Ok, so today the weather was windy and somehow fresh, so I didn't feel like going to the beach, and decided to play around with sharky

(my X) after checking the fluids I noticed the following:
1- no missing engine oil after replacing some leaky "joint" at the dealer the last time.
2- the coolant is missing a little (one inch below the top) but i did not top it up... I topped it up few months ago with water, and i'm waiting for another few months before putting some antifreeze... (mysterious leak)
3- the ATF PS fluid is down a little, but i will top it up when the level goes lower... (I have a leaking pressure hose)
About the tyres, I inflated them to 2.3 (around 34psi) yesterday while hot, so today they were all at 2.05... what's the ideal temperature to measure the pressure? after 5 minutes drive? or cold? I also inflated the spare to an acceptable 26-27... it was under 20...
The windshield fluid was topped up with 4 liters and some Sonax appropriate cleaning agent...
then it was time to see the battery... after wresteling for few minutes and removing screws and some heavy weight lifting... i reached the battery...
My Question:
what is this semi-spherical device under the spare tire??? it has electrical cables... see the picture below
The battery is interstate battery (Mega Tron) with a 75month warranty. no date is written nor marked... I assume they replaced the OEM in 2005-2006 (after 4-5 years of manufacturing date) so if we add 6 years, I believe I should replace it in 2011 or 2012... since i intend to sell the X in 2015, it would be convenient to replace it in late 2011 or early 2012... I have it scheduled...