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Chapter Two - How a Slide Rule Works 9It is interesting to note that the mantissa of 375 is the same as the mantissafor 37.5 or 3.75 or 375,000,000! The characteristic tells us which number it is.Log 3.75 = 0.574Log 37.5 = 1.574Log 375 = 2.574Log 375,000,000 = 8.574Each successive characteristic represents a number that is 10 times, or onetenth, the number represented by the adjacent characteristic. But ... logarithmsof numbers less than 1 are slightly different! See end of this chapter.The Starting Point in Slide Rule Operation – MultiplicationThe basic scales, C and D, on a common 10 inch slide rule, are therefore 10inch rulers whose markings are not in uniform inches, but in the number ofinches of the mantissa for each number between zero and 10. The logarithm of2 is 0.301... and you will find the number 2 on the C and D scales 3.01 inchesfrom the left end. The logarithm of 3 is 0.477, and you will find the number 3engraved 4.77 inches from the left end. Adding the two distances gives one7.78 inches, and sure enough, the number 6 is 7.78 inches from the left end.You don’t actually have to add the distances to calculate the numbers. Theslide rule has already done this for you.To multiply 2 times 375, a slide rule adds the logarithms of the two numbersand reaches the logarithm of the answer. But... although the scales are spacedlogarithmically, they are labeled with the actual numbers, not the logarithms.So, you read the answers directly.2 (logarithm is 0.301) times 375 (logarithm is 2.574) = 750 (logarithm is2.875) The logarithms are added. The numbers are multiplied. Check it out!See photo below.Logarithms of numbers less than 1Pickett 160, 12.5 cmscales, plastic,simplex, USABut ... what about numbers less than 1?