is well known that a solution of chrome alum when
heated to 70° undergoes a change which is easily traced by
the colour changing from violet to green, and that on cooling
the solution remains for a long time green, but gradually
returns to its original state. Experiments were made on the
viscosity of a solution before and after being heated; the
results are given in the following Table, and shown graphically
in fig. 4:—
TaBLe XVIII.—Viscosity of ;% normal solution of Chrome
Alum. ‘
Mean| “Time. Pressure. pt Me Col eal
Temp. Seconds Shee of water at 15° (p).| 1000° bo] OPOUE OK EO:
)
16 1132 28°42 32°0 1-245 violet
16:2 1115 28°42 317 1-224 violet
29°8 817 28°42 23°2 896 violet
49:3 567 28°42 16:05 620 violet
58°8 483 28°42 13-67 ‘528 | colour changing
69-4 413 28°42 11-70 "452 green
49°35 528 28-42 15:0 ‘579 green
[had been heated
29°85 753 28°42 21:4 826 to 100°.]
green
16:05 1031 28°42 29:3 1-182 green
Experiments were also made with a solution which was
saturated in the cold with similar results.
This change of colour has been explained in two ways: (1)
that it is due to dehydration ; (2) more recently and _per-
haps more satisfactorily as due to the decomposition of the
normal chromium salt with formation of basic and acid salts.
The diminished viscosity may perhaps be taken to indicate a
decomposition of complex molecules into simpler ones, but
does not seem capable of discriminating between these two
theories. Probably osmotic pressure being chiefly dependent
on the number of molecules in solution would yield a crucial
method of experiment from the physical point of view.
The alteration of viscosity is so marked in this case that it
would be sufficient to show that a change had been produced
by heating ; hence it seems that in cases where there is no
alteration of colour determinations of viscosity may be used
Viscosity of Solutions. 231
to detect a change which otherwise might pass, or, perhaps,
has passed, unnoticed.
Hxperiments on Solutions of Calcium Chloride.
These were undertaken with a view to investigate the
viscosities of solutions of the same salt in different solvents.
For this purpose viscosities of solutions of calcium chloride *
[4, qb, sp normal] in water, ethyl alcohol, and methyl
alcohol were determined. Considerable trouble was taken
to purify the substances used. As no obvious relation appears
to exist an account of only a few of the experiments is given
in the following Table. The noteworthy result of these
experiments is that the increase of viscosity on adding
calcium chloride to either of the alcohols is much greater
than that produced when it is added to water. Perhaps the
explanation of this is to be found in the superior dissociating
action of the water.
TABLE XIX.
Thani Tempe- bee pee ‘| Differ- | Tempe- Vi t Differ-
ae rature. i ences. | rature. |’ *°°°"'Y" ences,
i CaCl, in water} 15 | 1-053 50 | «+543
RO tre teeta: srsieeies < 38 cal. — 7-6 X 105" cal.
The quantity of energy radiated per second at 1000° is
therefore about 600 times greater than the quantity commu-
nicated in heating from 0° to 1000°.
If, further, we have a platinum wire of r centim. radius
and 1 centim. length, then at 1000° the quantity of energy
lost per second by radiation M, and the quantity W commu-
nicated in heating from 0° to 1000°, are given by the formula
M=2rrx4:7, W=7r" x 21:5 x 38;
therefore W/M=87 xr.
We see from this that, with a wire about 7, centim. in
thickness, the energy radiated in a second and that commu-
nicated in heating from 0° are nearly equal. With thinner
wires the latter diminishes very rapidly in comparison with
the former.
Hxactly similar considerations of course apply to the case
of glowing and radiating platinum foil.
22. The method employed for the determination of the .
radiation gives it, in the first place, according to order of
magnitude. The numbers just quoted show, in fact, how
extraordinarily great the radiation is. ‘The surface-layer must
therefore cool rapidly. The loss of energy thus caused is
instantly supplied by conduction from the interior hot. por-
tions at the expense of the work done by the current. Since
the outer portions are, in any case, cooler than the inner,
their resistance must be less. But the resistance measured is
a mean of the various concentric layers. ‘Therefore it is not
at once possible, without a thorough inquiry into the relation-
ships of conductivity for heat &c., to obtain a reliable conclu-
sion, from the observed resistances, as to the actual tempera-
ture of the radiating surface f.
* Comptes Rendus, |xxxv. p. 543 (1877).
+ Compare also (amongst others} the work of G. Basso, Natura, iii.
pp. 225, 304.
U2
, TE
256 Prof. E. Wiedemann on the
The influence of these disturbing circumstances may be ‘
determined by heating a platinum wire to a definite tempera-
ture in an air-bath and measuring the intensity of the light
emitted at a definite part of the spectrum, and at the same
time determining its resistance. Then the wire is heated by
means of a current to the same brightness and its resistance
determined again. From the difference in resistance observed
in the two cases account can be taken of the complications in
question. The experiments should be made with wires of
different thickness.
Comparison of the Amyl-acetate Lamp with Glowing Platinum.
23. From these determinations we will turn to the definite
evaluation of the amyl-acetate lamp in absolute measure.
Care must be taken that the platinum wire is linear, but
the amyl-acetate flame, on the other hand, flat ; 7. ¢. so that
the rays from the former traversing the slit only fill a portion
of the objective, whilst those from the latterly entirely fill it
so soon as the flame is sufficiently near to the slit, as is the
case in our experiments.
How account is to be taken of these circumstances in their
influence on the brightness is explained in the following.
(a) First, we calculate the quantity of energy reaching
unit length of the slit from the platinum wire.
Let A be the diameter of the diaphragm in the collimator
which limits the pencil of rays issuing from it, e its distance
from the slit, 7 the distance of the wire from the slit, and 6
the thickness of the wire. The pencil of rays drawn from the
diaphragm through a point of the slit intersects on the surface
of the wire an area which, projected on the meridian-plane at
right angles to the axis of the collimator, has a breadth 6 and
a height y, as calculated from the proportion
iy eee
ys Hail sce, aye $
é
The quantity h/e occurring here can be calculated as follows.
Ata distance a of 35 centim. from the slit a scale was placed
at right angles to the axis of the collimator and to the length
of the slit, and a light was moved along the scale until an
observer at the telescope announced that the light could no
longer be seen. On moving the eye sideways right or left the
distance of these two points was 2°2 centim.: then
2°2
io Va 35-0 =) 0G3:
Mechanics of Luminosity. 257
Let us take, as a first approximation, the law of cosines*
as holding good for the radiation, then we replace the semi-
eylindric surface of the wire radiating to each point of the
slit by the rectangle yé=/.
Let the quantity of energy radiated by each square centi-
metre be EH, then the surface 7 gives, on the whole, the
quantity of energy H/.
If the width of the sht is s, then the unit of length of the
slit receives a portion which is to the total radiation as the
surface of the slit corresponding to the unit of length s. 1 is
to the half surface of a sphere of radius 7. (In the quantity
E determined by experiment we have only the quantity of
energy radiated outwards, and not that radiated towards the
interior of the wire.) This fraction is s/277.
Hence upon the unit length of the slit there is radiated
from the surface 7 of the glowing platinum wire a quantity of
energy ae
A=5-5 b= D3 E=(°) iE
: e 217? e / Qa
In our experiments
h/e=0°063, 6=0°026 cm., »=4:4 cm.;
consequently 0-026
(6) We will now calculate the similar expression for the
energy sent to the slit-by. a flat-shaped source of light of con-
siderable extent, like that of the amyl-acetate lamp, or the
Bunsen flame co!oured with sodium, which is so near to the
slit that the cone passing through the diaphragm of the colli-
mator and a point of the slit in its prolongation towards the
flame is completely filled with luminous particles.
The cone from the diaphragm through a point of the slit
cuts the flame in a circle; if the flame is at a distance 7’ from
the slit, and if 6 is the diameter of this circle, then the
* The validity of the law of cosines may, upon theoretical grounds, be
open to doubt. As is well known, it is established by regarding as the
radiating quantity that contained in a parallelopiped whose base is the
radiating surface, and of which the edge forms a portion of the prolonga-
tion of the rays under investigation, equal to the depth from which, in
general, rays still issue. But it is certainly not the particles contained in
this parallelopiped which give the rays issuing in the direction in question,
since in their introduction the refraction from metal into air is neglected,
of the existence of which (even before the direct proof given by Herr A.
Kundt) evidence was offered by the strong polarization of the emergent
light. Further experimental investigations are required to explain the
contradiction between theory and the observations of Herr Moller ( Wied.
Ann, Xxvi. p. 266), which tend to confirm the law of the cosine.
258 Prof. E. Wiedemann on the
radiating surface is
If a square centimetre emits a quantity of energy KH’, then
our surface yields a quantity of energy,
ouat
Of this the fraction which reaches the unit length of the
slit is s/47r7’”._ We must here divide by the whole surface of
the cone, since the sodium flame is transparent to its own
rays. The quantity of energy actually falling upon the slit is
therefore :
(ied OS aS 4 12 at (2) pmo oh’
eae 7?B' = =,(~) H’=00;25 oB’.
The distance 7! thus does not occur in the final result, since
the radiating surfaces increase as the squares of the distances.
We may say that the quantity A’ is the fraction of the total
energy which passes through the diaphragm. Strictly speak-
ing, account should also be taken of the circumstance that the
flame represents not a space bounded by two parallel very
large surfaces, but a cylinder. Nevertheless, what we thus
neglect is small in comparison with the other sources of error.
We have further neglected the fact that the slit is not a
portion of the sphere, but occupies a tangent plane.
(c) We therefore obtain for the ratio of the energies
which reach the slit from an extended source of light, and a
narrow linear source
Naame a Qarn Bi’ #18) poke
AT 16 \C). Ocak ay h} 2arn A
With the dimensions of our apparatus in particular
H’ A’ !
pnl24q> B/ =0-24 0.
The ratio of the energy of a source of light with a con-
tinuous spectrum, and that of the platinum wire at a definite
point of the spectrum is obtained at once from the readings
of the photometer. We have seen above that the brightness
of the platinum is 1°827 times greater than that of the amyl-
acetate lamp for the yellow in the neighbourhood of the D
line. Hence ie UNS
A'/A=0'547,
and we obtain for the energy of unit surface of the amyl-
Mechanics of Luminosity. 259
acetate lamp expressed in terms of that of the glowing
platinum for the yellow )
K’=0°24 .0°547 H=0°13 E.
~ Comparison of Sodium Flame and Glowing Platinum.
24. After this determination we may further ‘compare the
brightness of the amyl acetate lamp for the yellow with that
of a gas-flame coloured yellow by sodium, according to the
method of Herr Ebert*, and thus the latter also with the
brightness of the yellow of glowing platinum.
If, then, we wish to determine the ratio of the radiation of
the sodium flame corresponding only to the yellow sodium
lines and the total energy of radiation of the glowing plati-
num, we must first determine the ratio of the latter to the
radiation which reaches a definite portion of the yellow.
For this purpose we will make use of the results of
Mouton}, by assuming, without doubt correctly, that the
temperature of the platinum wire in our absolute measure-
ments is nearly equal to that of the platinum wire in
Mouton’s Bourbouze lamp.
Tf this is not exactly the case, and consequently the final
value is not quite accurate, yet its order of magnitude can in
no case be affected.
In order to obtain a part of the radiated energy which
belongs to a definite portion of the spectrum situated in the
neighbourhood of the D-line, the following method was
adopted. A curve was drawn upon paper according to
Mouton’s numbers, which represented the distribution of
energy as a function of the wave-length. The wave-lengths
were measured in ly, the energies in any convenient unit
By division of the weight g of a piece of the curve-paper of
known area by the weight G of the area included between
the curve and the axis of abscissee, we obtain for the fraction of
the total energy corresponding to unit area
ee
* Wied. Ann. xxxii. p. 345 (1887).
+ Compt. Rend. lxxxix. p. 295, 1879; Beibdl. iii. p. 868, 1879. The
following calculation of course proceeds upon the assumption that we
obtain the whole quantity of radiated energy in the bolometer or the
thermopile, or that the substance of the bolometer absorbs even the extreme
infra-red rays. This may be tested experimentally by comparing the curve
of energy determined by the bolometer with the total expenditure of
energy as measured by resistance and intensity. I should have liked to
have determined the distribution of energy for the wire employed by me,
but unfortunately this was not possible with the very unfavourable con-
ditions of the Erlanger Institute—it is so exceptionally damp that it is
not zeae to set up rock-salt prisms &c. for the purposes of an extended
research.
260 | Prof. E. Wiedemann on the
In our ease |
a=0°0,83.
If we make the slit so wide that when illuminated by homo-
geneous light of wave-length X it has a breadth in the spectrum
corresponding to a difference of wave-length A at this place,
and if we now illuminate it with white light, then every point
at the same place receives rays between the wave-lengths A
and X+A.
If the ordinate corresponding to the wave-length X in the
energy-curve is y, and that corresponding to X+A is y;, then,
since A is always small, the area included by the ordinates y
and y,, the curve, and the axis of abscissa is
poy
2
and the corresponding energy is
yr
a> A.
The breadth A of the slit illuminated by the sodium flame
in our experiments amounted to 0°22 of the distance between
the sodium and lithium lines in the spectrum; the wave-
length of the sodium line is 0°59, of the lithium line 0°67.
Each point of the spectral image receives then rays between
the wave-lengths 7=0°59 and 7+A=0°59+ (0-67—0°59)
0°22=0°6076. Further, to the abscissee 0°59 and 0°6076 cor-
respond the ordinates y= 11-35 and y,=13°33 ; the above-
mentioned surface is therefore
11°35 + 13°33 ee 68
But to this surface there corresponds a fraction & of the
total energy
£—0-0,83 x
x 0:0176.
24°68 1
a x 0-:0176=0-00180= 556"
Having thus determined the energy corresponding to this
definite breadth of slit from measurements with our apparatus,
we find for the sodium flame the whole, but for the platinum
wire only the s1¢ of the total radiated energy.
A’ and A are the measured brightnesses of the sodium
flame and of the platinum wire, in reference to that of the
amyl-acetate lamp ; they are proportional to the squares of ea
cotangents of the readings on the photometer.
A'=const. cotan?a', A=const. cotan’a,
where the constants have the same value.
is —_—- - na a
-
Mechanics of Luminosity. 261
Hence A! _ cotan*a!
A ecotanza ’
therefore 21
B= 0-94°082 ep,
cotan’a
In our case :
a=a0° 30), H=4°7, -and@ £=-!,
so that
4-7 cotan?a! . cotan?al
556 cotan? 365 = Mee cog BeL cm. g. sec. cal.
i —()°24
Coefficient of Total emission of 1 gr. sodium in absolute
Measure.
25. In order to test, in the first place, the dependence of
the emission of light upon the quantity of sodium chloride
contained in the unit volume, two solutions of sodium chloride
were scattered into a flame in the mode described by Herr
Hbert, exactly in the same way. They contained in 1 cub.
centim. respectively
(a) M=0-0304 gr. sodium, (b) M,=0-0182 gr. sodium.
Their density was nearly unity.
A portion of the flame was placed opposite to the slit, which
appeared uniform in the whole section. Its diameter is
2 cub. centim.
The readings a’ on the photometer and the corresponding
cotan’a’ were for
@) al=31"; cotan’a’ = 2°770,
(b) a, =42°, cotan?a,’=1°233.
Therefore, very nearly,
M : M,=cotan’a’ : cotan’a,’,
er 00304 : 0°0182=2°770 : 1°233.
The brightness therefore increases nearly proportionally to
the quantity of salt present, which is also what Herr Gouy*
has found.
For solutions of sodium carbonate, which contain in the
unit volume the same quantities of sodium as the above
sodium chloride solutions, the same brightnesses were found.
26. We will now calculate the quantity of sodium which
in the first of these solutions yields the observed brightness,
and the corresponding quantity of energy.
2100 cub. centim. of gas-mixture pass through the burner
per minute+. The velocity at this point is, therefore,
* Ann. de Chem. et de Phys. [5| xviii. p. 5 (1879).
Tt Cf. also H. Ebert, Wied. Ann. xxxiv. p. 83 (1888).
262 Prof. EH. Wiedemann on the
2100 ;
Z14xL =670 centim.
7. é@. in each minute a column of gas 670 centim. long passes
in front of the slit. In 380 minutes 1°025 gr. would be
scattered, therefore in 1 minute 0°034 gr. A column of
1 centim. height and 2 centim. diameter contains therefore
0°034 _ st
and in 1 cub. centim.
OX MOR ae Ne
oS =) 59 x 10 gr. fluid dust.
With the concentration chosen 1 cub. centim. of the flame
contains
4°8 x 10-7 gr. sodium.
Let us now calculate the quantity of sodium in a parallelo-
piped of unit height and breadth, therefore of the unit of
radiating surface and of the thickness of the fame as depth,
2.e. 2 cub. centim.; it contains in round numbers
9°6 x 10-7 gr. sodium.
This quantity of 9°6 x 1077 gr. sodium therefore radiates
the quantity of energy per second
Hi’ =0-002 er
ey d1
n’ 364
The coefficient of ne emission of sodium, i.e. the quantity of
energy radiated by 1 gr. sodium in the two yellow lines of the
Bunsen flame amounts to
=0°00308 cm. g. sec. calories.
3210 g. calories per second,
from which we obtain upon the assumption (no doubt not
strictly correct) of equal brightness, 1600 gr. calories ee
second for each line.
An atom of sodium weighing 1:7 x 10-2 gr. emits per
second
5°) x 10—* gr. calories.
27. We found before that 1 gr. platinum radiates on the
whole 2°2 x 104 gr. calories per second, now we find that with
sodium for the two isolated spectrum lines the same value
amounts to 3°2 x 10°, whichis not so much less. It is as if the
energy emitted, which with platinum is distributed through-
out the entire ’ spectrum, were with sodium concentrated in
the two lines.
In the case of sodium we have besides the energy of the
infra-red rays present according to the researches of Hd.
alr re
Mechanics of Luminosity. 263
Becquerel *, so that the coefficient of total emission of sodium
for all rays together is greater than 3°2 x 10°.
True Coefficient of Emission of 1 gr. Sodium. Comparison
with Platinum. Application of Kirchhof’’s Law.
28. From the data for the coefficient of total emission for
sodium, and the breadth of the sodium lines, we may obtain
the true coefficient of emission for the unit breadth in the
spectrum (cf. p. 161) for 1 gr. sodium.
For this purpose we have only to divide the energy emitted
by the breadth of a sodium line; this according to diffraction
experiments (see below 32, p. 265) is 4 of the distance be-
tween the centres of the two sodium lines—that is 0°15 py.
The true coefficient of emission is then, if we take 1 wy as unit
for the wave-length, 1600
ial: We
2.¢. 1 gr. sodium in a region of the spectrum of the breadth
1 wy would emit per second 10700 g. cal., or in round num-
bers 1:1 x 10* if the brightness throughout this region were
alike.
29. We may further compare the true coefficient of emission
of sodium vapour with that of solid platinum. We have
seen above (p. 259) that since the ordinate of the curve of energy
of platinum at the point which corresponds to the sodium
line is 11°35, the energy eradiated within the region of the
spectrum of breadth 1 wy by platinum is
& H=0°0,83 x 11°35 x 0001 x H=9:4 x 10-5 E.
Thus 1 gr. platinum emits (c/. p. 254) in this region
9-4 x 10-° x 2°2 x 10*=2°1 cal.
The ratio of the true coefficient of emission of sodium Sy,
and platinum Sp; is therefore per gramme
Syna hou, 1-10 107
Spt = 21
The coefficient for sodium is thus much greater than that
for platinum.
30. A film of platinum of 1 sq. centim. area and 10-5
centim. thickness, which contains 2x 10-4 gr. platinum is
almost opaque.
According to Kirchhoff’s law a film of sodium vapour
which for equal area contains less substance in consequence
of its greater coefficient of emission for its particular rays,
* Kd. Becquerel, Compt. Rend. xcix. p. 374 (1884).
= 10700%
=e:
264 Prof. E. Wiedemann on the
must also be opaque; 7. ¢. a film which contains per square
centimetre
2 >< 10
5x he:
In the sodium flame examined by us there is present in a
layer of 1 square centimetre 6°9x1077 gr., that is about
twenty times as much as would be necessary to produce such
opacity with the platinum.
If, therefore, Kirchhoff’s law is to hold good here the
flame must be absolutely opaque for the yellow rays. In fact
such a flame shows reversal ; 7. e. in the centre of each of the
yellow sodium lines a dark line appears when a ray of white
light traverses it, nevertheless the absorption is by no means
so great as one would have expected according to Kirchhoff’s
law, since the dark line is confined to the centre. Hence
it would seem that in the sodium flame luminescence
phenomena appear together with with the usual luminous
phenomena. In fact, highly complicated chemical processes
occur in such a flame ; further researches will show this more
clearly.
Direct Comparison of the Coefficients of Total and True
Emission of Platinum and Sodium.
=4 x 10-8 gr. Na.
31. In continuation of the foregoing, an experimental
arrangement was employed, which will find frequent applica-
tion in later investigations.
In one and the same flame sodium was distributed and a
platinum wire was heated to luminosity, and the brightness
of each was compared with the amyl-acetate lamp.
The apparatus shown in fig. 3 (Pl. IIL.) wasemployed. In
the interior of an Ebert’s* burner, B, a thin platinum-wire 0°26
millim. thick was fastened at a; it had thus the same thickness
as the wire previously investigated, which was heated by the
current; at its upper end it was attached to a small hook
which was suspended to one arm of a lever, movable about
the horizontal axis e, which was capable of being adjusted
as to height. The lever was weighted on the other side by
the weight fin order to keep the wire stretched when hot.
Then water only was scattered in the flame, which was
colourless, and the brightness of the platinum wire was
measured ; then by a slight movement of the support the wire
was put out of the field of view, the flame was fed with
sodium solution, and its brightness measured again. ‘These
measurements showed that the ratio of brightness of the pla-
* Wied. Ann. xxxu. p. 345 (1887).
Mechanics of Luminosity. 265
tinum wire to that of the sodium flame was almost the same
as in the previous experiments in which the wire was heated
by a current. There is no object in giving the particular
values here.
In exactly the same way experiments were made with solu-
tion of strontium chloride, which yields a spectrum of bands,
solutions equivalent to the sodium chloride solution being
scattered in the flame. ‘The result obtained was that the
total brightness is of the same order as that of the sodium
flame, which also may be inferred from the strong colora-
tion of the flame.
Here, therefore, nearly the same total energy is distributed
over a series of bands.
32. We will now determine the ratio of the true coefficients
of emission of two sources of light. For this purpose let
us consider the following points:—
If we have a narrow spectral line whose boundaries are at
A, and A,, and if we examine this with a spectral-photometer
of small dispersion, it appears in the spectrum of the same
width as the slit. Let the dispersion be so chosen that the
edges of the slit correspond to wave-lengths \ and X+A in
the spectrum. If then, by means of a spectrophotometer,
we compare the brightness of the spectrum-line » and of a
continuous spectrum, then each point in the image of the
slit, corresponding to the line-spectrum, receives rays between
A, and Ay, and in the image of the slit corresponding to the
continuous spectrum each point receives rays between
Aand A+A. If the intensities corresponding to the wave-
length » are in the two cases v’ and 2” respectively, then the
total intensities J; and Jz in the first and second image
respectively are :—
MS AA ES
Ji = vdnr and Jo = ( dn.
hs Se
The quantities 7’ and 7” are proportional to the true coefficients
of emission ; the ratio of the intensities is therefore
A2 | A+A |
v=| 2’dnr ‘| "dr.
Ke A
In the simplest case we may assume that 2’ and 2” are con-
stants, 2. e. that the spectral lines between ), and A,, as also
the continuous spectrum between Xand A+A, possess every-
where the same brightness, then
a” vNe—Av
Sere an et
The observed ratio of intensities is therefore proportional to
266 Prof. E. Wiedemann on the
the ratio of the true coefficients of emission multiplied by
(4y—r)/A.
e may determine 2'/2’’ directly, if we observe with a
spectrophotometer possessing so great a dispersion that the
line also appears as a continuous band, for then the slit
appears illuminated by homogeneous light of a width which
is distinctly smaller than the spectral image of the line, it
behaves therefore as a portion of a continuous spectrum ;
instead of A»—2A, we have A, and that the more accurately
the greater the dispersion, and the ratio of brightness measured
in the apparatus is itself 7’/2”.
In order to determine the ratio 2'/2’ for a sodium flame and
the amyl-acetate lamp, the following arrangement was made:—
The spectrum apparatus consisted of two telescopes belonging
to Herr Hbert and a plane Rowland’s grating. The colli-
mator was provided with an arrangement for symmetrically
narrowing down the slit, and had an aperture of 65 millim.
and a focal length of 1 metre; the observing-telescope an
aperture of 75 millim. and a focal length of 1 metre. The
grating had a divided surface of 46 x 386 millim., and possessed
very good definition. The slit was made very narrow. For
the determination of the maximum of brightness a totally-
reflecting prism was placed before one half of the slit; the
beam of light from an arc lamp fell upon the uncovered half of
the slit, after having traversed two adjustable Nicols. The
light from the sodium flame or amyl-acetate lamp entered
the apparatus through the totally-reflecting prism. First the
sodium flame was brought before the prism, the apparatus
adjusted for the greatly expanded sodium lines of the fourth
spectrum by turning the grating, and the spectrum of the
arc lamp weakened by turning one of the Nicols until it
appeared of equal brightness with the sodium lines in that
part of the spectrum.
Then the sodium flame was replaced by the amyl-acetate
lamp, and adjusted for the yellow of the first diffractive
spectrum. Since the light of the electric lamp was much
brighter than that of the amyl-acetate lamp it was weakened
by clouded glasses of known strength till the two spectra
were of equal brightness. A direct comparison of brightness
between the amyl-acetate lamp and the sodium flame in the
fourth spectrum was not possible, because in the fourth
spectrum the first was hardly visible. But since for all
sources of white light the degree of weakening in passing
from one spectrum to another is the same, and all continuous
spectra are dispersed in the same degree, the ratio of bright-
ness of amyl-acetate to arc-light must be the same in the
Mechanics of Luminosity. 267
spectra of different orders. This is also confirmed by a
simple experiment. If an equality of brightness between the
are-light and the amyl-acetate light had been established in
the first spectrum by the use of clouded glasses, this equality
was also observed in the second and third spectra.
The comparison in brightness between the arc lamp and
amyl-acetate lamp was made at a point a little distance from
the yellow, on the side of the green, so that it might not be
disturbed by sodium contained in the arc. The results of
experiment are as follows :—The breadth of a sodium line is
1 of the distance between the two lines. The brightness
diminishes from the centre rapidly, then more slowly, and at
the edges more rapidly again. The measurements were made
at about 1 of the breadth from the edge after the brightness
of the arc-light had been made equal to that of the sodium flame
by rotation of the Nicol, it had then to be reduced to 34 to be of
the same brightness as the amyl-acetate lamp.
The brightness of our sodium lamp therefore for rays
situated about 1 of the breadth of a sodium line from its
edge is 34 times greater than that of the amyl-acetate lamp
at the corresponding point.
We may now apply the above results to the experiments
on p. 261, where the brightness of the amyl-acetate lamp was
compared with that of the sodium flame.
We will take 7’ to refer to the sodium flame, and 7” to the
amyl-acetate lamp. In the sodium double lines the breadth
of a single line is } of the distance between the centres of
the lines, so that the total breadth of the two together is 4
this distance ; the distance of the centres is known to be
00006 p, consequently the quantity A,—A,=0°0003 w; further
V was found to be 2°7, since A=0°0176 w (p. 259) therefore
pi) Be oyOiT6,
The direct determination for a point about } from the edge of
the weaker line gave - = 34. It follows from the difference of
these numbers, which agree as to order of magnitude, that the
above assumption as to the distribution of brightness is not
strictly correct, but that the brightness of a sodium line must
increase rapidly in the centre, which is also confirmed by the
appearance to the eye. This further indicates the possibility
that in spite of the breadth of the spectral lines, interferences
may occur with differences of path up to more than 100,000
wave-lengths, such as have been observed by several expe-
rimenters. [To be continued. |]
[268 4
SKY, On a Relation existing between the Density and Re-
fraction of Gaseous Elements and also of some of thew
Compounds. By Rey. T. PEtuam Dates, M.A.*
i my former paper which I presented to the Society f I
touched upon the empirical relations discoverable be-
tween the specific refractive energies of selenium and sulphur.
The present state of the data, however, relating to these sub-
stances is so far unsatisfactory that we are not furnished with
refractive indices and density taken from the same specimen
at the same temperature. ‘Thus there is a doubt as to the
density to be chosen as normal, in consequence of the differ-
ence due to the allotropic conditions in which these substances
are found. This difficulty may be to a certain extent eluded
by taking both densities and calculating the specific refractive
energy for both. The result is, in the case of selenium and
sulphur, that in both substances the mean values are not very
far apart.
The question, however, of the relation between the refrac-
tive indices of the elements is of so great interest, that it
appeared advisable to calculate the value of aes of all
chemical elements for which data existed, giving both refrac-
tive index and density in the state of gas or vapour. This
would include the refractive indices of hydrogen, oxygen, and
nitrogen, and the importance of these is obvious. Then, again,
the calculated densities derived from atomic weights might
be used in cases where an observation was wanting, and as a
check where these existed. A very few tr ials revealed
relations which it was impossible to overlook.
These relations among the numbers found are set forth in
the accompanying Tables.
These tables are arranged in columns. The first, column L.,
contains the name of the substance. Column II. its index of
refraction less unity, or w—1. Column III. its density.
Column IV. its specific refractive energy, or poe Column
d
V. the ratio of ~—1 in the substance to the similar number
for hydrogen. The upper row of numbers in each line are
natural numbers, and those immediately under are the man-
tissee of their common logarithms. Hxamining this table in
detail, it is seen at once that the logarithms of the specific
* Communicated by the Physical Society: read May 25, 1889.
+ Phil. Mag. Jan. 1889, p. 50.
On the Density and Refraction of Gaseous Elements. 269
refractive energies of nitrogen, chlorine, and phosphorus are
nearly identical, as also of sulphur and oxygen. It will also
be observed that in N, Cl, P this log. is double of that of
H, and § and O three times that of half the log. specific re-
fractive energy of hydrogen. In the same way, the log. of the
specific refractive energy of mercury is 8 times, and arsenic
9 times this quantity.
If we turn to column V. we find that oxygen has nearly
double the refractive energy of hydrogen, mercury 4, arsenic
8, sulphur, but not so closely, 12 times.
Now all these coincidences arise from observation only, and
are independent of theory altogether. The probability that
they should be fortuitous is very small in so large a number
of instances.
When we turn to the compounds, we again see indications
of the same law. Thus N,O has log. specific refractive
energy half of similar log. of CO; and the refractive energy
of Cy is very nearly 6 times that of hydrogen. All these
numbers may, roughly it is true, be united under a single
Be: thus, os fee de 15606 atallnanrittnn 10508,
and half this is 09789 ; this is according to Prof. Hverett’s
data. Mr. Lupton’s give (09374. If we multiply these suc-
cessively by 1, 2,... and 10, we shall find that almost all the
logarithms range between these two products, being less than
the greater and greater than thesmaller. It is worth noticing
that 5 =1°57079, log . = 19612—a curious coincidence
which, if quite fortuitous, will nevertheless prove a help to the »
calculator.
I have not as yet attempted to express these relations under
an algebraic formula, although it is obvious that it might be
very readily done. I prefer to call attention to the existence
of these empirical relations, which hitherto seem to have
escaped notice. ;
In some of the instances set forth in the Tables the density
was checked by calculation from the equivalents. This also,
it appears, opens another field of great interest. The well-
known relations between molecular weight and density lead
us to expect a relation between molecular weight and refrac-
tion, and this relation has been abundantly worked out in the
case of liquids by my friend Dr. Gladstone. I have not as
yet had time to work out this part of the subject com-
pletely, as though the calculations necessary present no
Phil. Mag. 8. 5. Vol. 28. No. 173. Oct. 1889. xX
270 Rev. T. P. Dale on a Relation between the
difficulty they require a numerous and bulky array of
figures which must be carefully verified and checked, and
also because more data are needed. It is also unfortunate
that no data exist, which are accessible to me, of the absorp-
tion-spectra of chlorine, bromine, or iodine, or of sulphur
and selenium, comparable with the observations here used
as the basis of the calculations in the Table. It is in the
hope that some of these data may be supplied that I venture
to put this paper before the Society.
Some interesting relations are observable between the
equivalents and refractions* of gaseous elements and com-
pounds, which I hope to present in a future paper.
Note—The data are taken from Prof. Everett's ‘Units and Physical
Constants,’ 2nd ed, 1886 (marked E) ; and from Mr. Lupton’s Numerical Tables,
1884 (marked L).
iE, II. III. IV. V.
Sy. Ref Ratio of
Sub- | Refraction,} Density. PG "| Refraetion Remarks,
stance.| p—l. d. Lane, to that of
d. Hydrogen.
| =.
O.
N.
Cl. L 7720 |E 380909 | 24986 4°27
14208 | 94630 |E 19578 L18749 Another value of log.
u—l
9706 | 14107 | 19182] 1-95 q. ‘Lupton’s data of log.
43933 | 14943 |B 28290 | 29025 |L 27993 ae
p-l
a
2977 12393 | 24241 2°14
47378 | 09318 |H 38060 33170 378134 do.
88762 | 49009 | 89753 | 62992 } Density given by Everett.
50243 | 38159
Cl. L 7720 |L 318 | 24274 \ Density and Index according
PS
He. | L 5560} 100xH}| 62918 4-00
to Lupton.
L 16290| 96xH|]| 19202 11-7 hoe ain totan ee:
1:21192 | 98227 | 28335 | 06984 Seay EC Oe eect.
L 13640 | 62xH}| 24895 9°84 \ Density calculated from equi-
1:13481 | 73869 | 389612 | 99273 |; valent.
74507 | 94630 | 79877 60299 \ Calculated from hydrogen.
As. L 11140 | 150xH| 74268 8:03 | Ditto
J
1:04689 | 17609 | 87080 90479
* I propose to call the quantity »—1 the refraction, p the index.
——|
Ja 0001387 |00008837} 15696 1-00
Density and Refraction of Gaseous Elements. 271
I. IT.
Sub- | Refraction. Peat:
stance.|| p—l.
—_———$——. —_—_—_——
ITI.
N,O.} EH 2975 |H19433
1-47349
NO. | E 5159
71257
co. | EB 3350
52504
So, | E 7036
| 84733
Cy. | E 8216
91466
NH,. 385
5855
HCl. 449
6522
HS. 665
8228
CH,. 443
6464.
C.H,. 678
8312
28554
E 13254
12235
E 12179
29024
E 26990
43120
E 22990
36154
0-761
8814
1-64
2148
1°52
1818
Cale.
8554
Cale.
8554
Compounds.
IV. V.
Ratio of
Sp. Ref. Refraction
ee |e tosthatror
A eee
15309 2°14
18495 30141
38924 3°72
59022 33141
22947 O27
36720 57049
26070 5:07.
41613 70525
35737 5:92
55312 77258
2°78
7041 4434
3°24
4484 5107
4:79
6410 6807
2:02
7916 3040
49
7328 6900
Remarks.
All these are calculated from
experimental data of both
index and density from
Prof. Everett.
Se
Calculated from Lup-
3969 ton’s numbers.
Density calculated from hy-
drogen and equivalent.
ood ——-+--—_——_—_— -_———
These to four places are evidently of less value than those above.
Note by Prof. A. W. Rucker, /.#.S., on Mr. Dale’s Paper.
It has been shown that the volume of the molecules in unit
volume of the substance which they form is (u?—1)/(y?+ 2),
where yp is the refractive index.
If is nearly equal to unity (as in the case of the gases)
this expression reduces to 3 (u—1). Hence if 6 is the density
of the body, v and m the vias and mass of a molecule and
n the number of molecules in unit volume,
p—l
ee
}
_ 3d nv
2 nm
3 Ov
| 2m
272 Mr. J. C. M¢Connel on Diffraction- Colours,
For the same substance the right-hand side should be a
constant, and it has been shown that it nearly fulfils this
condition.
Mr. Dale now states that for different substances
log ae = TG
where ¢ is a constant independent of the nature of the
substance, and a is an integer. This at once leads to the
relation v/m=¥%e,., which would indicate that the ratios of the
volumes to the masses of the molecules are in geometrical
progression, or, more shortly, the densities of the molecules
are in geometrical progression.
Tf, then, Mr. Dale’s conclusions are correct this would be
the theoretical inference to be drawn from them.
XXXVI. On Diffraction-Colours, with special reference to
Corone and Iridescent Clouds. By James ©. M°ConneL,
M.A., Fellow of Clare College, Cambridge*.
[Plate X.1
N a previous paper f I have explained the occurrence of
bright colours in certain clouds near the sun on the
hypothesis that the light is diffracted by thin needles of ice
or by fine drops of water. In the present paper I give a more
complete determination of the actual colours produced, based
on Maxwell’s observations of the colour-relations of the solar
spectrum. The first section contains a mathematical investi-
gation of the light diffracted by clouds of filaments and of
spherules respectively. The second is devoted to calculating
the colours and setting them out on Maxwell’s diagram. And
I have been tempted to mark also on the diagram the colours
of the sky and sun. Ina future number of this Magazine I
hope to publish some additional remarks on iridescent clouds
and allied phenomena, including Bishop’s ring.
1. MATHEMATICAL EXPRESSIONS.
Rectangular Aperture. Point Source.
We will first take the case of a rectangular aperture
(sides ab) in an opaque diaphragm inclined to the incident
light at an angle y, and discuss the illumination on a
spherical screen of very large radius /, whose centre O coin-
* Communicated by the Author.
+ Phil. Mag. November 1887.
with special reference to Corone and Iridescent Clouds. 273
cides with that of the aperture. The side a is at right angles
tothe incident light. In fig. 1 3
only a quarter of the aperture Fig. 1.
is represented. %
O is the origin of coordi-
nates ; the axis of z is drawn
towards the source of light,
while the axis of z is parallel
to the side a of the aperture.
P(zyz) is a point in the
aperture.
M(& 7 %) a point on the sphe-
rical screen.
The source of light is small
and very distant.
Let the vibration at O be
represented by cos «vt, where
t is the time, v the velocity,
and «=27/d. The intensity
is then unity. The vibration M
at P iscosx(vt+2).
We now break up the primary wave into its secondary
components over the plane of the aperture, which is not a
wave-front. The disturbance at M due to the element dz dy
-at P is
-52 SMO ees 0), aes 4m 261) 4B)
where p= MP.
Now
p= (w—£) + (ya) + (2-0), and B4a Oa;
“yz are small compared with &7€; so, neglecting their
squares, we have
p> =f? —2x2& —2yn — 226.
In the last term we can put €=—/f, and obtain
+
P=2es ( 1— a”),
In the denominator of (1) we may write p=/f. So the vibra-
tion at M is 7
= (si K (ve —f+ ety) da dy,
b sin y
2
* Encyc. Brit., art. “ Wave Theory of Light,” p. 429.
the limits of # and y being + 5 and + respectively.
274 Mr. J. C. M¢Connel on Difraction- Colours,
Hence, as usual, the illumination on the screen is given by
a7? sin? vy oe rey ‘ahe fxr
=P) ee when
i 4 Fe ae
The field is crossed by two sets of parallel dark bands, given
by a&/fA and bsiny n/fr being positive or negative integers
other than zero. ‘There is a large central rectangle of dimen-
sions 2/A/a by 2/r/bsiny, surrounded by others of similar
shape but only a quarter the size. The brightest point is the
centre, and along the two principal directions the succes-
sive maxima have approximate values 0:046, 0°017, 0-0085,
0:0050..., that at the centre being unity, and are found at
distances given by
a/fN=1:48, 2°46, 3°47, 4:47.
Along the diagonals the numbers for the successive maxima
are the squares of the above, viz. 0:0021, 0:00029, 0:00007...,
so the diminution is much more rapid.
It is obvious from (2) that the linear dimensions of the
diffraction-pattern are proportional to A, and its brightness
proportional to X—?._ Thus, if the source send out white light,
the central patch will be bluish in the middle and tinged with
yellow and red at its edges. Along one of the principal direc-
tions, ¢. g. n=0, we have, governing the colour of the light,
the factor __ Tak
sin ia (3)
As will be explained in the next section, the colours are those
of Newton’s rings, though their relative brightness is very
different. Along the diagonals for which af=bsinyy, the
colour-factor is
M sint TF Ms LL
So that the tints are much richer, though the intensity is very
feeble.
Babinet’s Principle.
Suppose now that bsiny is much greater than a, so that
our aperture becomes a narrow slit. We are intending to
deal, not with slits in an opaque screen, but with filaments in
the open sky. This case may be immediately derived from
the other with the aid of Babinet’s principle. But it is
desirable, I think, to examine the application of the principle
in some detail. Replace the slit by a very much larger aper-
ture, say 500 times as long and 10,000 times as broad. The
with special reference to Corone and Iridescent Clouds. 279
screen is so far away that our expression (2) still applies ; in
other words, the diffraction-pattern is not supplanted by a
geometrical image of the aperture. But the diffraction-
pattern is enormously reduced in size, and outside it there is
no light. In this outer region the illumination wiil be the
same whether we block up all the aperture except the original
slit, or block up the slit by an opaque filament Jeaving the
rest of the aperture open. Tor the two portions of light must
be able to neutralize each other. So we may replace the slit
by a filament of thickness a and length 0, inclined to the inci-
dent light at the angle y, lying within our large aperture, and
(2) will still hold good except within a negligibly small area.
If then, according to (3), at any point in the screen the light
is, say, green, to an eye placed at that point the aperture will
appear a green speck. As the green light is not in any way
altered by increasing the size of the aperture, it is clear that
it must come from the region immediately surrounding the
filament, and that the filament will look green even when the
diaphragm is entirely removed.
Cloud of Filaments.
The effect then is the same, whether it be produced by slits
in an opaque diaphragm or by filaments in an open space.
The calculations are simpler in the case of slits, but practically
_we have to deal with filaments. So in future we shall speak
of filaments only, and in treating of the illumination of the
screen we shall refer only to the diffracted light and ignore
that which comes direct.
As ais made small compared with bsiny, the diffraction-
pattern is stretched out into a long strip, very narrow in the
y direction. If there be a large number n of filaments equally
inclined to the axis of z and evenly distributed round it, the
illumination is. found by summing the illuminations due to the
individuals. Practically we have to distribute the light we
find, according to (2), onany circle round the axis of z evenly
over the whole circle and then multiply it by n. Owing to
the narrowness of the strip we can treat & as constant for
points on the circle where the illumination is sensible. So of
the three factors on the right-hand side of (2), it is only the
last that varies. This third factor may be written p=sin? w/v”,
wherew=vbsiny.n/fr. If & and —€ be the points where the
circle cuts the plane y=0, the average value of p. over the
whole circle is, remembering that the strip is cut twice,
Vpdn|n€.
