First:
There are many reasons why your voltage would go up. As suggested by @jippie it can be heating in the boost converter in the pack. It can also just as easily be heating in your resistors, causing them to increase resistance and as such reduce drained current.
What's worse, slight imbalances between the two resistors' values will cause slight heating differences, which will cause bigger differences due to different heating, causing bigger differences in heating, etc etc, cause larger and larger measurement inaccuracy.
As @NickAlexeev suggests, if you are writing this for a mass-read publication you need to take this seriously or not do it at all. You will either mislead a large group of people with your findings or be quickly debunked by any one of "us professional EE engineers" living in your country. Best case scenario it's all wasted effort, worst case you're helping the world to yet more misunderstandings about EE and batteries and there are already way too many.
You need to:
- Keep the current controlled and constant, so you can rely on your data and know that for every single measurement you can rely on it, exactly and accurately. Research current sink circuits and if you need ask more clarification later. The best solution will be one that either doesn't get hot at all (heatsink+fan), or one that is compensated for heat. Or preferably both.
- Preferably measure back that current accurate to a percent or better (which in this sense is less than one percent), since a 1% error in your current will easily build up to a decent skew in your data. But at least, if it's fixed and controlled, you can know that all your measurements will be skewed the same.
- Measure the voltage with a reliable set-up, if you want you can do it with an Arduino, but not using your load as a divider. That's basically pointless. You need the voltage to be reliable as well, that goes for the one you measure and the one you measure against. Which is either a decent reference, or a very stable and reliable power supply. Most people choose the reference, but it's not unheard of to make a 0.5% stable and repeatable 5V supply for something like this, but it's harder. The Arduino (Atmel MCU) has internal references, but also a pin that you can connect a reference to. I suggest the external option, since the internal one isn't very much more accurate out of the box than its supply voltage from a linear regulator.
- Make sure you have a very accurate time-base. There are arduinos that use the internal RC oscillator of the processor: these are not in any way, shape or form accurate. You need one with a Crystal Oscillator that is capable of keeping decent time.
Once you've done all that, if your time also happens to cost something, you are going to have spent much, much more in materials, tests and research than the $199 for the battery tester that Nick linked in a comment, so you may as well go for that.
And you need to, but this is when you buy the tester as well:
- Read up a lot about how these packs work (what's a boost converter? how efficient are they on average?), what the batteries do and what the risks are with low grade electronics or batteries, because for a good, or even decent, article you will need to explain this well and clearly to your readers. Plus it helps you understand what you are actually measuring. Oh, and don't forget to think about what the mAh rating means and how that relates to the boosted voltage. the "mAh" number that's printed (on usually the more crappy ones) is for the internal battery, which is rated at 3.7V, not the 5V output. That's a free-bee you get from me.
Ask yourself this, can I remove the battery from the laptop and still have it run fine if it is plugged in? I am assuming this is a yes. This would mean that the load is being met by the supply from your battery charger. So, so long as you have the same continuous current capacity from your battery pack that you do from your charger you should be set.
If we assume that that rate is less than 5amps, (you have a pig of a laptop if it is that much) then you are golden as almost all genuine 18650 cells can source at least that much. Many source up to 15-30amps even.
You are also asking if it is safe to have too high of a discharge capability of your cells: No, not really. If you draw only 5amps out of a cell that can source 30, that is fine. The cells will always run a cooler than if you were taxing it more. So that is good.
If you want a bit more help, I would recommend the sanyo ncr 18650 ga cell. It can source up to 10amps continuously. You only need <5amps so it will run nice and cool. It also has one of the highest capacities of all the 18650 cells available these days so your battery will last nice and long between charges.
Best Answer
Using a constant current load you'll get a nice curve if you plot the voltage over time.
The C rating is given by the manufacturer as an indication of the safe maximum constant current draw from the battery.
Some searching turned up that it is standard to make the discharge curve over 20 hours. So this would be like 0,05C. I speculate that this will avoid some thermal effects, Because your battery would probably get hot from a 1C discharge.
If it is a AA battery, set the current to about 100mA. AAA - 50mA if it is another kind of battery, guess or measure how much more or less volume it has compared to the AA battery, and factor that into the current. It is just a way of guessing capacity. So if the battery looks 4 times larger than a AA, set the current to 400mA.
You can do this guessing because battery capacity is proportional to volume. After you've done this, you have measured the capacity of your battery, and you can make more precise measurements. Good luck