with amendments suggested by Sarah Hill

The first considerations for survival must be those of obtaining adequate food, shelter and warmth. It may well be that these can only be obtained with certainty by travelling to a more favourable environment and one where the chances of rescue are improved. To be able to travel back to camp after a foray in search of food without getting lost is also a necessity. The navigation and the measurement involved can be achieved with no other instruments than those that can be made from natural materials. If our predecessors were able to survey their surroundings, navigate for long distances, measure the size of the earth, the size and distance of the moon and sun by the use of primitive instruments, keen observation, and a clear understanding, then we ought to be able to do likewise. Mental survival is as important as bodily survival. It can be obtained by occupying the mind with a succession of soluble problems which bring the satisfaction of achievement at the end of each. The following shows what can be done with just sticks, stones and some sun.

I was on the stony shore of a bay at the edge of what was probably a lake whose ends were obscured by rocky points falling steeply into the water with pine trees clinging to the upper rocks. Pine woods also backed the bay but on a gentler slope. Although the sun was shining, it only fell at the extreme left of the bay. Where I was felt damp and chill. A little exploring was necessary. I walked away from the sunny end of the bay, noting that the shore became sandier and less stony as I progressed. On reaching the rocks, I looked to see if they could be skirted where they dipped into the water but they dipped too steeply. Judging the depth of the water to be over 6ft within a foot of the shore, I climbed. The surface was so broken that the climb to the top of the ridge was easy. I was now in full sun and it was pleasantly warm. At the crest of the ridge, the view was still obscured by the pines. The ground there was dangerous: jumbled rocks from 1 to 6ft in size, covered in moss and with the cracks disguised with ferns. It would be easy to break a leg there. I proceeded with the utmost caution.

On the far side of the ridge the lake again came into view. It ran straight from where I stood although it looked as if the shore was indented with bays like the one that I had left. The opposite shore seemed to be parallel to this and about half a mile away and it also seemed to be sunnier.

The exercise had cleared my mind and so I sat down on the edge of a rock in the sun and considered what had to be done. I had sufficient food, so my first priority was to find shelter, preferably in the sun, and the next to find out where I was.

I retraced my steps, this time paying more attention to my surroundings. The plants seemed familiar. The ferns looked very like the Male fern and the Lady fern. The trees were certainly pine but whether Scots or not would need closer investigation. The implication was that I was in the northern hemisphere. The rocks were basalt and other metamorphic rocks.

The sun had now disappeared from the bay and it was cold, so I hastened over to the other side of the bay and climbed the other headland. This was narrow and afforded a view of the end of the lake where there was a wide sandy bay with a stream flowing into the lake. The bay was backed by low deciduous woods and it was in full sun.

It was altogether a better place to be. I moved all the stores to a place of safety in the rocks at the right hand side of the bay. Now for shelter and a fire. For shelter I had a choice between the woods behind the bay or the rocks beside the – I opted for the former, mainly because the ground was likely to be softer. If it rained tonight then I would have to make for the rocks. If I was to get a fire going, I would have to be quick as the sun was past its highest. What I was looking for was a quartz pebble with a fairly smooth surface.

It took half-an-hour to find one but then I was lucky for the one I found was about 3in. in diameter. Filling one of the empty cans with water I went back to my ‘camp’ collected some dry grass and made a pile of it on the sand. Dipping the quartz pebble in the water to clear the surface I used it as a lens and focussed the sun onto the dry grass. The image was not as sharp as I would have liked but it looked as if it might produce a sufficiently intense image. Unfortunately, the water quickly dried from the surface so the stone had to be dipped repeatedly into the can of water. It took about a quarter of an hour to get the paper smouldering and that only by dribbling water over the quartz while I held it in place. With a little blowing the fire was kindled. More dried grass and driftwood soon produced a good blaze. Next time I would make the fire in an enclosed fireplace of rocks and turf to concentrate the heat. I must also improve the lens in some way.

Having got the fire going, I stove in the top of another tin, mixed in some more potato powder and heated the mixture. It tasted delicious, a great improvement over the cold version earlier in the day. The sun had sunk low by now and the night would be fine and probably cold. Until I had made a knife I would not be able to make a shelter nor a comfortable bed. Making a knife could wait until tomorrow but in the meantime there was still enough light for me to collect materials to find out my latitude.

It did not take long to find a straight branch about 5ft long and another about 3ft long. I stuck the longer stick upright in the sand until its top came just below the level of my eye. I now waited for dark to see whether I was in the northern or the southern hemisphere.

If I were in the northern hemisphere, I would easily be able to pick out the Plough and the Pole star. If I were in the southern hemisphere, I would have to spend a sleepless night guessing around which point in the sky the stars circled. The vegetation looked distinctly northern to me. Only in Chile and Tierra Del Fuego did I think I would find these temperate forests in the southern hemisphere, but the species looked too familiar for there. I wished that my knowledge of southern hemisphere species was adequate but unfortunately, I would be likely to recognise only those from South Africa and Australia. I awaited dusk with some excitement.