The integration extends over the region for which p is sensible,
and we are of course at liberty to extend the limits to +x.
=
276 Mr. J. C. M¢Connel on Dif'raction- Colours,
+° sin? u
Now 2 du =7 is a known result, and
—o
mb sin y dn/frx=du.
So \ pdn/wé =fr/rb sin y é.
Hence the illumination on the screen at points in the plane
y=0, due to a large number nz of equal regularly distributed
filaments making an angle y with the axis of z, is by (2),
in? wag
nvbsiny f fr
a Ne E Tee e e ° ° ° (5)
oS
To extend this to the case when the filaments are uniformly
distributed in all directions we must replace né sin y by 2dsin y.
If they occupy the fraction e@ of the field of view looking from
the screen, and the summation be extended over an angular
area w equal to that of the sun, we have
awf?= Lab sin y=adb sin y.
Now the direct illumination of the sun at the cloud is, by
hypothesis, unity, and it has the same value where the observer
stands, 7. e. at the imaginary screen. And it is obvious that
the apparent brightness of the sun and cloud are in the same
ratio as the illumination due to equal angular areas of each.
So, finally, the brightness of the cloud of filaments is in terms
of that of the sun,
awm TEN Tee ° ieee ° ° ° (6)
On p. 431 of my former article are given expressions for
the brightness of the first, second, and fourth bright rings in
a cloud of filaments, obtained in a different manner. It will
be found on examination that these expressions agree with (6).
In a cloud of filaments, of diameter a, the first four maxima,
according to (6), are proportional to 1, 0°215, 0-076, 0:035;
the ninth being 0:00386, and the central maximum being infi-
nite. This last result is not surprising, for we have supposed,
throughout the greater part of the argument, the source of
light to be indefinitely small.
In sunlight the colour is defined by the factor
sin? PM
These are the colours produced when the source is a luminous
with special reference to Corone and Iridescent Clouds. 277
line and the diffracting aperture a parallel slit, for the blurring
is of the same nature as that involved in the transition from
(2) to (5).
Diagonals of Square Aperture.
Before giving the accurate expression for the illumination
when the diffracting aperture is circular, it will be instructive
to examine a case which presents
the same peculiarities in an exag- Fig. 2.
gerated form. The main difference
between a circle and a square, as
regards diffraction in directions
parallel to the sides of the square,
is that in the former the outlying
portions, where the phase-differ-
ence is greatest, are relatively
small. This feature is still more
marked in diffraction by a square
parallel to its diagonals (see fig. 2), |
and this is a case we have inci-
dentally solved.
Let ¢ be the diagonal of the square, and ¢ the distance of
the point on the screen from the centre of the figure in a direc-
tion parallel to the diagonal. Then, putting y=7/2 in (2),
we obtain
ts es
: g 38 DFR :
— Af?n? meee ° ° e ° ° ° ( )
167%04
The dark points are given by c€=2mfa, where m is any
integer other than zero; and in general corresponding points
are twice as far out as in directions parallel to the sides of a
square of side c. As we have already seen, the diminution of
brightness is much more rapid, and the colours, when sunlight
is used, are purer.
Circular Aperture.
The expression corresponding to (2) for a circular aperture
1s aR? 45 .2(2)*
am BD, PU he) CO)
where e=2rRr/fnr ;
R is the radius of the aperture, and r the distance on the
screen from the centre of the diffraction-figure. The dark
* “Wave Theory,’ p. 432.
278 = Mr. J.C. MtConnel on Diffraction-Colours,
rings are given by
gjm=1'22, 2:23, 3:24, 4:24,...
and the maxima of the bright rings are given by
e/m= 1°60, "2 Goswell.) A(z eee
and have the values ,
0:0175, 0:00416, 0°00160, 0:00078,
that at the centre being unity. Thus corresponding parts
are rather further out than in the principal directions for a
square of side 2R, and the brightness falls off much more
rapidly. It seems legitimate to assume that the colours also,
when sunlight is used, are slightly purer.
Cloud of Water-drops.
To pass from the illumination on a screen, due to a single
circular aperture, to the brightness of a water-cloud, we
follow the lines of the previous argument, with, however,
considerable simplification, owing to the orientation of a
sphere being a matter of indifference. We have to multiply
(Y) by the number n of drops within an angular area equal to
that of the sun, and this number is given by
nt? =af7o.
So the brightness of the cloud, in terms of that of the sun, jg
aR? 4J,?(z
®@ o, se ) Wet tate =. eke oad (10)
The remarks we have made on (9) apply equally well to (10).
The colour-factor in both cases is J;’(z). For the two kinds
of clouds, compare the values of the maxima given under (6)
and under (9). We are enabled to make a fairly complete
comparison by the following result. When z is great,
J7(2)= = sin? (2— r) nearly*,
giving a colour-factor
a 7
Asn (2 7).
Kiven at the first bright ring the approximation is fair, for it
gives the first maximum at z=1-7167 with the value 0:0162;
and it rapidly improves as 2 increases, though always hetter
at the maxima than at intermediate points. The expression
(6) may be written in the form
* ‘Wave Theory,’ p. 432.
with special reference to Corone and Iridescent Clouds. 279
where zy =7ak/fn.
To secure corresponding points, let
T
Sl rin
and let us choose such values of R and a that the angular
_ distance from the sun is the same (=@) in both cases. For
this,
ab =2RO—D/4 ;sx
and, since by hypothesis z is great, a? amounts to several
wave-lengths ; and this equation is satisfied by nearly the
same values of a and 2R throughout the visible spectrum.
The ratio of the brightness of a water-cloud to that of an ice-
cloud is then 8R?z,°/a’z*, or 2z,/z. Thus the outlying spectra
from water-drops are about twice as bright as those from ice-
filaments, when the drops and the filaments occupy the same
fraction of the field of view, and corresponding spectra are at
the same distance from the sun.
Influence of Transparency.
We have incidentally assumed that drops of water and
needles of ice can be treated as opaque objects. Now ifa
single hexagonal filament be placed with one of its faces
normal to the sun’s rays, it is clear that the light, transmitted
through the part that behaves like a parallel plate, must inter-
fere with the light that passes on either side of the filament,
and should be taken into account. But with the varying
orientation of the filaments, the quantity and relative retarda-
tion of the transmitted light would alter to such an extent
that the practical result in the case of a cloud would merely
be the addition of so much white light.
The case of a spherical drop of water does not admit of the
same variety. And it would seem that, when the size is uni-
form, the transmitted light should be taken into account.
The investigation would be complex, even if it be possible
with our present knowledge ; but we see at once that a large
part of the light must be retarded relatively to the uninter-
rupted light by about a third of the diameter of the drop.
Thus the character of the effect would change completely with
small changes in the size, and in ordinary clouds we shall not
be far wrong in treating the drops as opaque. It is probable
that the comparative poorness of water iridescences is partly
due to this cause.
The legitimacy of adding the illuminations due to the dif-
ferent drops, without reference to phase, has been shown by
280 Mr. J.C. MeConnel on Diffraction- Colours,
Lord Rayleigh to depend on “ the light being heterogeneous,
the source of finite area, and the obstacles in motion.”
2. CURVES ON THE CoLouR DIAGRAM.
In a very interesting paper (Trans. Roy. Soc. Edinb. July
1886) Lord Rayleigh has set out a curve representing the
series of colours of thin plates on Maxwell’s form of Newton’s
diagram. Before such a calculation had been made, it would
have been impossible to predict from theory, except in the
very roughest manner, the nature of these colours, though the
exact composition of the light in terms of wave-lengths were
thoroughly known. The reading of this paper made me
anxious to obtain a more complete theory of the splendid
colours of iridescent clouds, and I have incidentally deter-
mined some of the colours of various diffraction-patterns.
This led to the discovery of a serious blunder which I
made in my former paper on iridescent clouds, in supposing
that the central band in the diffraction-pattern of a slit was
colourless. IJ was following high authority, for Verdet says
(Legons @ Optique Physique, § 70), “‘on apercoit au centre du
phénomeéne une bande blanche et brillante, qui est située sur
la direction normale 4 la fente diffringente.” As soon as
attention is called to the matter, itis obvious that the edge
must be reddish, since the breadth of the band in homogeneous
light is proportional to the wave-length ; and, as a matter of
fact, this red fringe is the finest red of the whole series. The
centre of the band is a pale though bright blue. But this
depends on the introduction of the factor X—! in the expression
for the secondary vibration, the necessity for which was not
recognized in Verdet’s time. I do not remember seeing the
coloration of the central band distinctly pointed out, though
it is implicitly contained in a statement of Verdet in the very
section I have quoted. He says that, when white light is
used, the red bands correspond to the absence of the brightest
part (2. e. the yellow) of the spectrum. This is not quite
correct, for my results show that they correspond to the
absence of the blue-green.
As the three corners of his diagram, Maxwell (“ Theory of
Compound Colours,” Phil. Trans. March 1860) selected equal
widths on his prismatic spectrum, near the points marked on
his scale by 24, 44, and 68. Between any colour whatever
and these three a match can be made by altering the propor-
tions ; either a combination of three matching the remaining
one, or a combination of two matching a combination of the
other two. Thus, for example, unit width at any point of his
prismatic spectrum could be expressed as the sum of multiples
y ane
~
'
"with special reference to Corone and Iridescent Clouds. 281
of the three units, using negative signs when required.
Looking at the table below, we see .
(36) =0°48(24) + 1:25(44) —0:02(68) ;
which means that the mixture of 0°02 of (68) with unit width
of (36) is indistinguishable in hue, depth, or brightness from a
mixture of 0°48 of (24) with 1:25 of (44). The position of (36)
on the diagram is the centre of gravity of weights proportional
to 0°48, 1:25, and —0°02, placed at the three corners (24),
(44), and (68). The brightness of a colour is not indicated
by the diagram.
The most important property of the diagram is the follow-
ing. Let us define the brightness of any colour to be the
algebraic sum of the corresponding multiples of the three
corner units. Then if any colour C be composed of the colour
A of brightness «, and of the colour B of brightness £8, its
position on the diagram is the centre of gravity of weights «
at A, and @ at B, and its brightness is 2+. Hence all the
colours on any straight line are mixtures of the colours at the
two ends of the line, and, in particular, all the points on a
straight line drawn from the point white are of the same hue ;
the depth or purity increasing as we near the spectrum-
colours on the borders of the diagram.
Now Maxwell has determined the multiples necessary to
express unit width at any point of the spectrum in terms of
the three corner units. The sum for the whole spectrum
must represent white. And, if the relative brightness of dif-
ferent parts of the spectrum be altered in a known manner,
we can, by introducing the proper factors before summation,
find the resultant colour in terms of the three units. Lord
Rayleigh used a table, containing twenty-two equidistant
points of the spectrum, based on Mrs. Maxwell’s observations.
From this I have deduced the following abridged table, which
is sufficiently accurate for my purpose :—
Scale-number.| Wave-length.| (24) (44) (68)
20 663 +044 | ow... +0-04
28 608 +117 +0°32
36 563 +0°48 +1:25 —0-02
44 BZQRO AY CI, os +1-:00
52 500 —0.06 +0°51 +028
60 475 —0-05 +019 +0°75
68 BDA eythi alice hac wcyert lite seqaess + 1-00
76 441 OLOS) We anaes +0°69
84 GUIS) <= ptr aaa aie lad eal se +0°33
92 EPR, Lik TN: Ei gtc +0°15
282 Mr. J. C. MeConnel on Diffraction- Colours,
The white obtained by superimposing unit widths at the
ten points is given by
W =2°01(24) +.3:27(44) + 3:22(68).
The chief defect of this table is the omission of the red
corner (24). This has been in great measure allowed for by
modifying the coefficients for (20) and (28). At the same
time the white was brought to practical coincidence with the
white of Lord Rayleigh’s table.
On the diagram (Pl. X.) are marked the positions of sixteen
points equidistant in the prismatic spectrum, from 20 to 80 on
Maxwell’s scale, with the corresponding wave-lengths. These
lie, for the most part, outside the triangle. Rood has deter-
mined the places in the spectrum which, when diluted with
a suitable amount of white, match the colours of certain
pigments (‘ Modern Chromatics,’ p. 38). I had no data for
marking the true position of the pigments on the diagram, but
their hues (2. e. the radii from white on which they lie) are
indicated. I have also divided the diagram into five parts,—
blue, green, yellow, red, and purple, chiefly in order to name
the hues in the “ brilliancy ” curves described below. In this
I have been mainly guided by Rood’s ‘ Modern Chromatics.’
On the spectral colours his statements are definite. But the
limits of purple, founded on considerations of complimentary
colours, are more doubtful. The estimation of hue depends
greatly on the brightness of the light and the purity of the
colour ; and of course, at the best, the lines of division must
be rather indefinite. The pure yellow in the spectrum is a
very narrow band; so my yellow division consists mainly of
orange-yellow and greenish yellow.
In the previous section I have shown that to find the
colours in the principal directions of the diffraction-pattern of
a rectangular aperture, the proper factor to multiply each of
the constituents of sunlight before compounding them is
sin? ue For the colours of thin plates the appropriate
factor, “strictly applicable only to a plate of air bounded by
media of small refrangibility,” but practically sufficient for all
e e e T o e
ordinary cases, is sin?——. Thus identical colours are found
: nN
in the two cases, whenever the “ retardation ’’ V for the thin
plate is equal to the extreme retardation a&/f of light from one
edge of the aperture relative to light from the other. The
dotted curve (copied from Lord Rayleigh’s) represents these
colours, and the small figures at the side are values of a&/f
expressed, like the wave-lengths, in millionths of a millimetre.
PESTS Pee
with special reference to Corone and Iridescent Clouds. 283
At the central point of the diffraction-pattern (a&/f=0) the
brightness is a maximum (instead of being zero as in the case
of a thin plate, when V=0), and the colour-factor is —?.
Abont 250 the curve passes very near white, on the side
towards blue-green. The colour then becomes yellowish,
gradually improving, till at 450 a very fine orange is at-
tained. And so on through the well-known series. When
the retardation is large the curve approaches nearer and
nearer to white, and, in the case of diffraction, the brightness
diminishes indefinitely.
Along the diagonals of the pattern, where the colours are
the purest, the factor is
pia gunde
sin cn
I have determined two points on the curve, D, in the first red
(a&/f=500), and Dz in the second green (a&/f=810). The
curve starts from the point X~?, and afterwards for several
sweeps keeps outside of the thin-plate curve. The first orange-
yellow and the second blue of the latter admit of but little
improvement. But in the first red, which borders the central
spot, the diagonals are far superior to the principal directions.
We now come to the main object of the present paper, the
colours of iridescent clouds, formed by needles of ice. The
colour-factor is
make
cg
Av sIn ae
Comparing this with the factor for thin plates we see that the
greater wave-lengths have an advantage. So the curve is, on
the whole, displaced from the violet and towards the red.
This curve is laid down on the diagram with a continuous
line. Points actually determined are marked with small
crosses, with the values of a&/f annexed in bold figures*.
The rest of the curve has been drawn by comparison with the
thin-plate curve. The curve starts at the point A7~!, so the
central blue though bright is very impure. On the whole
the colours are superior to those of thin plates. The reds are
distinctly better, especially the third red. The second blue
is nearly as good, though the third is decidedly inferior. The
third and fourth greens are about on a par for purity, but
more inclined to yellow, while the first and second yellows
* The calculations were inadvertently made for \? sin? (waé/fd), and
the points given are put halfway between those thus found and the
corresponding points on Lord Rayleigh’s curve. All the calculations
were made with a slide rule reading to 545.
284 Mr. J. C. M°Connel on Diffraction- Colours,
are somewhat purer and more inclined to orange. The curve
ultimately circles round closer and closer to the point A, a
very pale orange-yellow.
The custom of speaking of the successive diffraction spectra
is apt to lead to the impression that each spectrum is purest
in the middle when it does not overlap its neighbours. In
the colours of the first two orders the exact contrary is the
fact. A better idea of the phenomenon is arrived at by con-
sidering the wave-lengths that are absent ; in other words, by
considering the dark bands in the spectrum into which each
colour could be drawn out. The fine yellows of the first two
orders are due to the upper part of the spectrum being nearly
quenched by broad dark bands, which as they proceed down
the spectrum give the blues of the second and third orders.
Before we can obtain a good green we must have two bands
to blot out both ends of the spectrum. This occurs at 1330
and 1830.
Fraunhofer (Verdet § 70) using white light measured the
deviations of the red bands in the diffraction-image of a slit,
and, finding they were in the ratiol1:2:3 .. , thought he
had discovered the law for the successive maxima of homo-
geneous light. The complete explanation of this may be seen
in the diagram; for the points 500, 1000, and 1500, corre-
sponding to the absence of wave-lengths in the neighbourhood
of 500, lie almost on the line from W to the red corner.
The fourth red was probably not measured by Fraunhofer.
The real maxima for wave-length 631 are at the points 0, 900,
1550, 2190.
Maxwell’s colour diagram gives us complete information as
to the hue and depth of each tint, but is silent as to the bright-
ness; and with cloud colours, which are necessarily more or
less contaminated with white light, the brightness is of great
importance. It is clear, too, that the power of withstanding
contamination depends on the depth as much as on the
brightness. It occurred to me, therefore, that it would be
instructive to draw a curve with retardations as abscissee, in
which the ordinates should depend on both these qualities,
and should represent what I will call the brillianey of the
colour. I have used the following principles :—(1) the bril-
liancy of white light is zero; (2) the brilliancy of standard
red light is reckoned equal to that of standard green or violet
light, when they are in the proportion in which they occur in
white light; (3) the brilliancy of any colour which is com-
posed of two standard colours is equal to the brilliancy of the
more brilliant component. ‘The third principle ensures that the
brilliancy of complementary colours should be equal. As an
with special reference to Corone and Iridescent Clouds. 285
example of the application, suppose that the red, green, and
violet components of two colours are °536, 338, °042; °260,
"114, -084 respectively. The components of white are 2°01,
3°27, 3°22. Reducing the first two triplets in proportion to
the components of white, we have ‘267, 104, °013; °132, :035,
"026. These may be considered as mixtures of two standard
colours with some white light. Subtracting the white light,
and taking the greater of the remaining components of each,
we find the brilliancies are in the ratio '254::106. Treated
in this manner the brilliancies of the ten points in the spectrum
I have chosen come out proportional to 20, 47, 39, 30, 18, 26,
31,19, 10, 5. The maxima fall in the orange and the blue-
violet. The intermediate minimum is in the green-blue, a
part of the spectrum where the colour is generally considered
poor. It seems probable that, when nearly swamped with
white light, the colours would assert themselves nearly in pro-
portion to their brilliancy. At the worst the brilliancy curves
will be useful for comparing colours of similar hues.
In Plate X. is given a curve representing the brilliancy of
iridescent ice-clouds in accordance with the expression (6).
Owing to the occurrence of £ in the denominator the bril-
liancy is infinite when & is zero, and decreases rapidly as &
increases. The ordinates of the latter portion of the curve
are drawn on a scale tive times as great as those of the former.
The points where the nearest approach is made to the pure
colours of the spectrum are marked by the letter p. Under
the most favourable circumstances in the clouds, when all the
filaments are of the same size, there are two important causes
of blurring. The first is the finite diameter of the sun, which,
of course, prevents the brilliancy from being infinite. When
the first purple is at 5° from the sun—about an average dis-
tance—the colours over a range of 40 of retardation will be
all mixed together. This effect will be less marked when the
particles are finer and the colours further out. Another
cause, more serious than the other, especially for large re-
tardations, is the effective diameter of the filaments varying
from 1 to 1°155.
Let us now deduce the successive colours from a study of
the two diagrams, assuming the particles are of such a size as
to give 100 of retardation to a degree of arc. Up to 1° or
13° from the centre of the sun the light is very bright and of
a perceptibly bluish hue. If the cloud be dense even the face
of the sun will be tinted blue. From 14° to 24° the light is
practically white. Then a yellowish tinge asserts itself, which
attains its greatest brilliancy at 34° and its greatest purity at
44°. Between this and 54° intervenes a narrow ring of
Phil. Mag. S. 5. Vol. 28. No. 173. Oct. 1889. ng
286 | Mr. J. C. MeConnel on Diffraction-Colours,
reddish orange. Then a bluish purple extends as far as 53°.
A broad band of blue reaches to 74°, a poor green to 84°, a
fine yellow to 94°, an orange-red to 104°, a reddish purple to
113°. The third blue (to 124°) is greener and decidedly
poorer than the second. The third green (to 133°) is much
inclined to yellow. The next noticeable colour is in the pink
at 155°. There is a faint green at 184°, and a faint pink at
214°.
On Feb. 25th last I noted down some rather fine colours in
ice-clouds, in which the tint seemed to depend mainly on the
distance from the sun; in order outwards, yellow, bright red,
purple, green, greenish yellow, faint pink. A few minutes
later the purple had altered to faint purple, bright blue, and
the outer pink was succeeded by purple and green. This is a
good illustration of the extent to which the theoretical colours
are realized in observation.
Partly for the sake of comparison and partly on account
of its intrinsic interest, I give the curve of brilliancy of thin-
plate colours, deduced from Lord Rayleigh’s figures, with
the addition of an ordinate I have calculated in the first blue.
The light is suppesed to fall at a uniform angle on a film of
varying thickness.
When the diffracting particles are spherical the colour-
factor is, as we have seen, J,?(z). When z is indefinitely
small J,(<) = 2/2; so the curve starts from the point A~”.
When z is great
Ie) Sap ee aie eae a 2
so the curve starts somewhat outside the filament curve and
after a time comes near coincidence with it, finally oscillating
about the same point >A. Ihave calculated the colour* for
2Rr/ f= 600. This is the point marked ©, on the diagram,
which happens to fall exactly on the filament curve. I think
we may conclude that from the first red upwards the colours
produced by filaments and by drops will be practically
identical.
In the previous section I have shown that for a not too
small distance 0 from the sun and for corresponding colours,
te when
af = 2RO — d/4,
the brightness of the water-cloud is about twice that of the
ice-cloud. Thus we may make a fair approximation to the
brilliancy curve of the former beyond the first purple by
* Using the table for d(m) = 2n—1J,(”) given by Airy at the end of
‘The Undulatory Theory of Optics.’
t
with special reference to Corone and Iridescent Clouds. 287
letting the curve, hues included, stand as it is, and pushing
the abscissze to the left through a distance \/4. The quarter
wave-length varies from 158 at the red corner to 114 at the
violet corner ; but it is sufficient to take the mean 136. Even
in the first red we find 2R@=600 corresponding to a@=485.
An easy way of seeing these colours to advantage is to
lightly sprinkle the object-glasses of a pair of field-glasses
with lycopodium seed and direct them to the neighbourhood
of the sun. ‘fhe poorness of the green of the second order
compared with that of the third order is well brought out, also
the blueness of the first purple compared with the second.
The green of the fourth order is quite distinct, and the corre-
sponding red just visible.
The most notable difference between the colours of ice-
filaments and those of water-drops is the superiority of the first
blue of the latter both in purity and extent. On the whole
this agrees with observation, for the best inner blues that I
have seen in water-clouds were superior to the best inner
blues in ice-clouds.
Colours of the Sky and Sun.
To lend additional interest to the diagram I have calculated
a few points representing these colours. It is now certain
that the blue of the sky and the reddish tinge of the setting
sun are mainly due to the scattering of light by particles
small compared with a wave-length. The theory of this
action is due to Lord Rayleigh*. All that we require for
our present purpose is the law that the scattered light varies
inversely as the fourth power of the wave-length. When the
various parts of the spectrum are compounded in this pro-
portion, we obtain the point marked A~‘ on the diagram.
This is a fair approximation to the blue of the sky near the
zenith. Lord Rayleigh’s preliminary measures gave the sky
a somewhat richer hue.
Since the scattered light varies as X—* it may be shown that
the transmitted light must vary as e~#a~", where x is the
length of path and & is a constant, depending on the size and
material of the particles and on their number in a given
space. The particles will, on the whole, be more numerous
where the air is denser, and it is reasonable to take x pro-
portional to the mass of air traversed. Capt. Abney has
found that if x be expressed in atmospheres and ~A in
thousandths of a millimetre (Ap=0°589), & has the value
* Phil. Mag. Feb., April, June, 1871, Aug. 1881.
WeZ
288 Mr. J. C. M*Connel on Diffraction- Colours.
0:0138*. An atmosphere is defined to be the mass of air
traversed by a line drawn vertically upwards from the level
of the sea. The value depends on two series of observations
on particularly fine days at South Kensington, when the air-
thicknesses were about 1°3 and 3°3 atmospheres. Taking the
colour of the sun outside the atmosphere as the point W, the
points Ss, Sic, S20, Sup on the diagram give the colour of sun-
light which has traversed 5, 10, 20, and 40 atmospheres
respectively. The first two are yellow inclining to orange,
the third a fine orange, and the fourth redder than red lead.
To the colour of the fourth, wave-lengths less than 529 con-
tribute nothing appreciable ; and even in the third the violet
sensation is mainly due to wave-length 663. Tor an observer
at sea-level the first three thicknesses occur when the
apparent zenith distance of the sun is 784°, 85°, and 872°.
For apparent Z.D. 90° the thickness is 35°5 atmospheres +.
The additional 4°5 atmospheres can be secured by ascending
a height of 330 feet, while from a height of 3000 feet the
coloration due to 50 atmospheres can be studied. The same
action is exhibited to some extent by clouds near the horizon
and by distant snow mountains. For example, the Alps seen
from Berne, forty miles away, look yellowish. But here the
colour is interfered with by the intervening “ blue sky.” In
other words, the particles, which sift the blue waves out of
the hght from the snow, send to the observer a by no means
negligible quantity of scattered sunlight.
It is only when the colour of the sun is white that the sky
is represented by X74. If sunlight be represented by 8;,, then
skylight will be represented by o;, slightly on the green side
of white. The paleness of the sky, when the sun is low, is a
familiar phenomenon. Similarly o49, a9, correspond to Sypo,
Soo. But itis clearly of no consequence whether the shorter
wayve-lengths are filtered out betore or after scattering. So
if we could look at the ordinary blue sky through a tube, filled
with air, 25 miles long it would appear pale greenish white.
In the same way the blue of the sky near the horizon is of
poorer quality than near the zenith. When the scattered
light either before or after scattering has had to traverse 40
atmospheres, its colour reaches the point oy) on the diagram,
2.é. it is really red. This is the red of a sunset sky. It is to
be noticed that the form of the curves W, S85, Sj, Soo, Sao, and
* Phil. Trans. 1887. His statements left me in some doubt as to the
position of the decimal points, but the evidence of his diagram was
decisive.
+ From Forbes’s values, quoted by Abney, which allow for refraction
and the curvature of the earth.
¢
Molecular Constitution of lsomeric Solutions. 289
A-4, O53, T10) F20) Ts IS given by the theory, but to find the
position of these points on the curves we require to know the
value of &.
Since the triangle in my diagram is equilateral, the colour
represented by any point P within the triangle can be ex-
perimentally obtained in the following way :—Let a prismatic
spectrum fall on a diaphragm with three adjustable slits,
whose centres are at wave-lengths 631, 529, and 457. Make
the breadths of the slits proportional to the perpendiculars
drawn from P to the sides of the triangle. Then the three
spectral rays, when compounded by a lens, will produce the
colour P. The dispersion of Maxwell’s spectrum is defined
by the wave-lengths I have given of the sixteen equidistant
points in his spectrum. In consequence, however, of indi-
vidual variations in the colour sensations great accuracy
would be thrown away.
Hotel Buol, Davos, July 10th.
“XXXVIT. On the Molecular Constitution of Isomeric
Solutions §c. By Dr. G. Gorz, F.R.S."
iy the present research, the “voltaic balance” has been
applied to the detection of differences of chemical con-
stitution of a pair of isomeric solutions; and to detect mole-
cular and chemical changes in them, caused by heat, light,
lapse of time, order of mixture, degree of dilution of ingre-
dients, &c.
According to the results of J. Thomsen’s thermochemical
investigations, as described by P. Muir (‘ Principles of Che-
mistry,’ 1884, pp. 434, 437), “when nitric acid and sodium
sulphate react in equivalent quantities in a dilute aqueous
solution, heat is absorbed; but when sulphuric acid and
sodium nitrate react under similar conditions, heat is evolved.
But the final distribution of the base between the two acids
will be the same in both cases, and, moreover, this distribution
will be the same when equivalent quantities of the two acids
(sulphuric and nitric) and the base (soda) mutually react.”
“When soda, nitric acid, and sulphuric acid mutually react
in equivalent quantities in a dilute aqueous solution, two
thirds of the soda combines with the nitric acid, and one third
with the sulphuric acid.” “The final division of the base
between the two acids is the same whether the soda were
originally present as sulphate or nitrate.’’ (See also ‘ Theories
* Communicated by the Author.
290 Dr. G. Gore on the Molecular
of Chemistry, by L. Meyer, translated by Bedson and
Williams, 1888, pp. 470, 485.)
Experiment 1.—I have examined this instance by means of
the ‘ voltaic-balance ” method with zine and platinum couples
(see Roy. Soc. Proce. vol. xlv. pp. 265, 268), and have obtained
the following results. Distilled water was used in making all
the solutions.
Taste I. Voltaic
energy.
“A.” Na,SO, +2HNO, gave between 73,313 and 81,579 at 18° C, Average 77,446
“B” 2NaNO,+H,80, , , 981,000 , 34444 , » 82,722
The solutions of each ingredient of these two mixtures were
considerably diluted previous to mixing.
The numbers obtained with the mixture “ A” are much
more variable than those obtained with the one ‘“ B,”’ and it
will facilitate the clear understanding of the subsequent parts
of this research if I here state that the mixture “A” is an
unstable one, and liable to change in molecular constitution
are Seal of energy both during its formation and after-
wards.
It is worthy of notice that notwithstanding the average
voltaic energy of sulphuric acid in water is about 3°9 millions,
and that of nitric acid in water is only about 3°2 millions (see
Table II.), the mixture “A” containing the latter acid has
about 2°3 times the amount of such energy of the one “B”
containing sulphuric acid: this is probably explained by the
changes of energy which occur during mixing.
The amounts of energy show that the distribution of acids
and base in the two isomeric liquids “ A” and “B” were
very different. It is evident that if one of the mixtures con-
sists of ‘‘ two thirds of the soda combined with the nitric acid,
and one third with the sulphuric acid,” the other liquid must
have a very different molecular arrangement; and that “ the
final division of the base between the two acids” is not
always ‘‘the same whether the soda were originally present
as sulphate or nitrate.” The amounts of voltaic energy, how-
ever, appear consistent with the statement that “ when nitric
acid and sodium sulphate react in equivalent quantities in
aqueous solution, heat is absorbed; but when sulphuric acid
and sodium nitrate react, under similar circumstances, heat, is
evolved.” The mode of preparing each liquid will be
described.
In each of these two solutions the following compounds
may possibly be present :—H,SO,— HNO,—Na,80,_N aNO,
i> 2HNOs, H,SO, — Na,SO,, H,SO, =r 2NaNO,, H,SO,—
Constitution of Isomeric Solutions. 291
Na,SO,, 2HNO;—NaNOs, HNO, — and 2NaNQ,, Na,.SO,;
besides the more complex aggregates and the total aggregate
formed by the feebler chemical union of these compounds
with each other (see Table [X.; also “‘ A Method of Detecting
dissolved Chemical Compounds and their Combining Propor-
tions,’ Roy. Soc. Proce. vol. xlv. p. 265). The following are
the relative amounts of voltaic energy of some of these sub-
stances :—
TABLE II. Voltaic
energy.
H,SO,. Between 3,690,476 and 4,111,466 at 19° C. Average3,900,941
HNO, 3,039,215 3,369,565 _—, 3,204,295
Na,SO, 1,914 21296 13 2,020
NaNO, 155 177 «(12 163
Be Ne 0O) 254,984 —287,037 17 —270,985
Speaking of thermochemical measurement in this case,
L. Meyer states “according to J. Thomsen’s experiments,
although the action of one acid upon the other, and the action
of the salts on each other, do not produce any effect capable
of measurement, still each acid produces a greater or less
thermic effect with its own salt.” And in the case of decom-
position of a salt by an acid, he says “ the extent of the de-
composition can be determined from the value of the thermic
effect.” ‘ But for this determination it is necessary to make
an extensive series of experiments, showing the thermo-
chemical effect. of each pair of the substances in question.
The action of each acid on the base must be separately deter-
mined, then the action of each acid on its own salt, and also
on the salt of the other acid, and finally the mutual action of
the two acids.” “The greatest possible care has to be exer-
cised in each individual determination, in order that the result
may be trustworthy ; if due caution is not observed utterly
false results are easily obtained.” ‘Secondary thermic re-
sults are also produced by the mutual action of the other
bodies.” (‘Modern Theories of Chemistry,’ pp. 466-468.)
According to J. Thomsen, the value of the thermal change
attending the reaction of dilute sulphuric upon dilute nitric
acid ‘is so small that it cannot be accurately determined ”’
(‘ Principles of Chemistry,’ p. 435).
If, however, we employ the “ voltaic-balance” method
instead of the thermochemical one, not only the chemical
union of each of the acids with each of the salts, and with
one another, and the individual salts with each other, is clearly
shown by a depression of energy, but even that of Na,SQ,,
2HNO;, with 2NaNO;,H,SO,, and of still more complex
2992 Dr. G. Gore on the Molecular
aggregates with each other are indicated. The numerical re- |
sults contained in the following Tables support this statement.
Kach definite compound formed is the one having the smallest
amount of voltaic energy, and its formula is indicated by a
Star).
The chemical union indicated by the minimum amount of
voltaic energy in Tables ILI. to IX. is a distinct phenomenon
from the chemical and thermal changes which occur during
mixing the constituent solutions of each pair of substances.
TaBLe IT].—HNO,;+ H,SQ,. Voltaic
energy.
3HNO,+2H,80,. Between 3,604,651 and 3,900,000 at 11°C. Average 3,752,325
A EEO oe » 8,000,000 ,, 3,300,000 ,, » 8,150,000
Do SPA is » 9,000,046 ,, 3,780,487 12 » 3,204,295
Taste 1V.—Na,SO,+ HNOs.
2Na,80,+5HNO,. Between 81,579 and 91,176 at 18°C. Average 86,377
2h oy tS poy Ral alo (3, 1a TS L509 yl ; 77,446
7s 2 OM Uy » SA00 2s 92,201 4 as _ 88,480
Taste V.—NaNO,+ H,SQ,.
3NaNO,+2H,S8O,. Between 33,695 and 87,440 at18°C. Average 35,564
ee oy eel ogi eg :, 31,000%,0° | S44e ‘5 32,722
5 » +2 ” ” 35,469 9 39,440 UB ” 37,454
TasLe VI.—Na,SO,+ H,SO,.
4Na,8O,+5H,SO,. Between 31,900 and 35,477 at 12°C. Average 33,689
4 ” aa! » =% 2 29,245 ” 32,291 oy) ” 30,768
A ao a r 32,631 ,, 386,046 _,, 34,338
TABLE VII.--NaNO, + HNO.
4NaNO,+5HNO,. Between 24,603 and 27,200 at 12°C. Average 25,901
A os ae ee Daa | 22,005 ” 23,372
Ah cine ea r 24,603 ,, 27,200 ,, r 25,901
Taste VIII.--_NaNO;+ Na,SQ,.
3NaNO,+2Na,SO,. Between 79 and 88 at 12°C. Average 83°5
Iai
4 iy) +2 » * ” 70°4 ” 79 ” ” 74-7
5 99 +2 ) ” 79 9 88 5D) ” 83:5
Taste IX.—Na,SO,, 2HNO,; +2NaNO;, H,SOx.
3(Na,8O,, 2HNO,)+4(2NaNO,, H,SO,). Between 2,583 and 2,870 at 138° C. Average 2,726
4 ,» Jaan ¥9 )* 33 27200) ,,) 2,0 1 n° 2,410
5( Dg ~)+4( ” ; ). 99 2,541 99 2,818 23 ” 2,679
Constitution of Isomeric Solutions. 293
It has already been shown by the voltaic-balance method,
that the action of chemical affinity between substances in
aqueous solution is not limited to small groups of a few dis-
similar kinds of molecules, such as those represented in
Tables III. to VIII., but extends to large aggregates com-
posed of a variety of molecules, the aggregates being appa-
rently without limit of magnitude or variety, but subject to
the law of chemical equivalence. The results given in Table
IX. further support this statement. The complex structure
in such cases is usually built up by making each addition
chemically equivalent to the whole of the previously existing
compound (see “A Method of Detecting dissolved Chemical
Compounds and their Combining Proportions,” Roy. Soc.
Proc. vol. xlv. p.. 265; also “ The Loss of Voltaic Energy of
Hlectrolytes during Chemical Union,’ Proc. Birm. Phil. wee
vol. vi. part 2).
Loss of Voltaic Energy during Mixing.
In order to arrive at the loss of voltaic energy which took
place during the mixing of the two constituents in each of the
above cases, the average energy of each constituent was mul-
tiplied by its chemical equivalent, and the two amounts added
together to obtain the total amount of energy of the consti-
tuents. The average energy of the compound was then mul-
tiplied by its molecular weight, to arrive at its total voltaic
energy, and the product subtracted from the total voltaic
energy of its constituents. The following are the results :-—
TABLE X.
Loss
Total loss. Per cent.
BEIN'O, = HSOM EA Sectensacusdee ens 80,433,388 = 10:23
ONnNO)-+ Na SQ. sac... 291,244 = 91-49
Na,SO,+2HNO,(Mixture A”) . 383,262,482 = 94°86
2NaNO,, H,SO,+Na,SO,, 2HNO, 28,283,264 = 95:62
2NaNO,+H,SO,(Mixture “B”)... 373,550,482 = 97-70
Wat S@, SE SO, chests oa, 375,154,388 = 97°81
ING@NOLREUNO} cxecchstesecsescecass +s 198,425,384 = 98:49
In each of these instances the loss of voltaic energy appears
to be due to chemical union of the two dissolved substances.
294 Dr. G. Gore on the Molecular
Influence of Proportion of Ingredients upon the Amount of
Energy.
With the object of obtaining graphic representations of the
influence of proportion of ingredients, the following series of
measurements were made. With each mixture, 1 part by
weight of each ingredient was diluted with not less than 1550
parts of water previous to mixing. The proportions of the
substances employed are stated in the form of molecular
weights. Only the “average” amounts of voltaic energy are
given.
TABLE XI.
Eup. 2.—Mixture “A.” Hap. 3.—Mixture “ BL”
HNO, at 19°C. 3,204,295 HSO, at lore: 3,900,941
1Na,SO,+ 12 . 21 305,045 | 2NaNO,+6 _,, rf 136,342
he oc ia algae is7918] 4 3° Hee : 56,724
Beatie ¥ 1686406) | acto 15 43,194
eset 23 GOW ESe ae 21 35,934
et ie fc Sea7r | 10 | eeu 3 33.429
Ge eh doe F. z 75/880 112) fF SER ap 19 » 30,872
Bec a Si 20 S1 800i tain, Cale 20 35,686
g Sag = i "9106112 -. 45 Oe i 31.250
Gai ae teiyee 23 56,795 bide) se 31 27 968
6. EV ie Gis 21 34,608 }12 , +3 ,, 19 20,813
ees eee in . 14.874 [15> 4 ope 21 13,568
Gute eee 3 O 364 [La oe ies aes 9,453
Na,SO, 13 2,020 | NaNO, 12 163
Bach of these two series shows the depression of energy at
the combining proportion, attending complete chemical union
of the two substances. The excess of either ingredient appears
to exist largely as uncombined mixture. The two chief
causes which appear to determine the magnitudes of voltaic
energy are, strength of chemical union of the dissolved sub-
stances with zinc, and dilution of the definite compound by
the substance in excess; at the combining proportion the
latter influence does not exist because there is no substance
in excess. In the upper part of each series these two causes
cooperate, whilst in the lower part they counteract each
other: in the upper part, the stronger substance being in
excess, enlarges the magnitudes ; in the lower part the weaker
one is in excess, and diminishes them. The influence of dilu-
tion appears to preponderate over that of chemical union
generally in each series. Variation of amount of excess of
acid has in each series a much greater effect than variation of
excess of salt. The following are the curves representing
the above numbers :—
Constitution of Isomeric Solutions. 295
| Mixture ** A.”’ Mizture “ B.”
100Cnds.
HERRMANN RE
PESCPEEEEE
ae
1000nds.
1a) ——
Aah 2) 2
NaSO, 1 2 3 4 5666 6 6 6 6 |NaNO, 2 4 6 8 10 12121212 12 12 12
296 Dr. G. Gore on the Molecular —
Influence of Degree of Aqueous Dilution upon the Molecular
Constitution &c.
Mixture “A.”
Experiment 4.—Six solutions were made, each containing
1 molecular weight proportion of anhydrous sodium sulphate ;
and six others, each containing 2 of nitric acid. These were
first diluted to different degrees, and then mixed to form six
liquids of the following degrees of strength :—
TABLE XII.—Na,S8O, + 2HNOs.
No. 1 contained 1 grain of the mixture in 10°34 grains of water.
99 2 ”) LP) 39 i tb)
” 3 ‘}) 1 99 9” 155-00 gy
9 + iB) 1 a” 99 310-00 »)
99 5 ” 1 9) ” 1,550:00 ”
55 4 1 + 4 15,500-00 +
Each of these solutions had to be further diluted previous
to measuring their energy. The amounts of their voltaic
energy were as follows :—
TABLE XIII.
No. 1. Between 30,511 and 33,917 at 12°C. Average 32,214.
” 2. a9 9 39 99 99 99 39 93
foe oH 32,493 ,, 30,714 ,, 125 be 34,103.
» 4 i 41,005 ,, 45,600 ,, 13 i. 43,302.
we 1D i (O45, 17,000 gulZ FA 73,977.
cy AG: A TROLO”.,, —SUaTS Bole 5 77,694.
The mixture which was formed by adding together the
weakest solutions gave the greatest energy and the same
amount as “‘A”’ in Table I.; and the ones formed from the two
strongest solutions gave the least energy and the same as “B”’
in that table. The only way in which I have been able to
form the isomeric liquid “A” has been by first mixing very
dilute cold solutions in the manner just described.
It is evident from the numerical results, that the degree of
strength of the original solutions of sulphate of sodium and
nitric acid at the moment of mixing largely affected the mole-
cular structure, the distribution of acids and base, and the
amount of voltaic energy of the resulting mixture ; and that
these were more or less determined or fixed at that moment,
and were not rendered alike in the different cases by the
subsequent dilution necessary for the voltaic measurement.
