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Experiment 2 was made with the same object as Experiment 1. A gold-
leaf electrometer was charged so that the leaves stood open, and then a cloud
was made to pass by the insulated leaves. As the cloud passed they were
both attracted. This experiment was attended with considerable difficulty,
as the moisture from the steam seemed to get on to the glass shade over
the gold leaves, and so form a charged conductor between the leaves and
cloud. The cloud was first formed by a jet of steam from a pipe, then by
the vapour from a vessel of boiling water, and lastly by a smoke ring or
rather a steam ring. By this latter method an insulated cloud was formed,
which as it passed was attracted by the charged leaf.

Of the two latter propositions I have not been able to obtain any
experimental proof. I made an attempt, but failed, through the bursting
of the vessel in which the cloud was to be formed. I hope, however, shortly
to be able to renew the attempt, and in the meantime I will take it for
granted that these propositions are. true. Faraday maintained that evapo-
ration was not attended by electrical separation unless the vapour was
driven against some solid, when the friction of the particles of water gave
rise to electricity. So that unless there were some free electricity in the
steam or vapour before it was condensed, none could be produced by the
condensation, and hence the cloud when formed would be uncharged.

In the same way with regard to evaporation, unless, as is very improbable,
the steam, into which the water is turned, retains the electricity which was
previously in the condensed vapour, the electricity from that part of the
cloud which evaporates must be left to increase the tension of the remainder.
So that, as a charged cloud is diminished by evaporation, the tension of the
charge will increase, although the charge remains the same.

I will now point out what I think to be the bearing which these pro-
positions have on the explanation of thunder storms. In doing this, I am
met with a great difficulty, namely, ignorance of what actually goes on in
a thunder storm. We seem to have no knowledge of any laws relating to
these every-day phenomena; in fact we are where Franklin left us we
know that lightning is electricity, and that is all.

It is not, I think, decided whether the storm is incidental on the
electrical disturbance or vice versa, i.e., whether the electricity causes the
clouds and storm or is a mere attendant on them. Nor can I ascertain
that there is any certain information as to whether, when the discharge
is between the earth and the clouds, the clouds are positive and the earth
negative, or vice versa. Such information as I can get appears to point
out the following law : that in the case of a fresh-formed storm, the cloud
is negative and the earth positive; whereas, in other cases, the cloud is
positive and the earth negative.



32 ON THE ELECTRICAL PROPERTIES OF CLOUDS [5

Again, thunder storms move without wind, or independently of wind ;
but I am not aware whether any law connecting this motion with the
time of day, &c., has ever been observed, though it seems natural that,
however complicated by wind and other circumstance, some such law must
exist. In this state of ignorance of what the phenomena of thunder really
are, it is no good attempting to explain them. What I shall do, therefore,
is to show how the inductive action of the Sun would necessarily cause
certain clouds to be thunder clouds in a manner closely resembling, and for
all we know identical with, actual thunder storms.

In doing this I assume that the thunder is only an attendant on the
storm, and not the cause of it ; and that many of the phenomena, such as
forked and sheet lightning, are the result of different states of dampness
of the air, and different densities in the clouds, and really indicate nothing
as to the cause of electricity. In the same way, the periodicity of the
storms is referred to the periodical recurrence of certain states of dryness
in the atmosphere. Thus the fact that there is no thunder in winter is
assumed to be owing to the dampness of the air, which allows the electricity
to pass from and to the clouds quietly. What I wish to do, is to explain
the cause of a cloud being at certain times in a different state of electric
excitation to the earth and other clouds, and of this difference being some-
times on the positive side and sometimes on the negative, that is to say,
why a cloud should sometimes appear to us on the earth to be positively
charged, sometimes negatively, and at others not to be charged at all.

The assumed condition of the sun and earth may be represented by two
conductors S and E acting on one another by induction, the sun being
negative and the earth positive. The distance between these bodies is so
great that the inductive action would not be confined to those parts which
are opposed, but would in a greater or less degree extend all over their
surfaces, though it would still be greater on that side of E which is opposite
to S than on the other side.