At last it came, and there was the Plough. Using the pointers of the Plough, I identified the Pole star. Lining up the 3ft stick to the south of the longer one, and then with it and the Pole star, I drove it into the sand until its top and that of the longer stick were exactly in line with the Pole star. I could now leave these until morning. I found a dry place on the sand, curled up and went to sleep.

I awoke at sun-up with a heavy dew on my clothes. The fire had burnt down completely but within the ashes were two glowing embers. Collecting strands of dry grass that had escaped the dew and some dry twigs, with great care I nursed the embers into life and made up the fire to a good blaze. Before breakfast there was an important task to do. I wanted a patch of bare earth likely to be in the sun all day. At the top of the beach I found an area that would do, where the sand had just been consolidated with lichens. I smoothed and levelled an area about 4ft square and into the centre I pushed a straight stick vertically into the ground until it projected by just the span of my right hand from the top of my little finger to the top of the thumb.

I knew that this was very nearly 10in. and felt that a known measurement might be useful in the future. I placed a pebble where the end of the shadow of the stick cane and intended to place more pebbles at the end of shadow at about half-hourly intervals during the day. The curve that these traced would give me valuable information.

After breakfast, I turned my attention to the sighting I had made of the Pole star. This time I wanted to make a reverse sighting onto the sand. I looked down from the tip of the taller stick to the tip of the shorter and memorised the spot of sand that they pointed to. There I placed a pebble would be my latitude (I had to make four tries the pebble was properly positioned. As steadily as possible, I drew a straight line between the base of both sticks to the pebble. With a stone, I carefully scratched the bark of the sticks where they entered the sand and withdrawing them carefully, laid them as near as I could judge at right-angles to the line. I them completed the triangle by drawing a line from the other ends of the sticks to the pebble. The angle at the pebble would be my latitude. I had to make a quick sketch in the sand to make sure that this was right!). I could only guess at this angle, but it looked about 50degrees. A more accurate answer than that was needed. I got another stick with two twigs sticking out from the same side about 3ft apart to use as a compass. Inserting one twig in the sand in place of the pebble, I slowly rotated it around the pebble position to draw a circle with the other twig. Then I withdrew the stick and inserted the twig where the base line of the triangle crossed the circle. From there I drew an arc outside the circle to cut it in two places. I placed the twig in one of these and repeated the process right round the circle. Now I had divided the circle into 6 parts and, with the intersecting arcs, these into 2, giving me 30 degrees angular increments.

My latitude line lay between the 30º and 60º marks. This 30º I divided again and then again. The latitude line fell very nearly on the 30º+15º+7.5º mark which I estimated to be about 54º. Later when I had time to make better instruments, I would try for a more accurate measurement. It would suffice to enable me to get a rough idea of the date. When I had made myself a measuring stick and a set of trigonometrical tables I could obtain a more accurate answer.

I had continued to mark the sun’s shadow with pebbles and the line of pebbles had passed their nearest approach to the stick. It was therefore past noon. I would continue to mark the shadow until evening and tomorrow would draw some conclusions from it.

In the morning, I had a look at the curve made by the pebbles marking the shadow of the stick. Removing the pebbles one by one I drew a line connecting them all. I carefully removed the stick that had been casting the shadow and with my stick and stone compass, I drew a circle, with the stick hole as centre, that cut the pebble curve in two places. Using the compass again, centred on these two points, I drew two intersecting arcs to allow me to bisect the curve between the two centres. From that intersection to the stick hole I scratched a line. This then was the meridian, i.e. the North/South line, and I already knew which end was north. With the stick which had been used to cast the shadow, I marked the shadow length along the meridian and also marked where the dampness on the stick showed the part that had been stuck in the ground. I transferred these marks to another stick and replaced the first in the ground.

Now I had enough information to work out the approximate date, or at least the interval to the summer solstice (the longest day) and in a few days, I would know whether the date was before or after the solstice. Although I knew that the calculation was possible, I also knew that I would have to work out how to do it. That could wait. I had to make a knife.

I noticed some flat stones on the first beach which at the time I thought would be ideal skimmers. Being flat meant that their cleavage plane was well defined and could be slate or shale. So I went back to that beach and gathered half a dozen flat stones. I hit one on the edge and it split to give a sharp but friable edge. The stones should do the job until something better turned up. Some flints would have been useful but I didn’t think there was much chance of finding them here where all the rocks seem to be igneous or metamorphosed, although I might be lucky and find some obsidian.

I climbed the steep side of the lake until I came to some fir trees from which I broke off as many branches as I could carry. Thus laden, it was not easy climbing down to the bay. Several times I slipped but without injury luckily. However, I decided that I would not carry more than one armful again when climbing: the risk of accidents was too great. In the shelter of the trees behind the camp I looked for a spot where I could arch saplings over to make the framework of a shelter. I found a spot that looked suitable and, although the shape of the shelter would be irregular, it would be firm.

