I discovered another Hutton today.  I thought that there was only one, James Hutton, the father of modern geology.  But Charles Hutton has come to light.  I vaguely remembered reading about someone who invented the contour line in Bill Bryson’s A Short History of Nearly Everything.  And seeing that this blog has a geographical theme, I went looking for the inventor of this most famous, most useful and at times most confounding. Well, I used to find it confounding when we first had to make our own contour maps back in our Survey 101 and Geography 101 days. I have since refined my skills somewhat and now think that contours lines are a wonderful invention.

So the contour line is a descendant of a rather noble pursuit – that of measuring the mass of the Earth.  The Royal Society had stumped up a wad of cash to work out how much our planet weighed. So how does one go about such a task? If you are a teacher, you may want to pose that problem to your class and let them come up with some ideas as to how to solve the problem.  If that is all too much trouble, or you are a student looking for the inside line, here is the answer.

The Royal Society appointed astronomer Neville Maskelyne to lead the project.  For four months in the summer of 1774, no doubt plagued by swarms of midges, a team of surveyors camped out in a remote Scottish glen to measure the volume of Schiehallion, a 1083 m high mountain that lies in the Grampian highlands.

Hundreds of spot heights - points of measured elevation - were taken of the entire mountain, and the task fell to Hutton to carry out all the tedious mathematical calculations that were required to work out the spot elevations. Think trigonometry. Lots of it. Don’t forget that there were no calculators, computers or even slide rules to assist back in the day so it was a long tedious job to calculate the thousands of figures by hand.

At the end of the day a map of the mountain was produced with dozens of spot heights scattered across it. A confusing mass of numbers to say the least, but then Hutton noticed that if he used a pencil to connect points of equal height, it suddenly became much more orderly. By interpolating between the spot heights, which were recorded in feet and inches, he could reduce heights to exact elevation figures (again in feet), and by joining up these points he could make sense of the shape and the variations in gradient of the mountain. He had just invented the contour line. And by using the contour lines, he was able to measure the volume of the mountain. 

To complete the story, Maskelyne drew on Newton’s gravitational law to measure the gravitational pull of the mountain, using the deflection of plumb lines from the vertical to do so. A mountain will deflect a plumb bob from the vertical due to its gravitational pull.  The deflection must be measured against the fixed background of the stars, which was where Maskelyne skills lay.

The mass of the mountain was worked out according to the simple formula that density is the mass divided by the volume.  Knowing the density of the rocks which underlie the mountain, and the volume, it is then relatively easy to calculate the mass simply by manipulating the equation.

Assuming that the rocks underlying the mountain had a density of 2.5, Hutton was able to calculate the weight of the mountain and then by extrapolation the weight of the Earth. The final figure was 5000 million million tons, which was 20 percent out from the modern, accepted figure.  Not a bad result for a summer’s work, all things considered – the mass of the Earth, estimates of the density of our planet and the invention of contours.