Tables of Logarithms of Numbers, and of Logarithmic Sines, Tangents and Secants, to Seven Places of Decimals: Together with Other Tables of Frequent Use in the Study of Mathematics, and in Practical Calculations

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Durrie and Peck, 1849 - 340 pàgines
 

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Pàgina 41 - If the number of degrees and minutes falls between 45° and 90°, the degrees must be looked for at the bottom of the page, and the minutes on the right...
Pàgina 13 - The logarithm of a quotient is equal to the logarithm of the dividend diminished by that of the divisor.
Pàgina 38 - I 15.314292 6240" + 22".5 = 6262.5 log 3.796748 Am. 11.517544 These two pages may be used in the same way when the given angle lies between 88° and 92°, or between 178° and 180°; but if the number of degrees be found at the bottom of the page, the title of each column will be found there also; and if the number of degrees be found on the...
Pàgina 41 - Tangent, fyc., of any number of degrees and minutes. If the given angle is less than 45°, look for the degrees at" the top of the table, and the minutes on the left ; then, opposite to the minutes, and under the word sine at the head of the column, will be found the sine ; under the word tangent, will be found the tangent, &c. The log, sin of 43° 25' is 9.83715 The tan of 17° 20...
Pàgina 12 - Thus the characteristic of the logarithm of 604.27 is 2, as the integral figures viz. 504 are three in number. And the characteristic of the logarithm of 2.036 is 0, because the number 2.036 has one integral figure. But if the number be only a decimal fraction, the characteristic of its logarithm is negative, and is greater by one than the number of ciphers at the beginning of the decimal. Thus if the number concerned be the decimal .087, the characteristic of its logarithm is — 2 or as it should...
Pàgina 14 - M" is the mnth power of the base b, mn is the logarithm of M". Therefore the logarithm of any power of a number is obtained by multiplying the logarithm of that number into the number denoting the power. 13. Finally, if M is a number whose logarithm is m, the logarithm of M...
Pàgina 11 - If the number is greater than 1, the characteristic of the logarithm is one less than the number of digits to the left of the decimal point.
Pàgina 32 - The course is given in degrees or points in the two exterior marginal columns, the distance is found at the top or bottom of the page, according as the course is less or greater than four points or 45?
Pàgina 13 - ... so that the characteristic of the logarithm of a decimal is negative, and is one greater than the number of ciphers at the beginning of the decimal ; as is stated in the second part of the foregoing rule.
Pàgina 33 - ... something to be wrong. Is it the Formula, the calculation, or the mechanical measurement? You repeat the mechanical measurement and find it correct ; you examine the calculation and find it just. You conclude, then, that the error lies in the Formula, and your conclusion is right. Here is the difficulty: the sine of an angle and that of its supplement are the same. 107° 10' is the supplement of 72° 50', and 9-9802 is the log sin both of 72° 50

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