Perhaps this quote might help, Jim. ;-)
There was an interesting incident occurred whilst we were making density
measurements, an incident which illustrates two aspects of research which were
later to become very important, the possibility of conceptual inversion and the
psychological difficulty such inversion inculcated.
To find the density of a piece of material one needs to measure two quantities.
The weight of the material – straightforward enough, just stick it on a balance
– and the volume of a material.
Finding the volume of a material is easy enough when the material is a nice
simple shape like a cube or a cylinder; you just make measurements and use the
appropriate mathematical formula.
When the material is irregular, like a roughly hacked piece of soil cement or a
king’s crown then there’s more of a problem as Archimedes realised. The
solution which came to him in his bath and led to him shouting Eureka and
running through the streets naked (allegedly) has never been improved upon and
it is his method, more specifically its inverse, which we used to find the
volume of our soil-cement pieces.
Nowadays Archimedes’ discovery is normally expressed in the form,
“The loss of weight in water is equal to the volume of water displaced.�
Strictly speaking, the loss of weight in water is equal to the weight of water
displaced but since 1 cc of water weighs one gram more or less, one of the
more useful features about the metric system, we can jump directly from loss of
weight to volume.
Using this principle then the volume of a lump of stuff can be measured by
hanging it by a thin thread from one arm of a lever balance to measure its
weight and then letting out the thread until it is immersed in a beaker of
water when its weight is again measured.
The original weight is its weight. The loss in weight is its volume. So the
original weight divided by the loss in weight is its density.
The Concrete Division were using just such a system for measuring the density
gradients of core slices cut from concrete roads. Because we didn’t have a
suitable lever balance we thought we would be clever and do it slightly
differently. Using a pan balance we measure not the loss in the weight of the
specimen but the gain in the weight of the water when we hung a specimen in the
water.
On day our Division Head was walking through the lab and he happened to see me
holding one end of the piece of cotton and calling out the scale readings to my
colleague. He stood and watched for a while looking puzzled.
“What are you doing Grimer?�
“I’m measuring the volume of these soil-cement slices, sir.�
“But the volume is equal to the loss in weight of the specimen. You are
holding the end of the string. How can you measure the loss in weight like
that.�
“I’m not measuring the loss in weight of the specimen, sir. I’m
measuring the gain in weight of the water.�
“Are you sure you can do that, Grimer?�
His incredulity was so palpable that I almost started having doubts myself. It
was like when your wife asks you for the third time if you turned the gas off
when you left.
“Pretty sure. After all, the weight has to go somewhere, doesn't it! It can’t just disappear.�
He walked slowly away looking very unconvinced. In retrospect I can’t
really blame him. When all your life you have been used to seeing a thing done
one way, its very difficult to accept that it can also be done in completely
the opposite way. Standing there holding one end of a thread with the specimen
dangling in a beaker of water at the other it must have seemed as though I was
engaged in some mystic rite of pendulum divination.