With my home-make knife I cut round the soft bark at the base of each sapling and made a slit in the bark up the side. I then peeled the bark off as best I could, trying hard to get some long strips. These I used to bind the saplings together at about 6ft from the ground, bending the saplings inwards to form a wigwam shape. The bark was difficult to tie, as it was so slippery, so I ended up by jamming the ends into the binding. When it dried, it would be very firm. With the help of the knife, I broke off as many thin branches as I could and wove them in and out of the sapling frame.

The knife wasn’t very good as its edge kept splitting but used as a saw it was better than nothing. I was still not sure what I would use to cover the framework with. No doubt something would turn up. The fir branches I laid like shingles on the floor of the shelter with the soft tips overlapping the inner end of the branches. This made a comfortable mattress so much so that I was tempted to give it a trial there and them as cutting the branches had been exhausting work. However, the weather still looked fine, I thought that I would cook a meal, have a good think while eating it, them have a good wash and go to sleep.

While I was sitting eating, comfortably settled on the sand, I began thinking more about the measurements I had taken of the sun. I could remember that the axis about which the earth rotated was tilted at 23.5º to the plane in which it swung annually about the sun (the plane of the ecliptic). By making a few sketches in the sand to clarify my thoughts, I could see that at midday at the summer solstice the altitude of the sun above the horizon would be 90-latitude + 23.5º and at the winter solstice, 90-latitude-23.5º, varying as a cosine wave between the two. From my measurements of the Pole star I knew my latitude to be about 56º and 90-latitude was then 34º. So the altitude of the sun would swing from 10.5º to 63.5º above the horizon at midday. However, I had no cosine tables to calculate the intermediate values and compare them with my actual measurement.

The construction of cosine (or sine) tables sounded a daunting task. However, it had been done before with little more in the way of instruments than I had. Still, I had compasses of a sort, and perhaps I could make a measuring rule. With the latter in mind, I returned to the stony beach to look for a flat stone that was at least the span of my hand across. I also looked for two small stones that were both hard and sharp. Here, I was lucky for in the rocks sloping down to the beach I found a band of shale and was able to knock off several large slices. From these I could make my measuring instruments. I bound one of the sharp stones to a thin dry branch at about half a span from the stump of a twig projecting from the branch. The stone would be my pencil and the twig the pivot of this compass.

Grinding the edge of my flat stones to as near a straight edge as I could, I held this upright against one of the other flat stones and scratched a straight line across the centre. I made this scratch fairly deep so that the compass pivot would sit in it. With the point of the hard stone, I ground an extra depression at about the centre of the line. With the compass point in this hole, I made two marks on the line, ground depressions at these marks and with the compass divided these half lines. I repeated this until the line was divided into eight equal parts.

This then was my unit of length from now on.

Fetching a long straight branch, I scratched eight of these units on it, to make marks about 10" apart. This would be my measuring rod and with the scratched stone, I could subdivide any of the larger units into eight. While I was at it, I made a protractor on one of the other flat stones in the same way as I had divided the angles in the sand when working out my latitude.

From each of the intersections of the angle lines with the circumference of the circle, I drew, as near as I could judge, perpendiculars to one diameter using the right angle line as a guide. If the radius of this circle is one unit then the lengths of these perpendiculars are the sines of the angles and lengths from where they cut the diameter to the centre are the cosines of the angles. For the moment these would be too small to measure accurately so with my measuring rod I drew a copy in the sand but with a diameter of ten large units. This enabled quite accurate measurements to be taken of the sines and cosines of angles from 0 to 360 in 7.5º increments. As I progressed I scratched the results on the stone version. As my long measure was divided into 80 parts and I could estimate fractions of these, I was able to get reasonable two-figure accuracy.

I was interested to see how the figures would turn out for I vaguely remembered that sine 30 is 0.5 and sine 45 is 0.707 and sine 60 is half the square root of 3 (if I could ever get that worked out). The figures that I obtained by my crude measurements were:

sine 15 = 0.26 sine 60 = 0.866

sine 30 = 0.5 sine 75 = 0.97

sine 45 = 0.71

Encouraged by these results, I divided the angles still further until I got down to 3.75º increments and calculated the sines for all of these up to 90º. The results were scratched on the stone as before. I really felt that I had achieved a great deal for this sine table could be converted into cosines and tangents and would be of inestimable use in measuring distances to remote points and for the date measurements to which I now returned. Using the sand as my blackboard I wrote what I knew at my latitude, the maximum altitude of the sun on June 21 would be 57.5º and the minimum altitude on December 21 would be 10.5º, i.e. a curve of (57.5-10.5)/2 = 23.5º amplitude and starting from 10.5+23.5 = 34º at the spring equinox, March 20 (or 21, I could not remember which). Getting the stick on which I had marked the length of the sun stick and the length of the shadow, I measured these and found that the length of the shadow was about 6.3 units. This meant that the tangent of the altitude of the sun at midday was 8.5/6.3 = 1.35. I now had to find out what that angle was. Using the sine table, I wrote out all the sines in one column, then all the cosines in the next column – i.e. the sines written in the reverse order. In the third column I wrote the value of sine over cosine, i.e. tangent. The results being:

Now read the book to see what follows:

'Survival Navigation, Measurement and Mapping' at Brabourne Books by John Locke