Several months ago I was looking at an old single-burner stove on ebay (no surprise, right?) and in one of those little photos which slide along the bottom of the screen I noticed a peculiar looking item. It kind of looked like a compass, but more intricate. I clicked on the item, which was listed under the title M2 Artillery Compass, to get a closer look.
I did a little research on Artillery Compasses, which are known as Pocket Transits to the civilian world, and learned that they’ve been around for over 100 years. This blog post by Northing & Easting has a good write-up about it’s history, and he’s got a lot of other interesting posts, too.
The Pocket Transit was an 1890’s invention by David W. Brunton, a Colorado mining engineer. It was a compass and a clinometer, that is, besides providing direction it is also used to measured angles, which then can allow the user to calculate heights of objects. When I read that, I begin to think about the times when I was backpacking or on a canoe trip and wondered about the height of an old tree or a high cliff. So, I watched the prices of M2 Compasses for a couple of months to see what they typically sell for and finally purchased one for $40. I believe it was made in the 1970’s or early 1980’s.
This Artillery Compass or Pocket Transit was in decent shape with a clear mirror, plastic case, good glass and decent paint, though it was missing the label on top and the seal around the needle lock pin was rotted away. I contacted Brunton and was able to get a replacement seal and a Sine/Tangent label. BTW – Brunton will service pocket transits for $125, though I’m not sure what they do for that. If I used one of these for my job, I probably wouldn’t hesitate to spend the money, because a new Brunton Pocket Transit can set you back $250-$450. After I installed the parts, I was ready to go, except . . . I needed to learn how to use this thing.
I searched around for a Pocket Transit manual and thankfully Brunton had one for their current pocket transits online and since these instruments haven’t changed all that much in over 100 years, it was good enough. While reading the manual, I came across a peculiar question in section 1.3. It asked, “Why are EAST and WEST switched?” I sat there a moment and thought to myself, “Huh? Wonder what that means?”. Then I got out the transit and opened it up and low and behold, E and W are swapped from a typical compass. Funny that I hadn’t noticed that until now. Go figure. The manual continues, “Because the pocket transit is a direct reading compass. Read azimuth directly where the needle points on the graduated circle.” Okay, well, this might mess me up for a while.
Another peculiar feature is the azimuth and clinometer units. It’s in mils, that is, instead of 360 degrees, the military divides up a circle by 6400. I found an online conversion calculator and quickly discovered that 100 mils – 5.6 degrees, and therefore 50 mils = 2.8 degrees, 25 mils = 1.4 degrees and 20 mils = 1.12 degrees. Since my primary purpose was to measure the heights of objects the conversion poses only a minor inconvenience. So, onward . . .
Section 5.2a of that same manual explains how to measure height using vertical angles. I walked outside my two-story work building and stepped off 30 paces which would be approximately 90 feet. I measured:
Angle up to top of building at 300 mils -> 16.8 degrees -> tan 16.8 -> .305
Angle down to base of building at 60 mils -> 3 degrees -> tan 3 -> 0.052
Add these .305 + .052 = .36
Multiply these by the distance, .36 * 90 =32.4 feet.
Well, that’s about correct.
Doing this in the field isn’t too bad. If I just recall that 100 mils = 5.6 degrees, I can mentally convert 300 mils to degrees; 3 x 5.6. As for the tangents, I have that new SIN/TAN table attached to the top of the transit, so I just look it up. The remaining calculation can be done on paper if necessary.
So, what just happened here? Well, I think that what happened was Small Old Herman Carried A Huge Tub Of Apples. Sheesh. I hadn’t thought about that in quite some time, and there seems to be plenty of mnemonics for remembering trigonometry ratios. Anyway, we’re concerned with the Tub Of Apples because, I’ll measure the angle θ with my nifty new transit device, and step-off the Adjacent side, and what I want to know is the Opposite. Recall that the tangent of an angle gives us the ratio of the opposite side to the adjacent side. The 30 paces from the building gave us the adjacent side at 90 feet. When I sight to the top of the building, I’m creating a triangle and take the angle measurement. When I sight down to the bottom of the building I create a second triangle and take its angle measurement.
So, tanθ = opp/adj and rearranging to solve for opposite we have (tan(up θ) + tan (down θ)) * adjacent side. BTW – If both the base and the top of the thing you’re trying to measure are above level, with respect to your eye, then you subtract tan(bottom θ) from tan(top θ)
Now, if I had a ranging device, I could measure the distance to the top of the building and have the hypotenuse instead of the adjacent side (the subject of an upcoming post?). Then I could take the sine of the angle and multiply by the hypotenuse (distance). Small Old Herman says: Sin θ = opp/hyp -> Sin θ * hyp = opposite.
One other thing to note about pocket transits. Mine is military and goes from 0-6400 mils. Brunton makes two other types, at least. One type is 0-360 like a typical compass and the other goes from 0-90 in quadrants. It basically goes from 0-90-0-90-0. It seems like this quadrant type has been the more popular version used by geologists, etc.
D.W. Brunton’s pocket transit is quite a nice little instrument.
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