Chain surveying can only measure distances, and that limitation is what forces it into small open sites. To survey anything larger you need the second half of the information — direction.
This post covers why direction matters, the systems used to measure angles, and the two ideas that underpin the whole of compass surveying: the meridian and the bearing.
Why Direction Is Needed
Recall the second principle of surveying — locate a point by at least two measurements. Chain surveying satisfies this using two distances, which is why it depends so heavily on triangles.
But there is another way to fix a point: one distance and one direction. Measure how far away something is and which way it lies, and its position is determined just as completely.
This is the basis of compass surveying — distances are measured with a chain or tape, and directions are measured with a compass.
The advantage is considerable. Fixing points by distance alone requires every station to be connected to two others by measured lines. Fixing them by distance and direction requires only a single line from one station to the next, which is why traversing can march across country in a way chain surveying cannot.
Systems of Angular Measurement
Before directions can be recorded, there must be a system of units. Three exist.
1. Sexagesimal System
1 circumference = 360 degrees (°)
1 degree = 60 minutes (′)
1 minute = 60 seconds (″)
This is the system used almost universally in Indian surveying practice, and the one every examination expects unless it says otherwise.
The name comes from sexagesimus, meaning sixtieth — because both subdivisions are into sixty parts.
2. Centesimal System
1 circumference = 400 grads (g)
1 grad = 100 centigrads (c)
1 centigrad = 100 centi-centigrads (cc)
The centesimal system divides everything by hundreds, which makes arithmetic simpler — no converting between 60s and 100s halfway through a calculation.
Why 400 and Not 100?
A sensible question, and the answer explains the design. With 400 grads in a full circle, a right angle is exactly 100 grads — a clean round number. Since surveying is full of right angles and quadrants, that choice is far more convenient than making the whole circle 100.
3. Hours System
1 circumference = 24 hours (h)
1 hour = 60 minutes (m)
1 minute = 60 seconds (s)
This system reflects the earth’s rotation — 24 hours for one complete turn — and is used mainly in astronomical work, which connects to the astronomic survey mentioned in the classification by purpose.
The Three Compared
| System | Full Circle | Right Angle | Subdivisions |
|---|---|---|---|
| Sexagesimal | 360° | 90° | 60 and 60 |
| Centesimal | 400g | 100g | 100 and 100 |
| Hours | 24h | 6h | 60 and 60 |
Useful Conversions
90° = 100g → 1g = 0.9° and 1° = 1.111g
360° = 24h → 1h = 15°
The 15 degrees per hour figure is worth remembering — it is simply 360 divided by 24, and it is why the sun appears to move 15 degrees across the sky each hour.
The Meridian
A direction cannot be stated on its own. “That way” means nothing unless you say relative to what. That reference is called a meridian.
A meridian is any fixed direction from which the direction of a survey line is measured.
The meridian is the zero of the direction system, exactly as a benchmark is the zero of a height system. Change the meridian and every recorded direction changes with it — which is why the type of meridian must always be stated.
The Bearing
The horizontal angle between the meridian and the survey line is called the bearing of the line.
Two words in that definition carry weight.
“Horizontal”
A bearing is always measured in the horizontal plane, never along the slope of the ground. This matters because a line running up a hillside still has the same bearing as its horizontal projection — direction and slope are separate pieces of information.
This is consistent with the point made in the introduction to surveying: plans and maps are graphical representations of features on a horizontal plane.
“Between the meridian and the survey line”
The bearing is always measured from the meridian to the line, not the other way round, and not between two survey lines. An angle between two survey lines is an included angle, which is a different quantity entirely.
How Distance and Direction Work Together
Once both are available, a survey can proceed as a traverse — a connected series of lines, each with its length measured by tape and its direction measured by compass.
Each line takes you from one station to the next, and because you know both how far and which way, every new station’s position follows from the last. This is the method that opens up the larger and more obstructed areas where chain surveying fails.
What Follows From Here
The remaining topics in this chapter are all consequences of the two definitions above:
- Because a bearing needs a meridian, we need to know what kinds of meridian exist — true, magnetic, grid and arbitrary.
- Because each meridian gives its own bearing, we get the types of bearings.
- Because a bearing can be written in more than one form, we get the whole circle and quadrantal systems.
- Because a line can be observed from either end, we get fore and back bearings.
- Because the magnetic meridian does not coincide with the true one, we get magnetic declination.
Quick Revision Notes
- Compass surveying fixes points using one distance and one direction, rather than two distances.
- Three systems of angular measurement: sexagesimal, centesimal and hours.
- Sexagesimal: 360° per circle, 60′ per degree, 60″ per minute.
- Centesimal: 400 grads per circle, 100 centigrads per grad, 100 centi-centigrads per centigrad.
- Hours: 24 hours per circle, 60 minutes per hour, 60 seconds per minute.
- In the centesimal system a right angle is exactly 100 grads, which is why the circle is 400 rather than 100.
- 1h = 15° and 1g = 0.9°.
- Meridian = any fixed direction from which the direction of a survey line is measured.
- Bearing = the horizontal angle between the meridian and the survey line.
Mistakes Students Commonly Make
- Saying the centesimal circle has 100 grads. It has 400; the right angle has 100.
- Assuming all three systems subdivide by 100. Only the centesimal does — the other two use 60.
- Defining a bearing as the angle between two survey lines. That is an included angle; a bearing is measured from the meridian.
- Forgetting that a bearing is a horizontal angle, independent of the ground slope.
- Treating the meridian as fixed by nature. It is any fixed direction chosen as a reference, which is why several types exist.
- Confusing grads with degrees in calculations. 1 grad = 0.9 degrees, not 1.
Conclusion
Compass surveying rests on adding direction to distance, and direction rests on two ideas. A meridian is whatever fixed direction you choose to measure from, and a bearing is the horizontal angle from that meridian round to your survey line. Angles themselves may be expressed in degrees, grads or hours, with the sexagesimal system dominating practice and the centesimal offering cleaner arithmetic. Everything else in this chapter — types of meridian, forms of bearing, declination and local attraction — grows out of these definitions.
Frequently Asked Questions
What is compass surveying?
Surveying in which the lengths of lines are measured with a chain or tape and their directions are measured with a compass, so that each point is fixed by one distance and one direction.
What are the three systems of angular measurement?
The sexagesimal system, the centesimal system and the hours system.
What is the sexagesimal system?
The system in which one circumference equals 360 degrees, one degree equals 60 minutes and one minute equals 60 seconds.
What is the centesimal system?
The system in which one circumference equals 400 grads, one grad equals 100 centigrads and one centigrad equals 100 centi-centigrads.
Why does the centesimal system use 400 grads rather than 100?
Because it makes a right angle exactly 100 grads, which is far more convenient for surveying work that constantly deals with right angles and quadrants.
What is the hours system?
The system in which one circumference equals 24 hours, one hour equals 60 minutes and one minute equals 60 seconds. It is used mainly in astronomical work.
How many degrees are there in one hour of angle?
15 degrees, since 360 degrees divided by 24 hours gives 15 degrees per hour.
What is a meridian?
Any fixed direction from which the direction of a survey line is measured.
What is a bearing?
The horizontal angle between the meridian and the survey line.
Is a bearing affected by the slope of the ground?
No. A bearing is measured in the horizontal plane, so a line running uphill has the same bearing as its horizontal projection.