The muscle cells eagerly suck out the food-stuffs, and breathe in the oxygen of the blood; at the same time, they pour into it their waste stuffs of all sorts, including carbon dioxid.

These rob the blood of its bright red oxygen color and turn it a dirty purplish, or bluish, tint.
The loops of capillaries again run together, as they did in the liver and in the lung, to form tiny veins; and these run together at the base of the thumb and in the wrist, to form larger ones through which the now poor and dirty blood is carried back up the arm over much the same course as it took in coming down it.

Indeed, the veins usually run parallel with, and often directly alongside of, the arteries.

The blood passes through the armpit, across the chest, into the great main pipe for impure blood, the vena cava, and through this into the right side of the heart, where it again meets the rich, but waste-laden blood from the food tube and liver, and starts on its circuit through the lungs and around the body again.
The blood reaches every portion of our body in precisely this same manner, only taking a different branch of the great pure-blood delivery pipe, the aorta, according to the part of the body which it is to reach, and coming back by a different vein-pipe.
Why the Arteries are more deeply Placed than the Veins.

In the limbs and over the surface of the body generally, the arteries are more deeply placed than the veins, so as to protect them from injury, because the blood in the arteries is driven at much higher pressure than in the veins and spurts out with dangerous rapidity, if they are cut.