Combined Temperature Scale

The genesis of this idea was a story by Kevin Kling on NPR yesterday (see link). He observed that in England people use Farenheit for when it is really hot, e.g., "it's bloody hot. Almost 100", and Celsius for describing cold weather, e.g., "its cold, like one below zero."

I propose combining the two so there is one scale that has freezing of water as 0 and mas-o-menos human body temperature for 100. However, a problem is that if you divide this in equal size degrees, you end up with a degree that is smaller than a Farenheit degree, namely, .68 of a Farenheit degree or .37 of a Celsius degree. The problem with that is that statements like it is one below zero no longer means something like -1 Celsius. And even "its 101" actually is only 100.68 deg F (not as big an issue).

To remedy that problem I propose a scale where the degree size varies from 0 to 100 such that the first degree is the size of 1 Celsius degree and the 100th degree is the size of a Farenheit degree. That way, you can still have freezing water and body temperatures as end-points, and have the degree size to be about right at each end-point. In between, the degree size changes smoothly such that the sum of the 100 degrees equal 68 Farenheit degrees. Someone more mathematically inclined can come up with the formula. It should be some sort of hyperbola with the values f(1) = 1.8, f(100) = 1, and a minimum around f(50). Sum f(i) = 68. I'll put my best math guy on figuring it out.