杏吧原创

Round and about

Question: While walking along a beach recently, I noticed that most of the
pebbles, whatever their size, tend to have an ellipsoidal shape, often
egg-shaped with two small axes of similar length, and sometimes flat, with all
of the axes different. Flat, round pebbles with two major axes the same are much
rarer, and spherical pebbles are very rare.

Is this related to the tendency of the waves to roll pebbles around and is
there some underlying mathematics that dictates the distribution of shapes and
the most common aspect ratios?

I would expect all pebbles to tend to the spherical, the shape which takes
the least energy to roll and to which particles will tend as their 鈥渃orners鈥� are
eroded. Or are all pebbles still on their way to becoming spherical?

Answer: Pebbles on a beach differ in shape and size simply because they have
different origins. Each pebble began as an angular fragment. The present shape
and size of the pebble depend on the shape and size of that original. In turn,
the shape and size of the fragment are controlled by the texture of the rock
from which it was broken.

Granites, in which crystals of quartz, feldspar and mica make a more or less
random texture, break into bits of roughly equal axes. Sandstones and
limestones, which usually have a layered texture, break into tabular slabs.
Shales and slates, which have a finer parallel texture, shatter into thin
sheets. The layers in some sedimentary rocks may also display a preferred
orientation of texture within the layer so that the two longer axes of a
fragment may differ to give a bladed shape.

Geologists distinguish between shape (for example spherical, tabular, bladed)
and roundness, which is the result of a softening of the corners and edges
during abrasion. When pebbles are bounced around in water they tend to maintain
their shape, reflecting their origins, but suffer a progressive increase in
roundness (but not an increase in sphericity).

Robin Bathurst

Ruthin, Denbighshire

Answer: Pebbles can be divided into three categories: those of roughly equal
length, width and thickness; those with two axes much longer than the other
(flat slabs); and those starting with an elliptical form.

On entering the sea, each type will undergo the same processes, turning the
first type into elliptical forms and the second type into flatter forms. Those
starting as ellipses will become more elliptical.

The mechanism causing this is essentially a single force鈥攖he
sea鈥攑ushing individual pebbles over the top of more pebbles. The steady
state of a rotating body will be about its major axis, so that the moment of
inertia is minimised.

In a roughly circular pebble, this causes abrasion along the major axis,
making the stone more elliptical in shape over time. In the case of the flat
stone, the easiest way that it can be rotated is about the axis perpendicular to
the flat sides. The abrasion between the bottom and side surfaces and the seabed
will tend to produce a flat, rounded pebble.

The reason spherical pebbles are rare is that these would only occur where
abrasion is equal on all of the surfaces if, say, a strong current moves a lot
of pebbles at the same time making them constantly roll over and into each other
(as in a ball mill).

Ben Ogborne

Westbury-sub-Mendip, Somerset

A natural ball mill might exist in the potholes mentioned
产别濒辞飞鈥抬诲

Answer: We have smooth, deep, cylindrical potholes in the sandstone beds of
local mountain streams. These produce smooth, well-rounded stones, sometimes
startlingly spherical. In contrast, stones in open stream beds take on smoothed
irregular shapes.

Jon Richfield

Dennesig, South Africa

Tongue torture

Question: Why do fizzy drinks produce the sensation they do? I鈥檝e heard that
they stimulate the pain receptors in the tongue.

Can it be true that when you drink a glass of sparkling water you are really
enjoying a form of low-intensity masochism?

Answer: Yes, it is true that the fizz produces a mild pain response. The
carbon dioxide in the bubbles forms a dilute acid on the tongue, another reason
that fizzy drinks are bad for the teeth, along with the ridiculous amount of
sugar in them.

Simon Scarle

Heanor, Derbyshire

Recent research confirms that carbonated drinks do stimulate pain
receptors in the tongue and cause mild pain signals to be transmitted to the
brain via the trigeminal nerve. The sensations arise when CO₂ dissolved in
a fizzy drink is converted by an enzyme in saliva to carbonic acid, a weak acid
that irritates the tongue. Those who enjoy the tingle of fizzy drinks might thus
indeed be enjoying a subtle form of masochism.

The alternative explanation, that CO₂ bubbles in fizzy drinks cause
their pleasant sensation by stimulating mechanoreceptors in the mouth as they
burst, now looks unlikely to be correct.

The key research has been carried out by Earl Carstens and his colleagues at
the University of California at Davis. Last year, we reported that these
researchers had found the origin of the fizz by studying a drug called
acetazolamide (New 杏吧原创, 19/26 December 1998, p5). The drug is used to
combat altitude sickness and has the unusual side-effect of dulling the tingle
from sparkling drinks, causing 鈥渃hampagne blues鈥�. They found that the drug works
by blocking the action of the enzyme in saliva that converts CO₂ to
carbonic acid鈥攊f there is no acid, there is no sensation. They then
confirmed that view by getting volunteers to drink fizzy drinks in a chamber of
the type used to decompress divers. In a high-pressure atmosphere, no bubbles
form in fizzy drinks, but there is still a pleasurable tingling sensation as if
the bubbles were there.

Now the same team of researchers has gone a step further (The Journal of
Neuroscience, 15 September 1999, p 8134) in experiments in which rats drank
carbonated water while measurements were made from nerves in their brains. These
experiments show that carbonated water causes increased activity in particular
areas of the trigeminal subnucleus caudalis, a relay station in the brain that
passes on pain signals from the tongue and mouth to higher centres. When the
rats were given dorzolamide, another drug that blocks the enzyme which converts
dissolved CO₂ to carbonic acid, there was no increase in neural
activity in this region, confirming that acid irritation causes the sensations
that pass to the brain鈥擡d.

This week鈥檚 question

Commuter conductor: As I waited for a train yesterday, I noticed that my
metal umbrella, resting on a damp patch of platform, tingled as I touched it.
The tingling stopped when I lifted the umbrella. Was this some kind of current
induced by the nearby overhead cables? Is it harmful?

Roger Nuttall

London