The conductor E must be surrounded by an imperfectly insulating
medium to represent damp air. The formation of a cloud may then be
represented by the introduction of a conductor C near to the surface of E.
Such a conductor, at first having no charge, would attract the positive elec-
tricity in E, and appear by reference to E to be negatively charged. If it
was near enough to E, a spark would at once pass, which would represent
a flash of forked lightning. If it were not near enough for this it would
obtain a charge through the imperfect insulation of the medium. Such a
charge might pass quietly or by the electric brush. When the cloud had
obtained a charge it would not exert any influence on the earth, unless it
altered its position. But if the heat of the sun caused part of the cloud



5] AND THE PHENOMENA OF THUNDER STORMS. 33

to evaporate, the remainder would be surcharged and appear positive. Or
if G approached E then G would be overcharged, and a part of its electricity
would return, and on its return it might cause positive lightning. Thus,
suppose that, after a cloud had obtained its charge, part of it came down
suddenly in the form of rain. As the rain came lower, its electrical tension
would increase, until it got near enough to the ground to relieve itself with
a flash of lightning, almost immediately after which the first rain would
reach the ground. It has often been noticed that something like this often
takes place ; it often begins to pour immediately after a flash of lightning,
so much so that it seems that the electricity had been holding the rain up,
and it was only after the discharge that it could fall. This, however, cannot
be the case, for the rain often follows so quickly after the flash, that there
would not have been time for it to fall from the cloud, unless it had started
before the discharge took place. If on the other hand G receded from E,
it would again be in a position to accept more electricity, or would again
become negative. In this way, a cloud in forming, or when first formed,
would appear negatively charged ; soon after it would become neutral, and
then if it moved to or from the earth it would appear positively or
negatively charged.

If the air was very dry, as it is in the summer, any exchange of electricity
between the earth and the cloud would cause forked lightning, in the winter
it would take place quietly, by the conduction of the moist atmosphere.

In this way then there would sometimes be positive, sometimes negative
lightning ; sometimes the discharge would be a forked flash or spark, some-
times a brush or sheet lightning. And if clouds are formed in several
layers, as would be represented by another conductor D outside G, then in
addition to the phenomena already mentioned, similar phenomena would
take place between G and D ; and if in addition to this we were to assume
that there are other clouds in the neighbourhood, the phenomena might be
complicated to any extent.

And if, further, the motion of the sun is taken into account, as the
conductor $ moves round E the charges in D and E would vary, accordingly
as they were more or less between S and E and directly under the induction
of 8 ; i.e., the charge in a cloud would appear to change owing to the motion
of the sun ; thus a cloud that appeared neutral at midday would, if it did
not receive or give off any electricity, become charged positively in the
evening.

With regard to the independent motion of the clouds, there are several

causes which would affect it. For instance, a cloud whether it appeared on

the earth to be negatively or positively charged would always tend to follow

the sun, though it is possible this tendency might be very slight. Again,

o. B. <*



34 ON THE ELECTRICAL PROPERTIES OF CLOUDS, ETC. [5

one cloud would attract or repel another, according as they were charged
with the opposite or the same electricities ; and in the same way a cloud
would be attracted or repelled by a hill, according to the nature of their
respective charges.

Such, then, would be some of the more apparent phenomena under the
assumed conditions. So far as I can see they agree well with the general
appearance of what actually takes place, but, as I have previously said, the
laws relating to thunder storms are not sufficiently known to warrant me
in doing more than suggesting this as a probable explanation.

In these remarks I have said nothing whatever about what is called
atmospheric electricity, or the apparent increase of positive tension as we
proceed away from the surface of the earth. I do not think that this has
much to do with thunder storms. If the law is established it seems to
me that it will require some explanation, besides merely that of the solar
induction acting through the earth's atmosphere on to the surface of the
earth. It would rather imply that the sun acts on some electricity in the
higher regions of the earth's atmosphere, and that electricity in these regions
acts again on the surface of the earth ; but, however this may be, the effect
of the assumptions described in this paper would be much the same.



6.



ON THE RELATIVE WORK SPENT IN FRICTION IN GIVING
ROTATION TO SHOT FROM GUNS RIFLED WITH AN
INCREASING, AND A UNIFORM TWIST.