Similar results occurred with a mixture of potassic iodide and
chlorine (Roy. Soc. Proc. vol. xlv. p. 440). Probably the
smaller amounts of voltaic energy of the liquids made from
the more concentrated original solutions were due to more
Constitution of Isomeric Solutions. 297
energetic chemical action occurring at the moments of mixing
of those solutions than during the mixing of the weaker ones.
Mixture “ B.”’
Experiment 5.—Four solutions, of different degrees of
strength, were also made of the isomeric mixture of 2 mole-
cular weight proportions of sodium nitrate and | of sul-
phuric acid, exactly in the same manner as those of “‘A.”
Taste XIV.—2NaNO,+ H.SO,.
No. 1 contained 1 grain of the mixture in 15°5 grains of water.
” 2 99 1 3? 39 155°0 9 7
3) 3 29 1 ” bed 1,550-0 ” ”
ee 1 » » 15,5000 __,,
The amounts of voltaic energy given by these, after suitable
dilution, were :—
TaBLE XV.
No. 1. Between 30,511 and 33,917 at 15° C. Average 32,214.
vias _ 3],000 ,, 34,444 ,, 18 - 32,722.
ge 3 : SU obi 5. vas, ld 5 LZ: 35 32,214.
That of No. 2 was not measured. The results show that
the mixture of sodium nitrate and sulphuric acid was much
more stable than that of sodium sulphate and nitric acid ; and
that variation of degree of dilution did not change the amount
of its voltaic energy, and probably also not the distribution of
acids and base in it.
According to the statements, that ‘ two thirds of the soda
combines with the nitric acid and one third with the sulphurie
acid,” and that ‘‘the final division of the base between the
two acids is the same whether the soda were originally present
as sulphate or nitrate,” considerable chemical change must
have occurred during the mixing of the ingredients of “ B”
(as well as during that of “A’’). And as the amount of
voltaic energy of completely decomposed ‘‘A” is the same as
that obtained at the outset with “ B” (see Tables I. and XV.),
the latter mixture attains completely its final state during the
process of mixing. The thermal phenomena also support this
conclusion.
In J. Thomsen’s experiments with each of the mixtures
“A” and “ B,” “ the quantity of water serving as solvent varied
but slightly, so that the results of the experiments only hold
good for dilute solutions’ (‘ Theories of Chemistry,’ p. 467).
Influence of Order of Mixing.
Experiment 6.—In each of the previous experiments a solu-
tion of the salt of sodium was first taken, and then one of the
298 Dr. G. Gore on the Molecular
proper acid added to it; but in the present case the two dilute
acids were first mixed and then a dilute solution of caustic soda
added to the mixture.
Three solutions were made, of different degrees of dilution,
of a mixture of 1 equivalent each of the two acids ; and three
others, of similar degrees of dilution, of 1 equivalent of caustic
soda ; the solutions of acid and alkali of corresponding degrees
of dilution were then mixed together.
TaBLe XVI.
No. 1 contained 1 grain of the mixture in 15:5 grains of water.
” 2 9” 9) 9 1,550-0 9 2?
29 3 99 1 99 9 15,500-0 9) 99
Their amounts of voltaic energy were then, after suitable
dilution, measured.
TaBLe XVII.
No. 1 gave between 30,511 and 33,917 at 15° C. Average 32,214.
OBI on) ABADI peso 810 |i: Pesos)
From the results of exps. 4, 5, and 6, it appears:—(1) that,
with sufficiently dilute solutions of the acid and alkali, if the
sulphuric acid was first added to the soda and the nitric acid
then added to the sulphate of sodium, the voltaic energy of
the mixture was about 73,977 ; (2) that with either concen-
trated or dilute solutions, if the nitric acid was first added to
the soda and then the sulphuric acid to the nitrate of sodium,
the energy was = 32,722; and (3) that with all except very
weak solutions, if the two diluted acids were first mixed
together and then the soda added to the acid mixture, the
energy was also 32,722 ; whilst with very weak ones it was
=51,123. The order of addition of the liquids to each other
therefore affects the amount of voltaic energy, the molecular
constitution of the liquid, and probably also the distribution
of acids and base in it.
Influence of Time.
Experiment 7.—A solution of the mixture of sodium sul-
phate and nitric acid was prepared from diluted ingredients.
It contained 1 grain of the mixture in 1550 grains of water,
and its average voltaic energy was = 77,694 ; but after stand-
ing in a dark place during 72 hours at about 11° C. its energy
was
Between 63,786 and 71,101 at 11° C. Average 67,443.
After standing an additional 48 hours its energy was
Between 57,407 and 63,786 at 12° C. Average 60,596.
_ ae oa
. i=
oe
E
Constitution of Isomeric Solutions. 299
The mixture “A” therefore slowly altered in chemical con-
stitution at ordinary temperatures towards that of “ B.”” . The
one ‘ B” did not change under these conditions.
Influence of Heat.
Mixture “ A.’
Experiment 8.—Dilute solutions of sodium sulphate and
nitric acid were mixed, and the mixture, containing 1 grain
of substance in 1550 grains of water, and giving, after the
necessary further dilution, the usual average amount of voltaic
energy, viz. about 77,000, was heated during two minutes to
100° C. in a closely stoppered glass flask, then cooled, agitated,
and its amount of energy measured ; it was
Between 30,511 and 33,917 at 15° C. Average 32,214.
The mixture was therefore an unstable one, and its voltaic
energy wis rapidly and largely reduced by rise of tem-
perature.
Experiment 9.—The solution of the same mixture, contain-
ing 1 grain of substance in 15°5 grains of water, the energy
of which had already been reduced to 32,214 by insufficient
dilution during its preparation (Exp. 4), was heated exactly
the same as in Hixp. 8; it then gave
Between 30,511 and 33,917 at 15° C. Average 32,214.
Its voltaic energy therefore was unaffected.
Experiment 10.—In order to diminish the amount of che-
mical change which took place during the mixing of the
ingredients of ‘“ A,” very dilute solutions of them were taken
and cooled to 3° C. immediately before mixing. The mixture
contained 1 grain of substance in 15,500 grains of water.
Its amount of voltaic energy was
Between 91,176 and 100,650 at 11°C. Average 95,913.
The lower temperature therefore diminished the amount of
chemical change which occurred during the mixing (compare
Exp. 4). This shows that under the ordinary conditions of
temperature, when making the mixture ‘ A ”’ some decom-
position occurred.
Experiment 11.—A precisely similar experiment was made
with less diluted ingredients, forming a mixture of 1 grain
of substance in 155 grains of water. Its amount of energy
was
Between 80,511 and 33,917 at 11°C. Average 32,214.
The influence of the lower temperature therefore in this
case was insufficient to neutralize that of stronger solution,
Acie ae em
300 Dr. G. Gore on the Molecular
and did not prevent the maximum amount of chemical
change taking place.
Laperiment 12.—A mixture, each constituent solution of
which contained 1 grain of the substance in 1550 grains of
water was heated to 50° C. during two minutes, the liquid
cooled, and its energy measured ; it was
Between 33,917 and 87,804 at 12°C. Average 35,860.
The temperature therefore was hardly sufficiently high to
entirely change the mixture into the fixed product during
the given period of time. —
The circumstance that, by using either stronger solutions,
or heated ones, of the constituents of the mixture “ A,” the
latter yields the same amount of voltaic energy as that given
by the final product of the mixture ‘“ B,” agrees with the
conclusion arrived at from thermochemical data that “ the
final division of the base between the two acids is the same
whether the soda were originally present as sulphate or
nitrate.”
Mixture “ B.”
Eaperiment 13.—The solutions of sodium nitrate and sul-
phuric acid, of the degrees of strength of Nos. 1 and 3
(Exp. 5), were mixed, the mixtnres heated to about 100°C.
during two minutes, cooled, agitated, and their amounts of
energy measured. Hach gave the same, viz. :
Between 30,511 and 33,917 at 14°C. Average 32,214.
The mixture ‘“B” therefore was evidently completely
formed and fixed in chemical constitution at the moment of
mixing, and whether the solutions of it were more or less
dilute, rise of temperature did not alter their amounts of
voltaic energy or their molecular constitution (see Table XV.).
Experiment 14.—In this experiment, the two diluted acids
were first mixed, and heated to nearly 100°C.; a dilute
solution of caustic soda, equivalent in amount to one of the
acids, and equally heated, was then added to them, and the
liquid cooled and agitated; it contained 1 grain of the sub-
stances in 1550 grains of water previous to dilution for
measurement of its energy. The latter then was
Between 30,511 and 33,917 at 14° C. Average 32,214.
HKeperiment 15.—The diluted constituent solutions of sodium
nitrate and sulphuric acid in the proportion of 1 grain of sub-
stance in 15,500 grains of water were also chilled to 3° C.
and mixed. ‘The energy was then measured, it gave
_ Between 51,682 and 35,227 at 10°C. Average 33,429,
Constitution of Isomeric Solutions. 301
The difference between the numbers obtained in this case
and in Exps. 5, 13, and 14 is not sufficient to prove that the
cooling had any real effect upon the amount of energy.
Influence of Light.
Experiment 16.—A solution of the mixture of sodium sul-
phate and nitric acid was prepared from diluted ingredients
which, when added together, produced a liquid containing 1
grain of the mixture in 1550 grains of water. Its voltaic
energy was
Between 73,810 and 81,578 at 18°C. Average 77,694.
After standing the liquid in the dark during five days, its
voltaic energy was
Between 57,407 and 63,786 at 12°C. Average 60,596
(see also “ Influence of Time ”’).
A second portion of the same prepared solution was ex-
posed in a colourless glass bottle to diffused daylight during
the same period. Its voltaic energy then was
Between 58,270 and 64,583 at 12°C. Average 61,426.
A third portion, the energy of which at the outset was
Between 69,160 and 76,001 at 25°C. Average 72,598,
was exposed in a similar bottle to direct sunlight during five
days; its energy was then reduced to
Between 43,055 and 46,407 at 20° C. Average 44,721.
In these experiments daylight had much less effect than
sunlight, probably in consequence of the higher temperature
in the latter case.
Influence of Magneto-Electric Induction.
Eaperiment 17.—A portion of the original solution “ A”’
possessing an average voltaic energy = 75,860 at 23°°5 C.
was placed in an annular glass vessel surrounding a voltaic
coil, and a strong and rapidly intermittent current from two
large Grove’s elements passed through the coil during one
hour, and the voltaic energy again measured ; it was
Between 57,407 and 63,786 at 26°C. Average 60,596.
To ascertain whether the change was due to rise of tem-
perature from the heat of the coil, a similar portion of the
original liquid was kept during one hour at the same average
temperature; its average voltaic energy had then been
similarly reduced to 60,596. Magneto-electric induction
therefore had no manifest effect.
Phil, Mag. 5. 5. Vol. 28. No. 173. Oct. 1889. Z
302 Dr. G. Gore on the Molecular
Behaviour of a Solution of Sodium Sulphate.
Experiment 18.—Dry crystals of the hydrated salt were dis-
solved in cold water, and the voltaic energy of the solution
measured ; it was
Between 1,414 and 2,126 at 9°C. Average 2019 (see
also Table II.).
The solution was now heated to about 100° C. in a closed
glass flask during two minutes and cooled; its amount of
energy now was
Between 1,839 and 2,039 at 9°C. Average 1939.
And after boiling the solution to dryness and redissolving
the salt, the average amount of energy at 9°C. was still
== 1 ok
General Conclusions and Remarks.
It is evident from the results obtained that the chemical
and molecular constitution of the liquid “ A,” and the distri-
bution of acids and base in it, are affected by several circum-
stances: Ist By the degree of dilution of the ingredients at
the moment of mixing. 2nd. The temperature of the in-
gredients at that moment, or to which the mixture has after-
wards been subjected. 3rd. The order in which the ingredients
have been added to each other. 4th. The amount of light to
which the liquid has been exposed. And, 5th, the period of
time which has elapsed since it was made. In addition to this,
the liquid “A,” even under the circumstances most un-
favourable to chemical change, suffers a great and variable
amount of such change during the mixing of its ingredients.
With regard to the mixture “ B,” it is well-known that it
suffers chemical change, attended by liberation of nitric acid,
during the mixing of its constituents. Thermochemical
researches have disclosed that it forms a compound, in which
one third of the soda is united to the sulphuric and two
thirds to the nitric acid, leaving two thirds of the former
acid and one third of the latter in a comparatively free state.
The. present research proves that its ingredients, at the
moment of mixing, at once form a comparatively fixed sub-
stance or mixture, unalterable by various circumstances which
greatly affect the mixture “ A;” it also shows that the ex-
pelled portion of nitric acid probably unites chemically with
an equivalent portion or one half of the free sulphuric acid;
and it further proves that under certain circumstances the
Constitution of Isomeric Solutions. 303
mixture A” is changed into a fixed product, having the
same amount of voltaic energy as that produced by the
ingredients of ‘ B.”
With regard to the statement that “the final division of
the base between the two acids is the same, whether the soda
were originally present as sulphate or nitrate,” the present
research indicates that this is only true, provided the mix-
ture of sulphate of sodium and nitric acid has been sub-
jected to such conditions or influences, either during or after
its preparation, as decompose and convert it into the same
product as that of a mixture of nitrate of sodium and sul-
phuric acid.
Whilst there is greater voltaic energy in the mixture “ A,”
there is more molecular momentum in the one ‘“ B;”’ and
whilst the chemical change in “ A” may be retarded by low
temperature or dilution, it cannot be much prevented in “ B”
by either of these causes or by both combined. In “ A” the
chemical change which occurs during mixing only proceeds
to a certain stage, if suitable precautions are taken ; in “ B”
it proceeds its entire course, and apparently with greater
velocity.
The fact that by using weaker and colder solutions of the
separate ingredients of the mixture “ A,” a larger amount of
voltaic energy in the product is obtained, proves that the
amount of chemical change which occurs during mixing is a
variable quantity, and suggests that it may be still further
reduced. The larger the amount of voltaic energy of the
freshly-made mixture, the smaller is the amount of chemical
change which has occurred during the mixing. As the
freshly-made mixture gradually loses voltaic energy at 20° C.,
the nitric acid gradually expels sulphuric, the proportion of
nitrate of sodium increases, and that of sulphate decreases.
Loss of voltaic energy does not always coincide with loss
of thermal energy ; for instance, in making the mixture “ A”’
heat is absorbed, but in making the one “ B”’ heat is evolved ;
whilst in both cases the amount of voltaic energy is diminished.
In making “ A” the loss of energy is 94°86 per cent., and in
making “ B”’ 97:70 per cent. (see Table X.).
The “ voltaic balance’ is a very convenient instrument for
detecting and measuring molecular changes in dissolved
chemical compounds. :
LZ 2
[ 304 |
XXXVI. On the Ratio of the Electrostatic to the Electro-
magnetic Units of Electricity. By Henry A. RowLAND,
with the assistance of H. H. Hatt and L. B. FLETCHER *.
HE determination described below was made in the
Laboratory of the Johns Hopkins University about ten
years ago, and was laid aside for further experiment before
publication. The time never arrived to complete it, and I
now seize the opportunity of the publication of a determina-
tion of the ratio by Mr. Rosa, in which the same standard
condenser was used, to publish it. Mr. Rosa has used the
method of getting the ratio in terms of a resistance. Ten
years ago the absolute resistance of a wire was a very un-
certain quantity, and therefore I adopted the method of
measuring a quantity of electricity electrostatically, and
then, by passing it through a galvanometer, measuring it
electromagnetically.
The method consisted, then, in charging a standard con-
denser, whose geometrical form was accurately known, to a
given potential as measured by a very accurate absolute
electrometer, and then passing it through a galvanometer
whose constant was accurately known and measuring the
swing of the needle.
Description of Instruments.
Electrometer.—This was a very fine instrument, made
partly according to my design by Edelmann of Munich. As
first made it had many faults which were, however, corrected
here. It is on Thomson’s guard-ring principle, with the
movable plate attached to the arm of a balance and capable
of accurate adjustment. ‘The disk is 10°18 centim. diameter
in an opening of 10°38 centim., and the guard-plates about
330 centim. diameter. All the surfaces are nickel-plated and
ground and polished to optical surfaces and capable of
accurate adjustment, so that the distance between the plates
can be very accurately determined. The balance is sensitive
to a millig. or less, and the exact position of the beam is read
by a hair moving before a scale and observed by a lens in the
manner of Sir W. Thomson.
The instrument has been tested throughout its entire range
by varying the distances and weights to give the constant
potential of a standard gauge, and found to give relative
readings to about 1 in 400 at least. It is constructed through-
out in the most elaborate and careful manner, and the
* Communicated by the Author,
Hlectrostatic and Electromagnetic Units of Electricity. 305
working parts are enclosed in sheet brass to prevent exterior
action. : :
As the balance cannot be in equilibrium by combined
weights and electrostatic forces, it was found best to limit
its swing to a ;5 millim. on each side of its normal
position. The mean of two readings of the distance, one to
make the hair jump up and the other down, constituted one
reading of the instrument.
The adjustments of the plates parallel to each other, and
of the movable plate in the plane of the guard-ring, could be
made to almost 7, millim.
The formula for the difference of potential of the two
plates is
v= 8ird?ug
A ;
where d is the distance of the plates, wy the absolute force
on the movable plate, and A its corrected area. According
to Maxwell :
i r a
A=jr] R+R2—(R?—R) = NL
where Rand WB’ are the radii of the disk and the opening for
it, and a = °221 (R’—R). The last correction is only about
1 in 500, and hence we have finally
"0002
ar ce
Standard Condenser.—This very accurate instrument was
made from my designs by Mr. Granow, then of New
York, and consisted of one hollow ball, very accurately turned
and nickel-plated, in which two balls of different sizes could
be hung by a silk cord. The balls could be very accurately
adjusted in the centre of the hollow one. Contact was made
by two wires about +4, inch diameter, one of which was pro-
truded through the outer ball until it touched the inner one;
by a suitable mechanism it was then withdrawn and the second
one introduced at another place to effect the discharge. This
could be effected five times every second. The diameter of
the balls has been accurately determined by weighing in
water, and the electrostatic capacities found to be
90°069 and 29.556 O.G.S. units.
A further description is given in Mr. Rosa’s paper.
Galvanometer for Electrical Discharges.—This was very
carefully insulated by paper, and then put in hot wax in a
vacuum to extract the moisture and fill the spaces with wax.
V=17,221d Vw E +
306. Prof. H. A. Rowland on the Ratio of the Electrostatic
It had two coils each of about 70 layers of 80 turns each, of
No. 36 silk-covered copper wire. They were half again as
large as the ordinary coils of a Thomson galvanometer. The
two coils were fixed on the two sides of a piece of vulcanite,
and the needle was surrounded on all sides by a metal box
to protect it from the electrostatic action of the coils. A
metal cone was attached to view the mirror through. The
insulation was perfect with the quickest discharge.
The constant was determined by comparison with the
galvanometer described in the American Journal of Science,
vol. xv. p. 334. The constant then given has recently been
slightly altered. The values of its constant are:—
By measurement of its coils. . . . . . . 18382°24
By comparison with coils of electrodynamometer 1833°67
By comparison with single circle . . . . °. 1832°56
Giving these all equal weights, we have 1832-82 instead of
1833°19 as used before.
The ratio of the new galvanometer constant to this old one
was found by two comparisons to be
10°4167
10°4115
Mean . . 10°4141
Hence we have G = 19087.
Llectrodynamometer.—This was almost an exact copy of
the instrument described in Maxwell’s Treatise of Electricity,
except on a smaller scale. It was made very accurately of
brass, and was able to give very good results when carefully
used. The strength of current is given by the formula.
gi¢VvK
i
‘sin a,
where K is the moment of inertia of the suspended coil, ¢ its
time of vibration, « the reading of the head, and ¢ a constant
depending on the number of coils and their form.
Large Couls.
Total number of windings . . 240
Depthvotyorooveey slat, «ic "84 centim.
Nihidithwot croovey 370-4 i. 215804 “86
Mean radius of coils . . a Loan
DP)
Mean distance apart of coils. . 138:786_,,
to the Electromagnetic Units of Electricity. 307
Suspended Coils.
Total number of windings . . 126
Wentieat sc00ve , sw. "41 centim.
Wudth aierooyve. . “. . °... POLE x,
Mcamensunaes ss). fw! ae 2100...
Mean distance apart . .. . 200,
These data give, by Maxwell’s formule,
c='006457.
In order to be sure of this constant, I constructed a large
tangent galvanometer with a circle 80 centim. diameter, and
the earth’s magnetism was determined many times by passing
the current from the electrodynamometer through this instru-
ment and also by means of the ordinary method with magnets.
In this way the following values were found :—
Magnetic Method. Electrical Method.
Dec. 16th, 1879 992i 19934
Jan. 3rd = 19940 "19942
Feb. 25th __,, 19887 19948
ren zoth *.,; 19903 AGO
March Ist __,, "19912 "19928
Mean . --19912 "19933
which differ only about 1 in 1000 from each other. Hence
we have for ¢
From calculation from coils . . ‘006457
From tangent galvanometer. . ‘006451
Mean . . °006454 C.G.S. units.
The suspension was bifilar, and no correction was found
necessary for the torsion of the wire at the small angles used.
The method adopted for determining the moment of inertia
of the suspended coil was that of passing a tube through
its centre and placing weights at different distances along
it. In this way was found
K = 826°6 C.G.S. units.
The use of the electrodynamometer in the experiment was
to determine the horizontal intensity of the earth’s magnetism
at any instant in the position of the ballistic galvanometer.
This method was necessary on account of the rapid changes
308 Prof. H. A. Rowland on the Ratio of the Electrostatic
of this quantity in an ordinary building*, and also becausea_
damping magnet, reducing the earth’s field to about one third
its normal value, was used. [or this purpose the ballistic
galvanometer was set up inside the large circle of 80 centim.
diameter with one turn of wire, and simultaneous readings of
the electrodynamometer and needle of ballistic galvanometer
were made.
Theory of Experiment.
We have for the potential
"0002
V=edV/w i t, ine
For the magnetic intensity acting on the needle,
Qanrec / K sin «
(7? +6) tand —
For the condenser charge,
Q= =27 a sin 5(1 +42)= Nae
lel
W hence
eGC’r? Ntvwd tan _tan g | 12 ane if
oe, VK (7 + b?)3 T s/sina 2 sind O Zz Re
oe BDAY HON
2 sin 3 0 =oD E -3(>) | nearly.
So that, finally,
eGC'r? NiBYw d
~ One VK (+82)? Ta/sina 8
A= 0; 0011; -0030 ; -0056; -0090 for 1, 2, 3, 4, 5 dis-
charges as investigated below.
B= i(b)-a(b):
* This experiment was completed before the new physical laboratory
was finished.
but’
and
[L—A—B-—C+D+E—F+]T].
to the Electromagnetic Units of Electricity. 309
ae
5-3)
F = ‘0013 for first ball of condenser and ‘0008 for other,
as investigated below.
I = correction for torsion of fibre = 0, as it is eliminated.
= constant of electrometer = 17:221.
= i ballistic galvanometer = 19087.
= radius of large circle = 42°105 centim.
= number of coils on circle = 1.
= constant of electrodynamometer = 006454.
K = moment of inertia of coil of electrodynamometer
b = distance of plane of large circle from needle = 1°27.
C' = capacity of condenser = 50°069 or 29°556.
D = distance of mirror from scale = 170°18 centim.
w = weight in pan of balance.
t = time of vibration of suspended coil.
=e iy needle of ballistic galvanometer.
8 = deflexion of needle on scale when constant current is
assed.
o = ere caused by discharge of condenser.
= distance of plates of electrometer.
N = number of discharges from condenser.
dX = logarithmic decrement of needle.
A = correction due to discharges not taking place in an
instant.
a = reading of head of electrodynamometer when constant
current is passed.
Lr
n
C
The principal correction requiring investigation is A.
Let the position and velocity of the needle be represented
by
= a)sin b¢ and v = a,b cos bt, where 6 = za
{4
At equal periods of time, ¢,, 2t,, 3¢,, &. let new impulses
be given to the needle so that the velocity is increased by v
at each of these times.
The equations which will represent
the position and velocity of the needle at any times are, then,
3810 Prof. H. A. Rowland on the Ratio of the Electrostatic
between 0 and i ea, SIE; v=ayb cos bt;
» t, and 2t,, c=a' sind(t+¢t'); v=adeaspi eae:
» 24, and 8t,2=a"sinb(t+t"); v=a"'b cos b(é+t") ;
&e. &e. &e.
At the time 0, t,, 2¢,, &. we must have :—
w— Ok Up=Agd ;
ao sin bt;=a! sin b(t, +t’); vp +. apd cos bt;=a'b cos b(t, +1’) ;
a’ sin b(2t,+¢’)=a" sin 0(2t, +t"); vy +. a/b cos b(24, 4+ #/)
=a'b cos b(2t, +t") ;
&e. &e.
Whence we have the following series of equations to deter-
mine a’, a", &e., and ¢’, t!, &.:—
Gg b=;
ah? ==ay°b? + U9? + 29a) cos bt; sin b(t, +1) = z ati
a!? 6? ==q?? b? + vy? + 2a! b cos b(2t, +2) ;
sin b(2t, +t!) = - sin 6(2t, +t!) ;
al!203 == q!2h? + vo? + Qupa"b cos b(3t, +1’) ;
N
sin b(3t, +2") <7, sin b (84 +2");
&e. &e.
When ¢, is small compared with the time of vibration of the
magnet, we have very nearly
f=—1t, M=—t, =—Bt, &e.
a? = 2aj'(1+ cos bt)=4a0(1—4(0h)"),
a? = 9a,.?(1—3(bt,)”),
al"? =16a,2(1—3(b4)”),
al!” == 25.a92( 1 — 2(bt,)”).
to the Electromagnetic Units of Electricity. 311
Whence a! = 2a) (1 —1 (bt,)").
a! =3a) (1—-} (bt))”).
al" =4ag Cae (bt,)*).
al" =5ay é _ (bt,)").
Now @, a’, a", al”, and a’ are the values of 6 with 1, 2, 3, 4,
and 5 discharges, and dp, 2a), 8a), 4a9, and 5a, are the values
provided the discharges be simultaneous.
Hence the correction, A, has the values 0, }(6t,)?, 4(0t,)?,
8 (bt,), and (dt)? with 1, 2, 38, 4, and 5 discharges. The
value of ¢, is about one fifth of a second, and hence (bt,)?=
‘009 nearly. The values of A are then 0, -0011, -0030, 0056,
and *0090.
This correction is quite uncertain as the time ¢, is un-
certain.
In assuming that the impulses were equal, we have not
taken account of the angle at which the needle stands at the
second and subsequent discharges, nor the magnetism induced
in the needle under the same circumstances. One would
diminish and the other increase the effect. I satisfied myself
by suitable experiments that the error from this cause might
be neglected.
The method of experiment was as follows:—The store of
electricity was contained in a large battery of Leyden jars.
This was attached to the electrometer. The reading of the
potential was taken, the handle of the discharger was turned,
and the momentary swing observed and the potential again
measured. The mean of the potentials observed, with a slight
correction, was taken as the potential during the time of dis-
charge. This correction came from the fact that the first
reading was taken before the connexion with the condenser
was made. The first reading is thus too high by the ratio
of the capacities of the condenser and battery and the mean
reading by half as much. Hence we must multiply d by 1—F,
where F=-0013 for first ball of condenser and ‘0008 for
the other. This will be the same for 1 or 5 discharges.
From ten to twenty observations of this sort constituted a
set ; and the mean value of = which was calculated for each
observation separately, was taken as the result of the series.
Before and after each series the times of vibration, ¢ and T,
and the readings, @ and «2, were taken. The logarithmic
decrement was observed almost daily.
3
Sa Ae
a
12 Prof. H. A. Rowland on the Ratio of the Electrostatic
Results.—The following Table gives.
January 15, 1879. January 17.
10 10 18 10 10 10 16
c ...| 50-069 | 50:069 | 50-069 || 50-069 | 50-069 | 50069 | 50089
* 2 2 2. 2 2 2 2
: 2-486 | 2-436 | 2436 || 2436 | 2436 | 2436 | 2-436
6 ...| 8403 | 3408 | 3382 || 3310 | 3810 | 3299 | 32°99
< | 4839 | -2400 | 4851 |) 4880 | 1624 | 0981 | -4900
N. 1 2 1 1 3 5 1
De
r ..., -03583 | -03583 | -03583 || -03424 | -03424 | -03424 | -03424
T ...| 67505 | 67505 | 6-7467 || 6636 | 6636 | 6631 | 6-631
a .../14 5617/14 5617/14 53 5/115 18 50/15 18 50|15 14 48/15 14 48
oe | 42 7-2 4-2 48 eae 18-3 3-7
vx10-§| 30059 | 29837 | 300-17 || 296-72 | 295:73 | 29650 | 297-84
February 4. February 6. February 7.
20 20 18 18 19 19
Os 29-556 | 29556 || 29-556 | 29556 || 29:556 | 29-556
t,t 3 3 4 4 4 4
hae 2-436 2-436 2-436 2-436 2-436 2-436
eae 33-08 32-72 33-19 33/18 32-27 32:44
< ue 17450 | -69525 || -29572 | -58823 |) -11986 | -19938
IN ted 4 1 2 1 5 3
Dee
Naeaen 03500 | -03500 || -03500 | -03500 0352 0352
UE 4 6822 6825 6811 6828 6809 6:809
Penn 14 47 95 | 14 35 45 || 14 51 0 | 14 43 40 |] 14 11 20 | 14 20 20
8% aN 45 2-0 33 18 73 4-7
»x1078 | 30182 | 30080 || 297-43 | 29656 || 297-38 | 298-75
* Approximate value
oa
to the Electromagnetic Units of Electricity. 313
the results of all the observations.
{ January 20. January 22. January 24. Jan. 27. || Feb. 3
) 18 18 18 18 18 18 18 20
50-069 50:069 50:069 50-069 50:069 50-069 50:069 29°556
2 D. 2 2 3 3 3 3
2°435 9°435 2-437 2:437 2436 2-436 2°437 2°435
30°43 33:18 33°60 33°60 84:53 34°30 33°64 33°79
4871 | -09759 || -15954 | -48065 || -19588 | -39279 || -o9777 || ‘17145
1] 5 3 1 2 1 4 4
0350 ‘0350 03578 03578 03507 03507 03507 08500
6693 6°689 6°792 6°783 6:°796 6°788 6°7944 6°8471
15 2 35/14 57 45/| 14 25 30/14 25 52/15 6 25/14 59 40||14 25 221115 14 10
41 16°8 10°8 Bw Nei. 4:0 13:3 8:0
298:90 | 296°37 29640 298°57 29861 299-05 296°43 297°24
February 11. | February 12. February 14. February 17.
18 18 18 18 18 18 18 18
29°556 29°556 29°556 29-556 29:556 29°556 29:556 29°556
2 2 2 2 1 1 1 1
2°436 2°436 2:436 2.436 2°4385 9-435 2°436 2°436
32°89 32°75 32°82 32°42 32°72 32°39 31°77 81°39
*417 16744 ‘16767 42264 39752 29647 “40215 30109
2 5 5 2 3 4 3 4
0356 0356 0354 0354 0361 ‘0361 0348 0348
6°8734 6°8557 6:860 6°854 6-890 6-890 6°788 6:778
14 13 35/14 7 15/1416 10\14 110/14 8 0/13 59 ‘oll14 17 30| f4 1 ‘oO
421. .93 10°3 43 6:2 9-5 86 9-5
297°78 296-87 | 296°31 300°19 298°66 295-02 296°75 295-22
for correction only.
314 LHlectrostatic and Electromagnetic Units of Hlectricity.
These results can be separated according to the number of
discharges as follows:—
1, 2. 3. 4. 5.
———$——$<$——=_ |
300°59 298°37 295:73 296743 296°50
300:17 298 61 296-40 297-24 296°37
296°72 297°43 29875 301°82 297°38
297°84 29778 298:66 295-02 296°87
298°90 300°19 296°75 29522 296°31
298'57
299:05
300°80
296°56
298°80 298'48 297:26 297°15 296°69
In taking the mean I have ignored the difference in the
weights due to the number of observations, as the other errors
are so much greater than those due to estimating the swing
of the needle incorrectly.
Tt will be seen that the series with one discharge is some-
what greater than those withalarger number. This may arise
from the uncertainty of the correction for the greater number
of discharges, and I think it is best to weight them inversely
as this number. As the first series has also nearly twice the
number of any other, I have weighted them as follows:—
Weight. »x10-°
Si ihessene 298°80
Aeon 298°48
Ol ast an's 297°26
2, eae re SVS)
her era 296°69
Mean 298°15
Or v=29,815,000,000 cm. per second.
It is impossible to estimate the weight of this determination.
It is slightly smaller than the velocity of light, but still
so near to it that the difference may well be due to errors of
experiment.
Indeed, the difference amounts to a little more than half of
one per cent.
It is seen that there is a systematic falling-off in the value
of the ratio. This is the reason of my delaying the publica-
tion for ten years.
Had the correction, A, for the number of discharges been
omitted, this difference would have vanished ; but the cor-
rection seems perfectly certain, and I see no cause for
t
—
Ratio of the Electromagnetic to the Electrostatic Unit. 315
omitting it. Indeed I have failed to find any sufficient cause
for this peculiarity, which may, after all, be accidental.
As one of the most accurate determinations by the direct
method, and made with very elaborate apparatus, I think,
however, it may possess some interest for the scientific
world.
XXXIX. Determination of v, the Ratio of the Flectro-
magnetic to the Electrostatic Umt. By Kpwarp B. Rosa,
Student in Physics in the Johns Hopkins University*.
cc investigation was conducted in the Physical Labora-
tory of Johns Hopkins University during the months of
March to June 1889, under the direction of Associate Pro-
fessor A. L. Kimball. The writer takes great pleasure in
acknowledging his obligations to Dr. Kimball for valuable
advice and encouragement throughout the progress of the
work.
The method employed is essentially that given by Maxwell,
vol. il. § 776. It was used by J. J. Thomson in his determi-
nation of v, published in the ‘ Philosophical Transactions’ for
1883. The following is substantially his description of the
method. Ina Wheatstone bridge, A BC D (fig. 1), the circuit
Fig. 1.
D
A B
B D is not closed, but the points D and B are joined to two
poles R and 8 of a commutator, between which vibrates the
armature p, which is connected with the inner shell of a
spherical condenser. When p touches § the condenser will
be charged, and there will be a momentary current through
* Communicated by Prof. Rowland.
316 Mr. EH. B. Rosa on the Determination of v, the
the various arms of the bridge, through the galvanometer ‘
from D to C. When p touches R the two surfaces of the
condenser are connected, and the latter discharges itself
through DR. If now the armature be made to vibrate con-
tinuously there will be a series of momentary currents through
the galvanometer, and by adjusting the resistance a (¢ and
d being large, fixed resistances), these interrupted currents
may be exactly counterbalanced by the steady current from
C to D, and the resultant deflexion of the galvanometer is
zero. When this is the case there is a relation between the
capacity of the condenser, the number of times the latter is
eharged and discharged per second, and the resistances in the ~
various arms of the bridge. Maxwell gives an approximate
value of this relation. Thomson’s more complete investigation
gives the following equation :—
a shaeee yea b Ta
7 ab ag \
@ i Stee! 1 laa +¢+ 9)
where n is the number of complete oscillations of the armature
Pp per second; Cis the capacity of the condenser in electro-
magnetic measure ; and the other letters the resistances of the
various arms of the bridge, as shown in fig. 1. In the present
case the values of these resistances were about as follows:—
a = 40 to 1900 ohms. d = 100,000 ohms,
b= O nearly. =) C000
e = 1,570,000 to 2,450,000 ohms.
Owing to the very high values of c and d as compared with
a, b, and g, the above equation may be replaced by the ap-
n
proximate one, C = = which is true to within a hundredth
,
of one per cent. ‘The electrostatic capacity, 0’, is determined
by calculation from the geometrical constants of the con-
/
denser. The ratio of these values of the capacities, a Is a",
the square root of which, v, is the quantity sought.
Advantages of the Method.
Thus there appears at once an important advantage of the
method of determining the ratio of the units from the values
of a capacity, namely, that v is the square root of the ratio of g
Ratio of the Electromagnetic to the Electrostatic Unit. 317
the*capacities, and any error in the latter enters into v by
only half its amount.
There are several important advantages of this method of
measuring the electromagnetic capacity. In the first place a
knowledge of the exact electromotive force and resistance of
the battery is not required, and their constancy is not essential.
In the second place, since it is a null method, such uncertain
- quantities as logarithmic decrement, torsion of the suspending
fibre, and period of the needle are not required; the galva-
nometer can readily be made more sensitive than a ballistic
galvanometer; its “ constant” need not be known; and the
field of force may be variable both in intensity and direction
without prejudice to the experiment. On the other hand,
the quantities which are required are the period of the
vibrator and the values of three resistances, quantities which
are capable of determination to a very high degree of accuracy.
In the present case the vibrator was either a tuning-fork or
else it was driven by a tuning-fork, and by the arrangement
adopted the uncertainty in its period was reduced to an
extremely small quantity. The difficulties and limits of the
method will appear under the head of Sources of Hrror.
Instruments.
1. Condenser.—This was made from designs by Prof.
Rowland. It consists of a hollow sphere whose radius is
12-7 centim., and within which may be hung either of two
balls of 10-1 and 8°9 centim. radius respectively. The con-
denser has a capacity of about 50 absolute electrostatic units
with the larger ball and 30 with the smaller.
The spherical surfaces are accurately ground, nickel-plated
and polished to a mirror surface. The ball is suspended by a
silk cord C (fig. 38) passing through a hole 7 millim. in
diameter in the outer shell, and attached to the insulated end
of a pivoted beam and counterpoised. By means of a rack
and pinion movement and vernier, the ball may be accurately
set in any desired position. Maxwell* objects to this form
of condenser on account of the difficulty of working the
surfaces accurately spherical, making them truly concentric,
and determining with sufficient accuracy their dimensions.
That these difficulties have in the present case been entirely
surmounted will, I think, appear from the discussion under
the heads of Displacement of the Ball (p. 323) and Hlectro-
static Capacity (p. 328).
* Vol. i. p. 321.
* Phil. Mag. 8. 5. Vol. 28. No. 173. Oct. 1889. 2A
318 Mr. HE. B. Rosa on the Determination of v, the
2. Galvanometer.—This was one of Elliott Bros.’ Thomson |
high-resistance, astatic galvanometers, made very sensitive.
3. Tuning-Forks.—Two of Koenig’s forks were used, whose
frequencies were approximately 32 and 180 per second.
They were driven by three or four Bunsen cells, the same
current in the case of the slower fork operating the vibrator
» (fig. 1). Their exact periods were determined by Michel-
son’s method *.
4, Vibrators.—The oscillating piece p in the case of the
slower fork was a commutator such as that used by Thomson f.
The action of this form of vibrator was regular and satis-
factory in the case of the slower fork; but with the higher
fork great difficulty was experienced in obtaining sufficient
uniformity, and finally it was abandoned and the following
plan devised as a substitute. T, T’ (figs. 2 and 3) are two
Fig. 2.
—— = —
U LLL IEEE
Pts thts Vit YA) UM 407%
MELEE ELIA GEE:
prongs of the tuning-fork, driven by the electromagnet M ;
the interrupter, attached to the end of one of the prongs, not
being shown. J, b! (fig. 3) are two fine brass wires, uniting
at n and tipped with platinum at p, p’, where they are bent
at right angles and fastened to the fork with an insulating
cement. V, V! are two small blocks of vuleanite attached to a
firm support A. Below the platinum points are two cavities
in the vulecanite which are filled with mercury, and as the
fork vibrates first one and then the other of the points dips
into the mercury. Thus the mercury cups, which are joined
to B and D respectively (fig. 1) answer to the posts S and R,
while the wires b, 0’ unite and, passing through the fine
glass tube G, reach the ball of the condenser at m. When
the prongs separate, p' dips into the lower cup and the
* Phil. Mag. [5] xv. p. 84 (1883).
+ Thomson, Phil. Trans. 1888, or Glazebrook, Phil. Mag. [5] xviti.
p. 98.
Ratio of the Electromagnetic to the Electrostatic Unit. 319
condenser is charged; when they approach, p dips into the
other cup and the condenser is discharged. The points
must be at least half a millimetre above the surfaces of
the mereury when the fork is at rest, in order to avoid
Fig. 3.
both dipping at once and short-circuiting the condenser.
With an amplitude of about three millimetres perfect con-
tact is made at each vibration, and the regularity of action,
_ as shown by the steadiness of the spot of light on the scale,
is extremely satisfactory. The deflexion of the needle when
the steady current is not balanced by the intermittent current
amounts in the case of the high fork to 125 scale-divisions
using the one-tenth shunt; or, without the shunt, as it was
used in practice, to 1250 scale-divisions. With its best action
the resistances were adjusted until closing the key would
eause a deflexion of less than half a scale-division, corre-
sponding to less than 1-2500th part of the whole current.
To obtain a regularity of action which permitted such
accurate observations required a very delicate adjustment of
the distances between the surfaces of the mercury and the
points above them, as well as clean surfaces and a steady
current.
9). Battery.-—About forty cells of a storage battery, with a
total electromotive force of about eighty volts, were used. A
higher electromotive force, at first proposed, was thought to
be unnecessary.
6. Resistances.—The resistance a was taken from a box of
Elliott Bros., the total resistance of which was about 12,000
ohms; the resistance d was a 100,000 ohm box from the same
firm. The first of these, box A, was carefully calibrated by
320 Mr. E. B. Rosa on the Determination of v, the
comparing the several coils on a Fleming bridge with three
standard coils of 10, 100, and 1000 ohms respectively. The
first was a Warden-Muirhead No. 292,10 B.A. U. Its value,
determined by Glazebrook, Oct. 1887, is 9:99416 at 16°5 C.
The otber two had heen previously carefully compared with
this. The values of the resistances of box A adopted were the
means of three different and closely agreeing determinations,
made at different temperatures. The several coils of box B
were carefully compared with the known resistances of A.
The temperature-coefficients of both boxes were also carefully
determined.
The resistance ¢ was of graphite. Plate-glass was ground
with fine emery and lines ruled upon it. Under a magnifying
power of several hundred diameters the layer of graphite
appears made up of patches which run together at numerous
points. The resistance of a strip of graphite of given length
and breadth depends upon how well these patches are joined
together. The glass and graphite are given a heavy coat of
shellac and thoroughly dried. A series of ten such resistances
were prepared and mounted, connexion being made at the
ends by tin-foil, held firmly in contact with the graphite by
rubber packing, wires passing out from the tin-foil. The
resistances were placed in cylindrical boxes with vulcanite
tops, in which were set binding-screws, joined to the wire
terminals. The boxes can be surrounded by water or other
material to lessen the temperature fluctuations. ‘These re-
sistances proved quite constant and reliable. Two were used
in this experiment, R, and R;, whose resistances were ap-
proximately 1,570,000 and 2,450,000 ohms. During the six
weeks preceding May 9, their alteration, aside from tempera-
ture fluctuations, was inappreciable. But between May 9 and
May 18, when not in use, from some as yet unknown cause,
both increased about one half of one per cent., and up to June
8, when last used, remained nearly constant at the new value.
