I really like the game worlds of the various GUMSHOE games I have (Fear Itself, Esoterrorists, Mutant City Blues) but haven't run it yet.  My big concern is that I've seen the "ablative skill system" kind of mechanic work very poorly in other games - players hoard their "uses," or use them all and then sit on their hands during the latter part of the game session because they know they're not going to be able to succeed at anything and trying will just get them killed.  

In GUMSHOE, your skills are a "pool" of points that you spend either for benefits or for adds to the dice when testing.  You basically roll d6 + spend vs a difficulty, typically 4 for general stuff but often going higher.  Fighting works the same way, so if you have a Scuffling pool of 8, once you've used them all, you know you won't live through any meaningful combat.  

For those that have run GUMSHOE or similar ablative systems, do you find that happening, and what are ways to avoid it?  I mean, I don't mind trying to capture the "downward spiral" but it risks characters just checking out if they don't think whatever plot is at hand is really worth all their lives.  "Let's try to save her next session..." 


Question: Change in Wavelength of a Photon Relation to Energy (specifically Compton Effect)
Answer: If $\Delta \lambda$ is much smaller compared to either $\lambda_1$ or $\lambda_2$(it doesn't really matter, it should be much smaller than both), then we can make the following approximation:

$$|\Delta E|= \left|\Delta \left( \frac {hc}{\lambda}\right)\right|\approx\left|\frac {hc\Delta\lambda}{\lambda^2}\right|$$