Elements of Surveying and Leveling: With Descriptions of the Instruments, and the Necessary Tables |
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Page 9
... logarithm of any power of 10 is equal to the exponent of that power : hence , the formula , If a number is an exact power of 10 , log ( 10 ) = log n = p . ( 3. ) • .... BOOK LOGARITHMS AND TRIGONOMETRY SECTION LOGARITHMS PAGE Of Logarithms.
... logarithm of any power of 10 is equal to the exponent of that power : hence , the formula , If a number is an exact power of 10 , log ( 10 ) = log n = p . ( 3. ) • .... BOOK LOGARITHMS AND TRIGONOMETRY SECTION LOGARITHMS PAGE Of Logarithms.
Page 10
... hence , we have the following RULE . The characteristic of the logarithm of any whole num- ber is positive , and numerically 1 less than the number of places of figures in the given number . When a decimal fraction lies between .1 and 1 ...
... hence , we have the following RULE . The characteristic of the logarithm of any whole num- ber is positive , and numerically 1 less than the number of places of figures in the given number . When a decimal fraction lies between .1 and 1 ...
Page 11
... hence , its loga- rithm lies between 1 and 2 , as does the logarithm of 74 . GENERAL PRINCIPLES . 5. Let m and n denote any two numbers , and p and q their logarithms . We shall have , from the definition of a loga- rithm , the ...
... hence , its loga- rithm lies between 1 and 2 , as does the logarithm of 74 . GENERAL PRINCIPLES . 5. Let m and n denote any two numbers , and p and q their logarithms . We shall have , from the definition of a loga- rithm , the ...
Page 13
... hence , the decimal part of the log ( n × 10o ) , is the same as that of log n ; which was to be proved . Hence , in finding the mantissa of the logarithm of a num- ber , we may regard the number as a decimal , and move the decimal ...
... hence , the decimal part of the log ( n × 10o ) , is the same as that of log n ; which was to be proved . Hence , in finding the mantissa of the logarithm of a num- ber , we may regard the number as a decimal , and move the decimal ...
Page 15
... hence , the mantissa of the logarithm of 6728.87 , is found by adding 57 to 827886. The principle employed is , that the differences of numbers are proportional to the differences of their logarithms , when these differences are small ...
... hence , the mantissa of the logarithm of 6728.87 , is found by adding 57 to 827886. The principle employed is , that the differences of numbers are proportional to the differences of their logarithms , when these differences are small ...
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Common terms and phrases
adjusted Applying logarithms axis azimuth back-sight base-line bearing chord clamp-screw column compass corresponding Cosine Cosine D course curve decimal DegDeg degree of curvature degrees determined difference of level divided double meridian distance draw east error example feet field-notes fore-sight given angle given line ground hence horizontal angles horizontal distance horizontal plane inch intersection LatDeg LatDegDeg LatDegDegDegDeg latitude and departure length limb line of collimation locating M.
M. Sine M.
M. Sine D mantissa marked measured method multiplied NOTE offsets parallel passed perpendicular plane of reference plot position prismoid protractor radius reading right angles scale of equal screws secant side sights similar triangles Sine Cotang slope spider's lines stakes station subtract surface survey taken Tang tangent theodolite traverse vernier plate vertical plane yards
Popular passages
Page 56 - ... the square of the hypothenuse is equal to the sum of the squares of the other two sides.
Page 12 - The logarithm of any power of a number is equal to the logarithm of the number multiplied by the exponent of the power.
Page 17 - The minutes in the left-hand column of each page, increasing downwards, belong to the degrees at the top ; and those increasing upwards, in the right.hand column, belong to the degrees below.
Page 37 - The circumference of every circle is supposed to be divided into 360 equal parts, called degrees ; and each degree into 60 equal parts, called minutes ; and each minute into 60 equal parts, called seconds ; and these into thirds, etc.
Page 12 - The logarithm of a quotient is equal to the logarithm of the dividend minus the logarithm of the divisor.
Page 10 - When a number lies between 1 and 10, its logarithm lies between 0 and 1; that is, it is equal to 0, plus a decimal; if a number lies between 10...
Page 9 - The logarithm of a number is the exponent of the power to which it is necessary to raise a fixed number, in order to produce the first number.
Page 11 - The logarithm of the product of two numbers is equal to the sum of the logarithms of the numbers.
Page 130 - MC; hence, the double meridian distance of a course is equal to the double meridian distance of the preceding course, plus the departure of that course, plus the departure of the course itself : if .there is no preceding course, the first two terms become zero.
Page 38 - The secant of an arc is the line drawn from the centre of the circle through one extremity of the arc, and limited by the tangent passing through the other extremity. Thus, 00 is the secant of the arc AB.