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ed to the logarithm, answering to the first four figures, will be the fe. quired logarithm, nearly.

Thus; to find the logarithm of 738582 ; the log of the first four figures, viz. 7385 .868350 the next greater logarithm

= 868409

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the sum 5.868398, with the proper index prefixed, is the required logarithm.

5. The logarithm of a vulgar-fraction is found by subtracting the logarithm of the denominator from that of the numerator ; and that of a mixed quantity is found by reducing it to an improper fraction, and proceeding as before, Thus to find the Logarithm of fi

from the log. of 7 = 0.845098 subtract the log. of 8 =

= 0.903090

Remainder = 9.942008 = the required log.

PROBLEM II.

To find the number answering to any given logarithm.

RULES.

1. Find the next less logarithm to that given in the column marked o at the top, and continue the sight along that horizontal line, and a logarithm the same as that given, or very near it, will be found ; then the three first figures of the

corresponding natural number will be found opposite thereto in the side column, and the fourth figure immediately above it, at the top of the page. If the index of tbe given logarithm is 3, the four figures thus found are integers; if the index is 2, the three first figures are integers, and the fourth is a decimal, and so on. Thus the log. 3.132580 gives the Nat. Numb. 1357 2.132580 gives

135.7 1.132580 gives

13.57 0.132580 gives

1.357 9,132580 gives

.1357 &c. 2. If the given logarithm cannot be exactly found in the table, and if more than four figures be wanted in the corresponding natural number ; then find the difference between the given and the next less loga

rithin's, to which annex as many ciphers as there are figures required above four in the natural number ; which divide by the difference between the next less, and next greater logariihnis, and the quotient en pexed to the four figures formerly found, will give the required natutul number. Thus to find the natural number of the log. 4.828991;

the next less log. is .828982 which gives 6735 ; the next greater log. is 829046

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4 therefore 1.4 being annexed to 6735, the required natural number, 67351.4, is now obtained.

TABLE I.

LOGARITHMS OF NUMBERS.

1

21
22

1.913814 83 | 1.919078 84 | 1.924279

86 | 1.934498

No. Log. No. Log. No. Log. No. Log.

No. Log. No. Log 0.000000 1.322219 41 1.612784 61 1.785330

81 1.908485 0.301030 1.342423 42 1.623249 62 1.792392

82 0.477121 23 1.361728 43 1.63346863 1.799341 4 0.602060 24

44 5 0.698970 25 1.397940 | 45 1.653213 65 1.812913 85 | 1.929419 60.778151 26 1.414973 | 46 | 1.662758 66 1.819544 7 0.845098 27 1.431364 47 1.672098 67 1.826075

87 1.939549 8 0.903090 28 1.44715848 1.681241 68

1.832509

88 1.944483 9 0.954243 29 1.462398 49 1.690196 69 1.838849 TO 1.000000 30

1.477121 50 1.69897070 1.845098 1.041393 31 1.491362 51 1.707570 71 1.851258 91

1.079181 32 1.505150 52 1.716003 72 1.857332 13 1.113943 33 1.518514 53 1.72427673 5.863323 14 1.146128 34 1.531479 54 1.732394 74 1.869232 15 1.176091 35 1.544068 55 1.740363 75 1.875061 16 1.204120 36 1.556302 36 1.748188 76 1.880814 17 1.230449 37 1.568202 57 1.755875 77 1.886491 18

II

89 1.949399 90 / 1.954343

1.959041 92) 1.963788 93 1.968485 94 1.973128 95 1.97772 96 1.982271 97 1.986771 98

1.255273 38 1.57978458 1.76342878 1.892095 19 1.278754

39 1.591065 59 1.770852 79 1.897627 20 1.301030 40 1.60 2060 60 1.778151 80

1.903090 1100

1.991226 99 1.995635

2.000000

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414973 5140415307415474 415641415808415974 416141416308416474 261 416640

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