Examination Specialties by FOR SALE BY ALL DEALERS PUGSLEY'S GUIDE, with complete instructions for those who wish to learn navigation and save the expense of attending school by preparing themselves for the U. S. Local Inspectors Examination of Masters and Mates of Ocean-Going Steam and Sailing Ships. Price, $.200. PUGSLEY'S NEW YORK PILOT and Guide to the U. S. Local Inspectors examination of masters and pilots for New York Bay and Harbor, with complete sailing directions from Sandy Hook to Yonkers and Great Captain Island. Covers inland examinations generally. Price, $2.00. PUGSLEY'S TIDES. A special work on computation of times of tides for applicants for U. S. Local Inspectors licenses. Contains full set of problems covering every known condition with detailed explanation for each one. Price, $2.00. PUGSLEY'S DEAD RECKONING. A book specially for the beginner. Contains every step in detail with a great number of problems covering every step in the computation of courses and distances and keeping account of a ship’s track. An examination specialty. Price, $2.00. PUGSLEY'S LOG BOOK for yachts and other small vessels; also for ship's officers to record their voyages. Every officer should have one. Price, $1.00. PUGSLEY'S LEARNER'S COMPASS CARD for those who wish to learn the compass. Printed name at every quarter point. Price, 50 Cents. PUGSLEY'S SEAMEN'S RECEIPT BOOK. A proper receipt for money paid for services to a ship by seamen and others. Price, 25 Cents. Any of the above books sent to any address on receipt of price by CAPT. R. M. PUGSLEY 17 South Street New York MATHEMATICAL SIGNS + Plus. The sign of addition: indicates that the quantity is to be added, as Lat. left 27° ogʻ 25" N. Long. left 68° 53' 45" W. Dif. + 2 Dif. + 2 I7 45 W. Lat. ship 30 03 10 N. Long. ship 71 II 30 W. - MINUs. The sign of subtraction: indicates that the quantity is to be subtracted, as Lat. left. 38° 16' 15" S. Long. left 35° 22' 15" E. Lat. ship -32 28 30 S. Long. ship - 33 46 45 E. Dif. 5 47 45 N. Dif. 35 30 W. I • DIVIDE. The sign of division: indicates that the quantity is to be divided, as 63° 15' 30" = 2, and is usually written thus: 63° 15' 30" 2)63° 15' 30" Ans. 31 37 45 2 = EQUALITY. The sign of equality: indicates that the quantities between which it is placed are equal, as in latitude 30°, departure 60' = difference of longitude 120'. . DECIMAL POINT. The sign indicating by its position the value of a number, as 151. is one hundred and fifty one. is fifteen and one-tenth. 15. I DECIMALS Of all the mathematical signs indicating operation or value, the decimal point is the most important, and is given the least consideration by many who study navigation and nautical astronomy. For that reason it is suggested that the student should not begin advanced work until the use of the decimal point is thoroughly known and practised. A decimal is a fraction having some power of ten for its denominator which is not used, the value being fixed by the location of the decimal point. Ciphers to the right of a decimal does not change its value; but between the decimal point and the figures, it does. ADDITION The addition of decimally expressed quantities is the same as whole numbers, if they are so placed that the decimal points, including that of the sum, are directly under the one uppermost. Examples: Add 45.63 10.II 90.43 .151 1.015 10.3 181.9 1.821 Ans. 318.975 Ans. 22.382 SUBTRACTION The subtraction of one decimally expressed quantity from another is the same as whole numbers if they are so placed that the decimal points, including that of the remainder, are directly under the one uppermost. In teaching subtraction, it is customary to place the smaller number under the greater. That cannot be adhered to in this work, as they must occupy a proper position. Examples: Subtract 273.54 8328.469 9321.4306 869.783 Ans. 9047.8906 Ans. 7458.686 MULTIPLICATION The multiplication of quantities expressed decimally is the same as whole numbers, except that the product must contain consideration. If the product does not contain a sufficient consideration, and if the product does not contain a sufficient number of figures place the proper number of ciphers to the left. Examples: Multiply 58”.68 3.7 5. X 7.35 x 16.5 29340 1 875 17604 22 50 41076 375 Ans. 431.2980 Ans. 61.875 DIVISION If the divisor contains decimals, the decimal point in the dividend must be moved to the right as many places as there are decimals in the divisor. Then divide as if a whole number. essen When numbers are to be multiplied or divided, logarithms may be advantageously used, as by doing so those operations are performed by simple addition or subtraction and are tial in the practice of navigation. The logarithm is composed of two parts: the index and the decimal portion. The index is fixed by the number of figures composing the number for which the logarithm is wanted. The decimal part is found in Table 42. The index is one less than the number of figures to the left of the decimal point. index is 3. .65925 45.63 4563. 66 2. I. 4.563 0. To take a logarithm from Table 42, find the first three figures in the first column and the fourth figure at either the top or bottom and the proper logarithm will be found at the intersection. When using this table, bear in mind that the numbers 1, 2, 3, 4, 5, etc., at the top and bottom of the table are not tenths. They are the fourth figures. The logarithm for a decimal is found in the same manner. If the number is a decimal without ciphers between the decimal point and the first figure, the index is 9. If there are ciphers between the decimal point and the first figure, subtract i from 9 for each cipher to obtain the index, as |