[From the Thirteenth Volume of the " Proceedings of the Literary and
Philosophical Society of Manchester." Session 1873-4.]

(Read October 21, 1873.)

THE object of this paper is to show that the friction between the studs
and the grooves, necessary to give rotation to the shot, consumes more work
with an increasing than with a uniform, twist; and that in the case of grooves
which develope into parabolas, such as those used in the Woolwich guns, the
waste from this cause is double what it would be if the twist was uniform. I am
not aware that this fact has ever been noticed. It must not be confounded
with the questions already at issue respecting the Woolwich or French
system of rifling guns. The advocates of the gradually increasing twist,
maintain that it relieves the pressure between the studs and the grooves at
the breech of the gun, where it would otherwise be greatest, while the
opponents argue that in order to obtain this otherwise advantageous result,
the bearing surface of the studs has to be so much reduced, that they are not
so well able to withstand the reduced pressure, as they are to withstand the
full pressure with the plane grooves. Now 1 bring forward a collateral point,
which has no bearing on the previous question, but which is, in itself, of
sufficient importance to influence the decision in favour of one or other of
these systems. I show that apart from any undue wedging or shearing of the
studs, that with nothing but the legitimate friction, the amount of work
wasted in imparting rotation to the shot is nearly twice as great with the
parabolic as with the plane grooves. This is important, for, although the
magnitude of this waste does not appear as yet to have been the subject
of direct inquiry, it will be seen from what follows, that with the plane

32



36 ON THE WORK SPENT IN FRICTION ON GUNS [6

grooves it amounts to more than one per cent, of the whole energy of the
shot, and, consequently, with the parabolic grooves it will amount to two
per cent, of the energy of the shot; this is, to say the least, important
as regards the effect of the discharge; and when we consider that all the
work spent in friction is spent in destroying the gun and the shot, we
see that it becomes a matter of the very greatest importance whether
the gun spends one, or two per cent, of its power, on self- destruction. It was
established as a fact in the trials of 1863-5, that the guns with an increasing
twist gave a lower velocity than those with the uniform twist. In the trial
with the two seven-inch guns made especially to test this point, the differ-
ence of velocity was such as to make three per cent, difference in the
energy of discharge a result somewhat greater than what would have been
due to the legitimate friction, unless the coefficient of friction between
the studs and the grooves was excessively high from some cause, such as the
cutting of the studs into the grooves. However, it would seem that the
conclusions at which I have arrived are in accordance with actual experience,
and help to explain what was otherwise to a certain extent anomalous.

Although these conclusions cannot be definitely proved without the aid
of mathematics, they may be shown to be true (or reasonable) under certain
circumstances, as follows :

The work spent in friction will, both with the parabolic and plane
grooves, be equal to the coefficient of friction multiplied by the mean
pressure on the studs, and again by the length of the grooves (or by the
length of the gun nearly). Now, the coefficient of friction and the length
of the gun are the same in both cases ; hence this work will be proportional
to the mean pressure on the grooves throughout the gun. Again, if the
pressure on the parabolic grooves is constant (which it is the object of these
grooves to make it), then the mean pressure in both cases will be inversely
proportional to the angle which the shot turns through while in the gun.
This follows directly from the fact that the speed, and consequently the
energy of rotation with which the shot leaves the gun, is the same in both
cases ; for this energy is nearly equal to the mean pressure multiplied by the
arc through which the studs turn*, and hence the mean pressure is equal to
the energy divided by the arc.

We have then the work spent in friction proportional to the mean
pressure ; and the mean pressure inversely proportional to the angle turned
through by the shot in the gun ; therefore the work spent in friction is
inversely proportional to the angle turned through by the shot in the gun.

Now, the angle turned through with parabolic grooves is half the angle

* This is always true for plane grooves, but it will only be true for parabolic grooves when the
pressure on the studs is constant all along the grooves.



