I hope you mean the myth of strength.
People generally spend way too much time on their chest with the goal that they will 'look bigger and stronger'.
Nothing wrong with that. But if strength is why you are training, start deadlifting.
El Guapo says, ""You can buy muscles, but you can't buy COJONES!"
"When I do the press, I seem to feel it more in my triceps than my chest."
You need a wider grip on the bar (might not be possible on some type of machines, but try to improvise). Experiment with different widths and at a certain point, you will be hitting your chest much more than your triceps. Heavy, low-rep(3-8), slow sets to failure are best. Rest at least 4 minutes between sets.
You can't make a man by standing a sheep on its hindlegs but if you get a group of men together you can create a herd of sheep.
Ok. I tried tiring my triceps before doing my vertical press. I could definately tell a difference. Thank, Hap.
As for the "myth of strength" - That doesn't bother me. I'll still be stronger than I am now. Plus, I'll look better, too. :) I don't ever plan on getting into a strength competition. Now, a bathing suit, well... that's another story. :D