senting the hundreds, thousands and millions, as 93 346 543, and look for relations between the divisions, first. 2. We see that there are three 3's, one in each division. It is also seen that the sums of the figures in the different divisions are 12, 13, 12. Taking the first division; there are two figures only, one of which is 3, and the sum is 12, therefore the other must be 9. This places the millions at 93. Then taking the third division, which has the same total, 12, we see that it, just as the first division, ends with its 3. The other two figures add to 9 and may be 90, 81, 72, 54, or the same numbers reversed. It is 54, a combination which makes with the last figure, a sequence reading from right to left, the right end being the known figure. 3. Now, consider the thousands division and note its relations to the others. The sum of the figures is 13, one of which is 3, leaving a possible combination of the others in order to make 10, of 91, 82, 64, or 55, or any of them reversed. Compare this division with the hundreds; one commences with the 3 and the other ends with the 3; carry on the sequence of the last division and we get 6 for the last figure of the second division, and the middle figure, therefore, must be 4, which is also the middle figure of the last division. Again, comparing the first and the second divisions, we see that the two 3's come together, also that the sum of the first and last figures of the second division equals the other figure of the first division. This reasoning is given here in detail, but with a little practice the powers of observation are so quickened that the relationships are al most instantly seen and in taking up any set of figures, the mind will instinctively look for them, and fix them in memory. The number is then remembered not as so many arbitrary figures, but as a lucid grouping, and in future revival of the impression, any one figure will recall all the others in their proper order, one after another, until the group is complete. It will surprise one who has not thus thought of numbers, to observe how relations may be established between the figures of almost any given number of four or more figures. Consider, for instance, the populations of the three American cities having over one million inhabitants New York, Chicago and Philadelphia: Note the arrange New York-4,766,883. ment of double 6's and 8's-the sum of the first and last figures equals the second figure-the second and third divisions each total 19. Chicago-2,185,283. Note the arrangement of the 1, 2, 3-the difference between the first and last figures of the third division equals the first figure of the second division, and the sum of the same figures equals the last figure of the second division-and the middle figures of these two divisions are the same. Philadelphia-1,549,008. Note the relationship of the 9's-first and last figures equal 9— first and second of the second division equal 9, which is the other figure of this division-and total of all figures equals 27, 9 times the number of divisions. Other relations will easily be found, but this will be sufficient to indicate the character of the relations that exist between figures, the observation of which will assist in the study of even the most mathematical works. This underlying principle of the mutual dependence of things on each other, and observation of the most prominent features, will assist in the recollection of a man's name from his style of dress, his size, appearance, office or employment; the name of an author from association with the title or character of his books; a date from association with something connected with the incident, etc. The association of ideas is of great importance and its practice will make it of valuable assistance in learning anything, but it does not do away entirely with the necessity of making written memoranda. Use these to save the exercise of the mind on the non-essentials, and back them up with the brain's record of the unchangeable essentials-first making sure that these essentials and the relations between them are thoroughly understood, and are not stored away as a heap of facts without connection or order. X PREPARATION OF MANUSCRIPTS The vast quantity of new material on technical subjects constantly appearing in the form of books and periodical articles is evidence of a growing tendency on the part of engineers toward literary work. Yet it is a fact that not one-half of the manuscripts submitted to publishers are accepted and published, and it may also be noted that a very considerable portion of these offerings are the first efforts of their writers in this particular form of composition. Some manuscripts show that much time and pains have been taken in their preparation, but a lack of acquaintance on the part of their writers with the elementary details of the publishing business renders these efforts ineffectual, and results either in the rejection of the manuscript or in the necessity of editorial revision and a consequent delay in its publication. On the other hand, some of these manuscripts are little more than hastily-written texts carelessly thrown together, with a bundle of crude drawings, which certainly does not complete the initial stages of a book, nor form a welcome contribution, from the publisher's point of view. These facts show the desirability of an explanation of some of the principles that should govern authors in the preparation of their manuscripts in order that they may gain literary recognition and that the profession may benefit by the information they convey. Before a manuscript is turned over to the printer it must have a title page, a table of contents or chapter heads, a copyright entry, a preface or an introduction, or both, and a list of illustrations, if they are of sufficient importance to warrant it. It must be standardized as to typographical style, punctuation, capitalization, and orthography; paragraphs and other divisions, italicized words, and positions and titles for illustrations must be clearly indicated; chaptertitles, sub-heads, section or paragraph topics, head-lines or "box heads," etc., must be inserted, and last, but by no means least, after the book is in type and made up into pages, a full and intelligently-made index must be provided. This work is known as "editing the manuscript." Besides these details it involves. many others which necessitate a considerable knowledge of the technicalities of typography. It consists essentially of preparing the manuscript for the printer, that is, in preparing the "printer's copy," in which nothing must be |