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through forms. Hence, then, the sooner the teacher corrects such ideas in the pupil, the better it will be for both.
IIL-Exact Observance of Rules imperative. Thirdly. Every element in the diagrams must, in form, combination, order, attachment, and connection, be drawn according to the rules, invariably and exactly. Pupils are prone to consult a supposed ease in drawing, or to give loose rein to their own crude fancies, and thus they take unwarrantable and destructive license in the construction of diagrams. If, in accordance with the pernicious doctrine so current, of giving the substance of things without regard to the exact form, they have the various figures drawn substantially correct, that contents them. And so their diagrams, like their figures in mathematics, or their penmanship, or their maps, are, for very deformity, the likeness of nothing in the heavens above, or the earth beneath, or the waters under the earth.
IV.-A regular Order of Construction required. Fourthly. Figures which are similar should always be drawn from one regular starting point, with the same steady and continuous sweep of the hand, with the same prevailing curves, and with the same exact completion or attachment.
(1). POINT OF COMMENCEMENT.
The proper point of commencement for all complete figures is at the extreme left point, or the middle of the left extreme, as this is the natural point of commencement in writing the elements included; it leads to the proper forward motion of the hand in drawing; and it is best calculated to secure an exact connection of the related figures.
(2). PROPER MOVEMENT.
For all such elliptical figures, also, the proper motion is from the point of commencement, upward and onward to the right, and then downward and by a reversed stroke to the left. Never begin with the downward motion, constructing the lower line first. And, as far as is practicable, draw every figure and line with a continuous sweep. Never resort to the vicious practice of drawing parallel straight lines, and patching up the ends with fragmentary curves. Apply such a method to the construction of capitals in penmanship, and see how ridiculous will be the result. But, it is no less unnecessary, and no less inelegant and mischievous, in the former case than in the latter.
(3). COMPLETION OF FIGURES.
Still further, let complete figures be neatly finished. Do not carelessly dash up the closing portion of a figure, leaving the ends of the lines either disconnected, running over each other, or bulging out in inconsistent curves or swollen joints.
The same general rules apply to the construction of incomplete figures. The minor variations necessary will suggest themselves, and will, in all thoughtful drawing, substantially harmonize with the general rules.
1.-The Crossing of Lines or Figures inadmissible,
Fifthly. In drawing lines of connection between principal and subordinate propositions, it is a cardinal law that one line must never cross another line or figure. Subordinate elements of this kind must be skillfully disposed to the right and the left, below, so as to be readily connected with their principals, by the waved lines, with
out any careless or confused crowding or crossing. Disregard this rule, and the diagrams for involved complex sentences will soon become “confusion worse confounded.”
VI.-The Æsthetic to be constantly regarded. Sixthly. Always have an eye to the symmetrical and beautiful, as well as to the symbolical. An ugly diagram is the next evil to a bad analysis. With this principle in view, let important diagrams be carefully re-studied and re-drawn, as a matter of simple art-practice. Very possibly, many teachers and pupils will be impatient of such strict restraint and repeated labor; and quite as possibly, it is the very training which they most need.
GENERAL DEFICIENCY IN THIS DIRECTION.
Hardly any accomplishment is more infrequent among even educated persons, than neat, exact, and symmetrical execution in the line of graphic representation. And while this continues to be so, it is too much to expect that a corresponding crudeness and defectiveness will not characterize the body of their learning or their thinking. Since, then, it is one object of the study of analysis to correct this evil, and since the diagrams are so admirably adapted to the uses of analysis in this direction, let the study of the diagrams run parallel with that of analysis ; and as, in the latter, the constant aim must be logical precision and thoroughness, so in the former, let it be graphic neatness and accuracy.
THE RULES ENFORCED BY INDIVIDUAL EXPERIENCE. In conclusion, the observance of these practical rules is pressed with the greater earnestness, for the reason that
the author's experience has shown clearly and constantly, that imperfect or vicious drawing in the construction of diagrams induces a crude or a false analysis, and engenders a dislike for the whole system. Such is the natural and necessary relation between the logical analysis and its graphic representation, that he who begins by debasing the latter, will end by detesting the former. “He who begins by hurting," says a distinguished writer, s will end by hating.”
EXAMPLES FOR PRACTICE IN. ANALYSIS, AND
CONSTRUCTION IN DIAGRAM.
EXAMPLES FOR PRACTICE IN SENTENCES OR PROPOSITIONS.
Preliminary remark—I. Scheme of Classification—1. Distinctions
common to sentences, propositions, and phrases—2. Belonging
PRELIMINARY REMARK. WHILE it is no part of the present design to enter into a systematic consideration of grammatical analysis, it is