What the two columns actually are
A course is a direction and a length, and it moves you a certain distance north and a certain distance east. The north part is the latitude, the east part is the departure, and both fall straight out of the azimuth: latitude is the distance times the cosine, departure is the distance times the sine. Azimuths are measured clockwise from north, so at 0 degrees the whole distance is latitude and none of it is departure, and at 90 degrees the reverse. This is the opposite of the convention taught in trigonometry, where an angle starts at the x axis and the cosine gives the horizontal. Swapping them is the single most common mistake made on a first traverse and it is close to invisible: the misclosure comes out identical, the perimeter is unchanged, and only the plot gives it away by being flipped about the north-east diagonal.
Once you accept that, the closure test is obvious. Walk a loop and you end where you began, so every north step has been cancelled by a south one and every east by a west. Both columns sum to zero. They never quite do, and the amount by which they miss is the sum of every angle read a few seconds off and every tape pull a few hundredths short.
Reading the default traverse
The five courses in the box are a loop of 1,734.90 feet round a parcel of a little under five acres. Reduce them and the latitudes sum to plus 0.055 feet instead of zero and the departures to minus 0.148. The straight line between those two leftovers is 0.158 feet of linear misclosure, and the perimeter divided by it is the precision ratio the page prints as 1 in 11,007. That ratio is the number most specifications are written against, which is why it is the headline rather than the raw misclosure: a tenth of a foot left over on a 200 foot loop and a tenth left over on a 20,000 foot loop are not the same day of work.
The page also prints the direction of the closing line. That is more useful than it looks. If the closing line runs roughly parallel to one particular course, the error is probably in that distance. If it runs perpendicular to a long leg, an angle at one end of that leg is the suspect. A misclosure that points in no meaningful direction at all is usually what a genuinely random spread of small errors looks like, and that is the one you can reasonably adjust.
The default field book is a worked example of exactly that. Its closing line comes out at S 69-41 E, and the second course in the book runs S 69-02-29 E. Those two directions are within forty minutes of each other, which is the signature of one distance booked short rather than a scatter of small angular errors — and it is, because that course was written down 0.16 feet under its true length. Adjusting by the compass rule would have quietly spread those 0.16 feet across all five legs and left every corner slightly wrong instead of one leg plainly wrong.
Compass rule and transit rule
Both rules take the leftover and hand shares of it back to the courses so the figure closes exactly. They differ in who pays. The compass rule, sometimes called the Bowditch rule, charges each course in proportion to its length: a leg twice as long takes twice the correction. That is the right assumption when the angles and the distances were measured with roughly matching care, which describes most modern work where one instrument did both.
The transit rule charges each course in proportion to the size of its own latitude or departure, which means a north-south leg absorbs most of the latitude correction and almost none of the departure correction. That suits an older pattern of work where the directions were good and the lengths were not.
Neither one is a check and neither one finds anything. If one distance was booked ten feet short, both rules will quietly spread ten feet across every course in the traverse and hand you a figure that closes perfectly and is wrong at every corner. The adjustment is the last step after you are satisfied there is no blunder, and the closure figures above it are the evidence you use to satisfy yourself.
Loops and links
A loop closes on the point it started from, so the target is zero in both columns. A link runs between two points whose coordinates you already hold, and the target is the difference between them. The arithmetic is the same; only the number the sums are compared against changes. A link is the stronger check of the two because it tests the direction of the whole traverse against known control, while a loop can be rotated bodily and still close perfectly. A loop that closes to 1 in 20,000 tells you nothing about whether your starting azimuth was right.
What this cannot tell you
It cannot tell you whether the traverse is good enough. That depends on what the survey is for, what the governing specification says in its own words, whether the misclosure is spread or concentrated, and the judgement of the person who signs the work. The page takes a precision figure from you and prints it beside the computed one because the comparison is useful; it does not turn the comparison into a verdict.
It also cannot make a boundary. Reducing a field book gives you a mathematically consistent figure. A property line is a legal object built from record research, monuments actually found in the ground, the rights of adjoining owners and the professional judgement of a licensed surveyor. The two are related but they are not the same thing, and no amount of decimal places closes the gap.
Questions people ask
What is the difference between latitude and departure?
Latitude is how far north a course takes you and departure is how far east. Latitude is the distance times the cosine of the azimuth and departure is the distance times the sine, both measured from north rather than from east. On a closed loop the latitudes sum to zero and so do the departures, because you finished where you began. Swapping the two is the classic first-traverse error and it is nearly invisible in the numbers, because the misclosure and the perimeter come out identical and only the plotted shape is mirrored.
How is traverse precision calculated?
Divide the perimeter by the linear misclosure and express the result as one in something. The misclosure is the straight line between where the traverse computed out to and where it should have landed, which is the square root of the latitude closure squared plus the departure closure squared. A 2,000 foot loop that misses by a fifth of a foot is 1 in 10,000. The ratio is used rather than the raw miss because it scales with the size of the figure.
What closure does a traverse have to meet?
That is set by whatever specification governs your work, and it is not something this page can supply. It varies by the purpose of the survey, by the jurisdiction, by the client and by the class of work, and it changes over time. The form has a field where you type the figure your own standard asks for, and the page prints it next to the computed one. Deciding whether the work meets it is a professional judgement, not an arithmetic result.
Should I use the compass rule or the transit rule?
The compass rule spreads the closure in proportion to course length and assumes the angles and distances are about equally good, which fits most work done with one instrument. The transit rule spreads it in proportion to the size of each latitude and departure and assumes the angles are better than the distances. Neither locates a blunder. If one course is badly wrong both rules will hide it by smearing it evenly across the whole figure, so satisfy yourself the misclosure is a spread of small errors before adjusting anything.
My traverse closes perfectly but the plot looks mirrored. Why?
You have almost certainly swapped latitude and departure somewhere, or you are feeding azimuths into a routine that expects angles measured from east. The misclosure is unaffected by the swap, so every numeric check passes, and the figure comes out reflected about the north-east diagonal. Check one course by hand: a bearing of N 26 E on 285 feet should give about 256 feet of latitude and about 126 feet of departure, not the other way round.
Does closing a traverse prove the boundary is right?
No. A closed traverse proves the measurements are internally consistent, and nothing more. A loop can be rotated bodily, or sited a hundred feet from where it belongs, and still close to 1 in 20,000. Tying it to known control tests the position and the orientation. Establishing where a property line actually runs is licensed professional work involving record research and monuments recovered on the ground, and it is not a computation.