Analogical transfer consists in making the assumption that if two situations are alike in some respect, they may be alike in others. This paper studies analogical transfer from the viewpoint of measurement theory. We show that analogical transfer can be seen as a similarity-based reasoning on "contour lines" in a qualitative similarity model: if a contour line is included in another at a given point, then it may also be included at other points that are not too (analogically) dissimilar.