A Table Of Logarithms Of Numbers, From 1 To 1000

Description

This section is from the book "The Engineer's And Mechanic's Encyclopaedia", by Luke Hebert. Also available from Amazon: Engineer's And Mechanic's Encyclopaedia.

A Table Of Logarithms Of Numbers, From 1 To 1000

Number 1 to 100, and their Logarithms.
1	.0000000	21	.3222193	41	.6127839	61	.7853298	81	.9084850
2	.3010300	22	.3424227	42	.6232493	62	.7923917	82	.9138139
3	.4771213	23	.3617278	43	.6334685	63	.7993405	83	.9190781
4	.6020600	24	.3802112	44	.6434527	64	.8061800	84	.9242793
5	.6989700	25	..979400	45	.6532125	65	.8129134	85	.9294189
6	.7781513	26	.4149733	46	.6627578	66	.8195439	86	.9344985
7	.8450980	27	.4313638	47	.6720979	67	.8260748	87	.9395193
8	.9030900	28	.4471580	48	.6812412	68	.8325089	88	.9444827
9	.9542425	29	.4623980	49	.6901961	69	.8388491	89	.9493900
10	.0000000	30	.4771213	50	.6989700	70	.8450980	90	.9542425
11	.0413927	31	.4913617	51	.7075702	71	.8512583	. 91	.9590414
12	.0791812	32	.5051500	52	.7160033	72	.8573325	92	.9637878
13	.1139434	33	.5185139	53	.7242759	73	.8633229	93	.9684829
14	.1461280	34	.5314789	54	.7323938	74	.8692317	94	.9731279
15	.1760913	35	.5440680	55	.7103627	75	.8750613	95	.9777236
16	.2041200	36	.5563025	56	.7481880	76	.8808136	96	.9822712
17	.2304489	37	.5682017	57	.7558749	77	.8864907	97	.9867717
18	.2552725	38	.5797836	58	.7634280	78	.8920946	98	.9912261
l9	.2787536	39	.5910646	59	.7708520	79	.8976271	99	.9956352
20	.3010300	40	.6020600	60	.7781513	80	.9030900	100	.0000000

NUM.	LOG.	NUM.	LOG.	NUM.	LOG.	NUM.	LOG.	NUM.	LOG.
100	0000000	150	1760913	200	3010300	250	3979400	300	4771213
101	0043214	151	1789769	201	3031961	251	3996737	301	4785665
102	0086002	152	1818436	202	3053514	252	4014005	302	4800069
103	0128372	153	1846914	203	3074960	253	4031205	303	4814426
104	0170333	154	1875207	204	3096302	254	4048337	304	4828736
105	0211893	155	1903317	205	3117539	255	4065402	305	4842998
106	0253059	156	1931246	206	3138672	256	4082400	306	4857214
107	0293838	157	1958997	207	3159703	257	4099331	307	4871384
108	0334238	158	1986571	208	3180633	258	4116197	308	4885507
109	0374265	159	2013971	209	3201463	259	4132998	309	4899585
110	0413927	160	2041200	210	3222193	260	4149733	310	4913617
111	0453230	161	2068259	211	3242825	261	4166405	311	4927604
112	0492180	162	2095150	212	3263359	262	4183013	312	4941546
113	0530784	163	2121876	213	3283796	263	4199557	313	4955443
114	0569049	164	2148438	214	3304138	264	4216039	314	4969296
115	0606978	165	2174839	215	3324385	265	4232459	315	4983106
116	0644580	166	2201081	216	3344538	266	4248816	316	4996871
117	0681859	167	2227165	217	3364597	267	4265113	317	5010593
118	0718820	168	2253093	218	3384565	268	4281348	318	5024271
119	0755470	169	2278867	219	3404441	269	4297523	319	5037907
120	0791812	170	2304489	220	3424227	270	4313638	320	5051500
121	0827854	171	2329961	221	3443923	271	4329693	321	5065050
122	0863598	172	2355284	222	3463530	272	4345689	322	5078559
123	0899051	173	2380461	223	3483049	273	4361626	323	5092025
124	0934217	174	2405492	224	3502480	274	4377506	324	5105450
125	0969100	175	2430380	225	3521825	275	4393327	325	5118834
126	1003705	176	2455127	226	3541084	276	4409091	326	5132176
127	1038037	177	2479733	227	3560259	277	4424798	327	5145478
128	1072100	178	2504200	228	3579348	278	4440448	328	5158738
129	1105897	179	2528530	229	3598355	279	4456042	329	5171959
130	1139434	180	2552725	230	3617278	280	4471580	330	5185139
131	1172713	181	2576786	231	3636120	281	4487063	331	5198280
132	1205739	182	2600714	232	3654880	282	4502491	332	5211381
133	1238516	183	2624511	233	3673559	283	4517864	333	5224442
134	1271048	184	2648178	234	3692159	284	4533183	334	5237465
135	1303338	185	2671717	235	3710679	285	4548449	335	5250448
136	1335389	186	2695129	236	3729120	286	4563660	336	5263393
137	1367206	187	2718416	237	3747483	287	4578819	337	5276299
138	1398791	188	2741578	238	3765770	288	4593925	338	5289167
139	1430148	189	2764618	239	3783979	289	4608978	339	5301997
140	1461280	190	2787536	240	3802112	290	4623980	340	5314789
141	1492191	191	2810334	241	3820170	291	4638930	341	5327544
142	1522883	192	2833012	242	3838154	292	4653829	342	5340261
143	1553360	193	2855573	243	3856063	293	4668676	343	5352941
144	1583625	194	2878017	244	3873898	294	4683473	344	5365584
145	1613680	195	2900346	245	3891661	295	4698220	345	5378191
146	1643529	196	2922561	246	3909351	296	4712917	346	5390761
147	1673173	197	2944662	247	3926970	297	4727564	347	5403295
148	1702617	198	2966652	248	3944517	298	4742163	348	5415792
149	1731863	199	2988531	249	3961993	299	4756712	349	5428254

