M 41 Deg. M N.S. IN.C.S. N.S.N.C.S N.S. N.C.S 06293277715 64279 76604 6560675471 60 955 696 301 586 628 452 59 2 977 678 323 3 63000 660 4 022 6418 346 548 368 M 608 162 945 041 262 896 30 C.S N.S. M M Nat. N. Co- Nat. N. Co- Nat. N. Co-M Sine. Sine. Sine. Sine Sine Sine 019 15 45 880 4323 151 236 401 46 67901 73412369172 72216 70422 70998 14 47 923 393 193 196 443 978 13 48 944 373 214 176 463 957 12 III. A TABLE of LOGARITHMS for NUMBERS; and IV. A TABLE of LOGARITHMIC or ARTIFICIAL SINES, TANGENTSand SECANTS. Explanation of the Table of Logarithms for Numbers. LOGARITHMS are Numbers in Arithmetical Progression, corresponding to other Numbers in Geometrical Proportion. As, Logarithms. 1000. 10000. Numbers. 0. 1. 1. 10. 2.. 100. 3. 4. The Logarithm for any Number less than 10 is a certain number of Decimals; for any number between 10 and 100 it is 1 with Decimals; for any Number between 100 and 1000 it is 2 with Decimals, &c. The whole Number in Logarithms, or the Number which stands at the Left hand of the Decimal Point is called the Index; and is always a Unit less than the places of figures in the whole Number for which it is the Logarithm: Thus, The Log. of 6543 is 3.81578 The Log. of a Decimal Fraction is the same as that of an Integer, only the Index is negative; and is distinguished from an absolute one by placing a Point or a negative Sign before it: Thus, The Log. of 0.6543 is 0.06543 .9.81578 or 1.81578 - 2.81578 By the following Table the Log. of any Number, containing three places of figures, whether whole Numbers, mixed Numbers or Decimals, may be found true at once. Look for the two first figures in the Left or Right hand Column, marked No. and for the third figure on the Top of the Page; against the two first figures and under the third will be the Logarithm. EXAMPLES. Required the Logarithm for 346 Look for 34 in the Column marked No. and for 6 on the Top of the Page, under which and against 34 you find 53908 to which prefix 2 for the Index, because the Number consists of three places of figures In the same way the Log. for 28.3 will be found to be 1.45179 And the Log. for 3.23 to be 0.50920 To find the Number corresponding to any Logarithm. Look in the Table till you find the given Log. without regarding the Index; the Number standing against it in the Column marked No. together with the figure on the Top, form the corresponding Number; whether whole, mixed or Decimals, will be determined by the Index. If you cannot find the exact Log. take the nearest to it. If the Log. of any Number between 10 and 100, with two places of Decimais, be required, take the nearest numberof tenths, which will be sufficiently exact for common practice. But, if great accuracy be desired, work by Natural Sines, in the manner pointed out in Trigonometry, and in the Introductiou to the Table of Natural Sines. Or, The Log. of any Number containing more than three places of figures, may be found by the Table in this Book, as follows : Find the Log. of the three first figures as before taught; sub |