Take off the lower shoots whenever your knife is sharp.  Do not let them grow another year.  Theoretically, the best time to remove them is toward the end of the dormant season, but if they are not large as compared with the whole growth of the tree, go to it any time.

Canning Olives.

What is the recipe for preserving olives by heat, and how long do they have to remain in the heated state?

Canning olives is a process, not a recipe, and it has to be operated with judgment.  It resembles, of course, the common process of canning other fruits and vegetables.  It has been demonstrated that heating up to 175° Fahrenheit is effective to keep olives in sealed containers for over two years.  The heating was done in the jars in the usual canning way for several minutes after 175° was reached, to be sure the contents were heated through.

Renewing Olive Trees.

I have olive trees on first-class land; no pest of any kind is apparent.  The trees look healthy in every way, and average about 12 inches at the butt and 30 feet high.  They have borne fruit, but for the last three years have not borne.  I am advised to cut back to stumps, 5 or 6 feet high, and start new tops.

Unsatisfactory olive trees may be cut back, but not to such an extent as you mention.  Thin out the branches if too thick and cut back or remove those which interfere, but to cut back to a stump would force out a very thick mass of brush which you would have to afterward go into and thin out desperately.  The branches which you decide to retain may be cut back to twelve or fifteen feet from the ground.  This would have the effect of giving you plenty of new thrifty wood, which is desirable for the fruiting of the olive, but we cannot guarantee that this treatment will make the trees satisfactory bearers.  Are you sure they are receiving water enough?  If not, give them more next summer.  Also give the land a good coat of stable manure and plow under when the land is right for the plow.

Growing Olives from Seed.

How are seedlings grown from olive seeds?

Growing olives from seeds is promoted by assisting nature to break the hard shell.  This can be done by pinching carefully with ordinary wire pliers until the shell cracks without injury to the kernel, or the shell may be cut into with a file, making a very small aperture to admit moisture.  The French have specially contrived pliers with a stop which admits cracking and prevents crushing.  Olive seeds in their natural condition germinate slowly and irregularly.  They must be kept moist and planted about an inch deep in sandy loam, covering with chaff or litter to prevent drying of the surface.  Before experimenting with olive pits, crack a few to see if they have good plump kernels.  Seedling olives must be grafted, of course, to be sure of getting the variety you want.  For this reason growth from cuttings is almost universal.