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Many Internet protocols and operational procedures use measurements to guide future actions. This is an effective strategy if the quantities being measured exhibit a degree of constancy: that is, in some fundamental sense, they are not changing. In this paper we explore three different notions of constancy: mathematical, operational, and predictive. Using a large measurement dataset gathered from the NIMI infrastructure, we then apply these notions to three Internet path properties: loss, delay, and throughput. Our aim is to provide guidance as to when assumptions of various forms of constancy are sound, versus when they might prove misleading.