An amusing incident early in my research career illustrates the kind of cognitive dissonance resulting from inverting one's view of things such as material strength.
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To find the density of a piece of material one needs to measure two quantities. Its weight and its volume.
Finding the volume of a material is easy enough when the material is a simple shape; you just measure and use the appropriate maths formula.
When the material is irregular, like a roughly hacked piece of soil cement or a king’s crown, then there’s a problem as Archimedes realised. It is his method, or rather the inverse, which we used to find the volume of our soil-cement samples.
Archimedes’ discovery is often expressed as,
“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 we can jump directly from loss of weight to volume.
Using this principle 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 Soils didn’t have a suitable lever balance we thought we'd be smart and do it differently. Using a pan balance we measured, not the loss in the weight of the specimen, but the gain in the weight of the water.
............
One day our Division Head, Dr.Maclean, was walking through the lab and he happened to see me holding one end of the thread 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 samples, sir.”
..........“But the volume is equal to the loss in weight of the specimen. You are
...........holding the end of the thread. 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 the completely opposite way. Standing there holding one end of the 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.
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