Inasmuch as glass and shellac are poor- conductors, the tem-
perature of the graphite resistances cannot safely be assumed
to be the same as that of the air within the box, unless the
latter has been kept constant for some time. In order, there-
fore, to avoid all uncertainty as to their values these resist-
ances were determined anew whenever used; and if their
temperature changed materially, both just before and just
after using. ‘They were compared with the resistances of
boxes A and B, two arms of a Wheatstone bridge, with a ratio
of 99°89, being taken from A. Here is a specimen observation
and calculation :-—
Ratio of the Electromagnetic to the Electrostatic Unit. 321
May 22. Bridge reading 24,430. Temperatures : Graphite
19°8, A = 20°3, B = 20°6,
’ aa A430) 4, A= 4443 5, = 4444 ,, 20%3
94.459
24,459 x 99°89 =2,443,200 ohms at 19°-8=temp. at which used.
This value is reliable to within one part in five thousand.
It is proper to add that if these graphite resistances are put
into a circuit where there is a large difference of potential
between their terminals, their resistance is immediately
diminished by heating. With three Bunsen cells used in
measuring their resistance no heating was perceptible. In
the determination of capacity there was a difference of
potential between the terminals always less than two volts,
and usually less than one. When the temperatures were
maintained constant, the resistance after use was always pre-
cisely the same as before. While, therefore, the use of high
graphite resistances is somewhat restricted where greataccuracy
is desired, they still may serve a very useful purpose in many
cases, and are the most convenient and reliable of any high
resistance, aside from metal wires, that I know anything
_ about.
Arrangement of the Apparatus.
The vibrators were fixed as near as possible to the condenser
to reduce the capacity of the charging wires to a minimum.
The condenser, galvanometer, and other parts of the apparatus
_ were insulated with great care, and yet in spite of all pre-
cautions leakage made its appearance on rainy days, and a
slight trace of leakage could usually be detected. Observa-
tions were consequently confined to fair weather. The
apparatus for the determination of the frequency of the forks
was always ready for use.
Sources of Error.
1. Reststances.—The constant errors in the resistances must
have been very small, and corrections were always carefully
made for temperature-fluctuations.
2. Luning-Forks.—Michelson’s method furnishes a very
exact determination of the period of an electric tuning-fork ;
but unfortunately the period does not remain constant. This
is especially the case with the higher fork, the charging wires
ae te ee, rr
te 7
322 Mr. HE. B. Rosa on the Determination of v, the
and spring-contact having a varying effect upon the rate in
different adjustments. But the slower fork with mercury
contact was not, even after making proper temperature-
corrections, perfectly constant. To avoid all uncertainty, and
obviate the necessity of applying a temperature-correction, the
rates of the forks were determined each time;‘anew, usually
before and after or in the midst of a series of observations on |
capacity. As stated, the apparatus for the purpose was always
ready for use ; and without stopping the fork or changing its
circumstances in any way whatever, by simply closing the
clock-cireuit and the primary circuit of the induction-coil, I
could in three to five minutes count a sufficient number of
flashes to give me the period of the fork true to within less
than one part in ten thousand. Occasionally a slight change
in the sound emitted by the fork, due to variation in contact
or current, suggested a possible change in the period; a
moment’s glance in the microscope would answer the question.
This method of dealing with the rates of the forks avoids the
introduction of smali constant and large accidental errors,
which may happen when the rates are determined once
for all.
3. Charging- Wires.—The vibrating armature p, the wires
b, b’, as well as the joining-wire e, have a certain capacity,
which adds itself to that of the condenser when they are con-
nected, but which may be determined separately by dis-—
connecting the charging-wire at m. Thus, on April 15, with
R, and fast fork, the resistance a was 1874°5 and 153 respec-
tively in the two cases mentioned, which gives 1721°5 as the
resistance corresponding to the condenser alone. This assumes
that the capacity of the charging-wire is the same when joined
to the ball as when separated. The capacity of the two and a
half centimetres of fine brass wire between the ball and the
shell (fig. 3) is nearly one per cent. of the capacity of the
condenser, determined experimentally. It would seem that
this capacity might be slightly greater when the wire was dis-
connected from the balland at a different potential; but being
lifted one or two millimetres in disconnecting, its capacity
would be thereby reduced. The effects of these two modi-
fying circumstances were separately very carefully studied.
With the rapid fork running very smoothly, a change of half
an ohm could be easily detected ; this would be equal to a
change of ss'55 of the capacity of the condenser. No dif-
ference, however, could be observed, although the trial was
several times repeated. The two effects have opposite signs ;
and if each is inappreciable, much more would their sum be
————
Ratio of the Electromagnetic to the Electrostatic Unit. 323
so. 1 therefore conclude that the difference between the ob-
served capacities of condenser and charging system together
and of charging system alone is a true measure of the capacity
of the condenser.
4, Displacement of the Ball.—The upper half of the
spherical shell was lifted and the lower half adjusted upon
its supports until the distance of the ball from the shell was
the same at all points on the equatorial circumference. The
upper half of the shell was then replaced, and by means of the
rack and pinion the ball was first lowered and then raised
until it touched the shell, the exact moment of touching being
indicated by an electrical contact, and several readings taken
on the vernier in each position. The mean of the readings
in the two positions gave the central position. In this
manner the ball was adjusted vertically to within 0:1 mm., and
equatorially within 0°2 mm. Thus the ball is centred to
within less than one per cent. of the distance between the ball
and shell, which is 25 mm. Thomson has investigated a
formula for the capacity of eccentric cylinders. The formula
shows that for a displacement of one per cent. the capacity is
increased 54, of one per cent. Evidently the capacity of
spherical shells is less affected by slight eccentricity than that
of cylinders. Therefore we may safely conclude that no error
is due to eccentricity. This conclusion was verified experi-
mentally, a displacement of four per cent. causing an in-
appreciable change.
5. Adjusting Resistances.—The accidental errors occurring
in adjusting the resistance a so as to produce zero deflexion
will be eliminated by a large number of observations. Their
magnitude depends on the strength of the current, delicacy of
the galvanometer, regularity of the vibrator, &c., and is
larger with the slow fork than with the fast. The stronger the
current and the more sensitive the galvanometer, the greater
the deflexion due to a certain error in the resistance a; but,
on the other hand, the greater the unsteadiness of the spot,
so there is a practical limit in that direction. That these
accidental errors are small is, I think, attested by the uni-
formity of the results obtained.
Electrostatic Capacity.
The electrostatic capacity of the condenser was calculated
from the formula
rr
C= —,
{PoP
324 Mr. E. B. Rosa on the Determination of v, the
where 7, 7 are the radii of the shell and ball respectively.
The radii are determined by finding the volume of water
which fills the shell and which is displaced by the ball. These
results are confirmed by direct measurement upon the dividing-
engine.
Ball A.
May 1.—Weight in air, 2903°83 g. Temperature, 18°-9 ;
Bar., 76°0 cm. Volume of ball, 4339 c. c. approximately ;
volume of brass weights, 340 c.c. approximately. Correction
for displaced air is consequently +4°83 g. .°. weight of
ball wn vacuo =2908°66 g. A second determination gave
290864 g. I therefore take for the true weight wm vacuo,
2908°65 g. The ball being lighter than water, a sinker was
attached and the following weighings made :—
May 3. Weight in distilled water,
balland sinker . . . . 210°62 oMaigiva one:
Ditto, sinker alone . . . 1635°59 g. at 17°10 C.
Difference . . 1424-97 g.
Correction for nae) Cre) air
8-4
displaced by weights. . “21
1424-76
Weight of ballin vaewo . 2908-65 g.
Loss of weight in water at
TOON Rte Fo) AB BB Ane ae
Ditto, at 4°C. . . . . 4338°68 g. =volume in
cubic centimetres.
Another determination at a different temperature gave 4338°87.
I take as a mean 4838°8, which makes the mean radius
7 ,=101180 cm. An error of 0°1 in the number 4338°8
would cause an error of less than a thousandth of a millimetre
in 7”.
Ratio of the Electromagnetic to the Electrostatic Unt. 325
Ball B.
Pow t Weiehtimar ... . 232140 g.
Correction for displaced air 3°20 g.=2324°60 g. in
VUCUO.
May 3. Weight in distilled water,
pall’anoesmier +2... .-. 208°96 o. at 16°°45 C.
Ditto, sinker alone . . . 807°86 g. at 16°70 C.
Ditterence) 20.5 . «598-90
Correction for air displaced
Byeweremts 4 2. ‘09
598°81
Weight of ball an vacwo . 2824°60 g.
Loss of weight in water at
HGeet Cee es ae LQOQS AT
Ditoaue O..> . .2)~ 292665 = volume. in
cubic centimetres.
This gives r’g = 8°8785. A second determination gave a
closely agreeing result.
In these weighings the bodies were lifted completely out of
water, replaced, and air-bubbles carefully removed at least
three times in each weighing. The mean of the several
values, which differed in the centigrams, was each time taken.
These differences were usually due to slight changes in the
temperature of the water, the balances being far more
sensitive than the thermometer. As, however, the tem-
perature was read to gy of a degree several times during
a weighing, and the mean taken, it is thought that the tempe-
rature is true to within 0°1; and this corresponds in the case
of the large ball to about 07 g. I think the values of the
radii given above are true to within two or three thousandths
of a millimetre.
Shell.
The weighings of water contained by the shell were made
by replacement. The shell was sealed about the junction of
its two halves with white paint, filled with distilled water, and
allowed to stand to absorb any air-bubbles which might have
escaped the brushing with a wire which was given the inner
surface after filling. The condenser was placed on the plat-
form of the scales, approximately counterpoised, and then
accurately balanced by adding weights to the platform ; about
100 c. c. of water was then withdrawn, temperature taken,
shell refilled (the space around the opening being thoroughly
326 Mr. EK. B. Rosa on the Determination of v, the
raked with a wire, to prevent error from small air-bubbles
which tended to lodge there), and weights again added to
balance. The following weighings were thus made:—
1380-7 ¢g. 130° ¢. 1812g. 181:3g. Mean=131-4.
13820 g. 13820g. 181:77g. 131-4 g. Mean temp., 18°4.
13l6g. 1814 ¢.
The condenser being emptied and carefully dried, required
the following weights to balance the same counterpoise:—
8650°3 g. 8650°8¢g. 8650°9¢g. 8650°9 g. Mean 8650°7 g.
8650°7 —131:4=8519°3= weight of water at 18°:4 in air. -
8531:8= a a 4°,
Correction for dis-
a 9-1
placed air
8540°9= Fs ‘5 5 2n vacuo
=volume cf the shell in cubic centimetres. This makes the
radius r=12°6805 cm. It seems reasonable to suppose that
the number 8540°9 is true to within less than a gram. This
would make the error in r less than ‘0005 cm.
These values of the radii are confirmed by the following
direct measurements, made on a dividing-engine, using
calipers and a standard metre-bar by Bartels and Diederichs,
Gottingen, whose length is accurately known. Three mutually
perpendicular diameters of the shell were found to be
25°357, 25°360, 25°358. Mean=25-3583,
giving r=12°6791, a very close agreement in view of the
difficulty of setting the calipers. More accurate measure-
ments on the balls were obtained.
Ball A.—Following are twelve diameters :—
20°2399 20°2372 20°2170
20°2358 20°2336 20°2348
20°2350 20°2382 20°2250
20°2250 20°2315 20°2401
Mean =20:2328, + Correction for the bar -0038, = 20°2366 ;
r/, = 10°1183 cm.
Ball B.—Following are six diameters :—
17°7468 17°7408 17-7429
17°7465 17°7452 17°7407
Mean = 17'7488, + Correction 0034, =17°7472 ;
r!, = 88736 cm.
Ratio of the Electromagnetic io the Electrostatic Unit. 327
It is perhaps somewhat accidental that these values coincide
so closely with the values of the radii found by the first
method. Their importance is not insisted upon further than
as furnishing satisfactory confirmation of the results of the
other and more accurate method.
It will be seen that in ball A no diameter differs from the
mean by as much as a tenth of a millimetre, and in B the
variation is still smaller. This deviation from perfect sphericity
has no appreciable effect upon the value of the capacity calcu-
lated from the ordinary formula. We now have
or, — 1276805 x 10°1180
A= 12-6805 —10°1180
__ 12°6805 x 8:8735
B 12°6805 — 8°8735
The radius of the hole in the shell through which the sus-
pending cord (C, fig. 3) passes is °35 cm., and its area gy5
of the area of the shell. The capacity is diminished in a less
ratio than the area ; therefore the capacity is diminished pro-
bably not more than a hundredth of one per cent.—a quantity
wholly negligible.
= 50°069.
C’ = 29°556.
Hlectromagnetic Capacity.
A series of observations on the electromagnetic capacity
by the method described was made, extending from March 28
to June 8, under a variety of circumstances as to weather and
external surroundings. The two graphite resistances, the two
tuning-forks, and different resistances from box A were
variously combined, and at temperatures varying from 17° to
25°C. The shell and ball were occasionally readjusted, and
between April 16 and May 4 the condenser was taken apart
and its electrostatic capacity determined. Further, in order
to measure the graphite resistances the apparatus as shown in
fig. 1 was each time disconnected and put together again.
All these variations must have had the effect of eliminating to
a large degree constant errors, while of course the single
observations do not agree so well among themselves as they
otherwise would. Following is the last observation made,
given as a specimen :—
Resistances a: ©) 1930:0—@ 194-0=1736:0
. ©) 1932-0—@ 1955 =1736°5
©) 1932-0 —®© 197:0=1735-0
™ 1932°5 —® 196-5 =1736-0
Temperatures: A=22°-3, B=23°-0, Graphite=23°-0.
328 Mr. EK. B. Rosa on the Determination of v, the
The wire was first in contact at m (fig. 3), and the re-
sistance a corresponding to joint capacity of condenser and
charging-system was 1930°0 ohms. The wire was now lifted
very slightly, and 194:0 ohms found to give no deflexion on
closing the key in the galvanometer-circuit. The wire was
then lowered to make contact, and the subsequent observations
in the order of the numbers made. Any leakage increases
the numbers alike in the first two columns, and “if constant
does not affect the differences, which give the capacity of the
condenser. But the leakages are not constant, so that small
differences are thereby introduced ; this accounts in part for
the differences above, though of course small differences are
inevitable if there be no leakage. On June 6 the wooden
base of the condenser was thoroughly wet with a cloth; and
the leakage thereby introduced changed the readings from
1924:0—186:0 to 19330—195°0, the difference, 1738-0,
remaining unaltered.
The mean of the above differencesis . . . . 1735:9
Correction: Excess at 20° C., 5-4; temp. corr.,+1:3 6:7
1742°6=a.
Box B=100,120 at 238°0=d.
R; (calculated as already explained), 2,435,800 =c.
Frequency of the fork, 1380°075=n.
1 B.A. unit=°98664 ohm.
C pe a le
~ ned ™ 98664 x 10”
denser in absolute electromagnetic units.
log ¢ = log 2,435,800 = 6°386642
log d = log’ 100,120 = 5-000521
C being the capacity of the con-
logn = log 1380:075 = 2°114194
log °98664x 10° = $:994159
22°495516
loga = log 1742°6 = 3:241198
lon Cy: = 20°745682
log C'= log 50°069 = 1:699568
log v? | = 20°953886
log v = 10°476943
v = 2°9988 x 10!° cm. per sec.
Group
EL
9
sf
Table of Results.
[The numbers in the columns headed v, when multiplied by
v.
Slow Fork.
30040
3°008 1
2°9993
29980
30009
30010
3°0036
3°0058
3°0007
3°0089
30069
3°0033
30073
3°0012
30105
30090
3°0059
3°0021
3°0036
29990
bo bo G2 © Go Oe DO | Weight.
C9 Go bo bo Co 9
bo bo bo oo Cor GO
Weighted
mean of
3-0012
(24)
30045
(16)
30043
(16)
——_— | ——_____ | —— ite
40
29996
3°0025
3°0022
30028
>
30017
(15)
v.
Fast Fork.
29947
2°9950
29966
2°9988
29978
2°9980
2°9980
2°9988
Ratio of the Electromagnetic to the Electrostatic Unit.
Co bo DO DO
ARR LORE CS | He HE
329
101°, give the values of v in centimetres per second. |
Weighted
mean of
group.
330 Mr. H. B. Rosa on the Determination of v, the
The results exhibited in the preceding Table have been
divided into four groups. ‘The first group consists of
seventeen values found before the condenser was taken apart
to measure its electrostatic capacity. During this time the
upper half of the shell was lifted, and the ball adjusted two
or three times. The values found by the fast fork are more
uniform than the others, and average somewhat lower. The
second group extends from May 4 to 9 inclusive, when the
condenser had been set upagain. There were two small glass
tubes, about 5 mm. in diameter (and drawn out considerably
smaller where they projected through the shell one to two
centimetres into the space within), which had once been used
to pass charging-wires through. ‘The wires had been with-
drawn, and it was supposed that the glass tubes had no
appreciable effect. The holes were together only = !g9 of the
area of the shell, and the tendency of the glass to slightly
increase the capacity would tend to counterbalance the
decreasing effect of the holes. When the condenser was
set up the second time, the tubes were intentionally left
out and the values of Group II. were noticed to be larger
than those of Group I. No cause could be discovered for
this increase (which indicates a less electromagnetic capacity),
but the tubes were replaced and Group III. taken. The mean
of this group is as large as that of the preceding group. The
tubes were now again withdrawn, and the holes covered with
gold foil, making the inner surface of the shell continuous.
Group LV. gave values averaging almost exactly the same as
Group I. The circumstances were alike in other respects so
far as is known, the usual variation in the circumstances of
the observations, as already explained, occurring in all the
groups. I do not think the presence or absence of the tubes
could affect the capacity appreciably ; they were altogether
too small, probably not filling over a thirty-thousandth of the
space between the ball and the shell. But that there was a
difference in the actual capacity of the condenser when
Groups I. and IV. were taken from its value when II.
and ILI. were obtained seems almost certain. As yet I have
not become satisfied as to the cause of this difference ; but it
seems probable that, in putting the condenser together, some
obstruction lodged between the two halves of the shell and
prevented them from coming completely together. Had they
been separated a few hundredths of a millimetre only, the dif-
ference in question would be fully accounted for. The surfaces
of contact are very accurately ground and polished, and
loosening the screws does not cause them to separate, as
proved by the capacity remaining constant. That the low
Ratio of the Electromagnetic to the Electrostatic Unit. 331
fork should give higher values for v, which means a lower
value for the capacity, than the high fork, is rather unex-
pected and not fully understood. The low fork gave only a
quarter the current given by the high one, and was less steady
in its action in proportion to the current ; consequently the
single observations were less reliable, but this alone does not
account for the nearly uniform difference.
In view of the uncertainty as to the cause of the variations
it is difficult to determine how best to combine the results.
The weight of each single value of vin the Table is deter-
mined by considering the number of observations from which
it is calculated, the uniformity of the separate observations,
the steadiness of the spot, &. If we give to Groups II.
and III. one half the weight of I. and IV., in proportion to
the sum of the weights of the separate values we have as the
mean for the fast fork 2°9994 and for the slow fork 3°0023.
Giving now double weight to the results of the fast fork, on
account of their greater accuracy and uniformity, we have, as
a mean of all,
v = 3:0004 x 10"° cm. per second.
Again, if it be found that the cause suggested is the true
cause of the excess of groups II. and III., then those groups
should be thrown out, and we should have 2°9982 and 3°0014
as the means, which would give for the mean of all
v = 29993 x 10° cm. per second.
These vaiues are based upon the value *98664 for the British
Association Unit.
It is proposed to resume this investigation next winter,
when more perfect insulation can be obtained, and several
improvements in the details of the apparatus will be made.
The smaller ball of the condenser will then be used also, and
the cause of the difference in the values given by the two forks
will be studied. Although we cannot yet say whether v is
greater or less than 300,000,000 metres per second, it seems
certain that it is within a tenth per cent. of this number, and
it is hoped in the continuation of this investigation to narrow
considerably further the range of uncertainty.
For convenience of reference the following values of v and
of the velocity of light as found by different observers are
added, the values of v being corrected to the value ‘98664 for
the B.A. unit:—
332
‘Dr. EB. van Aubel’s Researches on
v, ratio of the units.
Velocity of , light.
11856. Weber and Kohl- 1879. Michelson ...... 2-9991 x 10?°
mause lie ee ek 3107 x 10'° 1882. Michelson ...... ries a
21869. W. Thomson and ‘9986 x 10
ane te Pade cia) 1°02. Newt { 2-9981 x 10”
31868. Maxwell ......... 2°842 x 101° S74. Cornu eee 2°9850 x 10!°
Sali? = iMMiKichan 4. ses: 2-896 x 10% 1878. Cornu ees 3°0040 « 10!°
° 1879. Ayrton and Perry 296010! | 1880-81. Young & Forbes 3:0138 x 10”
SASSO; Shida. -t..%c00- 1 2-955 x 10?°
71883. J.J. Thomson... 2:963x 10"
8 1884. Klemencic......... 3019 x 10'°
91888: Himstedt. ......... 3009 x 10?!°
1889. W. Thomson 3004 x 10?°
* Weber and Kohlrausch, Electrodyn. Maasbestim., Abh. der Kénigl. Sachs.
Gesellschaft der Wissensch. y. p. 219 (1856); and Poge. Ann. 1856.
? King, Report of the Committee on Electrical Standards, 1869.
° Maxwell, Phil. Trans. 1868, p. 643.
* Dugald M‘Kichan, Phil. Trans. 1879.
° Ayrton and Perry, Journ. Soc. Tel, Engineers, 1879, p. 126.
° Shida, Phil. Mag. [5] x. p. 481.
7 J. J. Thomson, Phil. Trans. 1883, p. 707.
8 Klemencic, Wiener Berichte [3] lxxxiii. p. 88.
9 Himstedt, Wied. Ann. no. 9 (1888).
Johns Hopkins University, Baltimore,
June 15, 1889.
XL. Researches on the Electrical Resistance of Bismuth.
By EpmMonp van AvuBEL, Doctor of Science*.
GREAT many memoirs having been published relating
to the influence of temperature upon the electrical
resistance of bismuth, I think it advisable to sum up in a few
lines the actual state of the question, in order to show the
bearing of my researches on the solution of the problem.
In the present memoir I have examined the electrical
conductivity of bismuth between 0° and 100° only; I will
therefore confine myself to stating the results arrived at by
physicists between the same limits of temperature.
Matthiessen t, in conjunction with von Bose and other
physicists, has found the conductivity of bismuth at 0° to be
1:245, that of silver being taken as 100, and has expressed
the conductivity at ¢ as a function of the conductivity at 0°
by the formula
A= Ay(1—0°0035216 ¢ + 0°000005728 ¢?).
G. Wiedemann, Matthiessen, Holzmann, and Vogt have
* Communicated by the Physical Society: read June 22, 1889.
+ The works of the physicists, whose names will be mentioned later on,
are enumerated in the Treatise on Electricity by Prof. G. Wiedemann,
vol. i. 1882, p. 503 and the following pages.
t
the Electrical Resistance of Bismuth. 333
also studied the effect of the composition of the alloys Bi—Sn,
Bi—Pb, upon their electrical conductivity.
According to Matthiessen and Vogt, the electrical conduc-
tivity of the alloys of bismuth is modified by the first heating
and the first cooling. If, be the original value, and Ap, the
conductivity after cooling, we have the following results: —
Xe ne
Pb—Bi (2°27 vol. Pb to 100 vol. Bi) . 8101 7-633.
eG 1S yy 5 ») - £908 4-565.
These variations doubtless depend upon permanent changes
in the molecular structure.
The conductivity of molten bismuth increases as the tem-
perature is lowered; it diminishes rapidly when the metal
solidifies, according to the researches of Matteucci and
Matthiessen, and increases again as the solidified mass cools.
If small traces of tin or lead be added to the molten bismuth,
according to Matthiessen, the conductivity at first diminishes,
as in the case of solid metals, and afterwards increases.
Fr. Weber has found for the specific electrical con-
ductivity of bismuth (C.G.S.) 0°838 x 107-5; and L. Lorenz
has given for the same quantity the values
0-929 x 10-* at 0°; and 0:630 x 10-° at 100°.
M. Leduc* has observed that the electrical resistance of
wires made of an alloy of bismuth and lead increases when
the temperature is raised. He has also observed a difference
between the electrical properties of wires and of thin plates of
commercially pure bismuth, which he attributes to the method
of preparation and to the very different rates of cooling.
More recently f the same physi¢ist has found the following
results with bismuth which had been run into a tube and then
slowly cooled. When the bismuth is heated for the first
time, say to 100°, it undergoes an annealing the effect of
which is to diminish its initial resistance about 30 per cent.
During this operation, between the temperatures 0° and 100°,
the following formula is obtained, which must be received with
caution :—
rm =7, (1 +0-00344¢ + 0-000007722),
in which 7, and 7 are the electrical resistances at the tempera-
tures 0° and ¢° respectively. This formula gives the value
+0°00421 for the mean coefficient of variation of the re-
sistance between 0° and 100°.
* Journal de Physique, 2) iii. (1884) p. 362.
+ Leduc, Thesis for doctor’s degree presented in June 1888 to the
Faculty of Sciences of Paris.
Phal. Mag. 8. 5. Vol. 28. No. 173. Oct. 1889. 2B
334 Dr. EH. van Aubel’s Researches on
Afterwards the resistance varies, between the same limits,
according to the formula :—
1=1) (1 + 0°00375t + 00000827),
and the mean coefficient of variation of the resistance between
0° and 100° is then 0°00455.
For a thin plate of bismuth, Leduc has found that after.
annealing the resistance decreases, between 0° and 70°,
according to the following formula :—
rt=7)(1—0°00158t + 0:0000043727).
And this gives the number —0°00127 for the coefficient of
variation with the temperature between 0° and 70°. The re-
sistance of the metal thus prepared would be much greater
than that given by Matthiessen, perhaps more than double
the value found by him, no doubt because of the difference of
molecular structure of the specimens examined.
In 1884, Prof. Righi* published a very remarkable paper,
and we will sum up those of his conclusions which bear
directly upon our researches.
1. The resistance of commercial bismuth increases on heat-
ing between certain limits of temperature, and decreases
between others (generally it decreases at temperatures near
the ordinary temperature), and, by constructing a curve of
resistance, with the temperatures as abscissee, and the specific
resistances as ordinates, we obtain in general a curve in the
form ofan M. There is a maximum ata low temperature, then
a minimum, then a second maximum a little below fusing
point, and finally a second minimum after the change of state.
2. The resistance of commercial bismuth varies not only
with the temperature, but also with the manner in which the
piece has been prepared, and with the temper of the metal.
8. Chemically pure bismuth behaves like other metals ; it
is not sensibly affected by tempering, and at 0° its resistance
compared with that of mercury is 1°15.
4, The difference between pure and commercial bismuth is
due to traces of tin, which give to the latter properties
similar to those by which steel differs from iron.
5. On adding to bismuth tin in increasing amounts, the
specific resistance becomes much greater up toa maximum,
and then diminishes.
6. The presence of tin in increasing amounts modifies the
curve of resistance, in the same manner as a temper more
and more hard would do.
G. Wiedemannt thinks that the phenomena observed
* Journal de Physique, [2] iii. (1884) p. 3565,
+ Elektrictdt, Bd. 1v., 11., p. 1228.
the Electrical Resistance of Bismuth. 335
by Prof. Righi can be partly accounted for by the discon-
tinuity of the bismuth wires.
G. P. Grimaldi* has studied the thermoelectric pro-
perties of bismuth, and has confirmed the analogies which
Prof. Righi has found between pure bismuth and iron, the
bismuth containing tin and steel.
_ A. von Ettingshausen and W. Nernstt have obtained
results which are recorded in the following Table, where « is
the electrical conductivity in absolute measure, and a the co-
efficient of variation of the electrical resistance with the tem-
perature. The plates denoted by Bi were made of absolutely
pure bismuth; the other plates denoted by LI to LIV were
made of an alloy with tin.
Bismuth. | ‘Tin. x (G.8.). a.
Parts by | Parts by
weight. weight.
Bir eS 100 4:80x107-5 | ~—0-0012
is en 99-05 0:95 2461075 | +0 0016
TET CA 98°54 1-46 2;71<10-5 |. +0:0018
Bie .-) 5; 93:86 6:14 3-46 10-6 | +40:0024
EV <5. 869 13:1 56210-§ | +0-0025
The electrical resistance increases then (between 0° and
30°) for every alloy, when the temperature is raised; it
decreases on the contrary for pure bismuth under the same
conditions. On increasing the quantity of tin, the coefficient
of temperature « also increases. The conductivity decreases
rapidly by the addition of small quantities of tin, and increases
again afterwards.
C. L. Webert has found that the resistance of the metal
under consideration at first decreased up to about 100°, the
coefficient of temperature being —0°0006; and then in-
creased up to the melting-point. The position of the mini-
mum, however, is displaced by repeated heatings and coolings
between 80° and 120°.
The same physicist has also observed that the electrical
resistance of alloys of bismuth and tin, containing from 10
to 80 per cent. of bismuth, increases between 0° and 120°,
as the temperature is raised.
* Beablitter zu den Annalen der Physik (1889), No. 1, p. 25.
+ W. Nernst, Annalen der Physik, Neue Folge, Bd. xxxi. p. 783
(1887); A. von Ettingshausen and W. Nernst, Annalen der Physik (1888),
Heft 11. p. 474.
{ Annalen der Phystk, 1888, xxxiv. p. 576.
7D 2
336 Dr. E. van Aubel’s Researches on
In his Legons sur ? Eléctricité, Prof. Exner * mentions that
when bismuth is heated the resistance generally decreases,
and does not return to its original value on cooling, but
reaches a value which is higher as the cooling is more gradual.
Ph. Lenard and J. L. Howard+ have studied bismuth
wires obtained by means of a screw-press; these wires were
rolled into a spiral immediately, while the metal was still hot.
They found that in the case of pure bismuth the electrical
resistance increased with the temperature between 0° and 36°
by 0:0052 for every degree Centigrade.
Finally, in a preliminary communication, published last
year {, I took up again the study of the question. Although
bought at the best manufactories in Germany, all the bismuth
that I used was very impure.
I examined bismuth slowly cooled, hardened bismuth, and
finally compressed bismuth. The molecular structure exerts
a great influence upon the electrical properties of different
kinds of impure bismuth. All the alloys of bismuth and tin
which I studied gave an increase of electrical resistance when
the temperature was raised, although the bismuth specimens
which entered into the composition of these alloys produced
the opposite effect. I also proved, in these preliminary
experiments, the great influence of lead as an impurity
in bismuth.
If my first results and those of the other physicists be com-
pared with the conclusions arrived at in my present treatise,
the wide differences which can be caused by impurities in the
pieces of metal under examination will be very striking.
The modes of preparing and of suddenly cooling rods of
bismuth have been fully described in a preliminary commu-
nication§.
Analysis of different Bismuths.
We have measured the electrical resistances of several
different bismuths, which we will designate by
Latest Brommsdorff,
Classen I.,
Classen IT.,
Classen III.,
Classen IV.,
and pure electrolyzed bismuth.
The first is the metal as pure as it is possible to obtain it
* Vorlesungen iiber Elektricitdt, Wien (1888), p. 404.
t LElektrotechn. Zeitschrift, 1888, Bd. ix., July, Part xiv.
t Bulletins de 1 Académie royale de Belgique, 1888, 3rd Series, xv. No. 1
(Preliminary communication).
§ Phil. Mag. vol. xxv. p. 191; Proc. Phys. Soc. Lond. vol. ix. p. 124.
the Electrical Resistance of Bismuth. 337
commercially. It has been supplied to us by the well-
known chemical works of Herr Brommsdorff at Erfurt, who
has taken all possible care in its preparation. We have so
named this product to distinguish it from Herr Brommsdorff’s
other bismuths, which we treated of in our “ Preliminary
Communication.”
_ The qualitative analysis of this metal, made by Prof.
Classen, showed that it contains several impurities, princi-
pally copper.
The four following bismuths are products as pure as can be
obtained by chemical methods of precipitation; they were
prepared by Prof. Classen, who used every precaution. The
metals Classen J., II., and {II. were obtained by reduction
from bismuth oxychloride, Classen IV. by reduction from
bismuth nitrate.
Bismuth nitrate is a pharmaceutical product which, it
appears, can be obtained in a very pure state in commerce.
These different samples were subjected to a minute spectral
analysis, the results of which we will point out later, but we may
mention here that they all contained lead. Small quantities
of lead were always carried down with the precipitated bis-
muth; this experiment repeated even 13 times never resulted
in a pure product. It appears then that bismuth cannot be
obtained absolutely pure by precipitation.
The last bismuth which we examined, and which we have
called “ pure electrolyzed bismuth,” was prepared by elec-
trolysis. During the electrolysis of a solution of bismuth
containing traces of lead, pure bismuth was deposited at the
negative pole; and lead, in the form of peroxide of lead, at
the positive pole.
As to the lead or tin which were used in the alloys, they
eame from Herr Brommsdorff’s chemical works, and were
sold to me as pure. Besides, they were introduced into the
alloys in such small quantities that there was no occasion
to take account of any impurities they might have contained.
Purification of Commercial Bismuth.
First Method.
About 250 grams of the metal were dissolved in HNO;
the solution was brought to the boiling-point in a porcelain
dish into which concentrated HCl had been poured. In
order to transform all the bismuth nitrate into the chlo-
ride, the operation was repeated until the presence of HNO;
could no longer be detected. The residue was then dis-
solved in HCl, and alcohol added in successive small quan-
tities. Most of the lead was precipitated in the form
338 Dr. E. van Aubel’s Researches on
of lead chloride, which was removed by filtration. The
solution of bismuth was then distributed among 10 glass
beakers holding about 4 litres each. The bismuth was pre-
cipitated as oxychloride on addition of water. The precipi-
tate was decanted and washed until no trace of HCl could
be found. Then it was again dissolved in HCl, the bismuth
precipitated as oxychloride, and washed as before. And this
was done twelve times. The precipitate finally obtained was
carefully washed again, then dissolved in HCl. The bismuth
in this solution, to which water had been added, was precipi-
tated by the addition of ammonia and ammonium carbonate.
After decantation the precipitate was washed with water,
until all the ammonia had disappeared, and dissolved in HCl.
This precipitation was repeated three times.
Finally, the precipitate was dissolved in HCl, and the
chloride transformed into the oxychloride by addition of water.
The resulting precipitate, entirely freed from acid, was dried,
mixed with KCN, and reduced. ‘The metallic bismuth was
again purified by a second fusion with KCN.
The bismuths Classen I. and Classen III. were both pre-
pared under the direction of Prof. Classen in the laboratory
for analytical chemistry at the Polytechnical School at Aix-la-
Chapelle.
Classen I. was prepared by Herr Norrenberg ; Classen III.
was obtained by Herr Magdeburg by means of the “ Bis-.
muth Purissimum”’ from the Schucharell works at Gorlitz.
Finally, we are indebted to the kindness of Prof. Classen
himself for Classen II.
Second Method.
The product used in this second method was the “ bismuth
subnitrate purissimum’’ of Dr. Marquardt, at Bonn, which
was employed by Marignac in his determination of the atomic
weight of bismuth.
One kilogram of this product was dissolved in HCl, and the
solution was divided among 22 glass beakers, having a capa-
city of 4 litres each, and these were filled with water. The
recipitate of oxychloride was washed with water until all the
Clwas removed. The solution in HCl and the precipitation
by means of water were repeated three times. Then the preci-
pitate was again dissolved in HCl, precipitated with ammonia
and ammonium carbonate, and thoroughly washed with water.
These operations were also repeated three times.
Finally, the precipitate was once more dissolved in HCl,
the bismuth oxychloride obtained by the addition of water,
and reduced by means of KCN and soda.
the Electrical Resistance of Bismuth. 339
Third Method. |
The metal, after having been purified by the preceding
methods, was subjected to electrolysis to take away com-
pletely any trace of lead. Prof. Classen, who is at present
engaged in determining the atomic weight of bismuth, intends
to describe this electrolytic method in detail.
Researches with the Spectrum.
To produce the bismuth spectrum a large Ruhmkorff’s coil
with a Leyden jar intercalated was used, and the spark ob-
tained between rods of the metal. The spectrometer employed
was one of Meyerstein’s with a Schroeder direct-vision prism
composed of five separate prisms. The slit was made rather
open so as to give a very bright spectrum.
With a smaller dispersion, produced by a fine Merz
prism, the spectrum was still more luminous. It was inter-
esting to compare the method of observation which we have
just described with that which consists in sending an elec-
tric discharge between platinum electrodes, in a tube con-
taining a solution of a salt of the metal. This method was
also used, the rest of the apparatus remaining the same.
It can thus be proved experimentally, and this is of some
importance to chemists, that the first method 1s much more
sure and exact than the other.
On examining the bismuth “ Latest Brommsdorff”’ in the
spectroscope, sodium and copper were found to be present.
The two characteristic lines D, D, of sodium remained, even
when the surface of the bismuth rods had been well cleaned
by long immersion in nitric acid. The metal contained only
traces of lead.
The other bismuths contained no copper and no sodium.
The traces of lead, which were found in the bismuths Classen
I., I1., U., 1V., and in the “ Latest Brommsdorff,” were all
very faint; indeed we were not able to establish them with
certainty, except by the following process :-—
After having substituted, for the original rods of bismuth,
other rods of lead, so as to produce a good spectrum of this
latter metal, the point of cross section of the micrometer wires
of the spectroscope was placed upon the most visible line of
the lead spectrum, and then the rods of lead were replaced
by those of bismuth.
The bismuth Classen I. showed the very characteristic
line of lead, of wave-length 5610°4.
The same line was found in Classen II. and atest
Brommsdorff; but it was much more feeble. Classen III.
and Classen IV. also contained lead.
340 Dr. EK. van Aubel’s Researches on
To sum up, all these bismuths contained lead in variable
amounts, Classen II. and Latest Brommsdorff containing the
least.
But in the case of the bismuth obtained by electrolysis, no
impurity was discovered by spectrum analysis.
This very minute spectrum analysis of products, prepared
with the greatest care by such a distinguished chemist as —
Prof. Classen, warrants us in saying that pure bismuth cannot
be obtained with certainty by precipitation. The electrolyzed
metal can alone be considered as chemically pure.
In the successive precipitations the traces of lead are
drawn down mechanically.
In electrolyzing the solutions of bismuth, in which the
spectrum analysis had revealed traces of lead, a very thin but
perfectly visible coating of peroxide of lead was found at the
positive pole. |
Calculation of the Absolute Values of the Electrical Resistances.
The mode of measuring the electrical resistance has been
described in the preliminary communication.
In order to determine the absolute value of the electrical
resistances at 0° of the tempered rods, it was necessary to
calculate the mean section of these rods from their weight,
density, and length.
No sensible error is committed in taking 9°82 as the density
of bismuth or of the alloys which we have studied, as the lead
and tin contained in the latter were only present in very
small quantities. Besides, a much greater cause of error is
the exact determination of the length of the rods of bismuth
between the -two solderings.
In the case of the slowly cooled rods the difficulty is greater,
because the bismuth adheres very closely to the glass tubes in
which it is contained *, and because these tubes cannot be con-
sidered as cylindrical. In spite of every precaution it is impos-
sible to break the glass, so that the whole of the metal may be got
out clear without breaking the rod of bismuth. So I measured
with a spherometer the diameters of the bismuth rod at the
two extremities and in the middle ; and I considered the rod
as formed of two truncated cones joined together at the small
end. It was then easy to calculate the electrical conductivity
at 0°; for example, either using the formula given by Siemens
(Annalen der Physik, vol. cx. 1860, p. 38, or F. Kohlrausch,
Guide de Physique pratique, édition frangaise, p. 223), or
calculating the section of a cylinder whose height is the length
of the rod of bismuth, and whose volume is that of the two
* Righi, Journal de Physique, 2nd series, vol. iii, 1884, p. 182.
the Electrical Resistance of Bismuth. a4]
truncated cones joined together. The section of this cylinder
can then be taken as the mean section of the rod.
All the absolute values that I give further on are thus only
approximations, but they approach very near to the true
values.
Results of the Electrical Measurements.
The following Tables contain, in column W, the electrical
resistances as I have measured them, that is to say in Siemens
units, and at different temperatures given by a Centigrade
thermometer. I have given also, for each bismuth, the specific
electrical resistance Ry in C.G.S8. units at O° temperature ;
and the mean coefficient of variation of the electrical resistance
between 0° and 100°, 2. e. the quantity K of the equation
f= Ry(1 4- Kd).
|
| It is allowed to cool again slowly; and it is found that the
{values remain constant.
Bismuths.
(1) Rods which have been slowly cooled.
W. K
Bismuths. Tempera- Electrical Variation for R,.
tures. | resistances (Ol penween OStand 100° u
in US. :
e)
0 0-1390
Latest Bromms- 19 0:1462
OMS cues v0 49°1 0°1590 +0:00325 103 x 109°90
99-6 0:1840 ;
0 0:2875
19-1 0-2882 +0-00076
iassemi Ll, ecc.sce- 49-9 0:2929
99°6 0°3095
0 ae
16°7 1680 +0-00299 10° x 12469
Classen II.......... 49-6 0-1898
99°5 0:2096
0 0:2447
(2) Classen III. 20°5 0:2500 +0:00161
2nd rod. 49°8 0°2595
99°8 0°2841
0) 0:2407 |
(1) Classen ITT. 20-5 0:2439 +0-00132 10? x 156°74
lst rod. 49°7 0:2509
99°8 (2725
/ 0 0:2036
20°3 0:2063
99-8 0:2302 |
It is allowed to cool slowly.
: ie 0:2043
‘9 0:2066-
ae an < | It is heated to 100°, and allowed to cool slowly.
’ O 0:2048
20 0°2069 | +0:00126 103 x 170°07
52:5 02136 |
| 99:6 0:2305 |
|
342 Dr. E. van Aubel’s Researches on
Table (continued).
W. K
Bismuths. Ter ee Variation for Ry.
Pes | see 1° between 0° and 100°.
in U.S.
fe)
(VW, 0-1790
20°2 0:1806
| 99°8 0:1998
It is allowed to cool slowly.
0 | 01794
Classen IV au veel
Onn ede a palit i heated to 100°, and allowed to cool very slowly.
i 01798
|| 2 01810 +0-00113 10? x 168°35
50 01861
| 99°6 02000
It is allowed to cool again slowly, and it is found that the
(| values remain constant.
