In the second case, the difficulty experienced is the incompatibility of a suggested and (temporarily) accepted belief that the pole is a flagpole, with certain other facts. Suppose we symbolize the qualities that suggest _flagpole_ by the letters _a_, _b_, _c_; those that oppose this suggestion by the letters _p_, _q_, _r_. There is, of course, nothing inconsistent in the qualities themselves; but in pulling the mind to different and incongruous conclusions they conflict--hence the problem. Here the object is the discovery of some object (_O_), of which _a_, _b_, _c_, and _p_, _q_, _r_, may all be appropriate traits--just as, in our first case, it is to discover a course of action which will combine existing conditions and a remoter result in a single whole. The method of solution is also the same: discovery of intermediate qualities (the position of the pilot house, of the pole, the need of an index to the boat's direction) symbolized by _d_, _g_, _l_, _o_, which bind together otherwise incompatible traits. [Sidenote: (_c_) in explaining an unexpected event] In the third case, an observer trained to the idea of natural laws or uniformities finds something odd or exceptional in the behavior of the bubbles. The problem is to reduce the apparent anomalies to instances of well-established laws. Here the method of solution is also to seek for intermediary terms which will connect, by regular linkage, the seemingly extraordinary movements of the bubbles with the conditions known to follow from processes supposed to be operative. [Sidenote: 2. Definition of the difficulty]