A point H lies on a network Q according to some unknown distribution. A Searcher starts at a given point O of Q and moves to ...nd H at speeds which depend on his location and direction. He seeks the randomized search algorithm which minimizes the expected search time. This is equivalent to modeling the problem as a zero-sum hide-and-seek game whose value V is called the search value of (Q; O). We make a new and direct derivation of an explicit formula V = (1=2) ( + ) for the search value of a

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... ree, where is the minimum tour time of Q and (called the incline of Q) is an average over the leaf nodes i of the di¤erence (i) = d (O; i) d (i; O) ; where d (x; y) is the time to go from x to y: The function can be interpreted as height, assuming uphill is slower than downhill. We then apply this formula to obtain numerous results for general networks. We also introduce a new general method of comparing the search value of networks which di¤er in a single arc. Some simple networks have very complicated optimal strategies which require mixing of a continuum of pure strategies. Many of our results generalize analogous ones obtained for constant velocity (in both directions) by S. Gal, but not all of those results can be extended.