(| 0 | 01031 |
99°61 01490 +0°00447
It is allowed to cool very slowly.
Pure electrolyzed re | nae
Classen Bismuth, 4
0:1032 {from 0° to 19°'5 : +0:00412
Se en. It is allowed to cool again very slowly.
| 19°5 01115 from 0° to 55°: +0-00426
\
55 01274 |from 0° to 999-72: +-0:00447
99°72 | 01493
Ar 20 00912
| 99°6 0-1322
Pure electrolyzed | | It is allowed to cool very slowly.
Classen Bismuth, 4 0 0:0913 |from 0° to 22°-1: +0-00411
2nd rod*, 22:1 0:0996 from 0° to 56° : +0-00426) 10? x 107-99
| 56 01131 |from 0° to 99°:7: +0 00450
\| 997 | 0-1323
* We think it will be interesting to give, for the pure electrolyzed
bismuth, the values of the influence of magnetism on the electrical
resistance.
AW being the difference between the electrical resistance in the
magnetic field and outside of it.
AW Intensity of
Temperatures. | 100 We mapnetioiela
Sine at oe : a eres a ies
ae 0-415 about 1560 C.G.S. units.
the Electrical Resistance of Bismuth. 343
(2) Tempered Rods.
Ww.
Beth Tempera-| Electrical eee for R
ee tures. resistances TOs Seno and 100°: 0°
in U.S.
°
0 0:0965
Latest 17°6 0:0988 +0:00199 10? x 189-86
Brommsdorff. 49°3 0-1040
99°7 0:1157
0 0°1745
1 I Gs) 0-1729
Classen I....1|) 49-7 | 0-1687 —0-000603 10° 246-91
99-7 0:1640
0 0°1275
Classen II. | 16:7 01287
Ist rod. 49-7 071319 +0-00106 10° x 166°66
{| 99:5 01410
0) 071292
Classen II. 16:9 0-1310
2nd rod. 50°3 0°13853 +000128 103 x 157-48
99 0:1456
( 0 1 00-1205
18 071215
| 99°8 0°1342
- Classen II. | | It is allowed to cool slowly.
acd %| 0 01203
| 997 | 01343 +0:00116 10? x 163-40
A second observation showed that the resistances now remain
( constant,
{ 0 071135
19-7 01127
99°8 0:1139
It is allowed to cool slowly.
Classen ITI. 0 0:1128
Ist rod. my 071121 +0:00009 10° x 204°50
0-1114
0-11388
A second set of observations of the electrical resistances from 0°
to 100° showed that the values remained constant.
998
|
3
( me 0°1376
\) 9 0:1363
99 °8 01372
| | It is allowed to cool slowly.
0
\
Classen IIT.
2nd rod.
013864
As 01355 +0:00005 10? x 208°33
0'1346
a ‘8 0:1371
A second set of observations showed that the values of the
Tesistances remained constant.
d44
Dr. E. van Aubel’s Researches on
Table (continued).
Bismuths.
Classen IV.
Ist rod.
Classen IV.
2nd rod.
Pure electrolyzed
Classen Bismuth.
Ist rod.
Pure electrolyzed
Classen Bismuth.
2nd rod*.
—
|
|
(
|
|
\
W
Tempe- Electrical ie
: Variation for R,.
ratures. resistances 1° Between O° acne! o
in U.S.
fe)
16:6 0:1301
49:6 071285
oN 7 0:1301
It is allowed to cool rather slowly.
0 0:1307
16:6 0:1295
49:3 0:1281 — 000004 103 x 207-47
Seer 0:1302
A second investigation showed that the values of the resistances
remained constant,
16°5 0:1507
49°6 01486
99°7 0°1501
It is allowed to cool rather slowly.
0 01512
16°5 01500
49°5 0-1479 —0 00008
99°7 0-1500
A second investigation showed that the values of t
remained constant.
0 0-:0965 +0:00434
996 01382
0 0-°0952
99°6 0-1370
It is allowed to cool very slowly.
0 0:0950 ‘from U° to 21°-9: +0:00399)
21°9 0°1033 —_|from O° to 56°°1: +0:00422
56°1 01175 {from 9° to 99°°7: +0:00445
99-7 0:1372
10? x 212-94
he resistances
10? x 108-69
* We think it will -be interesting to give the value of the magnetic
action for this rod of hardened bismuth, as we have done elsewhere.
i AW Intensity of
Temperatures. | 100 We maenere acl
a
mo a eeg | about 1560 C.G.S, units.
the Electrical Resistance of Bismuth. 345
(3) Compressed Rods.
W. K.
Tempera-| Electrical | Variation for
Bismuths. tures. | resistances |1° between 0°
in U.S. and 100°.
oO
( 20°6 0:1300
It was observed that the electrical resistance
was permanently changed each time the rod
of bismuth was heated. Finally, after having
been heated from 0° to 100°, and been al-
lowed to cool from 100° to 0° several times,
ee
Classen IT.
eae | constant values were found. We cannot tell
oe ae what. is the cause of this considerable decrease
| in the resistance, but it is certainly not due
to an alteration of the connexions.
0 0-1250
| 22 01215 —0:00049 | 10? x 236-96
\ 99:4 0-1189
( 20°5 0°1353
Classen IT. | Same observation as above.
2nd rod. + 0 0°1352
| 21-9 071302 —0:00083 | 10? x 251-26
| 99°3 0°1241
OW 0-1019
18 00978
| 99°8 0:0913
Classen II. It is allowed to cool slowly.
3rd rod. 4 9 0°1024
}997 | 0:0016 | —0-00105 | 10*x 26810
| A further investigation showed that the re-
{_sistances then remained constant.
Alloys with Tin.
W. K.
Alloys. Tempera-| Electrical | Variation for
tures. | resistances |1° between 0° R,.
in U.S. and 100°.
Ist. Rods slow ly cooled.
0° 0:2670
19 0-2710 10° x 458-71
49 02715
99°6 0:2623
| 0 0-6790
Latest Brommsdorff
bismuth + Sn.
0:5 gr. Sn to 100 gr. Bi.
Bi Classen IT. + Sn.
0°53 gr. Sn to 100 gr. Bi.
16°7 0:6917 10° x 416°66
49:6 06890
99'5 0°6540
2nd. Tempered Rods.
| 0 0:1960
rae ee ee ry |” 02020 10° x 346-02
f Bete |}: 49:3 0:2083
0°5 gr. Sn to 100 gr. Bi. 99-7 0:2095
0 0-1795
Bi Classen IJ. + Sn. 17°5 01844 10° x 35461
0:5 gr. Sn to 100 gr. Bi. | ) 49-2 0°1905
99°7 O0-1915
0 0-2561
Bi Classen II. + Sn. f 16-7 0:2637 10° x 349°65
0-53 gr. Sn to 100 gr. Bi. ie 49-9 0°2735
99:5 0:2780
346 Dr. E. van Aubel’s Researches on
Alloys with Lead.
W. K.
Tempera-| Electrical | Variation for
set tures. | resistances |1° between 0° R,.
in U.S. and 1002.
———————_ | __ _________
Ist. Rods slowly cooled.
Latest Brommsdorff 0 0°2125
. 19-1 02122
ee eedun | 2
gr. to 100 gr. Bi. 99-6 0-2200
) 0:4037
Bi Classen I. + Pb. 19 0:3887 10? x 362-32
0-5 Pb to 100 gr. Bi. 49-1 03690
99°6 0:3530
2nd. Tempered Rods.
Latest Brommsdorft i ae
a 49:2 | 0:1400 10? x 245-70
0:5 gr. Pb to 100 gr. Bi. 99-7 0-1365 x
| 0 0-1475
Bi Classen I.+ Pb. 17-5 0-1485
0-5 gr. Pb to 100 gr. Bi. | a2 0:1470 10° x 274-27
99-7 0-1414
Conclusions.
I have observed that the electrical resistances of some rods
were changed permanently after the first heating ; but when
once the values remain constant they do not change again,
even after several months. Dr. Leduc* has observed a
similar phenomenon. Rods of the same bismuths, either
slowly cooled or hardened under the same conditions, give
nearly the same values for the resistance at O° and for the
coefficient of variation with the temperature. The methods
of tempering and of slowly cooling remain sensibly the same
for the different specimens. We must not then look to this
cause to explain the great variations which have been ob-
served between one bismuth and another.
The molecular structure, which I have changed by temper-
ing and by compression, makes a great difference in the
electrical properties of impure bismuths. On the other hand,
tempering appears to have no action whatever on pure bis-
muth ; thus, the electrical resistance at 0° is :—
* Thesis for doctor’s degree, p. 30,
the Electrical Resistance of Bismuth. B47
for electrolyzed bismuth, slowly cooled. . 10° x 107:99,
and for the same metal, tempered . . . 10° 108°69.
The coefficient of variation with the temperature’ and the
influence of magnetism are very nearly the same for these two
specimens. The coefficient of variation with the temperature
besides is posztzve.
In the case of impure bismuths the process of tempering
causes the coefficient K to decrease, and even to become
negative. The action of compression seems to be still
greater.
As to the absolute values of the electrical resistance at
(0°, they increase under the action of tempering and com-
pression.
If we compare the results furnished by the electrolyzed
bismuth with those given by the other bismuths, we see
that the effect of traces of lead is to produce a dimi-
nution in the value of K, and an increase in the value
of Ry. It can also be seen that, in the case of impure metals,
a high vaiue for R, generally corresponds to a low value
for K.
With regard to alloys of impure bismuth with lead and
tin, the results prove that these latter metals tend to increase
R,, and can even in certain cases give a negative value for K.
- But the molecular action, and above all the lead, produce a
much greater effect than the tin.
The electrolyzed bismuth presents a peculiarity which
is not seen in the impure kinds. The coefficient K remains
sensibly the same at different temperatures between 0° and
100°, and this may be considered as a proof of the purity of
the metal.
In short, one may say that, of all the methods both
physical and chemical, the determination of the electrical
resistance is certainly the most exact for ascertaining if the
bismuth be pure, and above all if it contain no trace of
lead. While spectrum analysis and the process of electro-
lysis have with difficulty discovered the existence of lead in
the bismuth Classen II. for example, the study of the elec-
trical resistance leads to very different results.
When one considers all the difficulties I have met with in
procuring the pure metal, and the number of electrical
measurements which I have been obliged to make, so to
speak, uselessly, it is plain that, before studying the physical
properties of a metal, it would always be wise to submit the
metal to a very careful spectrum analysis, to assure one’s self of
its purity.
348 Researches on the Electrical Resistance of Bismuth.
The differences, which I pointed out at the beginning,
between the results of other physicists are easily explained
by the rarity of pure bismuth.
Unfortunately I had not enough of pure bismuth to be
able to study compressed electrolyzed bismuth and its alloys
with tin and lead.
Considering the great influence of very small traces of
lead, it is allowable to. suppose that the presence of this
foreign metal modifies the molecular structure of the bismuth
to a considerable extent; unfortunately a microscopic ex-
amination could hardly give any result here.
Finally, if the results which we have obtained in this
treatise be compared with those which we published in our
“ Preliminary Communication,” it will be seen how much the
conclusions deduced from the experiments may vary accord-
ing to the nature of the impurities contained in metal. Also,
the question of the variation of the electrical conductivity of
bismuth with the temperature presents a difficulty of a chemi-
cal nature, and we strongly recommend physicists to make
known in their works the method of preparation, and if
possible the results of the analysis of the different bismuths
which they have examined.
By means of the two following Tables my results may be
easily compared with those of other physicists. It appears
by the results that the bismuths studied by Messrs. L. Lorenz
and Righi were pure.
Slowly cooled. Tempered. Compressed.
Bismuths. ee
R,- Kx. Ry: K. R,- K
Brommsdorff...| 10? x 109-90 | 0:00325 | 10?139°86 | 0:00199
Olassen E30... || et eteeee 0-00076 | 10? x 246 91 | —0-000603
Classen II. a...| 10°? 124-69 | 0:00299 | 10° x 16666 | +0:00106 | 10° x 236-96 | —0:00049
1B St eel | aecee hes oN AN 10° x 157-48 | +9-00128 | 10% 251-26 | —0-00083
DD 6 a2.) 9p tee ea ae 10° x 163-40 | +0°00116 | 10? x 268°10 | —0-00105
Classen IIT. a...| 10° x 156-74 | 0:00132 | 10° x 204:50 | +0-00009
TCO. ee ee 000101} 10° x 20833 | +0-00005
Classen IV. a...| 10? x 170-07 | 0:00126 | 10° x 207-47 | —0-00004
IV. d...| 10° x 168°35 | 000113} 10° x 212-94 | —0:00008
Electrolyzed Bi.| 10° x 107:99 | 0:00429 | 10° x 108°69 | +0:00422
* It is to be observed that all the coefficients of K in this column
posttive.
are
Notices respecting New Books. 349
Observations. Experimenter. Ry. K,
Lenz. 10° 82°36
Matthiessen. 10? x 131-50
Matthiessen. 10° x 125-70 | +0-00418
F. Weber. 10? x 119-33
L. Lorenz. 10? x 107-64 | +0:00475
Bi cooled slowly. Ledue. +0:00455
Bismuth plate. Leduc. —0:00127
Kighi. 10? x 10849
Bismuth plate. Von Ettingsh. & Nernst.| 10° x 208°33 | —0:0012
C. L. Weber. — 0-0006
Lenard & Howard. +0:0052
Bi cooled slowly. Edw. van Aubel. 10° x 107-99 | +0:00429
Bi hardened. Edw. van Aubel, 10? x 10869 | +0-00422
I have great pleasure in expressing my thanks to Profs.
Willner and Classen for having so kindly furnished me with
the valuable materials necessary for my researches.
Physical Laboratory of the Polytechnic School,
Aix-la-Chapelle.
XLI. Notices respecting New Books.
Force and Energy. A Theory of Dynamics. By GRANT ALLEN.
(Longmans, Green, and Co.: 1888. Pp. xiv+161.)
HOSE familiar with Mr. Grant Allen’s more popular writings,
whether in Natural History or Fiction, were hardly prepared
for his appearance as the Author of a new theory of Dynamics, a
branch of Science supposed to be among those the bases of which
are most firmly established, and verified by thousands of instances
of the accordance with its predictions of phenomena stch as the
recent “ Occultation of Jupiter by the Moon, the disappearance
taking place at 7 h. 4 m. August 7th, afternoon, at 25° from the
vertex...”
In a prefatory “ Apology” Mr. Allen explains that the present
book is the development of ‘‘a little twenty-page pamphlet, bearing
the same title, printed privately at Oxford in 1875 for presentation
to a few physical specialists.” The result of the earlier appeal, we
are told, was that “some said his theory was only what was already
known and universally acknowledged; while others of them said it
was diametrically opposed to what was already known ”—a resuit
not unlikely to happen, according as the specialist in dipping into
the brochure chanced to alight on one or another passage.
The “summum genus” of Mr. Allen’s theory of dynamical
science is “ Power,” of which “ Force” and “‘ Energy” are “ sorts,”
the former “‘initiating or accelerating aggregative motion, while it
resists or retards separative motion ;” the latter “resisting or re-
tarding aggregative, while it initiates or accelerates separative
motion.” ‘Gravitation, Cohesion, Capillarity, and Chemical
Affinity are Forces; Heat, Electricity, and Light are Energies.”
PeieViagees. 01 Vola 28, No. 173. Oct. 1889. 7A
300 Notices respecting New Books.
Here, then, ‘‘ Force” is used in the ordinary sense of “ Attractive
Force,” but “‘ Energy” in a sense wholly different from its usual
and accepted meaning, the power of doing work, the result and
equivalent of the work dene on the body in which the energy is
said to reside. Jt may be remarked that Mr. Grant Allen’s new
theory ignores work and momentum wholly. Instances adduced in
illustration of the above novel definition of Energy are, that ‘the
Moon is prevented from falling upon the Earth and the Earth from
falling into the Suu by the Energy of their respective orbital mo-
tions ;” and that “a ball shot trom a cannon into the air is pre-
vented from falling by the Energy of its upward flight.” Now
if in these instances for ‘‘ Hnergy ” is substituted its new definition,
‘a Power accelerating separative motion from the Earth ” (or Sun),
the total irreconcileableness of the “theory” with what is well
known is at once apparent. If Mr. Allen had contemplated the
case of the gun being pointed from above downwards (say from
the ‘‘fighting-top” of a ship’s mast upon boarders on deck) he
must have seen himself that the Energy of the shot would have
been the same in amount as before, but its effect would have been
‘‘agoregative” in his sense; while the smaller Energy of the gun
itself would have been “‘ separative.”
In these and such cases Mr. Allen fails altogether to realize the
conditions of the problem; but in mere descriptions of phenomena
(which occupy the greater part of the book) the facts are correctly
stated with characteristic lucidity and charm of style*. If therein,
with the alteration of a word or phrase occasionally, Energy were
understood in its accepted sense all would be ‘‘just what was
already known and universally acknowledged.” Much that may
have appeared to Mr. Allen as he wrote to plausibly support his
notion of a “separative Power” (in a retrospective sentence at the
opening of the concluding chapter is reiterated “ our theory of two
opposing Powers, aggregative and separative’) is perhaps due to the
sclection of instances wherein disintegration is an attendant cir-
cumstance: thus (p. 118) the Energy of the prime mover in the
water- or wind-mill is ultimately given up “partly in producing
separation, in opposition to cohesion, among the molecules of corn.”
It does not seem to have occurred to Mr. Allen that it might, by a
slight change of mechanism, have been employed in working a
small hammer which should have produced the opposite effect
among the “ molecules” of a bar or rod of iron.
A tolerably good idea of what the book is as a whole might be
derived from the supposition that Mr. Grant Allen had proposed
to himself to rewrite the late Balfour Stewart’s ‘ Conservation of
* Exception being made of occasional lapses into the “ slipshod,” such
as the following found in chap. v. of part ii.:—“so soon as we apply
heat to eithe:, they burn away”: “it is probable that they spontaneously
decompose....on any direct contact with external agencies.” An
instance of lapse into incorrectness occurs in chap. viil.: (the Earth’s)
‘orbital Energy and nutation which indirectly yield the phenomena of
winter and summer; ” where the inclination of the plane of the orbit to
that of the Equator is evidently meant.
Intelligence and Miscellaneous Articles. 351
Energy, adapting it to his peculiar ‘‘theory of two opposing
Powers ;” omitting all reference to work done by Force and intro-
ducing the principle of the ‘ Persistence of Force,” in the sense
that “the total amount of Force or Aggregative Power in the
universe is always a fixed quantity ”—a notion which at one time
so much exercised the mind of the great Faraday. Even “ elec-
trical units” when free are described as “‘rushing at once into a
state of aggregation with their fellows”! A notice of this book
should not conclude without mention of the perfect modesty—nay
“timidity ”—with which it is offered to the public. “If I am
wrong,” Mr. Allen assures us, “I shall expect to be frankly told
so: I shall accept demonstrations of my mistakes and misconcep-
tions with a good grace.” But ingenuously, though illogically, he
adds: “ Naturally I shall continue still to think myself right.”
To demonstrate, however, to Mr. Allen’s conviction the errors of
his theory would involve his submitting himself to a strict, if not
an extensive, course of training in orthodox dynamical science,
which being mastered the scales would at once fall from his eyes,
even if he should be forced to exclaim ‘* Pol, me occidistis, amici,
Non servastis .... cui sic extorta voluptas, Et demptus per vim
mentis gratissimus error !”—J. J. WALKER.
XLII. Intelligence and Miscellaneous Articles.
ON THE DEPENDENCE OF THE ELECTROMOTIVE POSITION OF
PALLADIUM ON THE QUANTITY OF HYDROGEN IT CONTAINS.
BY MAX THOMA.
— difference of potential of palladium wires charged with hy-
drogen, in dilute sulphuric acid, against zinc was determined by
comparing the deflexions of a Wiedemann’s galvanometer of 12,000
ohms’ resistance, as well as a Mascart’s electrometer, with that of
a Daniell’s element H=1-07 volt. The metals were placed in
glasses, which were connected with a third one between them filled
with dilute sulphuric acid.
The charge with hydrogen was defined by the expansion of a
palladium wire. The wire, along with the wire which served as
anode, was passed through a cork into a glass tube, and was bent
below into a loop and held by a glass rod. in each diagram.
(1-4) Para- = a,d Xe.
|
The symbol of Kekulé should give rise to four isomeric sub-
stitution derivatives when the introduced radicals are similar,
and to five when they are dissimilar (Wroblewsky Ber. xv.
p- 1023). The researches of Wroblewsky on the toluidines
(Annal. exci. p. 196) have proved that only one ortho- and
one meta-toluidine exist. (See also Lobry de Bruyn, J.C.S.
1885, abstracts, p. 972.) Kekulé has given an explanation of
the non-existence of two isomeric ortho-derivatives, which
is, however, very unsatisfactory. We shall not discuss this
point, because there are so many others which are in conflict
with his theory.
‘It may be pointed out that the angles abc and abe are
respectively 60° and 45°, whilst the angle enclosed by any
pair of valencies directed from the centre of a regular tetra-
hedron to its apices is 109° 28’, and it may therefore be
argued that the octahedral formule are in direct opposition
to the Van’t Hoff theory. But Van’t Hoff himself states
that the tetrahedron is not necessarily regular (see Dix années
dans (histoire dune théorie, p. 27). The author’s view of the
“tetrahedral theory” involves no arbitrary assumptions as
to the nature of chemical affinity or the shape of the atoms.
It is briefly as follows:—By means of the forces of chemical
affinity the carbon atom is able to unite with other groups.
These forces must act in four directions in space, which we
may call valency-directions. The directions are dependent
upon the nature of the associated groups. Only when they
are precisely similar will the valency-directions be perfectly
symmetrical.
In the octahedral formula for benzene we have one hydro-
gen atom on the one side of a plane drawn through a carbon
atom a perpendicular to ad (fig. 1). On the other side
of the Aromatic Nucleus. — A405
of this plane is a system of five carbon and five hydrogen
atoms. From this inequality it follows that the valencies of
the carbon atom a, and similarly of any other of the six
carbon atoms, will be unsymmetrically directed. The direc-
tions of the valencies of any particular carbon atom are
determined, not by the symmetry of the whole molecule about
its centre, but by the configuration and mode of attachment
of the rest of the molecule about the atom. Such a view is
not inconsistent with any of the facts which support the
theory of Van’t Hoff. ;
Armstrong has stated (J. C. 8. 1888) thatin ‘ the symbolic
system introduced by Van’t Hoff a double bond is represented
as the precise equivalent of two, and a treble bond as that of
three single bonds; which all observations show is a mis-
representation of the facts.” This appears to me to be a
misconception, for I have always considered the instability of
“unsaturated compounds” to be dependent upon the fact
that the forces of chemical affinity between two “ doubly-
linked” carbon atoms are not exerted in the imaginary
straight line joining the atoms, but have to act, as it were,
round a corner. Their effective value is weakened in accord-
ance with the laws of the resolution of forces.
It has also been stated that the formula of Thomsen is im-
possible, because it represents a system of atoms which
could not possibly be in equilibrium. ‘This assertion involves
the assumption that the forces which bind the atoms together
act only in the directions ab, bc,cd,de,ef, fa (taken in order)
and along ad, bc, and cf. It is in direct opposition to New-
ton’s third law of motion. THach atom offers resistance to the
interpenetration of its sphere of action by that of another
atom. ‘The force necessary to compress a liquid proves that
this resistance exists in the case of molecules. This point
may be illustrated by the fact that a model of Thomsen’s
symbol will hold rigidly together if made of six equal spheres,
of which the centres are connected by flexible and inexten-
sible strings ab, bc, cd, de, ef, fa, ad, be, and ef in such
a manner that the strings ab to fa inclusive are each equal
in length to the diameters of the spheres, whilst ad, bc, and cf
are each equal to this length multiplied by “2. (See fig. 1.)
The supposition that the spheres of action of the carbon
atoms in benzene are so related is the only one consistent
with the view that the atoms approach one another as nearly
as possible. If the longer strings be cut it will be found
possible to open out the model so that the centres of the
spheres form the angular points of a plane hexagon. I do
406 Mr. S. A. Sworn on the Constitution
not mean to imply by this model that the atoms are rigidly
fixed, but that a given atom is unable to shift its mean position
without altering the mean positions of each of the others.
The arguments by which I propose to distinguish between
these octahedral formule and Kekulé’s symbol may be thus
classified :— |
I. Evidence of direct linkage between symmetrically dis-
posed carbon atoms (para-linkage) will be brought forward.
Arguments derived from this evidence will support the
symbols of Meyer and Thomsen as opposed to those of
Kekulé and Armstrong.
II. Arguments for Thomsen’s as opposed to Meyer’s
formula will be based upon the constitutions of conine, of.
fluorene, and of the conjugated bodies, and upon the analogies
of ortho- and para-compounds.
III. The symbol of Thomsen will then be further developed.
This development will be supported by the crystallographic
character of benzene, and will afford a rational explanation
of the meta- and para- laws of substitution. A similar
consideration of Meyer’s symbol will fail to give this expla-
nation.
Arguments derived from the study of pyridine derivatives
will be applied by analogy to the derivatives of benzene.
Recent research entirely warrants such an assumption.
Hartley found the selective absorption of the ultra-violet
rays, characteristic of benzene and its derivatives, to be very
strongly marked in the case of pyridine, picoline, quinoline,
&c. (J. C.8. 1881, p. 153; 1882, p. 45). The recent paper
by Horstmann, on the physical properties of benzene, fully
bears out the analogy between the benzene and the pyridine
nucleus (Ler. xxi. p. 2220, footnote). We shall see also that
the independent consideration of benzene and pyridine deri-
vatives leads to the same conclusion.
I should propose by the term “ aromatic nucleus” to indi-
cate an octahedral arrangement of six carbon or nitrogen
atoms, characterized by a compactness of molecular structure
which is due to the existence of para-linkage.
It will be sufficient in most cases to use one of the pro-
jections of each octahedral symbol, viz. the diagonal symbol
of Claus and the star symbol of Ladenburg.
of the Aromatic Nucleus. 407
5 1 3 6 1 5
6 4 3 i é
x
6 2
5 3
4
(Claus. ) (Ladenburg.)
I. Arguments for Para-linkage.
(i) Anthracene consists of three symmetrically conjugated
aromatic nuclei. This view was formerly held, but had to be
given up by the supporters of Kekulé’s theory when Anschutz
and Hltzbacher, in achieving the synthesis of anthracene,
showed that the central carbon atoms are directly linked to
one another (Ber. xvi. p. 623). It is now asserted that
anthracene consists merely of two benzene rings united by a
paraffinoid .residue (CH—CH)!Y. Several considerations
show that the central nucleus is truly aromatic. In the
first place Ramsay has shown that anthracene has, like.
benzene, naphthalene, and phenanthrene, an abnormally low
molecular volume (J. C. 8. 1881, p. 64). Hartley has also
shown that the absorption of the ultra-violet rays observed in
benzene is much increased in the case of anthracene as well
as in those of naphthalene and phenanthrene. By means of
oxidation the two central methenyl groups become severed
and converted into carbonyl groupings. The body so pro-
duced is closely related to the quinones and its diketonic
constitution has been well ascertained. The carbonyls can
be reduced and the methenyls reunited. Such well-marked
reactions are characteristic not of paraffinoid but of aromatic
bodies. No instance is known in which a “ paraffinoid” single
408 Mr. 8S. A. Sworn on the Constitution
linkage can be broken and again set up in such a manner.
The formation of anthracene from benzene and acetylene
tetrabromide does not prove that the paraffinoid residue
(C,H,)!” exists as such in the anthracene molecule, any more
than Berthelot’s synthesis of benzene from acetylene shows
| that there are three such residues in benzene. The agegrega-
tion of other atoms to this residue causes it to assume the
most stable configuration, viz. that of two para-carbon
atoms in the aromatic nucleus.
| A direct proof of the aromatic nature of the central ring in
anthracene is wanting. The sulphonic radical, when intro-
duced by the direct action of sulphuric acid, invariably
attaches itself to one of the external nuclei. The naphthalene
derivatives, which we might expect to be the immediate pro-
ducts of the oxidation of anthracene, are at once further
| oxidized (Beilstein, Handb. der org. Chemie, ii. p. 188). It
should be noticed that a proof of the contrary view would be
| no argument against para-linkage because di-phenylene ethane
| can be as well represented by Claus’ as by Kekulé’s symbol.
| It has, however, been shown (Graebe and Caro, Ber. xiii.
i p- 99) that acridine (the analogue of anthracene) is oxidized
i to a quinoline derivative, thus :—
|
|
|
CH CH. 2 CH CH cH
i cH < C.COOH
|
| CH 5 c.COoH
i seu) Deities cH fi :
iW 5
Acridine. Pyr. a-8-quinoline dicarboxylic acid.
[ This reaction shows that the central ring (B) of the acridine
| molecule is a pyridine nucleus. By analogy it may be con-
| cluded that the central ring in anthracene is of a benzenoid
il nature, If this be admitted it follows, from the proved
| existence of a single linkage in this ring, that the benzene
molecule must have one and therefore three such linkages.
(2) Bamberger and Philip have shown pyrene to consist of
four benzene nuclei A, B, C, D, conjugated as in the diagram
(Ber. xx. p. 365). These chemists give the following formule
for pyrene and its quinone :—
of the Aromatic Nucleus. 409
Pyrenequinone, C,,H,O..
se Sots
> (et Len
ly
Pyrene. Pyrenequinone.
OE as se NS ee ae
PE:
It is quite inconceivable that the carbon atom Al should be
directly linked to C1 as in formula I; or A2 to C2 as in II.
I shall endeavour to show that the proved constitution of
this body is an important link in our argument. In the first
place, it is quite impossible to represent it as a conjugation of
four of Kekulé’s rings. :
410 Mr. S. A. Sworn on the Constitution
Symbols such as
‘s and
C;
would lead to the constitution C,)H, i C He for pyrene-
oe
quinone, whereas experiment shows that this. body must be
C;H,O oe
represented as Cy)H, ‘i C,H,0° (See pyrenic acid &e., Ber.
Kx ap. 615)
On the other hand, these bodies can be readily represented
as conjugations of Thomsen’s symbol (vide znfra for adapta-
tion of Meyer’s symbol).
cH
Pyrene, C,,H.,,. Pyrenequinone, C,,H,O, (a naphtha-
(Compare symbol on p.__..) lene deriv.). (Vide infra,
constitution of benzoquinone.)
The facility with which they can be thus represented affords
further evidence of para- as opposed to double-linkage.
Here we may pause to consider the views of those chemists,
who, in spite of recent research on the causes which deter-
mine isomerism, have refused to believe that in the symbol of
Claus the para- are to be distinguished from the ortho-di-
of the Aromatic Nucleus. 411
derivatives. This objection was legitimate and perhaps
necessary, so long as our chemical formulz were
only convenientmodes of representing atomic inter-
actions. We are told that instead of para-link-
ages there are linkages directed from the carbon
atoms towards the centre of the molecule, thus :—
Not a shadow of experimental evidence is brought forward
to show that the valencies are of such a nature. It is difficult
to conceive what function such valencies have. If valency
means the direction along which the attractive force between
two atoms can be exerted, rather than a vague notion of
prongs sticking out from the atoms, it is hardly legitimate to
suppose that a carbon atom can attract or be attracted by an
empty point in space. We shall not discuss the relation of
such a view to the “theory of open affinities,’ which is not
only in conflict with the facts of isomerism generally, but was
disproved by work on the isomers of propylene. It has
been stated that these valencies, being directed towards the
centre, are in a sense protected. If this is the case, and the
para-carbon atoms are not directly combined, it will be found
difficult to represent the constitution of pyrene, unless the
fundamental basis of modern organic chemistry—the tetra-
valency of the carbon atom—be given up. The formula
would consist of two distinct parts. These parts should
exist as molecular entities (C, and Cy, Hy), thus :—
Such a supposition is not only
unwarranted, but opposed to all
that we know of pyrene. If the
symbol merely represents, as is
sometimes said, the idea that a
given carbon atom is directly
united with each of the other five,
it is not easy to see how its sup-
porters can explain the occur-
rence of more than one isomeric
di-derivative, except by the con-
sideration of the positiens in space
of the atoms. What advantage
it would then have over that of
Claus I will leave to be pointed out by those who pro-
pounded it.
(3) Thomsen states in his paper (Ber. xix. p. 2944) that
the most stable bonds in benzene are those uniting para-
carbon atoms, and that additive compounds are produced by
the severance of one or more alternate peripheral bonds.
A. K. Miller has shown that such a view is inconsistent with
412 Mr. 8S. A. Sworn on the Constitution —
known facts (J.'C. 8. 1887, p. 214). Discredit has thus been
thrown upon Thomsen’s symbol for benzene. If, however,
we suppose that the para-linkages are comparatively weak
and that these are broken, the facts quoted by Miller cease
to be inconsistent with the formule. ‘Two carbon atoms may
be bound together by three kinds of single linkage, which
may be called ortho-, para-, and paraffinoid. By this | mean
merely a difference in distance between the two atoms. Ortho-
carbon atoms are closer together than two consecutive carbon
atoms in a paraffinoid chain, and these than para-carbon
atoms. ‘The strength of chemical affinity varies inversely as
a function of the distance between them. ‘These points I
hope to consider more fully ina future paper, and by defining
them more precisely to afford a basis for the treatment of the
physical properties of benzene. Meanwhile they afford some
explanation of the stability of the aromatic nucleus, and of
the formation of the additive compounds of benzene, pyri-
dine, &e.
We may first take the quinones. The diketonic formula
for benzoquinone seems to be placed beyond all doubt by
Pechmann’s synthesis of dimethyl-quinone from diacetyl (an
undoubted carbonyl compound) (Ser. xxi. p. 1417). Only
one benzoquinone is known, and this is a para-compound.
From Kekulé’s theory we should expect such a body to be
ortho-. Its formation from and reduction to hydroquinone
are best explained by the dissolution and re-establishment of
a para-linkage (wde supra, anthraquinone, p. 408). But what
becomes of the other two para-linkages in hydroquinone?
Is the formula of quinone
(exe) co
co
I am inclined to believe that when a para-linkage is broken
the nucleus opens out into a hexagonal ring, and the remain-
ing para-linkages are severed with the formation of true
olefinoid linkages. The work of Baeyer on the additive com-
pounds of terephthalic acid lends some support to this view
(Annal. cexlv. pp. 103-185). He has described a series of
four compounds—terephthalic acid and its di-, tetra-,and hexa-
hydro compounds. It is not impossible to explain his results
by the successive setting up of para-linkages in the passage
from hexahydroterephthalic acid to terephthalic acid. Buta
curious fact, and one which seems to indicate the existence of
of the Aromatic Nucleus. 413
olefinoid linkages in these bodies, is that the two intermediate
substances are much more readily disintegrated by oxidizing
agents than the others. I may quote Baeyer’s formule :—
CH.COOH Cc COOH
CH a CH, CH
cH, CHy cH, CH,
CH.C0OH CH.COoH
Hexahydro-acid (stable). Tetrahydro-acid (unstable).
Cc .cOOH c.cooH
cH | CH cH CH
CH cH, cH cH
A‘ dihydro-acid (unstable). Terephthalic acid (stable).
The behaviour of the intermediate bodies towards bromine
and hydrobromic acid, compared with that of terephthalic
acid itself, shows that they are (in a different sense) unsatu-
rated bodies.
~ Weshould rather expect a gradational change of properties,
if one, two, and three para-linkages were successively formed.
Whatever may be the view entertained of this question, it is
nevertheless true that the results of Baeyer’s work are incon-
sistent with Kekulé’s symbol for benzene. Baeyer states that
the obvious conclusion, from the reduction in one stage of the
dibromide of the A’® dihydro-acid to terephthalic acid—viz.
that terephthalic contains para- or meta-linkages—would
involve him in serious inconsistency. It seems to me that in
this respect he is illogical. Experiment justifies the belief
that double, and not para-linkages, are set up in the interme-
diate compounds ; but we are not thereby warranted in the
assumption that para-linkages are not formed in the end reac-
tion, which is admittedly of a different character. (In the
preceding year he stated that benzene has a double-bond,
because tetrahydro-terephthalic acid was thought to have
one, Ber. xix. p. 1797.) The ultimate formation of the
aromatic nucleus 1s brought about by a comparatively compli-
eated change. Three para-linkages are simultaneously set up,
and the atoms are drawn more closely together by the result-
ing pull towards the centre of the molecule.
The symbol which he proposed, and which I have already
discussed, has been somewhat improved by Marsh (Phil. Mag.
44 Mr. S. A. Sworn on the Constitution
Nov. 1888). This chemist has derived it from six regular
tetrahedra. It appears to me that Marsh’s representation is
inconsistent with the stability of the benzene nucleus, because
the ortho-linkages closely resemble those characteristic of
olefinoid compounds, which are admittedly a source of mo-
lecular weakness. Hach consists of two valency-channels
meeting at an angle (vide supra, p. 404).
The researches of Nietzki (Ber. xviii. p. 504; xx. p. 322)
on the secondary and tertiary quinones, and those of Meldola
and Streatfeild (Phil. Mag. 1887, xxiii. p. 513; J.C.8. 1887,
pp. 115 & 448), afford further arguments for the existence of
para-linkage in benzene.
(4) Hantzsch (Ber. xvii. p. 1512) investigated the conden-
sation of aceto-acetic ether with the aldehyde ammonias, and
showed that in the pyridine derivatives so produced the
y-carbon atom is identical with that directly attached to the
nitrogen of the aldehyde ammonia.
Knorr and Antrick (Ber. xvii. p. 2870) have shown that
y-oxyquinaldine (a quinoline derivative) is obtained by the
action of aniline on aceto-acetic ether. This body they proved
to be a “lactim”’ of the constitution
By direct alkylization it is converted into the “lactam” form
of methyl-y-oxyquinaldine, viz :—
CH N.CH 3
C
CH C CH,
CH CH
Cc
CH cO
That this body is not the “lactim”’ form of y-methoxyquinal-
dine, viz. |
cH C.OCH,
is shown by the fact that they prepared it by the action of
of the Aromatic Nucleus. Al5
aceto-acetic ether on methyl-aniline, a reaction which can be
represented only as follows :—
The formation of this body from y-oxyquinaldine necessi-
tates the change of the “lactim” into the “lactam form.”
This change can be satisfactorily explained only on the
assumption that in y-oxyquinaldine the nitrogen atom is
directly combined with the para- or y-carbon atom.
These researches, together with those of Ruhemann on
citrazinic acid (J.C.S. 1887, p. 403), and of Graebe and Caro
on acridine (Ber. xiii. p. 99), afford evidence of para-linkage
in the pyridine nucleus.
Finally, I would point out that arguments in favour of one
para-linkage in benzene are equally strong in favour of three,
for in no other way can the necessary symmetry of the mole-
cule be maintained. Such a deduction would not be strictly
logical in the case of the pyridine compounds, but the only
alternative ormula—viz. one with olefinoid linkages,
CH CH
CH
CH
is scarcely a representation of the stability of pyridine.
[To be continued. ]
# pemeee 5 N ce NCH,
1H ICH
ste 3 C6H4 C.cH
CgH 1 = C. CH.
: a O=—C.cH, =H,0O+ fp ma 4 | " 2 O-- CH,
| mn Sane CH ge
1 H+ CH x coal
a | \. 0H Co co
COOH > eh
Methyl- Aceto-acetic Hypothetical Methyl-y-oxyquinaldine
aniline. ether, intermediate body. (lactam form),
f 416 7)
XLVIII. On the Application of the Clark Cell to the Construc-
tion of a Standard Galvanometer. By Professor RicHarD
THRELFALL, 1/.A.*
[Plate XIV. figs. 1 & 2.]
Ee the instrument which forms the subject of this paper the
experience obtained with Clark’s cell is utilized to obtain
a simple means of standardizing a working current-measurer.
The construction of the instrument itself will be readily under-
stood from the accompanying figures. Its chief features are :—
(1) The arrangements which have been made for the sup-
port of the controlling magnet and for its adjustment: this
latter can be readily carried out without disturbing the sus-
pension.
(2) The damping of the needle by means of a thin copper
cylinder attached to a bit of fine wire and dipping in clove-oil.
(3) The mechanical arrangements of this part of the appa-
ratus, allowing of the easy suspending of the mirror and
adjustment of the cylinder in the oil.
(4) The arrangements for the testing of the galvanometer
by means of the Clark cell.
(5) The curving of the scale, so as to obtain direct tangent-
readings from a scale of equal parts.
The single coil of the instrument consisted of a rectangular
section of winding of 200 turns of No. 22 B.W.G. copper
wire. Resistance 2:02 ohms at 16° C.
This coil had an axial dimension of 1°3 centim., a radial
dimension of 1°3 centim., and the radius of the inner layer of
winding was 3°7 centim. The coil was supported so as to be
capable of sliding backwards and forwards with respect to
the suspended parts, keeping parallel with itself to a con-
siderable degree of accuracy. The slide was of carefully
crossed wood, the moving portion being kept in its position
in the grooves by means of half carriage-springs at each end.
A somewhat similar arrangement is adopted in the sliding
wooden parts of the Kew magnetometer.
There are three marked positions of the coil with respect
to the suspended needles.
Though the mirror is rather large the magnets are small,
in the ordinary sense, 7. e. about a quarter of an inch long.
A calculation was made by Mr. Adair on the law of deflexion
of the magnet by the coil at the three distances and up to
deflexions of about 15°. The method adopted in this calcula-
* Communicated by the Physical Society: read March 28, 1889.
Construction of a Standard Galvanometer. AIT
tion was the expansion in ‘Spherical Harmonics’ used by
Maxwell, part 4, chap. xiv. The tangent law was found to
be practically true, z. e. the deviation from it would never
introduce an error of more than about ‘5 per cent. The error
was greater the less the deflexion, and was negligible for
the accuracy required, which was of course not very great.
The error arising from partly neglecting the torsion of the
silk fibre was also investigated and found to be without
influence : the fibre was seven inches long.
The divided scale was one of Elliott’s scales, in which 360
divisions correspond to 229 millimetres. The distance from
the mirror to the scale was 1095-°7 scale-divisions, or about
seven hundred millimetres. The problem of finding the form
of the curve into which it is necessary to bend the scale of
equal parts so as to read direct currents was solved by Mr.
Adair ; as we could find no previous record of this solution, I
will give it here.
Let A B be a portion of the
curve required; let OA=/
the apsidal distance, @ the polar
angle subtended by AB, OB
=r the distance of the light-
spot from the mirror. ‘The
incident light falls along A O.
