Friday, March 24, 2006

How things start out #1.

Wondering and discovering: Applying knowledge to practical problems
(NB.For details of availability of this article,
please contact Robert L Fielding –


Robert L. Fielding

Walking the hills around my home in the north of England as a boy of fourteen, I found myself wondering about my height above sea level compared with the height of the hills in front of me. I wanted to know how high I had to climb before reaching the top of the next hill.

I had a map, and I had found the hill in front of me on it. What I didn't always know was my exact position on the map, and so I didn't know how high I had to climb to reach the summit.

I walked up to the top anyway, but I always wondered how I could determine my height relative to my destination.

The hills around my home had strange and wonderful names. I can still remember them. Alphin, dark and massive, looking across Chew Valley at Alderman frowning back, two giant sworn enemies, and more gentle Noon Sun basking in the afternoon sunshine.

Further into the moor, names like Black Hill, Laddow Rocks, and Kinder Scout conjured up images in my young head. I still love those names.

Although their names intrigued me, it was their heights relative to me, or to each other that really fascinated me. Standing on Laddow Rocks, Black Hill several miles away looked much higher. Bleaklow Hill in the distance looked lower, and yet I knew from the map that it was quite a bit higher.

The television aerial on Holme Moss dominated that part of the skyline, and Crowdon Great Brook fell away from my feet.

On some days, the wind buffeted us about, and we had to find shelter among the rocks to eat our lunch in comfort.

Paper was easily blown away, and we knew not to leave litter anywhere. I wanted to make a gadget that would help me determine the height of each hill, but I knew it would have to be made of something more substantial than paper to withstand the blustery Pennine weather.

So, I set about making a sort of template from the only kind of material I had: cardboard. In the days before plastic bags, in the days before supermarkets, Clifford at the Co-op put the things my mother bought into cardboard boxes.
"Do you want a ride on the bacon-slicer before you go, lad?' he would say cheerfully.
I had to carry the groceries home. By the time we reached our front door, my arms were dropping off, as we used to say.

Mum emptied the box, putting the things she had bought into their proper places. Meat and dairy products went into a kind of meat safe that was always a bit cooler than the rest of the kitchen. Tinned stuff, of which there was very little, went into the pantry with the rest. Last of all, came the potatoes. These weren't new ones. New potatoes came from my father's allotment at the back of the house. These were old potatoes, and they were dusty and brown. It was my job to take out the spuds and put them where they wouldn't get damp. My father had made some shelves with spaces between them so that the air could circulate and keep them dry.

When I had carefully placed each potato so that it wasn't touching another potato, I turned the box upside down to empty the dust and the dirt.

Sometimes, the boxes would be so dirty that they were only good for making compost to grow more potatoes, but sometimes they were practically spotless on the outside, and I used one such side to make my template. I had to make sure it was absolutely clean, otherwise I couldn't bring it back into the house. This particular day I had a nice flat piece that was clean and it wasn't creased either. It was perfect. I cut it from the rest of the box with a sharp knife my mother used to cut up vegetables. The knife was dry and it was clean. I made the cut and then used my mother's best scissors to clean up the edges.

I had a square of good, clean, stiff cardboard to work on. The next thing I had to do was to work out what I wanted to draw on it. I knew from my arithmetic teacher that a circle could be divided into 360 degrees, so a semi circle had to have 180 degrees. The semi circle I wanted to draw had to be no bigger than my pair of compasses could stretch to. They would open to about a five inch maximum. They were quite big.

I drew myself a semi circle with a base line ten inches long. Now I had to divide it up into degrees. I had to decide how many degrees between each division. I decided upon ten degrees.

This was my way of finding out how to calculate the height of the next hill. I knew a little about trigonometry, and although I didn't like it very much whenever I had to do it at school, I knew enough to be able to use what I knew to construct this template.

I divided the semi circle up into 10 degree sectors, and then used the other side of the cardboard to construct a table of numbers: distances in miles, height in feet, one for every angle on my template.

It was a bit difficult and took up all my time that evening, and the next.
I remember bedtime coming up quickly on those evenings.

I did finish it though, and showed it to my Mum and Dad. They both smiled at it as I showed them how it worked. I explained about sines, cosines and tangents. How you could find the unknown length of the side of a right angled triangle if you had either the lengths of the two other sides or one length and one angle. At least that's how I remember it.

I remember that I wrote the values down from my little red book of mathematical tables, which included trig ratios and values. At least that is what I can recall now.

After the longest week, I took my gadget, as my Dad called it, up onto the moor. I remember that it was a bit misty as it could often be that high up, about 1,700 feet above sea level, and facing the prevailing weather from the Atlantic Ocean via the Irish Sea. Anyway, visibility wasn't perfect, but the cloud cover was patchy, and every now and then a corner of clear blue sky would appear, a bright patch from the quilted autumn sky.

The brief window was enough to try the thing out. I took it out of my rucksack, and my friend, John held it steady for me as I lined it up with Pule Hill about four miles away. I got John to stand back a little to tell me if I was holding the thing level or not. I adjusted it and then took a reading. In fact, it was really quite difficult to do that, to take a reading in the wind, wondering whether the thing was really level or not. I took the reading and then we sat down in the heather and entered the numbers we had in our little notebooks. We had both made charts, with ruled lines to make it easier to enter the numbers.

We worked out that Pule Hill was either higher than Mount Everest, I think, or something ridiculous like that. We were both a bit disappointed, but laughed at our results too. There were problems with the device. We knew that. We had known that before we set out, but like the lads we were, we tried to ignore them, and convinced ourselves that they wouldn't make any difference.

Back home, I did try to think how it could be improved. I thought it might need my Dad's old spirit level sellotaping to the bottom, but I didn't dare take his tools up onto the hills. We could have done something with a pop-bottle half full of water, John said, but we both knew that it would make the thing too cumbersome and clumsy, so we didn't try it. It was a good idea but it had its faults. However, the principles behind it were sound, we both agreed.

I still have that bit of cardboard somewhere at my parents' house, and I take it out and look at it sometimes. Looking at the markings on the front, the tables and numbers on the back, and reading my junior version of my handwriting, much clearer than today's scribble, I remember that tall gangly lad I must have been. I remembered my freckle faced pal John, now a surveyor for an oil company somewhere, and I am grateful for those days, for that bit of cardboard, for the hills, the heather and the wind and rain, and most of all for the making of who I am now, up there with the wind in my face, and an idea in my head.

Robert L. Fielding


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