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"TAE MaRINE REVIEW ee | » 4 quart to the gallon and 2 pints to the quart, or thus, I5 X 4 X 2 = 120. Note.--In using the foregoing rule, numbers. should be considered as abstract, and not as denominate. A 'number used without reference to any particular thing is called an abstract number. Thus, 4, 7. 9 etc., are called abstract numbers. A number used in connection with something is called a concrete number. Thus, 5 degrees, 4 books 7 days,-8 dollars, are concrete numbers. In multiplication the multi. plier is always regarded as an abstract number. The multiplicand and product are like numbers. For sake of simplicity we have reversed this latter rule and made the multiplier a denominate number instead of an abstract. Thus, in the example: change 40° 15' to minutes; 40X 60' = 2400' + 15'=2415', The correct analysis of this would be: we multiply 60' by 40 because it takes' 60' t "4° ' ° there would be 60' 40+15' which is 2415', 2S Ae ee REDUCTION ASCENDING. Changing a denominate number to an equivalent num- ber of higher denomination is called reduction ascending. Change 480' to degrees. Ans. 8°. In this case we divide where we multiplied before; thus, 480' divided by 60, the number of minutes in a degree. The process of changing a denominate number to an equivalent number of higher denomination is called Re- duction to Higher Denominations or Reduction - Ascend- ing; as for example: How many degrees in 1740'? An- swer, as many degrees as 60' are contained times in 1740' because 60' = 1°. 60' are contained in 1740' 29 times, or 29" . * a Again, how many degrees in 90,000". Ans. 25°. ~Ex- planation:--Since there are 60" in 1', in 90,000" there are as many ' as 60" are contained times in 90,000", or 1,500'. Since 60' = 1°, in 1,500' there as many ° as:60' are con- tained times in 1,500' or 25°. * To reduce "' (thirds) to degrees we divide by 60 three times--once for ", once for ' and once for ° Rule.--Divide the given number indicating how many units of the given denomination make one of the next higher denomination. oS Proceed in like manner with this, and each successive quotient, till the whole is reduced to the required de- nomination. The last quotient, with the remainders, if any, annexed, will be the required answer. : 60 | 2,592,000°" 2,802:000 = 60 60 | 43,200" 43,200" = 60 60 | 720' 720 = OO i ; I Change 1740' to degrees. Ans. 29°. Change 104,400" to degrees. Ans. 29°. In a case of this kind we divide by 60 twice, once for minutes, and once for degrees; thus, 104,400" + 60 = 1740' and 1740' + 60. == 20.. Examples for practice: Change 17 yds. I ft. 9 in. to inches. Ans. 633 inches. Explanation:--Since there are 3 feet in 1 yard, in 17 yds. there are 17 times 3 feet = 51 feet, and 51 feet + 1 foot equals 52 feet. Since there are 12 inches in I foot, in s2 feet there are 52 times 12 inches = 624 inches and 624 inches + 9 inches = 633 inches. Hence, 17 yds. 1 ft. Noll Il II 9 ins. = 633 inches. Change 15 hrs. 16 mins. to seconds. Ans. 54,900 sec- onds. Since 1 hour equals 60 minutes, 15 hours equals 60 times 15, or 900 minutes plus 16 minutes equals 916 minutes; and as there are 60 seconds in one minute, in 916 minutes there are 60 times 916, or 54,960 seconds. Change 4 weeks 6 days 11 hours to hours. Ans. 827 hours. Se Since one week is equal to 7 days, 4 weeks will be equal to 4 times 7, or 28 days plus 6 days equals 34 days, and since 'one day -equals 24 hours 34 days equals 24 times 34, or 816 hours plus 11 hours equals 827 hours. : What part of a circle is it from XII to III on the face of a clock? Ans. go° The circle face of the clock is di- vided into 12 equal parts, or hours; therefore, 12 is equal to 360°, and 1-12, or 1 hour, is equal to as many degrees as 12 is contained times. in 360° (360° + 12 = 30°); hence, each hour is equal to 30°; and as there are 3 hour divisions - $200,000. between 12 o'clock and 3 o'clock 3 X 30° = 90°3 or as 3 1s contained in 12 4 times it must be 4 of the circle, or 90°. oe How much of an arc is it from IX 'to X on the clock? Ans; 30. - What part of a circumference it is from III to VII on the clock? Ans. 1-3, or 120°. as How much of an arc is it from 9 o'clock to 3 o'clock? Ans. 180°, From 9 to 3 o'clock is 6 hours and 6 X 30° = 180°, or 4% a circumference, __ - et : Imagine the minute and hour hand of a clock to be of the same length; the minute hand is on XII and the hour hand is on I. What is the angle formed by these two hands, also, how much is the arc from one hand to the other? Ans. 30°, that is, the angle is 30° and the arc of the circle is. 30.0, | ae ----__--- QUESTION AND ANSWER DEPARTMENT. | This department is conducted for the information and instruction it will render our subscribers in practical lake service, or otherwise. Primarily, its purpose is to be help- ful, rather than merely interesting. Are you puzzled by any question in relation to the science and practice of lake navigation, questions that concern your every-day naviga- | 'tion? State your question or problem in writing, and mail it to the Question Department of the MARINE REVIEW. If the question asked or the problem submitted is of gen- eral interest, the solution will be printed in these columns. If of merely personal interest, it will be forwarded by mail, provided an addressed and stamped envelope is in- closed for the purpose when the question is sent in. Rules for Question Department. Your real name and postoffice address must be on the sheet with the question, initials will not do. Your name is not for publication, but is an evidence of good faith. We reserve the right to decline to answer any question. not of general interest, i. e., unless the question and answer is helpful to others. LUMBER CARRIERS AND LABOR. The Lumber Carriers' Association has entered into sea- son agreements with the seamen and cooks. The seamen have practically the same schedule as last year with the addition of 25 cents an hour paid for all overtime in port. Cooks on lumber vessels carrying a crew of thirteen men are given $85 a month, which is an advance of $5 over last year's rate. The cook must, however, provide a sec- ond cook out of this allowance. In other respects the wages are the same as last year, on boats carying twelve men, $70 a month and on boats carrying eleven men, $60 a month. The wages for cooks on barges and schooners are the same as for seamen. An effort was made to dis- place women as cooks and it has probably been done by inserting the words "prior to 1905" to the agreement. This clause now reads: "It is understood that vessels of the Lumber Carriers' Association have the privilege of employing women cooks providing they have cooked on boatis of the Lumber Carriers' Association prior to 1905." This forbids the hiring of any more women cooks and excludes those who were hired last year. A bill to place a beacon light at the entrance of Milwaukee harbor has been recommended in committee. This light. is to be placed on the south end of the harbor of refuge pier, and will have a third order flash light and be equipped with a fog whistle. The tower containing the light will be about 100 ft. high and the original cost will be in the neighborhood of '