6] RIFLED WITH AN INCREASING, AND WITH A UNIFORM TWIST. 37

turned through with plane grooves (by a property of the parabola) ; hence
the work spent in friction with the parabolic grooves, is double what it is
with the plane grooves. This may be shown mathematically as follows :

I. To estimate the actual work spent in friction with plane grooves.

Let (j, coefficient of friction.

i = the inclination of the grooves.
K = the work spent in friction.

E = the energy of discharge or the striking force with which the
shot leaves the gun.

Then, K = ~ x E.

For if R = the mean pressure on the grooves, I = the length of the gun,
then



i^' .............................. (1).

And the energy of rotation



2 7?

- t L=li .............................. (2),



-



Hence (with a gun making one turn in 35 diameters) where i ' = y-r and



lit

The equation K = ~r E shows, what is otherwise quite obvious, that with

25

the plane grooves, the work spent in friction is independent of the dis-
tribution of the pressure within the gun, and is proportional only to the
energy of discharge ; and hence will be the same, whether the powder is
quick or slow, provided the shot leave with the same velocities.

This, however, is not the case with the parabolic grooves. It is obvious
that the friction will involve the law of pressure in the gun. Consequently,
we cannot calculate this work unless we make some assumption with regard
to the law of pressure.



38 ON THE WORK SPENT IN FRICTION ON GUNS [6

II. To estimate the actual work spent in friction with parabolic grooves
when the pressure on the studs is constant.

Let x = |- be the equation to the developed grooves, and let s be the
length of the grooves. Then, if we assume that -j-=- 1, and that K b (the



work spent in friction with the parabolic grooves) = pRl, we. have the
work of rotation



26/i

z
And the work of rotation



f ,-, dx ,

=\ R T y d y

7

K b .



=- .

Z



Since i ' = T



And for plane grooves



An expression for this work might have been obtained without assuming
-/ = 1, but so long as i is less than r-x the difference is very small

Hence we see that on this assumption the work spent in friction with
the parabolic grooves is twice as great as with the plane grooves. This
assumption is not an unreasonable one, for the declared object of the
increasing twist is that it may equalise the pressure of the studs on the
grooves throughout the gun. However, it is not to be supposed that this
object is always attained, for one kind of powder has a different law of force
from another. It is necessary therefore to consider other laws of force.
We cannot obtain a general expression which will include all, but we may
examine several laws of force, which will enable us to see how far the law
of force affects the results.



In all cases the force diminishes from the breech to the muzzle, and the
law may be roughly expressed by P = where y is the distance of the
shot from the breech, and a and X are constants for each class of powder.



6] RIFLED WITH AN INCREASING, AND WITH A UNIFORM TWIST. 39

Although with this value of P the equations of motion cannot be solved
rigorously, an approximate solution may be found as follows :

III. To find the ratio of work spent in friction with parabolic and plane
grooves when the law of force is



a + y

The equations of motion are



Neglecting the pR as small in (1), and taking p (the radius of curvature)

= b, we have if ~r = 1
as



2A, , a + y
T log



~TT I T> 7 M/V I / . . *

or K b = u,\ Rdy = ~ { (21, + a) log



fl t*

And for plane grooves p is infinite and , =i,



.. K = p, I jRc??/ = /u,Xt log ,
J a



a 1

7



i

log



If a = so that P = - ,

y



If a is very great, so that P = -



_
K ~2'

And the former law more nearly expresses the condition of most guns.



40 ON THE WORK SPENT IN FRICTION ON GUNS, ETC. [6

IV. If we take a law of force,

p= e ~^ iAnl *
the equations of motion can be solved.

And if i = r , = tan" 1 i.

o



We get K b = Y- [e* e - 1 - 2/a0 + ^ log (1

And for the plane curve



And therefore

log(l



From which, for any given value of 6, we may obtain the actual value
c Kb

Ofy.

When is small, so that we may neglect high powers without error,

*'<
# 2*

Which result is in exact accordance with those previously obtained, for,
it must be noticed, that with this law P is nearly constant. Hence we
arrive at the following conclusions:

(1) That when the pressure of the powder is constant,

Work spent in friction with parabolic grooves _ 3
Work spent in friction with plane grooves 2 '

(2) That when the pressure diminishes rapidly the above ratio = 2.

