TRIGONOMETRY.
801
44 Degrees.
M
2 ? 9.84527 09.85351-42 8 9 84540-5 9.85349 029q.84533-3 9.85335-6'30 9.84506-2 9-85324-2
bine.
0 9.84177 I9.84190-29.84203-39.84216-89.84229-49.842429 84255-59-84268-58 9.8428 1-5‘ 9.84294-6
l 0 9.84307-0
('
9.85693 ■9.85081 -t9.83669-09.85056-89.85644-69.85632-39-85620-19.85607-89,85595'f>9.85583-04 8557M
*1 9.84320-0 9.85558-8*2 9.84333-6 9.85540 5*3 9.84346 6 9.85534-2
14 9.84359-5 9S552L9
15 9.84372 5 9.85509-0J69.84385-5 9.85497-3
9334398-4 9.85485-09-84411-49-84424-39-84437-2
9.84450-2,
9 8 4463-19.84470-09.84488-99.81501-89.84514-7
bee-ant.
10.1441
9.85472-7
9.85460-3
9.85448-0
9.85435 6
9.S5423
9.85410-9
9.85398-0
9.85380-.'
4.85373-8
31
32
33
34
353037,3s
39
40
4|
42
43
44 g
459
46 y
47
484y
50
51
525o3455
365?5s59
9.84579 09.84591'99.846049 84617-59.84630 49.84643'29.84656-09.846689.84681 69.84694-4
9 84707 .9.84719 9:J -84732-79.84745-49.84758-29 84770 9
9.84783-69.8479o-4084809 I984821-8
9^4834^59-84847-29-84859 99.84872 69-84885-29 84897-99 84 910-6
4 -81923-9 84935-t9-349 4 8 -f
“O-sine.
10.1457
9.853! 1-89 85299-47 9.85286-99 85274-59.85262-09.85249 69.85237-19.85224-79.85212-29.85199
9.85187 29.85174-79.85162 29.85149 79.85137-29.85124-69 8511219 8509.9 09.85087-09.85074-5
9.85001-99.85049-39.85036-89.85024-29.85011-69 84999 09.84Q86-49.84973-89.84961-11 84948-5
10.1466.
10.1470
10.14775
10.14788
Sine.
10.1482510.1483810.1485010.1486310.1487510.1488810.1490010.1491310.14926
10.1493810.1495110.1496510.1497610.1498810.1500110.1501410.1502610.1503910.15051
Co-sec.
tv..
Co—ec.
Pangent
Co-tang
M
7 10,1582.
9.98484
10.015 1(
3 60
!■- 10.158 It
9-98509
10.0149
59
I It) 1579
9.98534
10.01461
3 58
3 10.1578-
9-98560
10.01441
I 57
5 10.1577
9.98585
10.014k
> 56
8 10.1575f
9-98610
I0.0139C
) 53
0 10 1574.
9.98635
10.0136.
>54
_ i 0.1573
9 98661
10.01331
J 53
4 111.1571 f
9-98686
10.0131-
52
7 10 1570.
9.9871 1
10.0128?
51
9 10.15691
9 98737
10.0126C
50
1 10.15671
9.98762
10.01236
49
3 10.1566t
9-98787
10.0121;
48
6 10.15653
9.98812
10.01188
47
8 10.1564C
9-98838
10.01 162
46
0 10.15687
9 98863
10.01137
45
3 10.15615
9.98888
10.01112
44
5 10.1560-
9.98913
10.01087
43
7 10.155$.
