Lol!
I'll break it down..........
The goose egg I'm going to assume is fertile, because she's the only female in the whole gang, and she's had many goslings in past years. Goose eggs have thinner shells than swan eggs.
When you "candle" an egg, you're putting a light source against the egg in a dark room and the inside of the egg becomes visible. With standard type poultry and waterfowl, you can identify the development of the embryo around 5-7 days. You'll see a network of blood vessels beginning to form and a small dark mass, which is the "baby". Swan eggs are just too thick to really identify anything, unless you go high tech.
Grabbed this off "Backyard Chickens". This is a Chinese Silkie egg, but it show what you're looking for.
This shows a developing gosling on the left and an infertile egg (clear, blank, or dud) on the right:
So by putting in a goose egg, which takes about 30 days to develop, I can candle that about every 5 days and get a good idea of how far along the swans are developing. The swans will take 4 days longer than the goose before they start to hatch or "pip", that's when they make their first attempt at breaking a small hole in their shell.
When the goose egg starts to pip. I know I need to stop the automatic turner in the incubator and transfer the eggs to a hatching rack that goes on the bottom of the incubator.
The "turner" in the 'bator" rocks the shelves from one side to the other, kind of like a BBQ spit that only turns your meat 180 degrees every 2 hours. This prevents the embryo from "sticking", as it develops, to the inside of the shell. The setting bird turns their eggs as they nest at about the same rate. A few days before the babies hatch, the mother (or father depending on what kind of bird) will stop turning them. What is left of the yolk is absorbed into the baby's belly through the umbilical cord. This will actually be used as a nutritional source for the baby the first 48 hours after it hatches. (that's why hatcheries can ship day old babies and not worry about putting water or food in the shipping box)
By candling, I can also tell if the humidity and temperature are accurate by observing the "air cell". That's found at the large end of the egg (not the "pointy" end), pictures on the bottom of the lower pics show the air cell, the white area. The air cell slowly gets bigger as the baby develops. If the air cell get too big, too fast, I need to put my temperature down and increase the humidity. The reverse if the air cell doesn't increase.
The goose egg is basically a way to gauge how the swans are developing, how close to hatch they become, and how well the incubator is being regulated. That's why it is my "control". I could use a lot of scientific terms but this is basically what I'm doing. Some people make it more complicated than it needs to be. After messing with the incubation process for a few years, I got to the point of just "set it and forget it". I'll put a quart of water into the water pan on the top shelf of the 'bator every day to top it off, and after a week, I'll start "misting" the eggs with water and pulling the trays out for 20 minutes to slightly cool, then pop them back in. Cooling and misting applies only to water fowl. It duplicates the mother leaving the nest, eating, getting in the water to stretch, and returning with moisture on her belly feathers.
That's the "short version"!