(3) That this ratio may have any values between these two, but that
it cannot go beyond these limits.



7.



ON THE BURSTING OF TREES AND OBJECTS
STRUCK BY LIGHTNING.



[From the Thirteenth Volume of the " Proceedings of the Literary and
Philosophical Society of Manchester." Session 1873-4.]

(Read November 4, 1873.)

THE results of the experiments referred to in this paper were exhibited
to the meeting.

The suggestion thrown out by Mr J. Baxendell at our last meeting
that the explosive effect of lightning is due to the conversion of moisture
into steam seemed to me to be so very probable that I was induced to try
if I could not produce a similar effect experimentally.

1. I first of all tried to burst a thin slip of wood by discharging a jar
through it, taking care so to arrange the wood that the discharge should be
of the nature of a spark, and not a continuous discharge ; this was done by
making the wood to form part of a discharging rod with balls on the ends.

This experiment was successful in the first attempt, although the results
were on a small scale.

It should be mentioned that the wood had been damped with water.

This experiment was repeated with larger pieces of wood with various
results.

2. It then occurred to me to try with a glass tube. This I did at
first with a very small tube, passing wires from the ends of the tube until
they were within ^ inch of each other.

The small tubes burst both with and without water.



42 ON THE BURSTING OF TREES AND OBJECTS STRUCK BY LIGHTNING. [7

3. I then used a larger tube (about ^ inch bore) in a similar manner.
The discharge without water produced no effect on this, even when repeated
several times, but when the tube was full of water (with the ends open)
the first discharge shattered that part of the tube opposite the gap in
the wire. This tube was bent in the form of a syphon, and the water stood
about 1 inch beyond the gap in the wire, on each side of it.

4. I then tried a stronger tube which I had been using for insulation.
It had a bore of ^ inch and was f inch in external diameter. It was capable
of sustaining a pressure of probably 10,000, and certainly 5,000 Ibs. on the
square inch, that is to say, a pressure from 2 to 5 tons per square inch.
It was about 14 inches long and bent in the form of a square-ended siphon.
The gap in the wire was about ^ inch, and the water extended about
1^ inches on each side of the gap. The ends of the pipe were open, and
the jar charged in the same manner as before, with about 100 turns of a
12 inch plate machine. The surface of the jar is about \ a square foot,
and the discharge, when effected with the common rod, took place through
about 2 inches of air.

This tube was shivered at the first discharge. That part opposite the
gap, and for some way beyond, is completely broken up into fragments, which
present more the appearance of having been crushed by a hammer, than
of being the fragments of a pipe burst under pressure. Some of the
fragments show that the interior of the pipe has been reduced to powder.

These fragments were scattered to some feet on all sides, but there was
nothing like an explosion. I held the pipe in my hand at the time of the
discharges, and the sensation was that of a dead blow. There was no noise
beyond the ordinary crack of the discharge.

The manner in which this pipe was destroyed clearly showed that a
larger one might have been broken. But as it was two o'clock and my fire
was out, I did not continue the experiments.

It is not easy to conceive the precise way in which a pressure of probably
more than 1,000 atmospheres could be produced and transmitted in a pipe of
water the ends of which were open. It might have been caused by the
sudden formation of a very minute quantity of steam, or by the expansion of
the water ; but whichever way it was, its effect was due to its instantaneous
character, otherwise there would have been an explosion.

When we consider the great strength of this pipe (which might have
been used for a gun without bursting), and when we see that it was not only
burst but that the interior of the glass was actually crushed by the pressure,
and all this by the discharge of one small jar, we must cease to wonder at
the bursting power of a discharge from the clouds.



7 A.



ON THE DESTRUCTION OF SOUND BY FOG AND THE
INERTNESS OF A HETEROGENEOUS FLUID.



[From the Thirteenth Volume of the " Proceedings of the Literary and
Philosophical Society of Manchester." Session 1873-4.]

(Head December 16, 1873.)

1. THAT sound does not readily penetrate a fog is a matter of common
observation. The bells and horns of ships are not heard so far during a
fog as when the air is clear. In a London fog the noise of the wheels
is much diminished, so that they seem to be at a distance when they are



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