NUM.	LOG.	NUM.	LOG.	NUM.	LOG.	NUM.	LOG.	NUM.	LOG.
350	5440680	400	6020600	450	6532125	500	6989700	550	7403627
351	5453071	401	6031444	451	6541765	501	6998377	551	7411516
352	5465427	402	6042261	452	6551384	502	7007037	552	7419391
353	5477747	403	6053050	453	6560982	503	7015680	553	7427251
354	5490033	404	6063814	454	6570559	504	7024305	554	7435098
355	5502284	405	6074550	455	6580114	505	7032914	555	7442930
356	5514500	406	6085260	456	6589648	506	7041505	556	7450748
357	5526682	407	6095944	457	6599162	507	7050080	557	7458552
358	5538830	408	6106602	458	6608655	508	7058637	558	7466342
359	5550944	409	6117233	459	6618127	509	7067178	559	7474118
360	5563025	410	6127839	460	6627578	510	7075702	560	7481880
361	5575072	411	6138418	461	6637009	511	7084209	561	7489629
362	5587086	412	6148972	462	6646420	512	7092700	562	7497363
363	5599066	413	6159501	463	6655810	513	7101174	563	7505084
364	5611014	414	6170003	464	6665180	514	7109631	564	7512791
365	5622929	415	6180481	465	6674530	515	7118072	565	7520484
366	5634811	416	6190933	466	6683859	516	7126497	566	7528164
367	5646661	417	6201361	467	6693169	517	7134905	567	7535831
368	5658478	418	6211763	468	6702459	518	7143298	568	7543483
369	5670264	419	6222140	469	6711728	519	7151674	569	7551123
370	5682017	420	6232493	470	6720979	520	7160033	570	7558749
371	5693739	421	6242821	471	6730209	521	7168377	571	7566361
372	5705429	422	6253125	472	6739428	522	7176705	572	7573960
373	5717088	423	6263404	473	6748611	523	7185017	573	7581546
374	5728716	424	6273659	474	6757783	524	7193313	574	7589119
375	5740313	425	6283889	475	6766936	525	7201593	575	7596678
376	5751878	426	6294096	476	6776070	526	7209857	576	7604225
377	5763414	427	6304279	477	6785184	527	7218106	577	7611758
378	5774918	428	6314438	478	6794279	528	7226339	578	7619278
379	5786392	429	6324573	479	6803355	529	7234557	579	7626786
380	5797836	430	6334685	480	6812412	530	7242759	580	7634280
381	5809250	431	6344773	481	6821451	531	7250945	581	7641761
382	5820634	432	6354837	482	6830470	532	7259116	582	7649230
383	5831988	433	6364879	483	6839471	533	7267272	583	7656686
384	5843312	434	6374897	484	6848454	534	7275413	584	7664128
385	5854607	435	6384893	485	6857417	535	7283538	585	7671559
386	5865873	436	6394865	486	6866363	536	7291648	586	7678976
387	5877110	437	6404814	487	6875290	537	7299743	587	7686381
388	5888317	438	6414741	488	6884198	538	7307823	588	7693773
389	5899496	439	6424645	489	6893089	539	7315888	589	7701153
390	5910646	440	6434527	490	6901961	540	7323938	590	7708520
391	5921768	441	6444386	491	6910815	541	7331973	591	7715875
392	5932861	442	6454223	492	6919651	542	7339993	592	7723217
393	5943926	443	6464037	493	6928469	543	7347998	593	7730547
394	5954962	444	6473830	494	6937269	544	7355989	594	7737864
395	5965971	'445	6483600	495	6946052	545	7363965	595	7745170
396	5976952	446	6493349	496	6954817	546	7371926	596	7752463
397	5987905	447	6503075	497	6963564	547	7379873	597	7759743
398	5998831	448	6512780	498	6972293	548	7387806	598	7767012
399	6009729	449	6522463	499	6981005	549	7395723	599	7774268

