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26 THE Marine REVIEW SCIENTIFIC LAKE NAVIGATION. By Clarence E. Long. PREFACE TO ARITHMETIC. This lesson is ittended to be self-explanatory; help from a teacher being unnecessary. The aim of the writer in the preparation of this first lesson--Arith- metic--has been to furnish a treatise on the subject of Arithmetic as applied to practical navigation. Complete, though not inexhaustive, it is a comprehensive manual for the self-taught student; and, there- fore, embodying every necessary form of illustration and exercise. In the writing and arrangement every consideration has been given to the peciliar conditions under which the 'lake navigator labors; and for this reason nothing has been stated that is not applicable to the theoretical learning and practice of scientific lake navigation by self- instruction. We have aimed to secure several results; namely, simplicity and clearness; how to reach and arrive at the fundamental principles of the study at once without unnecessary labor; and a proper under- standing of the reasons for the steps in the explanation of processes and the solution of problems. There aré many good Arithmetics in print, but none are devoted to this special study, nor adapted to self-instruction. While the ordinary Arithmetic contains much along this line, it is 'scattered through so many pages and so smothered by their surroundings that the untutored would be at a loss to even know where to start, let alone to understand it. In the present treatise, however, the whole subject is presented in a compact, though~»complete form, so that the student always starts at the beginning of the study and is led step by step. "Nothing is stated, only that which is absolutely necessary to a full understanding of the science; thus, the student is spared any chance of being led from the proper course of study. The treatment of every topic from the beginning to the end of the book, is thoroughly inductive. In this way, and by carefully constructed analyses, applied to all the various processes of the study, the pupil's mind cannot fail to be- come thoroughly imbued with clear' and accurate'ideas in respect to eath particular topic before he is required to learn, or apply to written examples, any set rule whatever. Definitions and principles should be carefully committed to. mem- ory. A definition is a basis for thought and reasoning, and every word which it contains is necessary to its integrity. With, a clear understanding of a definition comes the understanding of its principle and process. With the principle and process understood the rule or definition suggests itself. There are cases where the process explains the rule, instead of the rule explaining the process. In every-day practice the process ,eurned in the ordinary way-- parrot-fashion--are of little value because they are not the natural processes of the practical man. Students who learn to work exam- ples in a mechanical way often find themselves unable to solve, with certainty, .very simple probiems, because they have been taught a school method instead of a natural method. The author has therefore, adopted natural and practical methods of computation wherever they could be wisely substituted for the ordinary processes. The student should be careful not to advance too rapidly. The mind needs time to grasp' and hold firmly every new case, and then additional time to bring its new acquisition into relation with those preceding it. Hence, the need of frequent reviews, in order to give the pupil a comprehensive as well as accurate and permanent knowl- edge of the subject. Seek to cultivate the habit of selfreliance. This once atiained, leads to acquiring that most important of all mental habits, that of thinking and reasoning for yourself. One does not learn to think by mere thinking, but he learns to think correctly by thinking under guidance. There are many guiding posts in the lessons following so that the student will have every chance and opportunity of thinking correctly. Learn to be observing. Train yourself to be observing by cultivat- ing the mind in that direction. Think for yourself and reason for yourself; do not have, or expect, some one else to do it for you; and above all learn to rely upon yourself. These are necessary re- quirements for the student to acquire for a firm basis on which to build beneficial and lasting knowledge. The student should make it a point to investigate the 'whys' and "wherefores' of the various rules and principles involved in the different subjects so that he may intelligently understand what he is to do and why it is done. Never learn rules or Principles parrot- fashion. Learn the principles and processes, then if possible, frame your own rules. If you know why you are doing a certain thing you can always give a reason; this reason then should be your rule, Such rules will be living and lasting rules, not easily forgotten. The student should never permit himself to accept any statement as true which he does not understand. Learn it not by authority, but by practical demonstration, which he can always, in some man- ner or other, devise for himself. By these means the student is led to employ real methods of solution because they are generally natural methods, and to understand and explain every step in this process. A student who has been trained in this manner will never forget a process or a rule, because he can devise the process and frame the rule at will. As a rule, the average sailor is backward in Arithmetic--not be- cause he isn't able to learn it, but simply because he has not had the advantages of such training, and the practice of employing it. Arithmetic is practically the foundation of navigation, and is essen- tial to an understanding of same. When the practical man desires information of any kind, whether it be his distance off a rocky reef that he is about to pass, or the acquiring of any study that will tend to further his interests, he wants to proceed to business at once, without coming "in stays'? and beating back and forth. It is the main points that he wants, and if there be any beating and tacking to be done these are the points to tack on. This is precisely the man- ner in which these lessons are arranged. The order and arrangement of the subjects, though they are in some respects a departure from that usually given, will hasten the pupil's progress because one is a stepping stone to the other, and each subject follows in the order in which it is to be learned. This work is of sufficiently comprehensive scope to meet the de- mands of even the most advanced schools and standard books on navigation. The unusually practical character of the problems will be discerned by a mere glance through its pages. After the rules, principles and processes have been explained, practical examples are given to show their application in every-day lake navigation. This is the kind of knowledge that counts. Such knowledge is '"'real," not theoretical knowledge. The stiident should carefully read over several times, with due thought and deliberation, each subject in its order. In this manner he acquires a. theoretical knowledge of the principles underlying the subject. Then he is to go back and commence at the beginning of each subject, and put its theory into practice by acquiring its rules and working its processes. This is the proper course to pursue in order to obtain the necessary basis or ground-work, so essential to the thorough and comprehensive understanding of any study. The student should not become discouraged if he is unable to grasp the meaning of each principle at first sight. Should this at any time occur, after giving it the required amount of study, either throw it from the mind entirely for the time being, and take up the subject following it. Many times the student will be able to grasp the following subject more readily than the one preceding it, for. it may happen to appeal to him, whereas the other did not. Thus, the following subiect ofttimes helps to expiari the preceding subject, since one is a stepping stone to the other. The learning of one subject increases one's power to master an- other along the same lines. It is also a fact that the study of a branch of knowledge that trains several powers of the mind may in- crease its capacity to master other branches that appeal to these powers. Go slow and begin at the beginning. Be sure to do everything thoroughly that you attempt to do. ARITHMETIC OF PRACTICAL NAVIGATION. WRITTEN ESPECIALLY FOR THE BEGINNER. The arithmetic of practical navigation is extremely sim- ple and is included in the following: it is supposed that the four fundamental rules of Arithmetic are clearly understood by the student. LESSON I.--PART I. The first lesson in navigation is the arithmetic of navi- gation. ARITHMETIC OF THE COMPASS. The first thing to be done by the pupil is to learn and memorize the table of circular, or angular measure; in other words, the degrees °; minutes ', seconds ", into which every circle of circumference, is divided, and by which it is measured. This is very essential since this part of mathematics