Subordinate to these reasons for studying geometry are many others, exactly as with all other subjects of the curriculum. Geometry, for example, offers the best developed application of logic that we have, or are likely to have, in the school course. This does not mean that it always exemplifies perfect logic, for it does not; but to the pupil who is not ready for logic, per se, it offers an example of close reasoning such as his other subjects do not offer. We may say, and possibly with truth, that one who studies geometry will not reason more clearly on a financial proposition than one who does not; but in spite of the results of the very meager experiments of the psychologists, it is probable that the man who has had some drill in syllogisms, and who has learned to select the essentials and to neglect the nonessentials in reaching his conclusions, has acquired habits in reasoning that will help him in every line of work. As part of this equipment there is also a terseness of statement and a clearness in arrangement of points in an argument that has been the subject of comment by many writers. Upon this same topic an English writer, in one of the sanest of recent monographs upon the subject,[13] has expressed his views in the following words: The statement that a given individual has received a sound geometrical training implies that he has segregated from the whole of his sense impressions a certain set of these impressions, that he has then eliminated from their consideration all irrelevant impressions (in other words, acquired a subjective command of these impressions), that he has developed on the basis of these impressions an ordered and continuous system of logical deduction, and finally that he is capable of expressing the nature of these impressions and his deductions therefrom in terms simple and free from ambiguity. Now the slightest consideration will convince any one not already conversant with the idea, that the same sequence of mental processes underlies the whole career of any individual in any walk of life if only he is not concerned entirely with manual labor; consequently a full training in the performance of such sequences must be regarded as forming an essential part of any education worthy of the name. Moreover, the full appreciation of such processes has a higher value than is contained in the mental training involved, great though this be, for it induces an appreciation of intellectual unity and beauty which plays for the mind that part which the appreciation of schemes of shape and color plays for the artistic faculties; or, again, that part which the appreciation of a body of religious doctrine plays for the ethical aspirations. Now geometry is not the sole possible basis for inculcating this appreciation. Logic is an alternative for