80 years of the Triangulation Pillar

The BBC alerted me to this fact and I decided to blip one nearby. I had a wee walk through the blooming gorse onto Dalmahoy Hill to be buffeted by a strong norwesterly as I captured this image.

Having climbed all the 282* Munros in Scotland, and now working my way through the Corbetts, I've come to accept these concrete erections as part of the landscape rather than unwelcome intrusions. When the weather is gnarly and visibility is nil, there is something reassuring about the sight of a pillar on the mountain summit.
On the other hand, when the weather is fine, there's a ready-made camera tripod for you to capture the view. And that is main point - if the Ordnance Survey built one of these pillars, then you can be certain it has a good view. I can't remember the principles but they needed to have line of sight to multiple related pillars required for the accurate triangulation of Great Britain.

Whatsmore, it is such a simple calculation; by measuring angles to a remote point from known points at either end of a fixed baseline, rather than measuring distances to the point directly, the point can then be fixed as the third point of a triangle with one known side and two known angles.

So from Dalmahoy Hill (DH), I could see two notable trig pillars - Arthur's Seat (AS) in central Edinburgh and Allermuir Hill (AH) in the Pentlands. Lets say I already know from a previous calculation, the distance from Dalmahoy to Arthur's Seat. If I then observe the angle from Dalmahoy to Arthur's Seat and Allermuir, then the distance to Allermuir can be calculated.

Just for a laugh, I've done a bit of scribbling...

Calculated Distance* from DH to AS = 15km
Measured Angle** DH to AS = 80
Measured Angle** DH to AH = 100
Measured Angle** AS to AH = 215

*from google earth
**from a screen guess

Using laws of trigonometry, I can work out my three internal angles of th e triangle as 20, 35 and 125....

Calculated Distance from DH to AM = (15 x sin35)/sin125 = 10km
Calculated Distance from AS to AM = (15 x sin 20)/sin125 = 6.25km

Very rough of course, but sort of illustrate what they were up to those blokes in the 1930s.