Next question, are the tires folding or metal wire bead? If you bought them in an already circular state (as opposed to folded up in a box) they are probably wire bead which is good. 27 X 1 1/4 can safely sit on a straight wall rim up to about 80 psi and this is the normal pressure for that size tire if you weigh less than 220 lbs. 70 psi isn't a bad pressure either. I currently run straight wall rims with no problem but have pumped them harder than 80 and had the tire blow off. Have a spare tube handy before trying that experiment.

Keep in mind back in the 70's bikes were ridden on any kind of road and so tires were bigger and lower pressure to better fit the rugged lifestyles of hairy chested He-Wheelmen that dominated the roadways then.