Eis —s,
The form of the curve, assuming that the galvanometer
obeys the tangent law, is
a7 tan 2 |
or
ES ai) mie fs
d6 =fsec 9 5
and the differential equation giving 7 in terms of @ is
CP \ ae,
(a) ais == fa SOE 3
This is insoluble in general terms: but if the range of @ is
small we can develop in powers of 0, and assume r=f+A,
where A is the addition to the radius of the circle whose centre
is QO and radius f. Thus the differential equation for X
becomes, by retaining terms in @*,
OY=EOO 13
Phil. Mag. 8. 5. Vol. 28. No. 174. Nov. 1889. 2H
418 Prof. R. Threlfall on the Application of the Clark Cell
Writing 0’ fe & p we get
et Lg Ge l= val8t a5")
hence
Balls) V2 ae a} x 3
= 9-36 Toa fo [ie ol 0+ 7,0} a0].
Now /=0 when 6=0; therefore the arbitrary constant c=0;
and to the order of 6 retained we get
v= V2 — 1 6? + 4 — V2 64
2 96
='207 @ +°0269 @.
At the extremity of the scale @ is about 4 in circular measure;
thus at the end of the scale,
N= :0233,
and NX =25°5 scale-divisions.
Thus on the radius making the angle 0=19° 6’, whose
circular measure is 4, the theoretical curve is outside the circle
by a distance of 16 millim. Similarly, when 0=10°=:174
radius, A/=:006297, and therefore X=6°901 scale-divisions
— 4-4. millim.
With these numerical results the curve was laid out on
millimetre paper, a template was cut to the curve, and the
wooden back of the scale-holder was brought up to the tem-
plate. The scale itself was carefully pinned to the wood at
short intervals along its whole length.
The Clark cell supplied with the instrument had the same
area of surface as the “large cell”’ referred to in our previous
papers: it was tested from day to day alongside of the large
cell, master cell, &. The following particulars refer to this
testing.
Internal resistance (August 28, 1888), roughly 5:5 ohms.
August 29, at 16° C., hospital cell —master cell = —0-000852
volt. Terminal EB. MF. hospital cell, two minutes after short-
circuiting through 1426 legal ohms, taking H.M.F. of master
cell at 1:435:—
August 28. 1:4263 volt.
ee: ADO 3
Pee: e202 s
About ten minutes after short-circuiting, in each case the
E.M.F. fell further :0011 volt.
to the Construction of a Standard Galvanometer. 419
As the galvanometer was very dead-beat no calibration-
experiment need take longer than 20 seconds, so that this is
without effect.
In order to use the instrument the cell is coupled up in
series with a platinoid resistance of 1417 legal ohms; the
galvanometer-coil being itself 2°02 ohms, the cell about 5:5
ohms. Consequently the current used in testing is
1:4262
= 11174902 > 001007 ampere.
This is quite near enough for our purpose.
In order to set up the galvanometer once for all the follow-
ing dispositions were made. ‘The galvanometer-coil was
pushed up towards the suspended magnet as far as it would
go; this was known as position O. The controlling magnets
were then raised so as to give a mean sensitiveness; the
known current was put on and reversed and the double de-
flexion noted. This deflexion was indicated by a fiducial
mark on the scale. If at any time the sensitiveness of the
instrument changes, it is only necessary to bring the coil up
to its O position and raise or lower the controlling magnets
by means of the adjusting arrangement till the deflexion
reaches the fiducial mark.
When the coil is in the position A, ‘001 ampere corre-
sponds to 10 scale-divisions ; and at B, to 1 scale-division.
These points were found by using a very large storage cell,
whose H.M.F’. was tested whilst the calibration was going on,
and employing suitable resistances from a thick wire box.
The whole arrangement was tested by this means from ‘001
to ‘4 ampere, and it was found that the results were wonder-
fully consistent : this was possibly in part due to the mirror
not being very good, and consequently the observation is so
far wanting in accuracy. With the rather bad light-spot the
readings could not be taken nearer than to about 1 per cent.
at the end of the range, and 3 per cent. towards the centre.
Of course if currents of only three or four milli-amperes are
to be measured, these can be got with at least this accuracy
by using the coil at some convenient point near O, A and B
being rather far away. As an accuracy to about 5 per cent.
is all that is requisite in measuring currents for hospital work,
there can be no doubt that this instrument fulfils the purpose
for which it was made, having an accuracy in use of at least
five times this amount. I have to thank the assistants in my
laboratory for the excellency of their workmanship. |
poo «J
XLIX. An Improved Standard Clark Cell with Low
Temperature-Coeficient. By H. 8. Carwart.*
HE best form of Clark cell hitherto made is that of
Lord Rayleigh, described in the ‘ Philosophical Trans-
actions’ for 1885. The objections to this form are that the
temperature-coefficient is not the same for all cells, as is shown
in Lord Rayleigh’s paper, and it is so high as to introduce a
very troublesome and uncertain error because of the difficulty
of ascertaining the exact temperature of the cell; secondly, it
is not so constructed mechanically as to prevent the mercury
from coming into contact with the zinc when the cell is sub-
jected to violent jars in transportation; thirdly, a great
chemical defect is the facility with which local action takes
place between the zinc and the mercury salt. I might add
that the mercurous sulphate, purchased by Lord Rayleigh,
evidently contained considerable salt in the mercuric form, as
is shown by its turning yellow on mixing with the zinc-
sulphate solution.
All these difficulties I have, at least in large measure, over-
come. Respecting the materials, the greatest care is required
to secure and maintain cleanliness and purity in their pre-
paration. The mercury must be distilled zn vacuo after being
cleaned by chemical means. ‘The zinc sulphate should be free
from iron as well as other impurities, The mercurous sulphate
can be made almost or quite free from the mercuric form by
using plenty of mercury ; keeping the temperature down to
the lowest point at which action will take place; and letting
the mixture of salt, acid, and metallic mercury stand for some
time. I have made in this way a salt that remains white, not
only when the free acid is all washed out, but when mixed
with the standard zinc-sulphate solution. Further, it remains
white in the cell indefinitely if it is not exposed to a bright
light.
Hitherto the importance of the local action going on ina
Clark cell appears not to have been appreciated. It accounts
for some of the differences in temperature-coefficient, and leads
to some more serious results in some cells. The zinc replaces
mereury when in contact with the mercury salt. This amal-
gamates the zinc, producing a slight change in the E.M.F.;
and then the amalgam is liable to creep up to the top of the
zinc, where it attacks the solder. The copper wire is thus
sometimes loosened. The zinc sulphate follows up, and the
cell may be thus short-circuited by the zinc and the copper
wire. Upon taking down one cell, which was perhaps a year
* From an advance proof communicated by the Author.
j ;
7 ee ook pearl | ail a re er
See
On an Improved Standard Clark Cell. 421
old, I found that the zinc had been removed from the rod at
the surface of the liquid and had been deposited again upon
the rod at the surface of the mercury salt, in a solid frill round
the zinc. The copper wire in this cell became entirely de-
tached, partly because of the expansion upward of the marine
glue, which brought a severe strain upon the wire.
The local action then increases the zinc sulphate in the cell at
the expense of the mercury sulphate and amalgamates the zinc
rod. I have become convinced by some experiments extend-
ing over several weeks that this substitution process goes on
only when the zinc is in contact with the solid mercury salt.
The mercurous sulphate is only slightly soluble in a saturated
solution of zinc sulphate. I therefore prevent local action by
keeping the zinc and the mercury salt out of contact. The
same device operates to raise the E.M.F. about 0:4 per cent.
The following Table exhibits the observed and calculated values
of the H.M.F. of cells No. 17, 112, 113 in terms of No. 1
(old style) at 20° C. :—
No. 17. No. 112.
Temp. C. | Observed. | Calculated./| Temp. C. | Observed. | Calculated.
{e)
8:3 1:0108 1:0106 | 51 1:0124 1:0125
8:5 1:0103 1:0105 | 106 1-0106 10103
93 1:0104 1:0102 12°5 1:0098 1-:0096
11:8 1 0093 1:0092 15:2 1-0087 1:0086
13°8 1:0084 1:0085 195 1:0069 1-:0069
15:0 1:0080 1:0080 21-2 1:0062 1:0062
181 1:0069 1:0068 311 1-0024. 1:0024
19-4 1:0064 10063
19°9 1:0062 1:0061 No. 113.
20°3 1-0060 1:0059
20°8 1:0054 1:0057 A
21-1 1:0057 1-0056 51 1:0124 10125
216 1:0054 1:0055 10°6 1:0106 1:0104
29-4. 1:0050 1:0052 12:5 1:0098 10097
93-3 1:0048 1:0048 15-2 1:0088 1:0087
25:1 1:0044 10041 19-5 1-0070 1:0070
96-4 1:0035 1:0036 21-2 1:0062 1:0063
30°2 10019 1:0022 dl] | 1:0025 1:0025
ook 1:0014 1:0013 ;
39:1 0-999 1 09989
41°7 0:9980 0:9979
50-4 09949 0:9947
52-7 0:9939 0-9940
Cell No. 1 was always very near 20° C., and the reduction
to that temperature was made by means of Lord Rayleigh’s
reduction-coefficient, ‘00077 per degree C.
422 On an Improved Standard Clark Cell.
The equation for the E.M.F., derived from the observa-
tions on ia 17, is
ye 000387 (t—15) +°0000005 (¢—15)?].
The aie values for the three cells were all obtained
by this formula. The change for one degree C. is, then, the
following linear function of the temperature :—
— °000386 + :000001 (¢—15).
The temperature-coefficient ranges from ‘000361 at 0° C.
to ‘000376 at 25° C., and to :000361 at 40°C. At the highest
observed temperature in the preceding Table it was only
000348. The curve of H.M.I’. with temperatures as abscissee
is clearly concave upward, indicating a fall in the temperature-
coefficient with rise of temperature. The change is, however,
so small as to be quite negligible within the range of tempe-
rature to which a normal element is subjected in practice.
Lord Mayleigh’s cells show a change in the temperature-
coefficient directly the reverse of the above; that is, the
coefficient increases by a very appreciable quantity with rise
of temperature. For his No. [36] the coefficient ranged from
7000556 at 0° C. to ‘90101 at 25° C., if his equation holds
true for the higher temperature.
In making comparisons of E.M.F. I have used Lord
Rayleigh’s method, slightly modified, by means of which a
difference of one ten-thousandth part is observed directly and
with the greatest ease. In fact a difference of half that
amount is easily measured. A comparison of half a dozen
cells can be made in as many minutes without difficulty.
As to polarization, these cells show none with external
resistance greater than 30,000 ohms. At 30,000 ohms the
polarization is just discernible; and with 10,000 ohms it
amounts to only one ten-thousandth part in five minutes.
This fall in E.M.F. is less than the accidental differences
between different cells in general, and much smaller than the
almost unavoidable errors due to ignorance of the real tem-
perature of the cell. If the cell is not closed on less than
10,000 ohms resistance, and only for a few minutes, the
polarization may be entirely neglected.
As indicating the uniformity attained, the following relative
values of the H.M.F. of six cells, only four days old, may be
given :—9048, 9049, 9049, 9048, 9046, 9043. The last one
was still approaching the others when last observed. Six
cells of later construction gave the following relative values
when less than two days old:— 9182, 9182, 9182°5, 9182,
9182, 9182°5. The two sets of numbers do not represent at
all the relative values df one set as compared with the other.
Notices respecting New Books. 423
Ti will be seen from the Table that Nos. 112 and 113 never
differ by more than one part in ten thousand at the same
temperature.
Physical Laboratory,
University of Michigan.
L. Notices respecting New Books.
Watts's Dictionary of Chemistry.
Watts's Dictionary of Chemistry, revised and entirely rewritten.
By M. M. Parrison Morr, M.4A., ond H. Foster Mortey, M.A.
D.Sc. Vol. Il. Longmans, Green, and Co.
HE second instalment of this invaluable work maintains the high
character of the preceding volume. Commencing with Cheno-
cholic Acid, the work concludes with an article on Indigo which ter-
minates on page 700. The list of contributors contains the names
of some authors who contributed to the first volume together with
several new writers; the list is a sufficient guarantee that the editors
have secured the collaboration of some of the highest authorities
on the special subjects treated of. Among the longer articles are
those by Dr. Schunck on Chlorophyll, by Dr. McGowan on Cho-
lesterine, on Chromium by Mr. Muir, and on Cinchona bark by
Mr. David Howard. The article on Chemical Classification by
Mr. Muir occupies over 20 pages and is followed by a very useful
bibliographical list. The same author contributes the articles on
Cobalt and its compounds, on the Laws of Chemical Combination, and
on the Combining Weights of the elements. The article on Com-
bustion by Prof. Thorpe might with advantage have been extended ;
in its present form it is entirely historical. About 9 pages are
devoted to the subject of Crystallization, the writer being Mr. H.
Baker, and a long article (about 24 pages) on Cyanic Acids is
from the pen of Dr. Senier. Mr. Muir devotes over two dozen
pages to the Cyanides, and a short article on Relative Densities is
contributed by Miss Ida Freund. An excellent article by Prof.
Threlfall on Dissociation, which extends to 28 pages, must be noted
as one of the special features of the present volume, and an equally
valuable article on Chemical Equilibrium is from the pen of Prof.
J.J.Thomson. The article on Equivalency is written by Prof.
Tra Remsen, and that on Explosion is by Prof. Threlfall. Dr. 8.
Rideal contributes a somewhat sketchy article on Fermentation
and Putrefaction, and the bibliographical list of works relating to
this subject is not quite as extensive as could have been wished.
Prof. Thorpe writes on Flame, Mr. Veley on Formic Acid, and Prof.
Tra Remsen on Formule. The article on Geological Chemistry is
by Mr. F. W. Rudler, and is sufficiently excellent to make us regret
that more space could not have been devoted to this important and
little studied branch of the science. Prof. Japp contributes the
article on the Hydrazines and Hydrazones. A long article on
424 Notices respecting New Books.
Hydrogen by Mr. Muir, and 8 pages on Indigo by Mr. A. G. Green
conclude our list of the chief contributions to this volume. Al-
though we are bound to admit that the spirit of active research is
not so widely spread here as it is on the Continent, in scientific
literature we certainly can hold our own. ‘The present work is a
production which reflects the highest credit upon the editors and
their staff.
Bernthsen’s Organie Chemistry.
A Text-Book of Organic Chemistry. By A. BERNTHSEN, PA.D.,
formerly Professor of Chemistry in the University of Heidelberg.
Translated by Grorek McGowan, Ph.D. Blackie and Son.
TE author of this excellent little volume of about 500 pages has
long been familiar to working chemists in this country for his bril-
liant investigations in synthetical organic chemistry, and especially
for his well-known researches into the colouring-matters of the
Methylene Blue series. It will be instructive to British manu-
facturing chemists to learn that Prof. Bernthsen, after having held
a Professorship in a German University, has now become Director
of the Scientific Department of the world-famed ‘“ Badische Anilin
und Soda-Fabrik ” at Ludwigshafen on the Rhine. Such an in-
timate relationship between pure science and its applications as is
revealed by the transference of a University Professor to the
Directorship of a laboratory associated with a factory is the very
best illustration we have had in modern times of the way in which
industrial advancement is insured abroad. The book before us may
be described as a condensed epitome of the present state of know-
ledge concerning organic chemistry—full, accurate, and abreast of
the’ most recent discoveries. The original work has been revised
and brought up to date by the author expressly for this English
edition. The arrangement adopted is well calculated to impress
upon the student a sound knowledge of the chief characters of the
compounds of the various groups, and the author has throughout
kept in view the educational value of the branch of science on
which he writes by treating the subject as a logically connected
whole unburdened by the mass of purely descriptive detail which so
often repels the student of organic chemistry. The introductory
portion consists of thirty-two pages containing sections on the
usual general subjects, such as analysis, determination of formule,
isomerism and polymerism, homology, radicals, classification,
physical properties, and fractional distillation. The remainder of
the volume forming the Special Part deals with the different groups,
classified in the first place into the two great divisons of Methane
Derivatives and Benzene Derivatives. This is certainly preferable to
the usual designations of ‘‘ Fatty” and ‘‘ Aromatic.” The Methane
derivatives are treated of under fifteen groups, viz. hydrocarbons,
haloid derivatives, monatomic alcohols,alcoholic derivatives,aldehydes
and ketones, monobasic acids, acid derivatives, polyatomic alcohols,
polyatomic monobasic acids, dibasic acids, tri- to hexabasie acids,
cyanogen compounds, carbonic acid derivatives, carbohydrates,
Notices respecting New Books. A95
and lastly transition compounds to the benzene series. Under the
second class we have first of all an excellent summary of the differ-
ences between the two great classes, some sixteen pages being
devoted to the general theory of the constitution of benzene and
its derivatives. Then follow the groups of hydrocarbons, halo‘d
derivatives, nitro-derivatives, amido-derivatives, azo- and diazo-
compounds, sulphonic acids, phenols, alcohols, aldehydes, and
ketones, acids, indigo group, diphenyl group, diphenylmethane
group, triphenylmethane group, dibenzyl group, naphthalene, an-
thracene, and phenanthrene, pyridine and quinoline groups, terpenes
and camphors, resins, glucosides, albuminous substances, &c.
The translator has done his part of the work well, although we
detect distinct Teutonisms here and there. The proofs have had
the advantage of being revised by the author. We can confidently
recommend the work to both teachers and students, and we hope that
in afuture edition the translator will have an opportunity of modi-
fying the nomenclature in certain cases so as to bring it more
into harmony with that adopted in this country.
An Elementary Treatise of Mechanics, for the use of Schools and
Students in Universities. By the Rev. Isaac Warren, JA.
(London: Longmans, 1889. Pp. 144.)
It may be in the recollection of some of our readers that in our
issue for January 1887 the Rev. T. K. Abbott raised the ques-
tion, “‘ To what order of Lever does the Oar belong?” and proposed
to show that “the vulgar conception of the oar as a lever of the
first order is correct.” Our author, in a note, after stating that
the oar is commonly regarded by writers on Mechanics as a lever of
the second kind, proposes to reconcile these apparently conflicting
statements. We use the summary he himself gives of the results
he arrives at, viz. :—(1) The oar must be regarded as a lever of the
second order if the resistance acting at the rowlock be understood
to include, not only the external resistance to the boat’s motion,
due to the action of the fluid in which the boat floats, but also the
reactwon engendered by the person of the oarsman when he pulls the
oar. (2) If we consider only the resistance offered by the fluid to
the boat’s motion, it will be found that this resistance is related to
the effort employed by the rower at the handle of the oar zn exactly
the same way as rf this resistance acted at the blade of the oar, and as
if the rowlock were the fulcrum, i.e. practically as of the oar were
a lever of the first order. 'The author’s work will be found on pages
129, 150, and he concludes thus:—‘‘ Whether this result might
have been @ priort predicted from the circumstance that the row-
lock is a fixed point relatively to the rower, the author leaves for.
others to determine.” The text forms a handy book for junior
students, and is accompanied by full store of illustrative exercises,
with several specimen (Trinity College, Dublin) papers.
It should be mentioned that the present is the first part of the
complete treatise, and is concerned (in the text) with Statics only.
Phil. Mag. 8. 5. Vol. 28. No. 174. Nov. 1889. 21
[ 426. ]
LI. Intelligence and Miscellaneous Articles.
ON A RELATION BETWEEN THE SUN-SPOT PERIOD AND THE
PLANETARY ELEMENTS. BY CHARLES DAVISON, M.A., MATHE-
MATICAL MASTER AT KING EDWARD’S HIGH SCHOOL, BIR-
MINGHAM.
pve length of the sun-spot period was first estimated by its
discoverer, Schwabe, at about ten years. Some years later,
Rudolf Wolf, making use of a much more extensive series of ob-
servations, determined the mean period to be 11°111 years, with
an uncertainty of 0°307 year. The period of Jupiter being 11-86
years, it was at first surmised that there might be some connexion
between the two. But the idea was soon abandoned, partly on
account of the obviously considerable difference between the two
periods. i
A close approximation to the sun-spot period is, however, ob-
tained by taking the average of the periods of all the known planets
in the solar system, on the supposition that the determining effect
of each planet is directly proportional to its mass and inversely
proportional to the square of its distance from the sun. If m be
the mass of a planet, d its distance from the sun, P its period, the
average to be determined is
>(Pm/d°) = 3(m/d’).
In the following Table the values of m, d, and P are taken from
Herschel’s ‘Outlines of Astronomy’ (1873); the corresponding
elements for the satellites and minor planets bemg omitted as
unknown or unimportant.
Planet. Mass. |Distance. alae m/d?. | Pm/d?.
Mercury ...... 0:074 | 0387 88 0:494 43
Wes) yee... 0:895 | 0723 225 ert Ih 386
Barta gs... a: 1-000 | 1-000 365 1-000 365
Mats etre escort 0-134 | 1:524 687 0-058 40
Sp Oger hoo ae gas 343:125 | 5-203 | 4833 | 12676 | 54925
Sarum see seiner 102°682 | 9:539 | 10759 1:128 | 12136
Wiramushs eee 17-565 | 19:182 | 30687 0-048 1473
Neptune ...... 19-145 | 80-057 | 60187 0-021 1264
From these values we find that
Y(m/d*) =17°136,
>(Pm/d?)=70632,
and
=(Pm/d*) + X(m/d*)=4122 days, or 11-29 years.
lf the elements be those given in Newcomb’s ‘ Popular Astro-
nomy’ (1878), the value of this average is 11-27 years. The
effect of taking the moon into account is to reduce both these
estimates by 0°01 year. In either case the average is well within
the limiting values given by Wolf for the sun-spot period, namely
11:111+ 0°307 years.
Intelligence and Miscellaneous Articles. 427
ON THE LEAKAGE OF NEGATIVE ELECTRICITY CAUSED BY SUN
AND DAYLIGHT. BY T. ELSTER AND H. GEITEL.
In reference to the theory of atmospheric electricity propounded
by Arrhenius *, we have recently made a series of experiments
to ascertain whether sun- and daylight have the property of
eradually withdrawing the charge from negatively electrified bodies.
M. Hoor? alone has established such an action, while all other
observers, so far as we know, have not been able to discover
any. We have therefore been greatly surprised to find that not
only sun- but also ordinary diffused daylight can under suitable
conditions rapidly discharge a negatively electrified body.
A zine dish, 20 centim. in diameter, is exposed in the open on
an insulating support in such a manner that it is not acted on by
negative electricity, and is put in conducting communication with
a quadrant-electrometer or an Exner’s electroscope, and further is
so arranged that the dish can be put in the dark or light at pleasure.
The following phenomena can then be observed, which, it is true, are
already known from experiments on ultra-violet light. The dry dish
polished with emery completely loses a negative charge of 300 volts
in 60 seconds: an equally high positive charge is retamed. The
loss of the negative charge ceases as soon as the dish is put in an
entirely dark room ; it is considerably enfeebled if the sun’s rays
pass previously through a glass plate. A decided collapse of the
leaves of the electroscope takes place when the dish is merely
exposed to the blue light of the sky.
If the dish is filled with hot or cold water the action is com-
pletely extinguished; a moist cloth stretched over it acts in like
manner.
By being illuminated the finely polished plate acquired a sponta-
neous charge of +2°5 volts, which by blowning on the plate could
be still further increased.
The experiments are much simpler when the metals to be
illumined are directly fixed in the form of wire to the knob of an
Exner’s electroscope. If freshly polished wires are used—alumi-
nium, magnesium, or zinc—a permanent negative electrification in
the sunlight in the open is not at all possible. It is completely
discharged in less than five seconds. Magnesium and aluminium
wires act here more energetically than zine ones. There is a per-
ceptible collapse of the leaves when the former are used, even with
the action of diffused evening light.
It is also interesting to note that freshly polished wires of the
metals in question act as if an ignited body were attached to the
electroscope: If an electroscope so arranged is taken to an open
field, the leaves diverge with the use of freshly polished wires with
positive electricity, arising from the influence of the electricity of
the air.
In all these cases an abnormal diffusion of positive electricity
could not be observed.
* Meteorol. Zeitschrift, v. p. 297 (1888).
+ Rep. der Phys. xxv. p. 105 (1889).
428 Intelligence and Miscellaneous Articles.
‘The experiments were made from the middle of May to the
middle of June in this year (1889).—Wiedemann’s Annalen,
vol. xxxvill. p. 40 (1889).
ON THE PHOSPHORESCENCE OF COPPER, BISMUTH, AND MANGA-~
NESE IN THE SULPHIDES OF THE ALKALINE EARTHS. BY YV.
KLATT AND PHILIPP LENARD.
The results of a long series of researches on the phosphorescence
of the alkaline earths are summed up by the authors as follows :—
(1) The strongly luminous lime-phosphorescents are mixtures of
three essential constituents; sulphide of calcium, the active metal,
and a third body which, when present alone in calcium sulphide, is
not active. Itis very probable that perfectly pure calcium sulphide
does not phosphoresce.
(2) The bands which occur in the spectra of the lime-phospho-
rescents show that the active metals are manganese, copper,
bismuth, and a fourth metal which is not known. To each of
these metals a band corresponds which is invariable in position.
Extremely small quantities of the metal are active. The inten-
sity of the phosphorescence at first increases with its quantity, and
then decreases to zero. The quantities which exhibit the maximum
action are very small.
(3) The additions used by us as the third constituent are colour-
less salts, and all of them fusible at the temperatures at which the
phosphorescents are prepared. Hence they coat the surface of the
caleium sulphide causing the mass to sinter together, and the active
metal produces a delicate tint which is essential for the phos-
phorescence.— Wiedemann’s Annalen, vol. xxxviil. p. 90 (1889).
ON STEATITE AS A SOURCE OF ELECTRICITY.
BY M. MENTZNER.
Steatite, when rubbed with gun-cotton, or with Kienmayer’s
amalgam, or with fur, becomes negatively electrified, and in the
electrical series is on the extreme left. For these experiments
a prism with rounded edges, 8 centim. in length, 3°5 centim. in
breadth, and 3 centim. in thickness is used, in which there is a
hole for an ebonite rod. In the upper surface a semicylindrical
groove is cut by means of a glass rod and emery-paper. If a glass
or ebonite rod is drawn through it, it becomes positively and the
steatite negatively electrical.
A kind of electrical machine may be made from a cylindrical
rod of steatite fixed to a handle of ebonite; a loop of copper wire
is fastened round it, the ends of which are twisted together and
terminate in a knob, which is held over a flat metal vessel full
of bisulphide of carbon. When the steatite is struck with a fox’s
brush the bisulphide is ignited by the spark produced.—Zettschrift
fiir phys. und chem. Unterricht. 11. pp. 241-243 (1889); Berblatter
der Physik, vol. xxi. p. 707 (1889).
THE
LONDON, EDINBURGH, ann DUBLIN
PHILOSOPHICAL MAGAZINE
AND
JOURNAL OF SCIENCE.
[FIFTH SERIES.]
DECEMBER 1889.
LII. On the Law of Cooling, and its bearing on certain Equa-
tions in the Analytical Theory of Heat. By CHARLES
H. Luus, W.Sc., Berkeley Fellow of Owens College, Man-
chester *.
LTHOUGH it is a well-known fact that the temperature
of a heated body allowed to cool in air does not follow
“‘ Newton’s Law,” it has been usual to assume that law to hold
in cases in which the loss of heat of a body through contact of
its surface with air had to be taken into account. In calori-
metry the error thus introduced is probably small ; but it
becomes of much greater importance in those methods of
determining thermal conductivity in which the ratio of the
outer to the inner conductivity of the body is a quantity
determined experimentally, and this ratio used in conjunction
with a value of the outer conductivity +} (supposed to follow
Newton’s law) to determine the inner conductivity.
The method to which I specially refer is that of Briot,
Despretz, &c., in which a bar of the substance whose conduc-
tivity is required i is placed in a horizontal position in air, and
heated at one end. The equation of motion of heat in the
bar is then, assuming the isothermal surfaces to be planes,
pee (0°!) Pp, :
aia <.(boe)— gee orb: (1)t
* Communicated by the Author.
Tt The “ Conductibihté extérieure” of Fourier, or the surface emissivity
of Thomson, art. “‘ Heat,’ Encye. Brit. p. 577.
{ Fourier, Théorie Anal; ytigue de la Chaleur. Thomson, ‘ Collected
Papers,’ vol. ii. p. 42, or Encyc. Brit., art. “Heat,” p. 579.
Phil. Mag. 8. 5. Vol. 28. No. ioe Dec. 1839... 2K
430 Mr. C. H. Lees on the Law of Cooling, and tts bearing
where v == excess of temperature at a point « of bar above
temperature of air, which is supposed constant; ¢ = specific
heat, p = density, k = inner conductivity, h = outer conduc-
tivity, at temperature-excess v; p = perimeter of section of
bar ; g = area of section of bar.
Assuming, with Fourier, that c, p, &, 4 are constant, we
have for the “steady state” the equation
the solution of which is
kh ak
Ne eee ee
where A and B are constants of integration. By determining
the temperature at ditferent points of a bar thus heated, the
value of c can be found. Briot and Despretz determined
the temperature by means of thermometers placed in holes in
the bars. This would, on account of the different conduc-
tivities of the bars and the glass and mercury of the thermo-
meters, make the isothermal surfaces deviate considerably
from planes. The results, however, of both experimenters show
evidence of an increase of a Ph with temperature, especially
k
where the bars are of the poorer conducting metals, and
the effects of the holes therefore less. This is also the case
with the results of Wiedemann and Franz, who determined
the temperature by means of a thermojunction brought into
contact with the surface of the bar at different points.
From the experiments which follow it will be seen that h
increases about 50 per cent. as the temperature varies from
30° C. to 80° C., while & and c for a metal are not found to vary
more than about 5 per cent. in the same interval. The most
important source of error in the assumptions of Fourier is,
then, that introduced by the variation of h, and it is towards
a more accurate determination of this variation that the
following experiments have been conducted *.
A bar of infinite length originally heated to a uniform
temperature would, if allowed to cool in air, continue to satisfy
the condition oe =(, and it will be assumed that for the bars
used in these experiments this is still the case. Since the
* The experiments were carried out in the Owens College Physica]
Laboratory.
on certain Equations in the Analytical Theory of Heat. 431
temperature has previously been assumed constant throughout
any section perpendicular to the axis, this amounts to assuming
the temperature uniform throughout the whole bar. The
equation (1) then takes the form
Ov
PE
Or, multiplying both sides of equation by /, the length of the
bar, and writing more generally for v on right side /(v),
Bee! hous
qd
Pah o° Se hes
Or, writing m for plq, and s for the whole surface of the bar,
including the two ends,
v
om = SPC tat an ce haw \'s (2)
The bars used in these experiments to determine the form
of f(v) were about 26 or 27 centim. long and 1°9 centim.
diameter. They were nickel-plated, so as to give them the
same smooth even surface. At the extremities of a diameter
in the middle of the length of the bars, two small holes, about
‘7 millim. diameter and 2°5 millim. deep, were bored, and
into them an iron and a German-silver wire respectively were
soldered. The other ends of these wires dipped into mercury-
cups, in the circuit of an aperiodic Wiedemann’s galvano-
meter. The mercury-cups being provided with thermometers,
the arrangement formed a thermo-cireuit, and from the de-
flexion of the galvanometer and the temperature of the
mercury-cups the temperature of the bar at any time could
be found. The deflexion was read off by means of a tele-
scope and scale situated 2°5 metres from the galvanometer.
The correction of the extreme deflexion for the assumption
tan 20=2tan @ is less than °3 per cent. and is neglected.
The bars were at first suspended horizontally in the room by
means of two threads, and the temperature of the air observed by
means of a thermometer situated vertically under the bar and
protected from radiation by a small paper screen. On account of
the air-currents in the room, and the “‘lag”’ of the thermometer-
indications behind the actual temperatures of the air, the
cooling was ultimately carried out in a water-jacket 55 centim.
diameter and 75 centim. long. The change of temperature of
the jacket was then slow and regular, and the correction for
this change could easily be applied. The bars were heated
in an air-bath surrounded by water at 100° C. for three or
four hours, and at the end of that time the temperatures of
Pen 2
432 Mr. CO. H. Lees on the Law of Cooling, and its bearing
bath and mercury-cups, the deflexion, and the resistance of
the circuit were determined. The resistance was ascertained
by shunting into circuita known resistance, and observing the
diminution of deflexion. These observations give data for
reducing the observations of deflexion and resistance during
cooling to degrees Centigrade. During cooling observations
of deflexion were taken every two minutes ; of resistance, and
of temperatures of water-jacket and mercury-cups, every four
minutes.
Writing e for the product of the deflexion and resistance,
v temperature of junction in bar, v; temperature of mercury-
cups, é,v values of e, v when bar is in hot bath, C some con-
stant, we have, according to Avenarius*, for an iron-German-
silver circuit,
e=C(v—v,)(1 —-00034(v+0)),
é=C(v—r)(1 —'00034(0+ %) );
_(=_,.\ @ , 1— "00034 +0,)
pte) - 7 -00us oe
: Aer e( —"00034(0—v) ) approx.
e,e a) e e ° é ovr
Writing for v, in correcting factor, its approximate value rie
we have
yey Ot -e( 1—-000346 2=9),
é e
‘which determines (v—v,), in Centigrade degrees, from obser-
vation of deflexions and resistance.
By applying this equation to the observations made, we get
a series of temperatures of the bar at two-minute intervals:
and from this series the form which /(v) must have to best re-
present the variation of the outer conductivity is to be found.
We consider only simple forms of /(v), so as to complicate
equation (1) as little as possible, and commence with the
simplest.
The simplest form is /(v)= v, the usual assumption. Substi-
tuting in (2), we deduce
d /
— +at=C, where a= = (C is an arbitrary constant),
ee v=wve“, where v is value of v at time t=0.
If a in this equation be determined from the first eight
* Poge. Ann. cxxii. p. 199.
on certain Equations in the Analytical Theory of Heat. 433
minutes of the curve of cooling, when the mean temperature-
excess of the bar was about 64° C., it is always 30 or 40 per
cent. greater than a determined from the last eight minutes
when the temperature-excess was 11° C. Hence a increases
with the temperature, and we are led to the assumption :—
J (v)=0(1 4+ bv)*, which gives
“de
pean +at = constant,
or
: +b=Aec“%, where A is an arbitrary constant.
v
The constants of this equation, determined from observations
at times 0, 10, 20 minutes, are in one experiment
a— 0208 0—"0047,. A=0187 ;
and at 40, 50, 60 minutes, in the same experiment,
a= 07707 b=-0165; .A=:0284,
A similar variation was found in other cases, so that the
cooling is not well represented by making /(v) a quadratic
function of v.
Ceasing to consider integral powers of v, we write
fv)=0(a+ bo),
where m is some + quantity. This gives as integral,
ee a aL
a
Solving this by trial we find m=-2 approx. and a=0; and
we deduce as probable form /(v) =v”, where n> 1.
The equation (2) therefore takes the form :—
Ov
Tae ie Ao le ae ae la 0)
or the rate of loss of heat from the bar varies as the nth
power of the excess of temperature of bar above temperature
of air, supposed to remain constant, where n=1-2 approxi-
mately. |
So far the specific heat c has been considered constant ; but
* Kundt and Warburg (Poge. Ann. clvi.) make use of this to express
the cooling of a thermometer in a sphere concentric with its bulb. H. F.
Weber (Mon. Ber. d. Berlin Akad. 1880) considers some correction of this
form to be necessary in dealing with conductivities of bars.
A34 Mr. C. H. Lees on the Law of Cooling, and its bearing
the form of (2’) allows its variation to be taken into account
without materially affecting the integration. Writing
c=c(1+c'v),
where ¢p is the value of ¢ at the temperature of the air in the
experiments (about 17° or 18°C.), and c’ is some constant,
generally less than -001, (2’) becomes | | |
oe = —sh.v”.
Another small correction has to be applied for the change of
temperature of the water-jacket, which up to the present has
been assumed constant. Writing it now =V, where V is a
function of ¢ such that its value at the end of the experiment
=(), we have
mceo(1 + c’v)
ou
mcey(1+ cv) — Sp sh(v—V)”.
From the Tables aie follow, it will be seen that V/v is
generally less than 1003 so that if,in the left-hand side of the
above equation, 1 +¢’(v—V) be substituted for 1 + c’v, the error
introduced is generally less than z5),95- Also from these Tables
it is seen that, for an interval of twenty minutes, on is with
close approximation = —g o where g is generally less than
tho. Hence, for an interval of twenty minutes, we have as a
very close approximation,
Ov ore = HH
a on ea
or
Oe el Ov—V :
oo OU
and the equation of cooling corrected for all known variations
becomes
mej(l+cev—V) ov—V
Pe mepiige oT oe
Olle
\so-vy-4 c(v—V)'"bdv+ NOE = constant ;
or
re De ype _ sh1+g)m—1)
Ore) a 2—n~ ° . MCg eee)
Tables follow from which it can be seen how this equation
agrees with experiment.
on certain Equations in the Analytical Theory of Heat. 435
Nickel-plated Copper bar cooled in water-jacket.
—
>
A
= S) o vi [3 i S ral
> =| = > —! a = = ~ > =
‘3 f SS + S ~ als
LV rs = = S
y S
S
|
=
0 16°97 T3°4 “4040
2 17°05 68-1 102 Means
+: 63°3 168 of 5.
6 “15 58°8 236
8 54°62 299
10 “21 50°83 366
12 47-35 434
14 27 | 4419 | 499 Another
16 41-28 567 aa Save
18 31 38°54 633
20 36°06 700 0660 0653
22 35 33°67 770 68 61
24 31:60 839 67 60
26 36 29°71 896 60 54
— 28 28:00 958 59 53 | :003281 003264
30 38 26°26 5028 62 57
32 24-61 096 62 57
34 39 23°06 167 68 63
36 21-382 | 297 60 56
38 09 20°60 292 59 58 3288 3232
40 19:39 358 58 54
42 18°40 425 55 52
ae 17°34 489 54 52
46 “Oo 16°39 550 54 52
48 15°50 621 53 52 262 3209
50 1465 | 685 BT 56
52 13-90 751 55 54
54 ‘oor |, 13715 815 48 48
56 12°47 8835 56 56
58 11°88 943 Oi 51 3265 3247
60 11:26 6008 50 49
62 “40 10°69 079 54 53
64 1016 141 52 Bl
66 9-67 206 56 55
68 StS 79 52 51 3259 3272
70 40 | 876 | 337 52 51
72 8:36 | 399 48 47
74 795 | 467 52 50
76 7-58 531 48 46
78 ' “42 7.26 592 49 47 3241 3220
80 6:93 654 46 44
Mean...:003266 | | ‘003240
n=V-21. c, = 092. lig De 1 676
m=676 grams. ere 000231. Onis pie2) x oie % 163-4
$s =163'4 sq. centims.
='0640.
436 Mr. C. H. Lees on the Law of Cooling, and its jar
N ickel-plated Iron bar cooled in water-jacket.
’
t
minutes.
ved.
(w—-V)° C.
20s 1l+qn—1
mco
ee ee eee
65°10
57 60°72
56°74
67 53:04
49°73
(C4 46°92
43°70
78 40°92
38°42
81 36:02
33°91
85 31°88
50 00
87 28°28
26°67
89 25°09
23°78
93 22°55
21:25
96 20°00
19:02
98 17-91
16°96
99 16:16
15:2
19-01 14°51
13-79
03 13:06
12°41
03 11°84
11°25
03 10°71
10-20
03 9°79
‘21.
73°4 grams. ¢
62-2 sq. centims,
Another
0631 exp. gave
28 | 003149 003198
24 3136 3187
30 3146 3161
29 3141 3147
28 3139 3180
Mean... °003139 | 003179
h ‘00316 _ 573-4
6s eo 1622
= ‘0520.
on certain Equations in the Analytical Theory of Heat. 437
Nickel-plated Zinc bar * cooled in water-jacket.
ae
>
f
cj Ts
ee ie |
ee ee ale tlle
S af wa + oe i S
Ss Fs = a p
A 2
S
1
17:00 70°93 | -4050 Means
‘10 | 64:92 122 of 5.
59:02 215
20 54:01 297
49:33 rstell |
24 45°10 466
41:29 553
O7 37°98 637
35°00 ALT
ue 32°33 798
29:95 | 877 | -0827 | -0820 Another
299 | 27-70 964 42 37 Pee ENS
25°59 5045 30 25
-29 23°69 126 29 24
21-99 211 30 26 =| 004132 004100
20:30 301 35 33
18°98 374 21 19
29 1 aaron 447 10 08
16°60 531 14 12
15°42 614 16 15 4087 4087
14:43 693 16 16
“29 13°50 777 13 13
12°62 862 Ir¢ 17
11:83 946 20 20
11:05 ‘6031 20 20 4086 4109
"29 10°41 108 O07 07
Sere 185 El tt
9-22 268 21 21
8-62 353 22 22
8:08 440 26 26
29 7°64 517 24 24 4093 4112
Mean...:004100 004102
= Dle Ges O915; . A _ ‘00410 _ 573°4
m = 573-4 grams. c' = ‘000485. ae RE | * 1655
s = 1655 sq. centims. — -0676.
* Nickel surface not good, peeled in places.
438 Mr. C. H. Lees on the Law of Cooling, and its bearing
The constancy of the numbers in the columns of first differ-
wn") shows how well
0
ences (the columns headed 20 a
the assumption that the rate of loss of heat varies as the
nth power of the temperature-excess can be made to represent.
the actual fact by a proper choice of n. Within the limits of
the experiments, 7. e. 80° to 10° C. temperature-excess, there is
| d shn—1L
no definite secular change of the mean values of —————,, and
me
0
we thence conclude that the above law is a close approxima-
tion to the actual fact.
The values of h/c, deduced from the experiments are, for
copper, iron, and zine, respectively -0640, °0520, ‘0676, where
h is the amount of heat lost from 1 sq. centim. of the surface
in | minute, when the temperature-excess is 1° C.* and tem-
perature of air is about 18° C., and cy is the specific heat of
the material of the bar at 18°C.
Taking the specific heats at 18° C. as 092, 112, 0915 re-
spectively+, and dividing by 60, we have for the amount of
heat lost in 1 second under the above conditions :—
"0000981, °0000971, -000103.
On account of the uncertainty of the specific-heat values,
and the fact that the zinc bar had not so good a surface as the
others, not much weight is to be attached to the differences
between these three results. The value deduced from the
copper bar is probably nearest the truth ; and we have then
the loss of heat in 1 second from 1 sq. centim. of surface of
the bars used equal to -000098(v— V )! 7! heat-units.
The particular value 1:21 of the index n refers only to the
cooling in the water-jacket, but it seems not to depend to any
great extent on the presence or not of the jacket, for when the
cooling was performed in the middle of the room ata con-
siderable distance from any object the value of m which
best represented the cooling was less than 1:21 but greater
than 1:2.