NUM.	LOO.	NUM.	LOO.	NUM.	LOO.	NUM.	LOO.	NUM.	LOG.
600	7781513	650	8129134	700	8450980	750	8750613	800	9030900
601	7788745	651	8135810	701	8457180	751	8756399	801	9036325
602	7795965	652	8142476	702	8463371	752	8762178	802	9041744
603	7803173	653	8149132	703	8469553	753	8767950	803	9047155
604	7810369	654	8155777	704	8475727	754	8773713	804	9052560
605	7817554	655	8162413	705	8481891	755	8779470	805	9057959
606	7824726	656	8169038	706	8488047	756	8785218	806	9063350
607	7831887	657	8175654	707	8494194	757	8790959	807	9068735
608	7839036	658	8182259	708	8500333	758	8796692	808	9074114
609	7846173	659	8188854	709	8506462	759	8802418	809	9079485
610	7853298	660	8195439	710	8512583	760	8808136	810	9084850
611	7860412	661	8202015	711	8518696	761	8813847	811	9090209
612	7867514	662	8208580	712	8524800	762	8819550	812	9095560
613	7874605	663	8215135	713	8530895	763	8825245	813	9100905
614	7881684	664	8221681	714	8536982	764	8830934	814	9106244
615	7888751	665	8228216	715	8543060	765	8836614	815	9111576
616	7895807	666	8234742	716	8549130	766	8842288	816	9116902
617	7902852	667	8241258	717	8555192	767	8847954	817	9122221
618	7909885	668	8247765	718	8561244	768	8853612	818	9127533
619	7916906	669	8254261	719	8567289	769	8859263	819	9132839
620	7923917	670	8260748	720	8573325	770	8864907	820	9138139
621	7930916	671	8267225	721	8579353	771	8870544	821	9143432
622	7937904	672	8273693	722	8585372	772	8876173	822	9148718
623	7944880	673	8280151	723	8591383	773	8881795	823	9153998
624	7951846	674	8286599	724	8597386	774	8887410	824	9159272
625	7958800	675	8293038	725	8603380	775	8893017	825	9164539
626	7965743	676	8299467	726	8609366	776	8898617	826	9169800
627	7972675	677	8305887	727	8615344	777	8904210	827	9175055
628	7979596	678	8312297	728	8621314	778	8909796	828	9180303
629	7986506	679	8318698	729	8627275	779	8915375	829	9185545
630	7993405	680	8325089	730	8633229	780	8920946	830	9190781
631	8000294	681	8331471	731	8639174	781	8926510	831	9196010
632	8007171	682	8337844	732	8645111	782	8932068	832	9201233
633	8014037	683	8344207	733	8651040	783	8937618	833	9206450
634	8020893	684	8350561	734	8656961	784	8943161	834	9211661
635	8027737	685	8356906	735	8662873	785	8948697	835	9216865
636	8034571	686	8363241	736	8668778	786	8954225	836	9222063
637	8041394	687	8369567	737	8674675	787	8959747	837	9227255
638	8048207	688	8375884	738	8680564	788	8965262	838	9232440
639	8055009	689	8382192	739	8686444	789	8970770	839	9237620
640	8061800	690	8388491	740	8692317	790	8976271	840	9242793
641	8068580	691	8394780	741	8698182	791	8981765	841	9247960
642	8075350	692	8401061	742	8704039	792	8987252	842	9253121
643	8082110	693	8407332	743	8709888	793	8992732	843	9258276
644	8088859	694	8413595	744	8715729	794	8998205	844	9263424
645	8095597	695	8419848	745	8721563	795	9003671	845	9268567
646	8102325	696	8426092	746	8727388	796	9009131	846	9273704
647	8109043	697	8432328	747	8733206	797	9014583	847	9278834
648	8115750	698	8438554	748	8739016	798	9020029	848	9283959
649	8122447	699	8444772	749	8744818	799	9025468	849	9289077

