You mentioned that if the iPhone 4s is getting hot it may be overcharging not due to any mistakes with the Theory! :-)
I now can totally agree and I understand that. Thanks by the way!
But some possible malfunction with the iPhone regulation system is possible. So while charging it I forgot to mention or actually I left it out completely because it is a guess, not a measured result, but both the iPhone and the apple 5 watt source were what I consider to be excessively hot.
I dumped all power from the Iphone 4s and then recharged it on one of the apple 5 watt cubes where it is registering 6.5 watts draw. I calculated the 80% capacity level since I noticed by measurement that Apple IOS charge regulaters built into the device INTERNALLY, act very similar to my higher end solar controllers. From 0% to 80% there is the bulk charge level, maximum charging level, then at 80% the apple IPhone starts asking for less voltage. It is the same transition level as the solar controller has and they both went into the "Absorption" Phase where lower charge levels are applied to be able to fill the battery to 100%. After 80% of capacity was reached voltage on my meter started dropping down from 6.5 watts to 5.9 watts, then to 5 watts, this was at about 87% capacity, then down to 4.5 watts, then to 4 watts at 90% capacity and then to 3.7 watts, to 3 watts, and finally to 1.1 watts at 100% capacity where it stayed... Just like the "float" charge of a solar controller only with a higher percent level of float charge. But then one of the links you sent mentioned that apple IOS devices will still pulse charge for an hour after 100% is supposedly achieved, but that they deliberately kept the variations off the readable capacity so consumers would not get confused.
So yes they have an internal very smart charging and regulation system! But it isn't calibrating with what the specs should be! Charging time at bulk rate to 80% of capacity (1136 Mah as I calculated based on 1420 Mah full capacity at 3.7 volts ) was reached in 76.5 minutes. But that includes time spent restarting up the phone as I let it totally uncharge and shut down. On 3% it rebooted. At 5% charge I went into,settings and shut off data function, I shut off Wi Fi and engaged "airplane" mode. I also made all of those bottom icons get all wiggly, and shut them down too. :-)
So just by calculating approximate full charge period at bulk charge to 80% along with the time it took tells me nothing precisely. It does put charge rate at a bit less then 1C. However I am very aware that any number of voltage and wattage combinations could produce the same results. As you pointed out:
Scientific method must set up a defined set of parameters for a test, that when repeated by others with the same parameters produces the same results. I learned that through school (psych major) and my own readings of many books. ( not enough obviously )
I hope I made some sense in this post. Which I doubt. I also think I can narrow down the % of C that could produce a better "guess"
But I can't measure the power between the apple 5 watt source working at 6.5 watts between the phone and the power source! Very frustrating.