The value of n is, however, dependent on the nature of the
surface, and also on the cross section of the bar; for by
covering the iron bar with a shining black varnish n was
* That is, if the loss of heat varies for temperatures below 10°C. ex-
cess, as it is found to do from, 80° to 10° C. excess.
+ Naceari gives :— Cu :092
Fe +106 } Bedbl. xii. p. 326.
Zn ‘0915
The values for Cu and Zn agree with the results of other experimenters, but
that for Fe is too low. Brystrom’s value = ‘112 is taken. WNaccari’s
values for c' have been used in each case.
bedi» . & Rules ease
= son es
on certain Equations in the Analytical Theory of Heat. 489
reduced to about 1:16. The varnish was, however, slightly
softened at the highest temperature, so that the character of
the surface would change somewhat during the cooling.
The much larger square nickel-plated bars used by Mitchell
in his repetition of Forbes’s experiments on conductivity give
for the cooling experiment n = 1°26 (see p. 441). This increase
of n may be due to change of form of section, or to change
in dimensions, as both these circumstances affect the stream-
lines* produced in the air by the presence of the heated bars.
It seems probable, however, that the only part of the loss of
heat which is altered by alteration of the nature of the surface,
is that part due to radiation. |
From these facts we conclude that the loss of heat from an
element of surface of heated bar, due to the effects of radia-
tion, conduction, and convection into the surrounding air, is
‘proportional to the nth power of the excess of temperature
of that element above that of the surrounding air.
The fundamental equation for the state of heat along such
a bar becomes then :—
OPO fpOV) =P iz., /
Pa, pale) : eer ete (1. )
It is evident from this equation what a great effect the outer
conductivity has on the nature of the solution of the problem
of motion of heat ina bar. The solution in terms of expo-
nentials for the steady state used by Despretzt, Wiedemann
and Franz{, and others is replaced by a power of the tempe-
rature, and the solution for the “steady periodic”’ state first
given by Angstrém§ no longer holds. The above solutions
neglect also variations of £, and we proceed to consider the
effect of this.
Taking the case in which the temperature state is steady,
we have the equation
ok Se)—E hor + tue oeawy 14)
or taking f/, as a‘linear function of the temperature, thus,
ky=ky + k’v,
we have, on expanding the equation (4),
2 2
(ho + Hv) S% +e (8°) — 1 hon=0. eet #@)
* See for stream-lines, Lodge, Phil. Mag. xvii. p. 214 (1884);
Rayleigh, Proc. R.S. Dec. 1882.
Tt Ann. de Chim. et de Phys. xix, et xxxvi.
t Poge. Ann. Ixxxix.
§ Lbid. cxiv., cxyiii., xxiii.
440 Mr. C. H. Lees on the Law of Cooling, and its bearing
ae thie
As the term in () is often neglected in the mathematical
treatment of conductivity*, it is interesting to compare its
value, as deduced from experiment, with the first term of the
above equation.
Taking Mitchell’s figures for his iron bar, we deduce
Value of Value of
ist term. 2nd term.
At 50° C. excess. -011(5°5)="06 - 00001 (2500)= 025
[100 » « ‘O11 (18) ="14 00001 (12,000) =-12
From which it is evident that the neglect of the second term
will seriously affect the results, unless k’ is very small, 2. e. the
conductivity nearly independent of the temperature. In the
above case the conductivity has been taken as changing 10 per
cent. in 100° C., which, according to the experiments of
Forbes f, Kirchhoff and eeneeoneiari f, Lorenz §, and others,
is by no means an extreme case.
Those determinations of conductivity which involve the
assumptions k’=0, n=1, need not be considered, as the results
derived from them can only be rough approximations. Inte-
grating (4) with respect to w, between the limits x, and 2»,
we have |
afhes a = | pte ALS sy ee)
or the difference between the amount of heat flowing along
the bar at points 2;, w, is the amount of heat lost from the
sides between the two points.
If there be no “source or sink”’ along the bar except at
the origin, and the bar be long enough to make oe =0( at its
end, we have ou
gh 2° ={" pho ds, .. 6 re)
which determines &, from observations of v along the bar.
* The effect of this will be to raise the value of the conductivity as
deduced from experiment.
+ Trans. R.S8. H. xxiii., xxiv.
{ Wied. Ann. ix., xiii. Kirchhoff and Hausemann neglect, however,
the second term in equation (5).
§ Ibid. xiii.
on certain Equations in the Analytical Theory of Heat. 441
We have then in (7) the solution of the problem of deter-
mination of conductivity by the bar method, free from the
most serious of the errors involved in the usual assumptions.
The outstanding assumption is that of plane isothermal surfaces.
To confirm the deductions made in this paper, from the fact
that the loss of heat from a heated bar is proportional to a
power of the temperature-excess, I proceed to apply them to
the observations of Mitchell*, who has repeated Forbes’s
experiments on conductivity, after having the bars used by
Forbes nickel-plated. He gives the values of — O° for dif-
ferent temperature-excesses for an iron bar; and from this the
following Table is calculated :—
Temp. Cy Cy OU
excess in Qu specific ou y) 26 of
degrees | — AYA heat. mo a 4 1-26
Cent. x=. v
10 oh 1-01 “1111 18°19 ‘0611
20 26 1-021 2655 43°56 10
30 ‘43 1-031 4433 72°61 10
40 ‘61 1-041 635 104°5 10
50 807 1-052 849 138-4 14
60 1:00 1-062 1-062 173-9 07
70 1:19 1-072 1:276 211:2 05
80 1-405 1:082 1521 248-9 iW
90 1-605 1-092 1°755 289°8 06
100 1°83 1:103 2:018 331 10
110 2°04 1-113 2°270 373°4 08
120 2:28 1-124 2°563 4176 14
200 4:4 1:206 5307 792°5 "0670
250 6°12 1258 7699 1051 0733
The constancy of the quotient c, oe / v2 up to a tempera-
ture-excess of over’ 100° C. shows how well the index 1-26
represents the cooling in this case. Above 100° C. 2 appears
to increase.
Putting n = 1:26 in (7), the equation determining & from
the observation of temperatures along such a bar heated at
one end is
Ov OE 1:26.
hos, = [pte dx.
Mitchell gives v and — oP at different points along the bar, and
from these we have the following Table :—
* Trans. R. 8. E. 4 July, 1887.
442 Mr. OC. H. Lees on the Law of Cooling.
1:26
= 28 T 1:26 1. sai
x in feet. OF Or § vy) ax. ov a
x
"25 172-1 195:4 656'3 446 2°28
7) 125:25 | 132-2 439°7 311 2°35
“15 92'3 92 299-4 220 2°39
1-25 52:0 47°9 1453 113 | 2°36
1-75 30°39 29:2 73°7 60°38 2:09
2:25 18:2 15:2 38:7 39 2:18
2°70 11:15 10 20:9 19-2* 1:92
3°75 4:3 6:16
4°75 1:85 2:27
5°75 fh "96
The numbers given in the last column indicate a rise of
conductivity with temperature, which agrees with the result
given by Mitchell as his most reliable. As the integration
” 1.96
) v~ ax
@
is performed graphically, no great importance is to he attached
to small variations of results. The number 2°28 ought to be
increased about 5 per cent., as the index 1°26 in the cooling
experiment only holds up to about 100°C. temp.-excess. A
close agreement of the values of & with one another is pro-
bably not to be expected, on account of the deviation of the
isothermal surfaces from planes caused by the insertion of the
thermometers into the bar. The method of Forbes would be
much improved in this respect if the temperatures were de-
termined by thermo-junctions either set in the bar at different
points, or movable, such as Wiedemann and Franz used.
Finally, then, in the general theory we, have the equation
of continuity in the form
O00 ( OU a 0 ( Ov rs) Ov
Si a (ees face ee ey ee seg eae
“Pat Bak? Oa) Onn f = 4 52( : =
with the condition at surfaces in contact with gas
ov
On,
where n can only be taken =1 when temperature changes
of only a few degrees occur, but where ¢, and probably
i, may be taken as constant when changes of temperature
of not more than 50° C. occur.
be + hv" = 0,
* JTiable to an error of about 5 per cent. on account of uncertainty of
cooling &c. below 10° C. excess.
p13
LIf1. The Constitution of the Aromatic Nucleus. By 8. A.
Sworn, B.A., Assoc. R.C.Se.L., late Brackenbury Scholar
of Balliol College, Oxford.
[Concluded from p, 415. ]
II. Arguments against Meyer’s symbol.
(1) | has brought forward, as an argument
against Ladenburg’s symbol, the fact that dihy-
droxyterephthalic ether (a benzene derivative) is converted
by nascent hydrogen into succino-succinic ether (a hexa-
methylene derivative) (Ber. xix. p. 1797).
A. K. Miller and Ladenburg have each shown his deduction
to be faulty (J.C.8. 1887, p. 209). (Without a single ex-
ception the facts quoted by these chemists can be as well
explained by the symbol of Claus as by that of Kekulé.)
It would indeed be a serious objection to Ladenburg’s
symbol could it be shown that on hydrogenation the para-
linkages are successively split. Weshould thus expect to get
two trimethylene rings. Facts are in opposition to such a
supposition.
But this is not the only conceivable way in which the
reaction may occur. A hexamethylene ring may be formed
by the dissolution of one para- and two meta-linkages, the
atoms being supposed to open out into a hexagonal ring
(vide supra, p. 405). It is perhaps improbable that a stable
meta-linkage (corresponding to ortho-linkage in Thomsen’s
symbol) would be severed in favour of a much weaker
para-linkage. The fact, however, remains that the additive
compounds can be so derived. The hexamethylene ring so
obtained will differ from that derived from Thomsen’s sym-
bol in this respect—that the order of the six atoms will not
be the same. This is evident from the following diagrams:—
' } d 1
6 2 6 2
Thomsen’s ; will give
symbol.
; 5 3 5 3
4 4
444 Mr. §. A. Sworn on the Constitution —
1
6 2
Ladenburg’s
symbol. : 2
4
; l
6 2 5 3
will give opening out to
5 3 é 6
“4 4
: 1
6 2 4 3
or opening out to
5 3 6 5
a 2
A 1
6 : & 5
or opening out to
5 3 2 :
4 | 6
The difference may be thus defined :—
The symbol of Thomsen will give rise to a ring in which
each carbon atom is bound to what were in the benzene
molecule its ortho-neighbours; whereas in those derived from
Ladenburg’s symbol,a carbon atom would in no case be directly
attached to atoms which were previously its ortho-neighbours.
The ascertained constitution of conine helps us to dis-
tinguish between these two methods of notation... Conine is
undoubtedly the hexahydro-derivative of ortho-propyl pyri-
dine. (See especially the researches of Hofmann, Ladenburg,
Skraup, and Cobenzl, on conine aud picolic acid, described in
Pictet’s “La Constitution Chimique des Alcaloides Végé-
taux.) |
Its optical activity is due to the presence of an asymmetric
of the Aromatic Nucleus. 445
carbon atom. No exception to this rule is at present known
(see especially “ Die années dans Vhistoire dune théorie,” by
Van’t Hoff). When derived from Ladenburg’s symbol, the
formule for conine cannot possess an asymmetric carbon atom.
This is evident from the following symbols :—
NH NH NH
cH CHC,Ho’
2 a7 CH CH, cH, cH,
or
cH, CH, 4 A z cH, CHa CH,
H . a
CH, cH, C H.C3H,
From Thomsen’s symbol. From Ladenburg’s symbol.
Moreover Ladenburg’s theory would indicate the possible
existence of two position isomers derived from a-allyl
pyridine.
The properties of conine, when thus considered, afford
direct evidence that pyridine is to be represented on Thomsen’s
type and not on Ladenburg’s. This deduction is confirmed
by the fact that Knorr and Antrick’s researches (vide supra,
p. 414) prove by direct synthesis the existence of ortho-linkage
between the nitrogen and the a-, 8-, and y-carbon atoms in the
pyridine nucleus of y-oxy-quinaldine, thus :—
(a) Pyr.
(8) Pyr.
(y) Pyr.
(The proved ortho-linkages in thick lines.)
(2) It is commonly stated that Ladenburg’s symbol will
not account for the conjugated derivatives of benzene. This
is not altogether true, although there are difficulties which do
not exist in the case of Thomsen’s symbol.
In the case, for example, of naphthalene it is necessary to
sever two para-linkages and to set up an ortho-linkage in each
aromatic nucleus (II.). The symbol (ILI.) which Meyer
gives is complicated by the improbable supposition that the
atoms 3 and 3’, 4 and 4’, are directly linked together, and by
the fact that phenanthrene cannot be similarly represented
(vide infra).
Phil. Mag. 8. 5. Vol. 28.-.No. 175. Dec. 1889. 2 Li
CH cH cH CH
446 Mr. S. A. Sworn on the Constitution
a 2 ; @
iH 1 2 8 Z 3
4 e + a G 4
5. 5 7 5
From Thomsen’s symbol. From Ladenburg’s symbol
: Ce
5! 5
Meyer's symbol.
III.
Naphthalene as thus constituted (II.) could hardly be said
to consist of two aromatic nuclei. That it does consist of two
such nuclei is evident from the fact that, like benzene, it has
an abnormally low molecular volume, and gives substitution
products by direct nitration and sulphonation. Moreover, in
the formation of these derivatives the action appears to follow
as closely as possible the laws of substitution which hold for
benzene derivatives. Hartley found the absorption of the
ultra-violet rays characteristic of benzene to be even greater
in the cases of naphthalene, anthracene, and phenanthrene.
The same difficulties hold with regard to the other conju-
gated bodies. Unless ortho-linkage is set up it is difficult to
account for the ascertained constitution of phenanthrene,
more especially its formation from stilbene.
I may quote the formulze which might be assigned to phen-
anthrene and pyrene.
CH CH .
Phenanthrene, C,,H,, Phenanthrene, C,,H,,
(from Thomsen’s symbol). (from Meyer’s symbol).
of the Aromatic Nucleus. 447
Pyrene, C,,H,, (from Meyer’s symbol).
Compare with p. 410.
(3) It is generally admitted that closed chains of more than
six atoms do not exist. If this be so, it is difficult to account
for the constitution of fluorene on Ladenburg’s theory, as it
is then necessary to assume the existence of a closed chain of
seven carbon atoms. In the formulation of this body from
Thomsen’s symbol this ring consists of five carbon atoms only.
The relationship of fluorene to phenanthrene, through diphe-
nylene ketone and diphenic acid, proves it to be a di-ortho-
compound. The argument is evident from the following
symbols :—
CH xC (a
cH C meen C ES ALS CH
WAY) eae
CH CH CH oH
Fluorene, C.;H,, Fluorene, C,;H.,
(on Ladenburg’s symbol). (on Thomsen’s symbol).
In this connexion I may quote the following passage from
Watts’ ‘ Dictionary of Chemistry’ (new edition, i. p. 800) :—
“ Ortho-compounds readily give rise to products of condensa-
tion in which the side chains may be supposed to be joined in
the form of a ring ; this tendency is observed to some extent
in the para-series but not at all in the meta-series.”
(4) The analogies between the ortho- and para-derivatives
of benzene as opposed to the meta- have been cited by
Koerner (J. C. 8.1876, i. p. 240) and by Lellmann (Ber. xvii.
| 2L2
AA8§ Mr. 8. A. Sworn on the Constitution
p- 2720) in favour of ortho- and para-linkage. It must be
confessed that these arguments depend upon hypothetical
views as to the cause of such analogies, and are therefore not
very conclusive. Stuart has similarly brought forward the
results of his experiments on the benzolmalonic acids (J.C.S8.
1886, p. 357) in support of Kekulé’s formula—a formula
which is at variance with so many facts.
III. Thomsen’s Symbol.
The preceding discussion affects merely the nature of
the atomic linkage, and shows that the diagonal symbol of
Claus is alone consistent with all the facts. The argument
is not merely based on hypothetical analogies between ben-
zene and pyridine derivatives. The independent consideration
of these groups of bodies clearly shows that they must be
formulated on the same type.
(1) Thomsen’s symbol is a development of that of Claus,
but the positions of the hydrogen atoms are not considered.
It is most natural to suppose that any given hydrogen atom
is attached to its carbon atom, in such a manner that the
direction of the valency falls within the solid angle formed
by the three other valencies which unite that carbon atom to its
ortho- and para- neighbours. If, forexample, we assume that
this valency is equally inclined to the other three, it will make
an angle of 148° 36’ with them (or 31° 24! with the diagonal
of the octahedron).
But whatever may be the true angle of deviation it is
evident that, whilst the meta- and ortho-carbon atoms are
equidistant, the meta-hydrogen atoms (or rather their mean
positions) would be closer together than the ortho-.
If the configuration of the benzene molecule as a whole
were octahedral, we should expect the crystals of benzene to
belong to the regular system. Butthey arerhombic. Schrauff
has considered this point (Wiedemann’s Annal. Neue Folge,
xxxi. p. 540), but the positions which he assigns to the
hydrogen atoms give a symbol which would indicate the
existence of two isomeric mono-substitution derivatives.
Further, any space formula for benzene, which represents
all the atoms in one plane (see Claus, Ber. xx. p. 1425),
would lead us to suppose that benzene would crystallize in
the hexagonal system.
(2) The development of Thomsen’s symbol which I have
proposed in no way affects the questions which were pre-
viously discussed (I. and I1.).
It affords a basis for an explanation of the so-called para-
of the Aromatic Nucleus. 449
and meta-laws of substitution (see Armstrong J. C. S. li.
. 259).
‘ (a) “et us consider the continued action of sulphuric
acid upon benzene. The sulphonic group first introduced is
itself sulphonized, and for the moment an unstable body (B)
is formed. This compound gives off a molecule of water, the
hydroxyl (n) being eliminated with one of the ortho- or meta-
hydrogen atoms (0, 0g m, m3). Simultaneously with this
change the two sulphonic groupings (a and b) become dis-
united, and (b) takes the place of the eliminated hydrogen
atom. As in a large number of such molecules, the hy droxyl
(2) will be more often in closer proximity to a meta- than to
an ortho-hydrogen atom, and always closer to one of these
than to the para-hydrogen atom (p), we shall get the forma-
tion of meta- and ortho- to the exclusion of para-benzene-
disulphonic acid, and of these the meta will be the chief
oe These changes may be graphically represented
thus :-—
Be (Nya @) ee a
H a
Intermediate Body (B). Benzene meta-
di-sulphonic acid.
H---(%)
(Plan).
Benzene sulphonic acid, C,H, SO,H.
450 Mr. 8. A. Sworn on the Constitution
(6) This explanation is dependent upon the nature of the
radical first introduced. If this radical has no tendency to
form addition products, the further substitution must be
effected by the momentary dissolution and re-establishment
of one of those aromatic linkages which attach its ortho- and
para- neighbours to the carbon atom whose hydrogen is al-
ready displaced. (This explanation is admitted for the mono-
substitution derivatives.)
Meta-derivatives are not obtained because there is no meta-
linkage, and para-derivatives are formed in greater quantity
than ortho- because the para- is less stable than the ortho-
linkage. The formation of o- and p-dibromobenzenes, by the
direct bromination of benzene, may be thus represented. (See
page 451.)
(c) In a similar development of Meyer’s symbol the ortho-
hydrogen atoms would be nearest to one another, and similar
arguments would lead us to ortho- and para-laws, and the
formation in each case of meta-compounds in small quantity.
Attempts have been made by Schiff (Annalen, cexx. p. 303),
by Lossen (Annalen, cexxv. p. 119), by Horstmann (Ber.
Xx. p. 766; xxi. p. 2211), by Briihl (Annalen, ce. p. 228),
by Thomsen (YVherm. Unt. iv. pp. 61, 273), and others
to determine the constitution of benzene from its physical
constants. The calculations of these chemists presuppose the
existence of paraffinoid and olefinoid linkages alone, and lead
to conflicting results. Moreover they are based on so-called
‘‘laws,’”? such as that of Kopp, the general application of which
(in the case of molecular volumes) has been disproved by
numerous researches.
It is certainly true that the linkages in aromatic com-
pounds are not directly comparable in such a manner with
those in fatty bodies ; and it is therefore impossible to make
use of arguments based upon the measurements of specific
volumes and refractive indices and upon thermochemical
data, until some quantitative connexion has been made
out. ne
In a future paper I hope to bring forward some calcula-
tions based upon space formule and made with the object of
advancing this question.
451
of the Aromatic Nucleus.
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[ 452 ]
LIV. The Measurement of High Specific Resistances. By
R. THRELFALL, M.A., Professor of Physics, University of
Sydney, N.S.W.*
[Plate XIV. fig. 3.]
Te experiments which form the subject of this paper
were begun almost immediately after my arrival in New
South Wales, in June 1886, and have been continued at
intervals ever since. The original object was to measure
accurately the resistance of certain gums produced by trees
growing in the Colony. The only gum thoroughly examined
however, up to now, is that produced by the “ grass tree”’
(Xanthorrhea hastilis). This gum, in spite of many attempts
to improve it by various methods of purification and by
mixing with other substances, turns out to be useless as an
insulator, having in fact no higher resistance than, say,
ordinary samples of resin, that is about 4:1 x 10° megohms
per cubic centimetre. Besides this, the gum in question is
faulty in other ways. It is of the nature of shellac, but
cannot compete with the shellac as ordinarily supplied either
in price or purity. In addition it has the two fatal defects of
being partly soluble in water and of decomposing before it
melts. Long-continued gentle heating does not seem to im-
prove itin this latter respect; while the texture of the material
becomes looser, it grows friable and very dark in colour.
Benzoic acid appears to be given off in large quantities
during the process. In spite of many attempts I have
hitherto failed to obtain any considerable quantity of the
fig-tree gums which are said to be produced in large quantity
in the northern parts of the Colony. This paper therefore
will be devoted to a description of the method adopted in
measuring these resistances, a method which ultimately
reached a considerable degree of perfection; partly on ac-
count of the modifications introduced in the construction of
high-resistance galvanometers, and partly on account of the
peculiar property of Clark cells. The method has since
been empioyed for other measurements, as will be shown
later on.
I do not wish to claim any superiority for the galvanometer
over the electrometer methods, except that, given the gal-
vanometer and cells, it is certainly more easily applied,
especially when the determinations are numerous. I was
forced to adopt the galvanometer method in this instance
through not having an electrometer ; but I was by no means
* Communicated by the Physical Society: read March 23, 1889.
On the Measurement of High Specific Resistances. 453
unwilling to do so, because I have long been of the opinion
that the galvanometer as usually constructed is susceptible of
considerable improvement for delicate work by simply pushing
the ordinary conditions of sensitiveness nearer to their limit.
GENERAL DESCRIPTION OF METHOD.
Measurement of Resistance of Gums.
The substance to be tested forms a layer of very exactly
estimable dimensions between two plates of conducting
material. The experiment consists in obtaining equal de-
flexions of a sensitive galvanometer—(1) when a known
fraction of the H.M.F. of a Clark cell is allowed to act
through a megohm in the galvanometer circuit ; and (2) when
the E.M.F. of a known number of compared Clark cells is
allowed to act through the resistance to be measured.
The apparatus, therefore, consists of the plates with the
substance to be investigated, the galvanometer, the standard
cells, and a megohm.
The Resistance-plate Arrangement.
This consists of two brass plates accurately rectangular and
scraped flat on one surface. The dimensions of the plates I used
were—length 15°2 centimetres, breadth 12°7 centim., thick-
ness 16 centim. These rather exact numbers were obtained
by filing. The measurements were made (a) by beam com-
passes, (8) by the dividing-engine. Neither the corrections
which had to be introduced for temperature nor the com-
parison of the dividing-engine scale and the beam compasses
with the standard metre are given, as no absolute measure-
ments of pure substances have been made. Several measure-
ments of each plate were made by both methods. The surfaces
were made flat by scraping, and this process was continued
till the contact was sufficiently perfect for one plate to lift the
other when laid on it, both surfaces being clean in the
ordinary sense. The upper plate is furnished with a solid
handle something like the handle of a flat-iron, and is pierced
by three holes, through which pass the micrometer distance
screws (see Plate XIV.). The screws are 4 centim. long, and
the threaded portion is ‘55 centim. in diameter (they would
have been better if twice the diameter). The micrometer-
heads are divided into a hundred parts each, and the mean
pitch of the screw, as determined by a comparison with the
millimetres of a standard scale by means of a measuring
microscope, is 39°5 divisions to a millimetre; that is, one turn
is equal to °5063 millimetre at 20°C. ‘The points of the
1D Oe ee, Ce eee
454. Prof. R. Threlfall on the Measurement
screws are conical, and the distance from the end of the thread
to the point of the screw is 5 centim. The screws are of
steel tempered to the blue, the heads of brass; and the tap
used to produce a thread in the holes through the brass plate
was identical with one of the screws; the lathe being set to
use the same part of its screw and of its change wheels
during the making of each; the measurement showed that
the screws were very good especially in the middle portion ;
they were also practically exactly alike. The goodness of the fit
in the brass plate was shown by the fact that an increase of
temperature of 20°C. was sufficient to “bind” the screws
very perceptibly. Indices similar to the indices of spherome-
ters were erected in the upper plate of the apparatus—one
index for each screw. All the workmanship being accom-
plished, the plates were next platinated by a process given in
Gore’s ‘ Hlectro-metallurgy’ under the name of “ Roseleur’s
Process ;”” a previous experiment showed that when the
directions are faithfully carried out, this process will yield a
hard bright deposit of platinum. The bath, however, is very
troublesome to keep in order since no solution of platinum
takes place to supply the place of that deposited. To prepare
the plates for platinating, they were first heated to the tem-
perature of boiling water and rubbed on the scraped surfaces _
with a solution of caustic potash. Finally, they were rubbed
with a bit of fine pumice dipped in dilute caustic potash.
This is by far the best laboratory method known to me for
preparing surfaces of brass for electro-plating; a clean
surface is obtained with comparatively little abrasion. Before
I found this out, l was much troubled to secure a good deposit.
After platinating, care being of course taken to prevent the
deposit being unequal, the plates were carefully washed and
dried. It was noticed that the metallic surfaces were covered
with a faint bloom of black platinum. On placing the plates
together and moving the top one slightly, the lower plate at
once adhered, and though weighing several pounds could
easily be lifted by the upper one. On pulling the plates apart
the ‘ bloom” was found to be burnished practically all over
both surfaces, showing of course that the platinating had not
sensibly altered the planeness of the surfaces. For this
accuracy | am much indebted to the university assistant,
Mr. James Cook, who, being accustomed to prepare optically
flat surfaces, was led by the application of experience gained
in that way to the happy result above mentioned.
The exact position of the two plates with respect to one
another was secured by cementing the plated surfaces to-
gether with hard paraffin. Two lugs of thick brass were
of High Specific Resistances. 455
made fast by screws to each plate, and brought as near to one
another as consistent with leaving an air insulating space
between them. These were then bored to fit slightly conical
steady pins. A rim was also screwed round the lower plate,
so that when the top plate was removed the bottom plate
resembled a tray. ‘The rim projected about ‘8 of a centimetre
on each side of the surface, and extended to a height of about
half a centimetre above it.
The gum was introduced between the plates in the follow-
ing way. The micrometer-screws were carefully cleaned and
screwed through their holes till they made contact with the
lower plate; the point of contact was almost as easy to
estimate as in the ordinary use of the spherometer. At all
events three or four consecutive attempts to fix the point of
contact did not differ from each other by more than about one
half of one of the micrometer-divisions. The accuracy with
which the contact-point can be fixed depends mainly on the
workmanship of the screw, which must fit perfectly ‘“ tight
and free,” to use the mechanic’s very expressive term. The
contact-points having been found, they were permanently
scratched on the micrometer-heads and called zero points.
The next operation consisted in screwing each of the screws
through a known number of turns. In one experiment this
amounted to making the distance of the plates apart = °02
centim.; and in another the distance was reduced to ‘OL
centim. with equally good results. It is not advisable in any
absolute measure to reduce the distance to much less than
this, because the error of the micrometer, depending as it
does (as in this case) chiefly on the small irregularities of
the screw, must not be allowed to become sensible. ‘There is
no doubt, however, that with first-rate appliances the micro-
meters might be easily madea hundredfold as accurate as mine,
and their travel actually measured in situ by a suitable
reading-microscope. In this case it would be important to
make the screw portion much thicker to avoid any risk of
permanent distortion (twisting) when the screws are finally
screwed back while partly held by the gum™*.
The screws being adjusted, the plates are slowly heated in
a gas-oven till some gum laid on the surface of the lower one
is in a state of quiet fusion. The great object is to avoid
any distortion of the plates. With this aim in view the
plates described were cast about twice as thick as they finally
required to be in order that the “ shell,’”’ supposed to be in a
* Since this was written an improvement of the above micrometer-
screw has been devised, entirely getting rid of the difficulty here referred
to.— Oct. 5, 1889.
456 Prof. R. Threlfall on the Measurement
different state of strain to the interior, might be approximately
removed. The plates were planed first on one side and then
on the other till the right quantity of metal was removed ;
the last cuts being taken very fine. The handle affixed to
the upper plate was of course arranged so as to fit loosely,
and not in any way constrain the free expansion and con-
traction of the plates; the temperature having been often
violently changed (by heating for cement &c.), it is hoped that
the plates may be considered fairly well annealed. ‘There 1s
no doubt, however, that for complete satisfaction in an abso-
lute measurement the plates should be capable of being
optically examined during the process of heating. This
would require to be done in the gas-oven or other uniform
field of temperature and at the time the experiments were
made. I had not the requisite appliances.
It was found by several trials that the best way of obtaining
a layer of gum free from bubbles between the plates, was to
float the lower plate or tray pretty full of gum, and also to
obtain a layer of gum free from bubbles and in quiet fusion
on the upper plate. In the case of the grass-tree gum this
could only be obtained by heating the gum for some time at
a temperature higher than the one at which it was when the
plates were brought together. This was accomplished much
in the same way as is sometimes done in microscopy—when
the cover-slip is placed on the slide with one edge down and
the other end gradually lowered. The freedom trom bubbles
of the layer of gum obtained in this way was tested by allow-
ing the plates to cool, and then heating the lower one till its
surface reached the temperature of the melting-point of the
gum, the upper one being kept cool. This being done the
upper plate could finally be lifted, leaving only a small portion
of the gum on the lower plate—owing to the small heat-con-
ductivity of the gum. The layer of gum was left thick on
one occasion for the purpose of this test, and when the
manipulation described above was properly carried out there
were no bubbles; the layer in fact was very homogeneous
indeed. ‘The only danger left so far as the insulating material
is concerned is that it may tend to crack away from the
plates during cooling. In the cases examined this did not
seem to be the case, because in the first place a thick layer of
the same substance rapidly cooled on a thin plate showed no
tendency to crack. Again, a great many insulating substances
are more or less plastic, or rather viscous, down to tempera-
tures very nearly approaching those at which experiments
are usually made (in this country 23°C. is a not unusual
temperature). Again, the massiveness of the plates being
of High Specific Resistances. 457
considerable no distortion of them ought to be caused by the
gum, if the ordinary precaution of allowing them to cool
slowly be observed.
In the experiments hitherto made the cooling took place
during the night in the gas-oven, which being coated with
non-conducting material took a long time to cool. On the
other hand, in all experiments of the sort one is in a dilemma.
If the substance is placed between conducting-plates there are
dangers of the kind mentioned; if, on the other hand, the
material itself be worked with a view to making it take a
prescribed form, the difficulties, especially in the measurement
of its thickness, become great. I began by making some
attempts of this kind, using blacklead to make the gum-sur-
face conducting, and plating this electrolytically. The diffi-
culties arising in the shaping of the plates are, however,
practically prohibitive with friable material. Besides this I
have often noticed that in electrotyping it is difficult to
prevent the deposit being “spotty” at first, and this has
shaken my faith in the perfect continuity of ordinary black-
lead surfaces. Possibly platinating with an induction-coil
may be really the best way.
However, to finish the description of the case in point :—
The gum was carefully scraped away from the edges of the
plates as soon as they were cool, and the screws were screwed
back. This could not be done with any ease at first because
of the cementing action of the gum. ‘This was got over by
heating the head of the screw with a Bunsen flame : finally,
the screws were retracted far enough to be quite out of the
way*. A correction to the area of surface has of course to
be made for the three screw-holes. If the thickness of the
gum be considerable compared with the diameter of the hole,
this may be very complicated. In the present case it was
negligible. Thus the whole area of the gum-plate was
193-04 centim. less the area of the three screw-holes —°7128
centim., 2. ¢. 192°3272.
Now it is clear that, owing to the curvature of the lines of
flow round the edges of the holes, the real correction will be
less than the one made. The deposit of gum, however, is
pierced by a hole corresponding to the conical end of the screw
and, consequently, only very small.
* Nore, Dec. 1888.—The difficulty is, however, serious, and has led to
new hollow screws being made. Through the holes bored down the
centres of the screws gold-plated copper rods pass; these are pinned to the
screws till it is required to retract them; the ends of the screws them-
selves are flush with the lower surface of the upper plate, or very near so.
458 Prof. R. Threlfall on the Measurement
Finally, the steady pins are taken out of the plates and the
gum is ready to be measured.
In order to measure the resistance of good insulation by
means of this arrangement, it is clear that it will be ad-
vantageous to have a galvanometer of the highest degree of
sensitiveness. ‘This is desirable both because the thicker the
insulating layer the less will be the experimental error in the
determination of its thickness; and the smaller the electro-
motive force required the less will be the difficulty of estimat-
ing it exactly, as will be shown in the proper place. I there-
fore attempted to obtain sensitiveness by pushing the ordinary
conditions further than is usually done. My first experi-
ments were on a galvanometer of about 9000 ohms’ resistance,
made by the Cambridge Scientific Instrument Company. It
was soon very evident that when the current reached the value
of about 10-7 ampere, the torsion of the suspension became
important. My first modification was to increase the length
of the fibre to about 12 inches; this led to considerable
difficulty of adjustment, but increased the sensitiveness about
fifty-fold. It then became clear that the next step must be
to get the magnets more perfectly astatic and to reduce the
weight of the mirror. The reducing of the weight of the
mirror turned out to be more difficult than I anticipated ;
however, it was finally arrived at, and at the same time the
astaticism was made more perfect. Some experiments showed
that it was very difficult to get two sets of steel bars of the
kind ordinarily employed even reasonably astatic. The
difficulty les partly in the magnetizing and partly in obtain-
ing exactly equal quantities of steel in the two systems of
magnets. In fact it is necessary that the steel bars be mag-
netized zn situ, otherwise they can hardly be perfectly
arranged and are sure to demagnetize each other more or
less. Now when the two magnet systems are only separated
by a bit of aluminium, say three inches long, it is impossible
to thoroughly magnetize one system without demagnetizing
the other more or less. Consequently it is necessary to set
up an arrangement so that both systems can be magnetized
at once. The following is a description of the arrangement
adopted :—It consists of two small electromagnets with
extremely soft cores, and movable pole-pieces most carefully
worked so as to fit the ends of the cores. Hvery precaution
was taken to make the electromagnets as much alike as
possible; the iron was cut off the same rod, it was bent to
the same templet, the annealing of both cores was done in
a box of asbestos at the same time. The four brass bobbins
of High Specific Resistances. 459
carrying the wire were also made as much alike as possible,
and the same number of turns of wire were put on each
bobbin by means of a revolution-counter. The winding was
quite uniform, No. 18 B.W.G. wire being used. As a check
the resistances of the bobbins were measured, when it
fortunately happened that two were about one half per cent.
higher than the other two, and so they were paired. The
wire, it need hardly be added, was wound on to the four
coils under a constant strain. The two electromagnets
were then mounted on a permanent stand—one being kept
steadily in a fixed position, and the other being capable of
sliding parallel to a line drawn perpendicular to the lines
joining the centres of the poles of each magnet. The pole-
pieces were bevelled off from the top side ; but the area of
the ends remained large compared with the size of the mag-
nets to be magnetized. The condition as to equality of
quantity and quality of steel in the galvanometer magnets
was next considered. After some reflexion I decided that the
most probable way of securing equality would be to discard
bar-magnets entirely and use disk-magnets. I therefore
procured a small piece of sheet steel about as thick as
ordinary thin writing-paper, and had a die constructed so as
to stamp small disks from this sheet. The sheet was fairly
hard, and it was found that the disks “‘ stamped” better when
the sheet was taken in its natural state than when it was
softened. A considerable number of disks were stamped out
of the sheet, and these were then laid on a bit of flat iron and
raised together to a bright red heat ; they were then plunged
together into a jar of cold water. On examination they all
seemed to be glass-hard, and some of them remained flat.
The four flattest ones were chosen and prepared for mounting.
A bit of aluminium wire was cut to the right length and
beaten out flat at each end. The disks were then cemented
with shellac varnish, one on each side of each flattened end
of the aluminium wire. The wire was thus much more ac-
curately the centre of rotation of the magnetic system than is
generally the case. Attempts were then made to get a good
light mirror. About three ounces of small microscope cover-
slips were examined by aid of the reflected image of the bars
of a window, and from these about twenty were selected
and silvered by the Rocheile salt process. They looked very
good, but on mounting for trial without strain they all turned
out disappointing. I finally made use of a small portion of a
larger mirror that had got broken. This was cemented on to
the flat surface of one of the steel disks and was found not
to be sensibly distorted. After trying very many cements, I
See
Se
460 Prof. R. Threlfall on the Moasurencae
incline to think that nothing is better than a trace of slow-
drying white paint. Amongst other experiments I tried
cementing two very thin glass disks together, selected so as
to mutually correct each other by the drying of the cement.
I also tried a method of using plaster of Paris. As plaster of
Paris expands on setting I covered the back of a thin mirror
with a layer of it about +, in. in thickness on drying, this of
course forced the mirror into a concave form. The back of
the plaster was rubbed away on a fine file till it was only
about =!5 in. thick, and the mirror still remained very con-
cave. Since cementing magnets on to disks with shellac
varnish invariably forces the mirror to become convex, I
hoped that I should obtain a correction of the concavity pro-
duced by the plaster by the convexity which the shellac tends
to provoke. My anticipation was completely realized ; the
mirror on examination turned out all that could be desired,
but, alas, was too heavy for the purpose for which I required
it. I can, however, most strongly recommend the process to
anybody who desires a mirror to be flat and does not mind it
being heavy. ‘The best way is to use very little plaster and
then to leave the mirror concave. ‘This concavity can be
removed by painting on small successive films of shellac ; it
must be remembered that shellac films go on contracting for
several days after they cease to be sticky. Equally good
results can of course be obtained by cutting out (with a
rotating tube and emery) disks of the size required from
previously examined thin sheet glass. The surfaces generally
require regrinding. ‘The advantage of the process described
is that it enables thin cover-slip glass, which is generally to
hand, to be kept flat.
The mirror having been mounted on the steel disks, these
last were magnetized by the apparatus mentioned above. In
carrying out this operation the following precautions have to
be observed :-—
1. The distance between the pole-pieces requires to be the
same for each magnet. This was attained by setting them
to touch a carefully prepared brass rectangular bar.
2. To annul the effect of any small outstanding differences
between the cores of the magnets the current was supplied to
them in multiple arc, and was strong enough to magnetize
the cores beyond the saturation point.
The approximate moment of inertia of the magnet system
was easily calculated, and it was found that the astaticism
was at least ten times as good as the best I had been able to
obtain with small bar-magnets mounted on mirrors or mica,
and magnetized with a small horseshoe magnet. Of course,
——
rr oo yor
ia 7
of High Specific Resistances. 461
as has been pointed out by several observers, there is danger
of rapid variation of the magnetization ; but it was thought
better to risk this than to force it by artificial “ageing” by
heating or otherwise. As will be seen hereafter, the magnets
were never exposed even during the experiments to anything
but the smallest electromagnetic forces, and the controlling
-magnet was weakened and introduced from high above the
galvanometer, and only lowered sufficiently just to make its
influence on the combination really felt. “This is a delicate
operation with ordinary arrangements, but becomes simple
when the construction of the galvanometer is modified in a
way to be explained directly. If one desires to keep the
astaticism perfect, it is necessary to be mindful not to use the
controlling magnet so as to produce demagnetization ; nor must
the currents through the galvanometer ever rise to much
greater values than those corresponding to the effects to be ob-
served. From an examination of the investigation in Maxwell,
vol. ii. articles 487 and 438, both Mr. Adair and I came to
the conclusion that the disk form of magnet would retain its
magnetization pretty well. This has turned out to be the
case, for after more than a year’s hard use, for all sorts of
purposes, the galvanometer has still a sensitiveness of about
one division for 10-° ampere. The galvanometer is in daily
use for testing cells with a view to their application to the
resistance measurements at present under discussion.
This galvanometer, however, never came to be relied on to
measure currents of less than 10-° to 10-° ampere. In the
course of reading on the subject I consulted the paper by
Messrs. T. and A. Gray in the Proc. Roy. Soc. 1884, vol. xxxvi.
p- 287. These gentlemen made use of a new arrangement of
magnets and coils, which, however, can hardly be understood
without referring to the picture, loc. cit. The coils and magnets
were so arranged that the poles of the magnets were normally
situated in conical holes containing the axes of the coils.
The two horseshoe magnets were suspended from a frame of
aluminium wire by one or two silk fibres of considerable
length. The coils themselves were composed of very fine
wire and had a high resistance. I lost three months’ hard
work in making and testing this arrangement, which certainly
has the advantage of being practically perfectly astatic. The
suspended arrangement being rather large was most trouble-
some to mount and balance, and had the additional dis-
advantage of having so great a moment of inertia that its
period of vibration often amounted to 70 or 80 seconds.
This sluggishness had the property of making it most difficult
Phil. Mag. 8. 5. Vol. 28. No. 175. Dec. 1889. 2M
462 Prof. R. Threlfall on the Measurement
to use, for it was hardly possible to distinguish the motion
due to the electromagnetic forces from the never-ceasing
motion due to air-currents. Though the instrument was well-
protected by a glass case, and this generally supplemented by
a wooden box, I never succeeded in eliminating the effect of
air-currents, though it must be added I never succeeded well
enough with it in other respects to make it worth while to
apply the ‘‘subjective’’ method of mirror observation. In
any case it seems to be essential to have a means of adjusting
the coils to the magnets as well as the magnets to the coils;
but the adjustments are very tiresome even with the facilities
which in the later forms of this instrument I had for making
them. My coils had not quite so much wire as those of the
Messrs. Gray because I used all 1 had and could get no more
in Australia. However, the aggregate number of turns —
amounted to 59,900, and the resistance at 20°C. was 15,852
B.A. units as against 62,939 turns, and a resistance of 30,220
ohms attained by the authors quoted. The authors also state
that the wire was approximately uniformly distributed
throughout their coils, though in my case this was found im-
possible, keeping the external dimensions quite constant, and
therefore there was a slight difference between the coils,
which, however, was compensated for by their arrangement in
the instrument. Ido not think that the diminution of the
number of turns had much effect, because the diameter of the
coils had reached 5°8 centim. Feeling that my non-success
was probably to be traced to my inferior skill as an experi-
mentalist, I undertook a long series of trials with a view to
discovering the best way of hardening the magnets and their
best position in the coils when at rest; amongst other ex-
periments the following will do for description. Three bits
of Stubb’s steel wire were carefully cut and filed to a uniform
length of 4,4, in., their diameters being @, in. These will be
called A, B, and C. A was made glass-hard throughout; B
was hardened through a distance of from ? to 1 inch at each
end ; C was hardened from a distance of from } to + inch at
each end. ‘These bits of wire were then magnetized by being
placed between the massive poles of a very large electro-
magnet. The cores of this magnet were 3 inches in diameter
and about 25 inches long. The pole-pieces were very broad
and thick. The magnetization of the steel was carried nearly
to saturation, and the magnets were found by filings to be
free from consequent poles. On taking the times of vibration
the following numbers were obtained :—
of High Specific Resistances. 463
A made 25 vibrations in 125 seconds.