NUM	LOG.	NUM.	LOG.	NUM.	LOG.	NUM	LOG.	NUM.	LOG.
850	9294189	880	9444827	910	9590414	940	9731279	970	9867717
851	9299296	881	9449759	911	9595184	941	9735896	971	9872192
852	9304396	882	9454686	912	9599948	942	9740509	972	9876663
853	9309490	883	9459607	913	9604708	943	9745117	973	9881128
854	9314579	884	9464523	914	9609462	944	9749720	974	9885590
855	9319661	885	9469433	915	9614211	945	9754318	975	9890046
856	9324738	886	9474337	916	9618955	946	9758911	976	9894498
857	9329808	887	9479236	917	9623693	947	9763500	977	9898946
858	9334873	888	9484130	918	9628427	948	9768083	978	9903389
859	9339932	889	9489018	919	9633155	949	9772662	979	9907827
860	9344985	890	9493900	920	9637878	950	9777236	980	9912261
861	9350032	891	9498777	921	9642596	951	9781805	981	9916690
862	9355073	892	9503649	922	9647309	952	9786369	982	9921115
863	9360108	893	9508515	923	9652017	953	9790929	983	9925535
864	9365137	894	9513375	924	9656720	954	9795484	984	9929951
865	9370161	895	9518230	925	9661417	955	9800034	985	9934362
866	9375179	896	9523080	926	9666110	956	9804579	986	9938769
867	9380191	897	9527924	927	9670797	957	9809119	987	9943172
868	9385197	898	9532763	928	9675480	958	9813655	988	9947569
869	9390198	899	9537597	929	9680157	959	9818186	989	9951963
870	9395193	900	9542425	930	9684829	960	9822712 \|	990	9956352
871	9400182	901	9547248	931	9689497	961	9827234	991	9960737
872	9405165	902	9552065	932	9694159	962	9831751	992	9965117
873	9410142	903	9556878	933	9698816	963	9836263	993	9969492
874	9415114	904	9561684	934	9703469	964	9840770	994	9973864
875	9420081	905	9566486	935	9708116	965	9845273	995	9978231
876	9425041	906	9571282	936	9712758	966	9849771	996	9982593
877	9429996	907	9576073	937	9717396	967	9854265	997	9986952
878	9434945	908	9580858	938	9722028	968	9858754	998	9991305
879	9439889	909	9585639	939	9726656	969	9863238	999	9995655

It is not our province, in this brief article, to explain the use of the larger Logarithmic Tables, as whoever possess such have of course their author's own explanations, and therefore the following illustrative examples are selected to suit the table here given.

Multiplication, as already stated, is performed by the addition of Logarithms, thus:-

To multiply 368 by 22.5, we place opposite to each other the

	Numbers and their	Logarithms.
	368 .......	2.5658478	Add.
	22.5 .......	1.3521825	Add.
Product of Numbers	8280. .......	3.9180303	Sum of Log.

