Francis
sent me this search page for "on the tree," asking if the instances of its usage are incorrect. This is my response to his question:
Examples one, two, five, six and nine on this search page refer to excrescences of a living organism known as a tree--to wit, leaves or fruit (with the one exception of lights which are attached to a tree, example two, but nonetheless constitute excrescences of a tree). Example three is incorrect, although native English speakers would understand it. All of the other examples, except example eight, refer to tree used in a figurative sense, and not as a reference to a living organism. So in fact, "while on the tree walk" is an example of the preposition "on" being used with the noun "walk," and "tree" being used to descriptively modify the word "walk"--it is a tree walk, as opposed to any other type of walk (readily understood by native English speakers, this would mean a walk one takes to look at trees). In the example "Pressing ENTER while on the tree display . . . " refers to a display, i.e., on the display, with "tree" used as a descriptive modifier of display--i.e., a display which has "branches" as does a tree. The same applies to the final example on that page. The eighth example uses tree in a very specialized sense, which is quite uncommon, and only seen in that context. In that entry, "tree" refers to the cross upon which the putative Jesus was crucified--when christians refer to the cross as a "tree," the use of "on" is no different than the use of on in the phrase: "Jesus was executed on a cross."