B 93 yy) 124 os)
C ay) 93 105 7}
After remagnetizing the magnets with about half as much
current again round the electromagnet, it was found that
A made 25 vibrations in 123 seconds.
i 7}5) 7) 107 4)
C 7) 99 107 yp)
B therefore was improved; A and C remaining about the
same. The deviations were probably produced by the un-
avoidable shaking and jarring in mounting the magnets,
though this was done with considerable care.
These magnets were next observed with respect to their
behaviour with one of the coils. Coil “ No. 8” was selected
for this purpose. It was placed on the table, and above it
hung a specially fine spring-coil of wire forming part of a
Jolly’s balance. The magnets were hung from the end of
this spring by a loop of silk, and could be adjusted to pene-
trate the coil to a greater or less extent. In general five
positions were taken :—
Position 1. Magnet-end flush with the upper windings of
the coil.
» 2 Magnet-end at + of the length of the hole
through the coil.
» 3 Magnet-end at the centre of the coil.
» 4. Magnet-end at 2 of the length of the hole
through the coil.
» 9 Magnet-end flush with the bottom of the coil.
Three Leclanché cells were allowed to run for four hours
through the coil before the experiment began. The coil had
a resistance of 3130 ohms.
First, a series of observations was taken by observing on
the glass scale the equilibrium position of the magnet with
the current direct and reversed. The magnet was then
lowered to position 2, and so on; then it was reversed and
the experiments repeated. Two complete sets each way were
made for each magnet, 7. e. forty observations of distance and
forty reversals of current. The experiment was a very pretty
one, and I never remember to have seen any apparatus work
better. The following set is given as a sample from the note-
book. -The numbers, of course, have no significance except
with respect to the actual coil and magnet taken.
2M 2
464 Prof: R. Threlfall on the Measurement
Magnet B.
Pasion an Coil. Tonle displacement with Number of
current + and —. experiments.
uxt edge) of ‘coil 2 ‘43 centim. 3
qoway tp), 6 7 ae ae TA Waa 2
oy nee Re eta SS £03. ye 2
3 - PN aks LO cee Z
Near bottom of coil . . 04 2
(4 inch off )
Magnet B reversed, otherwise everything the same.
ise 5; Displacement current Number of
Position. : + and — experiments
INE TOCCOA veeoy) cade adele °415 Seah
PAV Up kcge Gog aye. the! ike o ite Mae 2
2 se eg Cae NN IOS Ginn 2
a a ae geriiclene th tlc hic tanes 2
re (OLS? GOUT Ser pe ae ina O° Lee 2
The nett result was that all the magnets behaved best when
they started from three quarters to the whole way in, and
that B was best, C almost as good as B, and A distinctly the
worst. On reducing the observations it turned out that the
ratio of the mean displacements of A and B was about °782,
while the ratios of the magnetic moments was °755. This
relation is of about the order one would expect, seeing that
the length of the magnets was about 9°6 centim. and the
dimensions of the coil were :—axial 3°8 centim., radial at one
end 2:4, radial at other end 2°5. The external surfaces of
the coils were eylindrical.
The ratio of the greatest displacements was 643, It may
be conceded, therefore, that the questions of magnetization
and placing received a fairly complete answer. In the final
arrangement of the galvanometer with horseshoe magnets,
like those described by the Messrs. Gray, the Jengths of the
yokes of the magnets was 8°5 centim., and thus this was the
distance between the centres of the coils, The legs of the
magnets were 3°8 centim. long, and they were magnetized
like the trial magnet B. When in position, the magnet-legs
projected into the coils to an extent of about % the axial
dimension of the latter. The suspension was two washed silk
fibres (one would not carry the load) 16 centim. long.
The test for sensitiveness was made by running a large
Clark cell (already described) through 10,000 legal ohms, and
a certain small resistance taken out of an ordinary Brid ge-box.
The terminals of the Bridge-box were coupled up through the
of High Specific Resistances. 465
galyanometer toa megohm. The accuracy of this method of
testing has been already established.
The distance from the galvanometer-mirror to the scale was
155 centimetres ; and the light-spot was very good, showing
the wire image as sharply as the lines on the scale. The
scale itself was divided into millimetres. In the final test the
period of vibration of the magnet system was 80 seconds, and
the resistance out of the Bridge-box was 100 ohms. The
E.M.F. acting through the megohm and galvanometer and
100) :
100 ohms was therefore 10100 Clark cells, say °0145 volt.
Th t was therefore 275" = 1-26 x 10-7 amperes
e current was therefore 77g) 9= peres.
Employing the method of vibrations and neglecting the
correction for the extremely small log. decrement, the battery
being of course reversed and several experiments made, it was
found that the double deflexion amounted to 5 scale-divisions
(millims.). Hence the deflexion corresponding to 1:26 x 10~7
amperes is 2°5 divisions. Now I do not think that, bearing in
mind the lengthy period of the system, it would be possible to
read to more than ‘5 division. The difficulty comes in in
eliminating air-currents ; as far as the scale went I could read
certainly *2 division, so there is no advantage to be gained in
having the scale further, or even so far away. We may
therefore say that five times the least measurable deflexion is
given by 1°26 x 10-* amperes, or that the least measurable
deflexion itself is given by 2°5x 10-8 amperes. ‘This, I may
mention, is only to be obtained when the magnets are
judiciously kept from swinging by an extra controlling
magnet, worked carefully from a distance till the vibrations
get small, so as to jam against the side of the coil. Some
fine quartz threads were also prepared by Boys’ method, but
no appreciable improvement introduced by their use could be
detected. This may, however, have been on account of their
thickness ; for they could be seen, with a little practice, in a
good light, and when laid on a bit of black silk. I therefore
came to the conclusion that neither I nor my instrument-
maker (who is fairly good) could hope to compete in such
delicate work with the Messrs. Gray, who, using this type of
galvanometer, attained a sensitiveness of one half millimetre-
division with a current of about 10—"' amperes, and that with
a scale fairly close to the instrument, and with a manageable
period of vibration.
In consequence of this failure I determined to use the four
coils constructed for the Gray galvanometer, for an expe-
466 Prof. R. Threlfall on the Measurement
riment in which they were employed in the usual manner.
They were therefore roughly mounted, and provided with an
astatic combination of the kind previously described. ' The
results were so encouraging that the same methods were pur-
sued further. In the final form the suspension was a quartz
fibre, 85 centim. long, suspended in a carefully chosen glass
tube. With such long suspensions the tube must be very
straight, and the arrangement for raising and lowering the
suspended parts must be very good. After trying several
arrangements for this, I adopted a pointed piston working
into the tube and passing through a stuffing-box. The coils
were of course anything but suited, as far as shape goes, for
their present arrangement; however, they did what was
requisite, though I have no doubt that coils might be made
to increase the sensitiveness tenfold.
The mirror was in this case suspended midway between the
magnets, and, for want of a better, was so thin that it gota
little pulled out of shape by the paint which was used to fasten
it to the aluminium wire. ‘This fortunately turned out to be
an advantage in some respects, for the vertical wire and the
paint on the back of the mirror, by a happy accident, made
the figure of the mirror practically that of a portion of a
cylinder with a vertical axis; consequently, using a very good
lens of 40 inches’ focus, a good image of the light-spot was
obtained ata distance of three metres. It became evident at
once that the two real difficulties in securing sensitiveness
lay in preventing air-currents and in adjusting the controlling
magnet.
The first was finally attained by making the instrument
practically air-tight ; and, by means of a diaphragm, stopping
down the beam of light to very nearly the size of the mirror
—in this case of about 1 centimetre diameter. During the
measurement of the resistance of an impure sample of sulphur
this protection against air-currents was found to be insufficient,
and the galvanometer was further protected by enclosing it
in a cardboard box. If it ever becomes necessary to make an
instrument to be sensitive to, say, 10~'8 amperes, I shall have
the support for the controlling magnet absolutely independent
of the galvanometer-case, so that any vibrations set up in
adjusting the magnet shall be transmitted only through heavy
masonry. In the galvanometer now being described the con-
trolling magnet could be raised by a nut and screw combina-
tion, itself sliding on a brass tube attached to the case of the
instrument. The glass tube containing the fibre was clamped
at its upper end to a very heavy stand of brass and lead, and
this practically sufficed when the sensitiveness got to be of the
order of one division to 10—"! amperes.
of High Specific Resistances. | 467
The arrangement for adjusting the distance of the control-
ling magnet was arrived at after several trials. It consisted
of an apparatus sliding and clamping on the brass tube, with
a nut and screw for fine adjustment. It was intended to use
a worm-wheel and screw for the adjustment in a horizontal
plane; but this was found after a little practice to be un-
necessary, although it would be convenient.
The details of this arrangement for raising and lowering
the magnets will be understood from the drawing of the gal-
vanometer for medical purposes on Pl. XIV. figs. 1 and 2, see
p- 416, supra. Many experiments were made in order to decide
the relative merits of quartz and silk fibres. At first it was
thought that silk did as well; but after a time a great deal of
trouble with the zero was traced to the silk, and attempts were
made to use finer quartz threads. In this, owing to the skill
acquired by Mr. Pollock, I was finally successful. As I have
had about a year’s experience in drawing quartz threads, Ladd
the following notes on the process in hope that they may
prove of use to others. The difficulty is to get a large enough
bit of quartz fused onto a suitable handle. The best way of
managing this is first to heat a bit of rock crystal red-hot in
an ordinary crucible and keep it heated for about an hour.
On cooling, it will be found to have split into fragments of all
sizes ; one of these is chosen, and supported on a bit of lime
or on a massive bit of iron, and is then fused under the oxy-
hydrogen (not oxy-coal gas) jet. When it has once been got
glass-like it never cracks again, no matter how suddenly it
may be heated. Porcellanous quartz draws into rotten threads,
as might be expected. Two bits of fused quartz having been
prepared they may be fused to the ends of two bits of clay
tobacco-pipe, and can then be manipulated in the oxyhydrogen
flame without trouble. There is no difficulty (when once the
short thick threads have been drawn by hand) in the subse-
quent shooting. I most cordially indorse all that Mr. Boys
says in favour of this admirable invention.
Another difficulty lies in the obtaining of a reasonable
degree of astaticism. It has already been shown that it is
practically possible to increase the astaticism of a magnetic
combination by careful methods cf magnetization and manu-
facture of the magnets: but the astaticism thus in general
obtained is by no means perfect. The investigation of this
matter was undertaken by Mr. Adair, and proved to be diffi-
cult and unsatisfactory. In the first place it was necessary to
determine the coefficient of torsion of the silk fibre to be used
in the experiments. This fibre was about thirty inches long,
and before mounting had been boiled in a tube of water. A
copper disk, made up with a mirror so as to have about the
468 On the Measurement of High Specific Resistances.
same weight as nearly as possible as the astatic combination
to be examined, was suspended from the fibre in a vibration-
box furnished with a long glass tube. The copper ultimately
employed was supposed to be electrolytically pure. The
combination at first was slightly diamagnetic, but became
much less so as the paint-cement dried, and was finally almost
indifferent to any means we could find for testing it. From
experiments with this disk, whose weight and moment of
inertia were known, the coefficient of torsion of the fibre was
found to be T=:000115 C.G.S., with a load of :287 gram.
Two astatic combinations were next mounted and tested.
The first was the one that had already done some work in the
galvanometer, the second was carefully made for the purpose.
The moment of inertia of the first was found to be :02126,
and of the second (03274.
With both combinations two sorts of experiments were
made. The time of vibration of each was determined, and
the change of zero produced by twisting the upper end of the
fibre through a known angle, generally 27. From these
well-known methods it was found that the systems had a
period of vibration of about 2°51 seconds only. This corre-
sponded toa value for the moments of the forces of about
"1270. The magnitude of this number, as well as the positions
taken up by the combinations, showed not only that the asta-
ticism was far from perfect, but also indicated the cause of
this: the magnets were not really in one plane. Tentative
twisting of the aluminium wires was then resorted to, with
the result of bringing up the periods of vibration to 11 and
128 seconds respectively. In this latter case the moment
was reduced to ‘0064. ‘The needle that had been brought to
a free period of 11 seconds was mounted in the galvanometer,
and by means of the controlling magnet was brought to have
a period of 36 seconds, corresponding to a magnetic moment
of about ‘0007 C.G.S. During the experiments on resistance
the period was got considerably longer than 35 seconds.
The next paper, on the Resistance of Impure Sulphur,
contains the details of the method employed to find both the
specific resistance of the gums mentioned and of sulphur. As
no useful result is to be expected from a publication of the
long series of experimental numbers obtained in the work on
Gums, I refer to the following paper for the description of
the method employed, since it remained constant throughout.
a”
He 26%.
LV. On Measurements of the Resistance of Imperfectly
Purified Sulphur. By Prof. Richarp THRELFALL, and
Artruur Pottock, Esg.*
HE galvanometer having been brought to a state of
sensitiveness of 5 scale-divisions for 10~1! amperes, the
measurement of the resistance of the sample of sulphur in
question became a tolerably easy matter. The sulphur had
been supplied by Messrs. Hopkin and Wilhams as “ precipi-
tated, washed.” It looked clean when melted ; but on
examination turned out to have the following substances
existing as impurities : —
Calcium sulphate.
Ferric oxide.
Organic matter.
Dr. Helms, Demonstrator of Chemistry in the University of
Sydney, was kind enough to investigate a sample of this
sulphur with a view to discovering whether it contained
selenium ortellurium. The result of his examination of about
two hundred grammes of the substance was, that neither of
these substances was present in quantity large enough to be
detected. The examination was carried out by means of the
oxidation and sulphurous acid method; and also by the
cyanide method. We desire to express our thanks to Dr.
Helms. The importance of this result, so far as our work is
concerned, lies in the fact that it shows that pure sulphur
ean probably be obtained from the sample at hand by means
of distillation. The following measurements refer to the
unpurified sample ; the only substance existing in any con-
siderable quantity was calcium sulphate. The sample was
probably rather more pure than ordinary “roll” or flour
sulphur. The general arrangement of the apparatus will be
clear from the following diagram (p. 470).
By means of the key K, a current can be sent in either
direction through the resistance R and the galvanometer G.
The source of this current is a suitable number of small
Clark cells SC. The E.M.F.’s of these cells and of the large
one LC were watched during the experiments with the aid of
an auxiliary galvanometer and balance arrangement not
shown in the diagram. The key Ky allowed the upper metal
* Communicated by the Physical Society : read March 23, 1889.
470 Messrs. Threlfall and Pollock on Measurements
plate of the resistance arrangement to be put in communica-
tion with the last cell so as to charge up without allowing the
R WLMLLLZTLT LL)
current to rush through the galvanometer. After charging,
the connexions were altered so as to allow the current due
to the leak through the sulphur to pass through the gal-
vanometer. The H.M.F. of the small cells was not changed
by this amount of leaking, and the fall of the large cell was
measured at the time in the usual manner. The experiment
consisted in taking plugs out of the box 8 till the gal-
vanometer vave the same deflexion whether the current was
sent through it by the number of cells through the sulphur,
or by the adjustable fraction of the H.M.F. of the large cell
through a megohm. ‘The sum of the resistances of S and R
was always 10,000 legal ohms. The arrangement of the
observations was such that they interlocked in time.
The absolute value of the result, therefore, depends chiefly
on the value of the megohm. Respecting this standard I
wrote to Messrs. Elliott to inquire what degree of reliance
could be placed on it, and was informed in reply that it had
been tested against a standard in blocks of 100,000 ohms each,
and was right within the variation produced by one degree
of temperature. The wire was of German-silver. As the
present results are interesting only with respect to the
method and the resistances of the sample under varying
H.M.F.’s, the absolute value of the megohm is of com-
paratively small importance.
The following table gives the data of the experiments on
the resistance of the sulphur :—
ere
of the Resistance of Imperfectly Purified Sulphur. 471
|
Dat E.M.F. of large
ae Temperature | No. of small | E.M.F. of set | cell short-cir-
1888 of room. cells used. | of small cells. | cuited through
: 10,000 L. ohms.*
2 volts. | volts.
Oct; 20. ;). 17:0 C. 20 28°661 1°432
rh es NEOLC. 40 57312 1-432
7] ee 16:2 C. 40 57312 1°432
7) ee 16:2 C. 20 28 661 1°432
Date. Resistance | Thickness | Area of : ;
taken out | of layer of | layer of Roe oe lea
1888. of 8, | sulphur. | sulphur. epee ceoe aa a
L. ohms. | centim. | sq. centim.
Oct= 20 °... 90 0:05 189°8 8:°575 x 10! 1. ohms.
15°0 0:05 189°8 LO2BGSclOLs = =
rd] aw 10-7 0:05 189°8 £30710!
De 58 0:05 189°8 14-4 K LOR ag
* Lord Rayleigh has kindly pointed out to us that by a mistake in our method
of reduction we have slightly underestimated this value. The result will be that
the absolute value of the resistances as given are very slightly too large.
The following is a sample of the readings taken :—
Deflexion of Galvanometer with current from 20 Clark Cells
sent through the Sulphur.
Deflexion.
Double Zero from Observed
defiexion. deflexion. zero.
Right. Left.
Divs. of scale. Divisions. Divisions. Divisions. Divisions.
+60. +145 - 85 +102 +. 95
+50 +145 95 + 97 +100
+60 +148 88 +104 +100
+70 +150 80 +110 +100
+6) +143 78 +104 +100
+75 +150 75 +112 + 98
+68 +143 i) +107 + 98
+70 +135 65 +102 + 90
+40 +135 95 + 87 + 88
+60 +140 80 +100 + 85
+45 +133 88 + 89 + 8)
+35 +115 80 + 75 + 80
472 Resistance of Imperfectly Purified Sulphur.
Deflexion of Galvanometer with fraction of current from large
- Clark Cell.
: Defiexion.
pene? Double | Zero from | Observed
a ES deflexion. | deflexion. Zero.
Ores Right. Left.
Tae oheG Divisions of | Divisions of | Divisions | Divisions | Divisions
: seale. scale. of scale. of scale. of scale.
10 +55 +150 95 +103 +105
9 +60 +143 83 +101 +1038
9 +60 +145 85 +101 +103
8 +68 +140 72 +104 +103
8 +70 +140 70 +105 +103
9 +60 +145 85 +101 +100
8 +63 +130 67 + 96 + 90
9 +50 +133 83 + 91 + 90
9 +45 +130 95 +. 92 + 85
9 +35 +120 85 + 77 + 80
9 +35 +120 85 + 77 + 80
8 +40 +115 75 + 77 + 78
8 +40 +115 75 + 77 + 80
Rejecting those observations with the sulphur in which
the zero from the deflexions differs from the observed zero by
10. divisions and over, the mean double deflexion with a
current from 20 Clark cells sent through the sulphur is 85°5
divisions, and the mean deflexion with the current from the
large Clark cell when S=9 ohms is 85:9 divisions.
The difficulties which had to be met during these measure-
ments seemed to arise from what, following Mr. Bosanquet, we
at first called “ ghosts.”” These phantoms, however, seem to
have arisen from people opening and shutting doors with iron
locks ; as a general rule the galvanometer was got properly
sensitive overnight, and it was found that if on the following
morning the light-spot was where it had been left, then the
observations were practically successful ; if, on the other hand,
the light-spot had gone off the scale, then there was not much
use in going on. The disturbance of the fibre consequent
on restoring the old zero did not seem to wear itself out
under at least twelve hours. It is practically impossible to
et a galvanometer of this degree of sensitiveness to work
with a silk fibre, the zero being always on the move. In
order to get rid of air-currents the ventilators of the room
required to be covered up, and the well-made galvanometer-
case had to be enclosed in a cardboard box. The insulation
at first gave great trouble. It is necessary to support the
Fluorescence and Arrangement of Molecules. 473
wires on insulating stands of the paraffin-bottle form, the
cells, resistance-boxes, galvanometer, &c. on sheets of glass,
themselves resting on small cylinders of paraffin. The insula-
tion of the handles of the keys requires attention. Paraffin
keys are much better than ebonite ones.
In pushing the sensitiveness of the galvanometer beyond
this point, the following precautions should be observed be-
sides those already mentioned. The arrangement for sup-
porting the magnets should be quite independent of the
arrangement for supporting the suspension. The base of the
instrument should be of gun-metal and all the framework of
metal, The adjustments of the controlling magnets must be
capable of being made with extraordinary accuracy. The
mirror must be good enough to be used in a telescope. The
quartz fibre should be at least six feet long; it must be
cemented to its counexions with hard paraffin. The whole
apparatus should, we think, be placed in a thick soft iron
cylinder, but about this we are not sure. We are tolerably
certain, however, that it is in anybody’s power to construct a
galvanometer on these lines with a sensitiveness of 10-8
amperes per scale-division and a time of swing of about 40
seconds. Such an instrument, however, could only be used
in a tolerably non-magnetic building, and one steady enough
to be free from the vibration caused by people walking about.
Our best results were got at night and on Sundays, and this
in spite of the room having a concrete floor reposing on
twenty feet of broken stone and all the instruments being
supported on slate benches.
As to the results quoted, no discussion will be given here
as we are investigating pure samples of sulphur. It may,
however, be mentioned that the resistance depends con-
siderably on the time the current has been flowing, on the
electromotive force, and on the temperature.
LVI. On the Relation between Fluorescence and Arrangement
of Molecules. By B. WaAutTER*.
A is well known that the intensity of the fluorescent light
from solutions of many fluorescing materials at first
increases with the dilution and afterwards decreases again.
In order to understand this phenomenon rightly one must
conipare, for different degrees of concentration, as Stokes
* Communicated by the Author, and translated from the MS. by James
L. Howard, D.Sc.
A774 | B. Walter on the Relation between —
has already done, the ratios of the amounts of light emitted
by a given quantity of fluorescent substance to that absorbed
by it; since it is obviously upon these that the fluorescibility
depends. From theoretical considerations Stokes* showed
that in such solutions this quantity first increases with
the dilution and then finally becomes constant. Lommel,
on the contrary, in one of his numerous works on the theory
of fluorescence, has maintained that the fluorescibility, his
factor #, continually increases with increasing dilution f.
A. decisive answer to this question can only be obtained by
actual measurement of the quantities involved in it.
My first observations of this kind, which I began in the
winter 1887-8, and in which, for want of sunlight, the multi-
coloured light of a petroleum lamp served to excite the
fluorescence, could yield no decisive result on account of the
theoretical difficulty in making a comparative estimate of the
separate energies of fluorescence of different wave-lengths tf.
On account of this I determined to repeat the experiments
with homogeneous sunlight, for which the bright spring of
1888 offered a favourable opportunity. Experiment now
decided undeniably in favour of Stokes. At the same time, on
considering the special results of my measurements in con-
nexion with some phenomena previously only slightly noticed,
the cause of that remarkable behaviour of fluorescing solutions,
which Stokes has not explained, became evident.
The following notice is an abstract of my complete paper § :—
I. Measurements of the Fluorescibility.
As fluorescing substance ammonium fluorescein (more
shortly fluorescein) was taken in aqueous solution; and 23
different solutions of it were experimented upon, whose
degrees of concentration varied from 0:000001 to 40 per cent.
of salt. The exciting pencil of monochromatic sunlight was
obtained by throwing a spectrum on the screen A B by
means of a slit §,, the prism Pj, and the lens L,; then by
means of a second slit S, in the screen A B the desired rays
could be sifted out and rendered parallel again by a cylindrical
lens L,. But before this pencil of rays fell upon the solution
of fluorescein under investigation, and contained in the cell
G,, it had to pass through a fairly dilute solution of the same
* Stokes, Phil. Trans. 1852, p. 535.
+ Lommel, Pogg. Ann. clx. p. 76 (1877).
t Walter, Wied. Ann. xxxiv. p. 316 (1888).
§ Walter, Wied. Ann. xxxvi. p. 502 et seg. (1889).
Fluorescence and Arrangement of Molecules. 475
salt in the vessel G,, and the fluorescent light from the latter
served as the standard with which the intensities of light
from the 23 solutions mentioned above were compared.
With the fluorescent light emitted from G, and G, in all
directions there was mingled a comparatively large quantity
of light from the exciting pencil, scattered at the sides of the
vessels G, and G,; this had necessarily to be separated from
the fluorescent light itself. As this was only possible by a
spectroscopic method, the photometer chosen was that of
Vierordt (K), which is nothing more than a spectro-
scope with two slits, one immediately above the other, at S;.
In this case the slits were each covered with a totally reflect-
ing prism, so that one of them received light from the left,
the other from the right. Jn the figure only one of these
prisms can be shown. ‘These prisms received the fluorescent
light from the two vessels G, and G, respectively. After the
widths of the slits had been adjusted until they gave, on looking
through the eyepiece, spectra of the fluorescent light of equal
brilliancy, tlf ratio of these widths, which were measured by
micrometer-screws, gave directly the intensity of light from
the substance under examination in the vessel G,.
The ‘ fluorescibility,”” however, depends not only on the
intensity of the fluorescent light, but also on the quantity of
light absorbed ; and, moreover, it is evident that in the latter
term we must take into account the absorption of the
fluorescent light itself. Now there is a simple theory, for
which my original paper must be referred to, according
to which the fluorescibility 7, as given by the experiment, is
476 : B. Walter on the Relation berscen
obtained with sufficient accuracy by the formula
r
S= l—aa see: 30°?
in which IF is the intensity of the fluorescent light from Gg,
measured as stated above ; and the fractions a and a denote
the “ coefficients of transmission ” (Langley) of the fluorescent
light emerging from Gy, for the film of liquid in Gg. They
therefore express in what ratio the light incident on Gg is
weakened on emergence again. These coefficients were like-
wise determined by the Vierordt spectrophotometer, and thus
all the data requisite for the calculation of the fluorescibility
were obtained.
The following results were obtained :—
(1) The fluorescibility of very concentrated solutions of
fluorescein (from 40 per cent. down to about 3 per cent. of
salt) is zero, or at any rate very small; from this point it
suddenly increases very quickly as the solution is rendered
more dilute, the rate of increase being at first fairly uniform.
But from 5 per cent. downwards the increase becomes more
and more slow, and it ceases entirely when the solution con-
tains 0°02 per cent. of salt ; so that the fluorescibility remains
constant from this point onwards to the most dilute solutions,
the observations extending as far as a 0°000001 per cent.
solution.
(2) The alterations of the fluorescibility remain the same
whatever be the wave-length of the rays used to excite it;
in the experiments rays were used both below and above
those giving the maximum of absorption.
Alcoholic solutions of Magdala red of different degrees of
concentration showed the same fluctuations of fluorescibility,
except that in this case no solution could be obtained so con-
centrated that the fluorescibility became absolutely zero.
Il. Theoretical Deductions.
The fact that the fluorescibility remains constant in the
large number of solutions having a greater dilution than 0:02
per cent. must be regarded as the most important of the
results just stated ; for this means that under these circum-
stances the same quantity of substance always gives out the
same quantity of fluorescent light. This can lead to no other
theoretical conclusion than that the particles of fluorescein,
which give rise to the light, preserve the same constitution
unaltered throughout the whole of the range of dilution con-
sidered; and this conclusion agrees very well with the fact
Fluorescence and Arrangement of Molecules. A77
that the absorbing power of fluorescein also showed itself
constant throughout this range, whereas in stronger solutions
this was no longer the case. What is the cause then of the
irregularities in the fluorescibility and absorption in these
latter solutions? The second of the results stated above
points to the explanation. For since, according to it, the
fluorescibility alters in the same manner for all rays producing
the fluorescence, the decrease in this quantity in concentrated
solutions could hardly be produced by any mere weakening
of these waves (such as, for example, might be explained
by the fluorescein molecules being too crowded), for then
different wave-lengths would necessarily produce some
difference in the effect ; the explanation is rather to be sought
in the decrease in the number of those molecules by which
the fluorescence is set up. Fluorescein and similar com-
pounds must according to this view exist in solutions of
different degrees of concentration in at least two molecular
conditions, a fluorescing and a non-fluorescing one; and
indeed this hypothesis was soon placed beyond a doubt by
the discovery of avery remarkable phenomenon of fluorescence.
Before I describe this phenomenon I will, for the sake
of ease in referring to them, distinguish three grades of
solution of the bodies under consideration :-—
(1) Those in which only non-fluorescent groups of mole-
cules exist (Group solutions).
(2) Those in which these are gradually disintegrated and
pass into smaller fluorescing molecules (Transition solutions).
(3) Those in which this transition is completed (Perfect
solutions).
In perfect solutions we have, according to the above, to
deal only with molecules all having the same properties, which
for shortness I shall call “single”? molecules, and for which
this law holds good :—Every single molecule throughout the
whole range of dilution in which it preserves its single con-
dition absorbs always the same fraction of the quantity of light
falling upon it, and converts always the same fraction of the
absorbed energy into fluorescent light. But as soon as the
single molecules begin to arrange themselves in groups, as
is the case in transition solutions, the absorption becomes
quite irregular, and in the group the property of fluorescence
is entirely lost.
These and all statements in the latter part of this paper are
based upon the following phenomena. If a spectrum was
allowed to fall on a perfect solution of fluorescein or Magdala
red, one saw that each ray absorbed by it gave rise to a
corresponding quantity of fluorescent light; in transition
Pag. 3. o-1Vol 28. No. 175. Dec: 1889. -2N
478 B; Walter on the Relation hen wouae
solutions, on the contrary, a number of colours disappeared
by absorption in the liquid which gave no such light; and
indeed the production of fluorescence took place over exactly the
same range of wave-lengths as in the most concentrated of the
perfect solutions, while the absorption extended much further.
It follows clearly that in transition solutions also it is only
the single molecules which produce the fluorescence, and that
the portion of light absorbed by these solutions which does
not reappear as fluorescent light is taken up by the groups of
molecules. The fluorescibility of a transition solution must
therefore decrease with increasing concentration for three
reasons :—(1) because the number of single fluorescing mole-
cules is constantly getting reduced ; (2) because the groups
of molecules take up an ever-increasing proportion of that
light which can produce fluorescence ; and (#) because the
groups of molecules exert a constantly increasing absorbent
action upon the fluorescent light which is formed by the
single molecules still remaining. ‘This can be studied ex-
tremely well by observing the shrinking up of the band of
light at the less-refrangible end in the case of the spectrum of
fluorescent light, so that this alone affords a means of dis-
tinguishing at a single glance a perfect from a transition
solution.
Stated more exactly, the three laws deducible from the
above phenomena are the following :—
(1) In transition solutions there are present at the same
time both groups of molecules and single molecules; and as
the dilution increases the latter multiply at the expense of the
former.
(2) Only single molecules can give rise to fluorescent light,
not groups of molecules.
(3) The range of absorption by single molecules extends
between quite definite wave-lengtlis; groups of molecules on
the other hand absorb as a rule the neighbouring Be ts of the
spectrum as well.
The latter phenomenon was most striking in the case of
fluorescein and Magdala red ; for while the absorption spec-
trum of a very thick layer of a perfect solution ended quite
suddenly in the red with a sharp boundary, the absorption of
a transition solution, even when the absorbing layer con-
tained altogether less material, stretched beyond this boundary
and was gradually lost on the other side of it (between it and
the ultra-red). In the case of eosine no such difference was
found, so that in this compound the group absorbs hardly
any more rays than the single molecule.
These ideas were supported by another series of phenomena.
Fluorescence and Arrangement of Molecules. 479
The fluorescent light of transition solutions of fluorescein and
eosine increases in intensity considerably as their temperature
is raised, doubtless because warm water decomposes the
groups of molecules of these substances more easily than cold
water. In Magdala red the contrast is still greater; cold
water cannot decompose its groups of molecules at all, but
warm water effects the decomposition fairly easily. That
these phenomena cannot be ascribed to an increased freedom
of vibration, produced by the application of heat, is proved by
the alcoholic transition solutions of Magdala red, since in
them the fluorescibility decreased slightly on heating.
According to what has been said above this was rather a
proof that warm alcohol does not dissolve Magdala red so
easily as cold; and indeed a cold saturated solution of it
became turbid on heating, an indication that the solid sub-
stance was being deposited again.
A further circumstance which pointed to the existence in
transition solutions containing ammonium fluorescein of a
more complicated molecular arrangement than in perfect
solutions, was found in the fact that the former gave with
mineral acids an immediate dense precipitate ; the latter, on
the other hand, remained perfectly clear, and only after
several hours deposited fine crystalline needles of fluorescein
itself. Although it is generally not uncommon for a stronger
solution to yield a precipitate more quickly than a weaker
one under similar circumstances, yet the contrast is here so
great and the accompanying phenomena so remarkable that
one cannot refrain from bringing it into connexion with what
has already been stated with considerable certainty concern-
ing the differences in grouping of molecules.
Finally, concerning the non-fluorescent group-solutions of
fluorescein, it was noted that they all possessed a surface
colour, which became stronger with increasing concentration
but whose quality remained exactly the same ; even the solid
body itseli—of course not commercial acid fluorescein, but
ammonium fluorescein—possessed the same surface colour.
It is seen from this that fluorescein in its group-solutions
must still possess a stationary molecular condition, which
must be somewhat like that of the solid body. This theory
recelves great support from the circumstance, proved in a
later contribution*, that the index of refraction of these
solutions increases in the same ratio as the percentage
composition,
I cannot close this abstract without mentioning one obser-
* Walter, Wied. Ann. xxxviii. p. 117 (1889).
2N2
480 Dr. C. V. Burton on a Physical Basis
vation which has no direct connexion with the above, but
which may probably be of immense importance in the theory
of fluorescence, namely that fluorescein and its ammonium
salt, although they have quite different absorption spectra,
yet give out qualitatively exactly the same kind of fluorescent
light. We have then here, so to speak, two dissonant strings
of different materials ; and there is placed before us with
considerable emphasis this remarkable peculiarity of fluore-
scence as opposed to acoustic resonance, that the wave-length
of the light exciting the sympathetic vibrations is, within
certain fixed limits, of such slight importance.
Hamburg, Oct. 1889.
LVII. On a Physical Basis for the Theory of Errors.
By CHARLES V. Burton, D.Sc.*
1. ik deducing a law of error, two courses seem open to
us. We may make our assumptions as general as
possible, so that our results shall have the widest application,
and shall in the long run approach most nearly to the truth ;
or we may treat each separate case as a special problem in
probability, taking account of all that we know concerning
the actual conditions.
I shall here endeavour to illustrate the latter method i
means of some examples ; proceeding next to the resultant
law of error when two or more elements are combined which
are independently subject to error. The most advantageous
combination of fallible measures will then be shortly discussed,
and, finally, subjective or personal errors will be considered.
2. Suppose that we are given a series of numbers, known
correctly to any required number of places, and that from this
we write down the same series correct to four places. There
will be no uncertainty in the operation unless the digit in the
Sth place is 5, and all the remaining digits zero ; and (in
general) the chance of this occurring is indefinitely small.
The limits of possible error are obviously +:Q0C05, and all
errors between these limits are equally probable, unless from
our knowledge of the series we have a priori evidence to the
contrary. ‘The curve of error (as one may call it) is thus a
finite straight line A B (fig. 1), parallel to the axis of errors
LM, and bisected by the ordinate of no error, ON. If the
original table is carried only to (say) 5 places the case will
be somewhat changed. About 5), of the series of numer
will have 5 in the 5th place of decimals ; the remaining ,%
* Communicated by the Physical Society: read November 1, 1889.
for the Theory of Errors. 481
of the series will all be correct to 4 places, and will have
errors ranging uniformly between +°000045. Of the first-
Fig. 1.
A N B
GF fe) M
named 5/, of the series, half will have errors between +°000045
and +°000055, and half wili have errors between —-000045
and —-000055 ; the distribution between these limits being
uniform*., ‘The corresponding curve of error is given in fig. 2.
Fig. 2.
L | 0 M
3. A similar case is the following. Suppose we have to
record successive positions of an index upon a fixed scale,
which is graduated in centimetres, and that readings are to
be taken to the nearest centimetre. If our judgment were
infinitely acute, the errors would lie uniformly between +°5
centim. ; but in practice there will also be subjective errors,
the consideration of which is left to a later section (§ 10).
4. Next let us consider the error introduced by friction
into the equilibrium position of a movable index. Suppose
that the index has one degree of freedom, and that if friction
were removed its vibrations would be simple harmonic ; the
frictional coefficient being the same at rest and at all speeds.
During a half-swing—say to the right—there will be a con-
stant force (or a constant moment) of friction urging the
index to the left, and its motion during the half-swing will be
harmonic and in the same half-period as if friction were
absent, the only difference being that the mean position of
the half-swing lies somewhat more to the left. In the return
half-swing there will be the same half-period, the mean
position being equally displaced to the right. The amplitude
* That is, supposing that ‘00005 is added in the case of half of these
numbers, and subtracted in the case of the remaining half.
482 Dr. C. V. Burton on a Physical Basis
is thus decreased by the same amount at each half-swing,
until finally a half-swing leaves the index between the limiting
positions of friction, where it remains permanently at rest.
If the initial displacement (D) of the index was large com-
pared with the range of frictional error (+d), we may assign
the same probability to all displacements between D—2d and
D+2d; and since the final displacement differs from D by
an exact multiple of 2d, it immediately follows that all final
displacements between +d are equally probable, larger errors
being impossible. The curve of error will be like fig. 1.
If friction is greater when the index is at rest, the result is
rather curious. Let +d’ be the limits of equilibrium under
statical friction; then there will be equal probabilities of
errors between the limits 2d—d’ and —d’, and also between
—2d+d' and +d’. Ifd’ is <2d, these ranges of error over-
lap, and the curve of error is like fig. 8; if d’ is > 2d the
curve is like fig. 4; if d’=2d, we have simply fig. 5.
Fig. 3. Fig. 4.
Fig. 5.
These results are easily obtained by considering initial dis-
placements between the limits 4nd+d’ and 4(n+1)d+d’,
where z is an integer ; they refer of course to the actual, not
to the observed position- of the index. If, while the index
was In motion, three successive excursions were read (with
perfect accuracy), the inferred position of equilibrium would
only be subject to an error due to deviations from the assumed
laws of friction.
5. Now let a declination-needle which is to trace a con-
tinuous record be subject to frictional error. If the black
line in fig. 6 represent the true declination-curve, the curve
traced by the needle will be something like the dotted line.
Here the law of error depends on the (variable) friction of the
needle, and on the kind of changes which occur in the quantity
for the Theory of Errors. 483
measured ; it will further be influenced by the moment of
inertia of the needle.
Fig. 6.
6. Enough has now been said to show that the law of error
to be adopted depends in some measure on the nature of each
special case ; we may next consider how to find the law of
error when two or more fallible elements are combined. To
commence with, take two elements whose curves of error are
of the type of fig. 1, the limits of error being +m, and +m,
respectively. Inthe rectangle AC DB (fig. 7), let AO=O B
Fig. 7.
C 7 Q M D
=CM=MD = the unit of length; and let a particle be
chosen whose mass is numerically equal to m,. If this particle
be placed at O P to represent an actual error = m,O P, it is
evident that the wniform motion of the particle from A to B
represents the distribution of errors between the limits m,OA
and m,OB, that is, between +m,. The second source of error
may be similarly represented by a particle of mass mm, which
moves uniformly from C to D. Whenm, isat Pand m,at Q,
the resultant error will be m,OP + m MQ = (m,+m,)NS,
where § is the centre of mass of m, and mp.
To form the most general series of combinations, let mz.
move backwards and forwards very rapidly between C and D,
always with (numerically) the same velocity, while at the
same time m, moves uniformly and very slowly from A to B.
By following the movements of the mass-centre along HF,
we shall find the law of frequency of the resultant error.
Join PC, PD, cutting EF in G and H;; then while m, is
passing through P, the mass-centre is moving uniformly
between G and H ; and as m, moves from A to B, GH moves
484 Dr. C. V. Burton on a Physical Basis
‘uniformly from the position in which G coincides with H,
until H coincides with F. The chance of an error lying
between (m,+m.)# and (m,+mz,) (x +6x) is equal to
bx Fraction of its time of flight during (1)
GH which G H includes the element Sz. ae
In general the curve of error will take the form ABCD
(fig. 8); where AO = OD = unit length, and absciss are
Fig. 8.
A " 2
to be multiplied by the constant coefficient m,+m,. Ifm,=ma,
BC vanishes, B and C coinciding with N ; if m, and m, are
very unequal, BC preponderates, and AB, DC are nearly
vertical.
7. Next to combine two independent sources of error, each
following any known law. In the rectangle A B DC (fig. 9)
Fig. 9,
let AM=MB=CN=ND = unit of length. Let the nume-
rical maxima of the errors be m, and my, and the curves of
error ¥;=¢,(a,) or ALU, and ye=¢o(x2) or VK D. Fol-
for the Theory of Errors. 485
lowing the method of the previous section, let the mass m,
move very rapidly backwards and forwards between A and U
or between A and B, having at each point of its path a velocity
inversely proportional to the corresponding ordinate; (adding
U B to the path makes no difference, since the velocity in this
_ part would be infinite). Similarly let m, move from C to D
with a very small velocity, which follows a similar rule. First
of all let the mass m, be passing through R (NR=2,), so that
the second error has the value m2, ; also in fig. 9 let MT=a,
TY’ =62,, OS=a’, SS’=52’. Then the chance of a resultant
error between (m,+ mp)’ and (m+ mz) (2 + dx’) = the chance
that m, is moving between T and T’
= yOu, + area ALU.
ay a 1M 5 area ALU.
LS:
For simplicity, let the scale of ordinates be chosen so that the
area ALU = VKD = unity ; then the chance that R may lie
between x, and x2-+da.=Y>o dao.
Hence, taking both movements into account, the chance of
an error between (m,+m,)a/ and (m,+m,)(a# +dz’)
7 = dx
/ ? e
me Say Yo Ako 5
y, and yz being connected by the relation
MX + Mga =(M, + Mg) z’,
and the limits of integration being determined by
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