9.98939
10.01061
42
i 10.1557b
9 98964
10.01036
41
2 10.15563
9.98989
10.01011
40
10.15550
9 99015
10.00985
39
7 10 15337
9.99040
10 00960
38
; 10.15524
9 99065
10.00935
37
10.1551 1
9.99090
10.00910
36
I 10.15498
9.991 16
10 00884
35
j 10.15485
9.99i4l
10.00859
34
10.15472
9.99166
10.00834
33
10.15461
9 99191
10.00809
32
10.15447
9 1)9217
10.00783
31
10.15434
9.99242
10.00758
30
10. 15421
9 99267
10 00733
29
10.1 j408
9.99293
10.00707
28
10.15395
9.99318
10.00682
27
10.15382
9.99343
10.00657
26
10.15371'
9.99368
10.00632
25
10.15357
9.99394
10.00606
24
10.15344
9.99419
10.00581
23
10.15331
9.99444
10 00556
22
10.15318
9.99469
10.00531
21
10.15306
9.99495
10.00505
20
10.15293
9.99520
10.004S0
19
10.15280
9 99545
10.00455
18
10.15267
9 99570
10.00430
17
10.15255
9.99596
10.00404
16
10.15242
9,99621
10.00379
15
10 15229
9.99646
10.00354
[4
10.15216
9 99672
10.00328
13
10.15204
9.99697
10.00303
12
10.15191
9.99722
10,00278
1
10.15178
9.99747
10.00253
0
10.15165
9.99773
10.00227
9
10.15153
9.99798
10.00202
8
10.15140
9.99823
10,00177
7
10.15127
9-99848
10.00152
6
10.15115
9 99874
10.00126
5
10.15102
9.99899
10.00101
4
10.15089
9.99924
10.00076
3
10.15077
9.99949
10.00051
2
10.15064
9 99975
10 00025
1
10.15051
0 0000
10.00000
0
Secant.
Co-taug.
Tangent.
VI
j-et'S. Z
The uses of the preceding Tables of Logarithms are sufficientlyexplained under the articles Logarithms and Trigonometry,and consequently need no further explication in this place. Wewill, therefore, only present the reader with Dr.ILdley’s very con-cise method of solving all kinds of questions in Compound Interest by Logarithms in a very few lines, which, by the common rulesof Arithmetic, is known to he extremely prolix and laborious, inorder to point out one more of the most important facilitiesof calculation which the Logarithmic Canon affords the arithme-tician. “As to the use,” says the Doctor, “ of Logarithms ,
; although they were invented chiefly to facilitate Trigonometrical! calculations; yet they are of use, vv’here-ever there is any occasionfor multiplication or division. Thus in the business of anatocism,or Compound Interest , e. g. At the rale of6 in 100, for one year. Lor then it will be as100 lo 106, or as 1 to 1.06, that is to l T -* 0 :so is the Principal to the Principal, increasedby the interest lor one year. And consequently'(he Principal is to he multiplied by 1.06, forthe first year; and the product of this musthe multiplied by 1.06, fot the second year;and so on, as in the annexed operation, ac-cording to the number of years, that thesum may be found (hat rises at the endof so many years. Instead of which con-tinued multiplications, the matter proceedsthus by Logarithms . To the Log. 0 f thePrincipal, add so many times the Log. of 1.06,as is the number of years ; this gives~the Log. of the sum, arising after that term of Years:and the absolute number answering to thisLo;.-. is the sum desired.
Examp. Let the principal be 15/. 17 a-. 6 d.English coin, that is, in decimal parts 15.875/.and let the inteiest be at the rate of 0 in the109, for one yeai, and to be continued in thatsame proportion lor 12 years. Therefore thenumber 15.875, isto be continually multipliedbp t.0(3 twelve times; from whence arises31.94362/. that is 31/. 18a. lO^d. nearly.Now the same is more expeditiously done byLogarithms , thus: The num. 1.06, expressing
the rate of Interest, its Log. is.0.02531
This multiplied twelve times, ac- ) o’JpggTcording to the number of years, is.. 4 ' 0
0 1;
875
95250
1 161
82750
00965
2 17
1
83715
070229
3 IS1
907379
1344427+
4 201
0418217+
2025093+
2443310 +2746599 -
5 2 1
]
6 22
1
5189909-f351 1395 —
7 23J
8701304—4322078 +
8 25
1
3023382—5181403 —
9 26
1
8204785 —6092287+
10 28
1
4297072—
7057824+
11
30 1354S96+1 SOS 1294—
Both these added together, make the) . -0^3 g
Logarithm.$ °
To which answers the absolute number12 319-to6l90— 31.94362, i. e. 31 /. 18s. 10 \d. nearly, as before.
Contrariwise, if giving the time and rate of Interest (as before)Jgether with the sum arising, viz. 31.94362/. it be enquired fromhat principal this must arise.
Then the Log. of the stint arising is.. 1.50438
tom whence subtract twelve times the Log. of 1.05, \ , ~
which is.5 0.30o07
15.876, whose Log. is.|
ut then, if front the fore-mentioned Log. of the sum )viz. 31.94362, which is...4
arising,
1.20071
1.5043S
. 0.30367
8>'c. 0.02531
- Also, the said re-
. 0.30367
. 0.02531
: years.
in
•no. 212.
9 S
TRIGUEKA,