The foregoing explanations as to the use of logarithms are cheifly for the benefit of those who have, by disuse, become "rusty" in the use of the tables; although any one may in a day or two become familliar with them and may, by their use, greatly lessen the drudgery of mathematical calculations. Such uses only have been explained as pertain to the simpler mathematical operations. EXPLANATION OF CHARACTERS. The following brief explanation is given of a few of the more common characters used in calculations, etc. and which are so frequently met with in mathematical and similar works. ( ) [ ] Proportion, = as 28:4:16 reads....as 2 is to 8 or, 2 is to 8 as 4 is to 16. The Vinculum or Bar indicates that all the numbers over which it is placed are to be considered as one quantity, thus, 2+ 8 + 2 = 5; or 5 X 8-2 = 30. Parenthesis or Brackets indicate, as in above, that all included figures are to be considered as one quantity, thus, (3 × 5) + 10 = 25; or 3 × [5 +10 ] = 45. Decimal Point. The Radical or Root sign when placed before a num ber indicates that the square root of the number is required, 164; 15+ 10 = 5. The degree of the root, other than the square root, is indicated by a figure placed above the radical, which figure is called the Index. 3 Cube root; N = 4th. root etc. Signifies Angle. " &c. § &c. " 235 &C. " Therefore or Hence. Because. The Ratio of the circumference of a circle to its diam- Greater and Less, a>breads - a greater than b. Degrees. Minutes, and Seconds of arc. when set superior to a number, that the square or cube when set superior to a number, the power to which the number is to be raised, thus 22 = = 4; 23 = 8; 25 = 32 &c. CONCLUSION. The public may claim that the author owes to them an apology for having presented an irrigation manual wherein no direction is given as to the detail workings of an irrigation plant, or any direction as to when, and how often, to irrigate, how to prepare the soil, &c. Such was not the object, as stated in the preface, but rather to present certain items of technical information, and such other matter as would tend to show the importance and practicability of irrigation in the Dakotas. The subject is one too vast to be treated fully in one volume, or in a score of volumes, such as this. More has been omitted than has been included, and much which was of value, and which it was desired to include, has been omitted because of the limited means and space, and the circumstances under which this little book was made. Should it become advisable to issue a second edition many additional features of interest and of value will be included. A start has, however, been made which it is to be hoped others will more successfully emulate until all of the people of these states shall have become imbued with the vital importance to themselves and to their children of this matter of irrigation; and until the thousands of acres of our now waste paradise shall have put on that cloak of perrennial verdure which is their due and their destiny. No more fitting conclusion can be made than to quote from the eloquent words of the late Hon. S. S. Cox, congressman from New York, delivered in his oration at Huron on July 4th, 1889. Words as poetic in sentiment as they are prophetic of truth. He said: "But yesterday your fruitful valley was whitened with the bones of the buffalo. Now it is an ideal farming area. It is a lesser Nile region, without its overflow. Artesian Wells give water where the sun once made drouth perrennial. The water power of your matchless valley is as yet immeasurable by ordinary mechanical standards. It is so prevalent that your people will utilize its specific gravity for the diversity of their industries. When its undiminished flow and steady pressure from the bosom of the earth are properly harnessed by mechanism, it will give its lucid lymph to make grasses for stock and lawns for beautiful homes. Its sunless currents, through the ingenuity of man, will_enhance the rich soil by quenching its thirst. Fabulous are the wasted energies of your water power, as we count it by the standard horse power of mechanics; but still more marvellous are the real energies of the soil which it would fructify. The beautiful and fruitful valley of the James may not be as redolent of historic association and traditions as another James River of the colonial days; but deeper than historical or traditional incident are Dakota's pure springs under a magic more enchanting than that of Aladdin, which leap from your modern Artesium. THE END. ་ Advertising Appendix. THE author, on behalf of the public for whom this Manual is intended and to whom it will come, acknowledges the obligation due to the advertisers herein; for from the proceeds of this feature of the book has, in chief, been derived the funds for its publication. Had it not been for this patronage the book could not have been made. It is hoped and expected that in no sense has this been a charity, but rather a good paying investment, for the goods advertised will be used in large quantities in these states and the advertisers deserve the patronage of our people not only because the largest and most responsible representatives in their respective lines, but because of the acknowledged excellence and reputation of the goods they rep resent. The information contained in this appendix will be of value to irrigators and others who often find difficulty in learning as to where to find reputable dealers with whom to deal. Such only have been solicited, and to such as are here represented our people fairly owe their patronage. James B. Clow & Son, LAKE AND FRANKLIN STREETS, * CHICAGO, ILLINOIS. Manufacturers of and Dealers in Wrought Iron Pipe, Well Casing, Line Pipe, Boiler Tubes, Well Tools, Fittings & Brass Goods ALSO Supplies for Plumbers, Gas and Steam Fitters and SEND FOR CATALOGUE AND PRICES. |