Here the first factor, 368, being a whole number, consisting of three figures, has for its index 2; and the second, 22.5, having but two figures, without the decimal part, has for its index 1. To these are subjoined the decimal portions of the logarithms taken from the Table, and the sum of the two being found in the Table opposite to 828, which would be the answer were the index 2; but as the index is 3, the answer must be made to consist of four figures, which is done by supplying to the right of the figures a cipher, making the answer, as above, 8280

Required the capacity of an excavation, whose length is 295, breadth 128, and depth 25 feet.

	NUMBERS.		LOGARITHMS.
	295	............................	2.4698220
	128	............................	21072100
	25	.............................	1.3979400
Product.	944000	............................	5.9749720 Sum.

Again, let the numbers 32. 25, 1.12, .125, .015, and 004 be continually multiplied together.

	NUMBERS.	............................	LOGARITHMS.
	3.2	............................	0. 5051500
	25.	............................	1. 3979400
	1.12	............................	0. 0492180
	125	............................	1. 0969100
	015	............................	2. 1760913
	.004	............................	3. 6020600
Product	.000672	............................	4. 8273693

The number in the table corresponding with the decimal part of the sum of these logarithms is 672, but as the index is 4 there must be three cyphers prefixed to this number to constitute the product or answer which is therefore •000672.

Division, being the reverse of Multiplication, and performed by subtraction of logarithms, requires but little explanation.

For illustration, let 944000 be divided by 3200, thus:-

	NUMBERS.		LOGARITHMS.
Dividend	944000	...........................	5.9749720	From
Divisor. .	3200	...........................	3.5051500	Substract.
Quotient	295	...........................	2.4698220	Difference.

Again, let .00815 be divided by .0025.

	NUMBERS.		LOGARITHMS.
	.00815	...........................	3.9111576
	.0025	...........................	2.3979400
Quotient.	326	...........................	1.5132176

Let 493 be divided by 937.

	NUMBERS.		LOGARITHMS.
Dividend.	493	..........................	2.6928469
Divisor. .	937	..........................	2.9717396
Quotient.	.526	..........................	1.7211073

Here the logarithm to be subtracted being the greater of the two, the index of the difference is 1, which renders the quotient a decimal.

Involution, or the raising of powers, is performed by multiplying the logarithm of the given number by the index of the power to which it is required to be raised, thus:-

Let 26 be squared, or raised to the second power.

	NUMBERS.		LOGARITHMS.
	26	..........................	1.4149733
			.2
Power . .	. . 676	..........................	2.8299466	Product.

Required the cube root, or third power of 9.

	NUMBERS.		LOGARITHMS.
	9	..........................	0.9542425
		..........................	3
Power. .	. 729	..........................	2 8627275

Required the 9th power of 1.05, which will be the amount of 1l in nine years, at 5 per cent. compound interest.

	NUMBERS.		LOGARITHMS.
	1.05	..........................	0.0211893
			9
Amount..	1.55 or 1l 11s.	..........................	01907037

From this example it is manifest that the amount of money laid out at compound interest for 50, 100, or any other number of years, can be found by logarithms with the greatest facility, though the operation by common arithmetic is very tedious, requiring a distinct multiplication for each year.

Evolution, or the extraction of roots, is performed by dividing the logarithm of the given number by the index of the root required. Let this be illustrated by finding the square root of 324.

	NUMBERS.		LOGARITHMS.
	324	...............................	2)2.5105450
Root. .	. 18	...............................	1.2552725

Required the ninth root of 1.55

	NUMBERS.		LOGARITHMS.
	1.55	..............................	9)0.1903317
Root. .	. 1.05	..............................	00211479

As it may occasionally be desirable to apply the foregoing table to numbers beyond its limits, the manner of doing so is subjoined.

To find the logarithm of a number exceeding three figures, it is evident that the logarithm of the first three must be augmented by such a proportion of the difference between it and the next greater logarithm, as the remaining figures of the given number bears to unity with as many cyphers as may be required ; thus - to find the logarithm of 47583, the logarithm of the first three figures to the first logarithm, gives 4.6774516 for the logarithm of 47583. On the contrary, if the number be required for a logarithm not to be found in the table, to the first three figures corresponding with the next less logarithm, are to be subjoined the result of the following proportion; viz. - As the difference between the next greater and next less logarithm is to unity, with as many cyphers as may be required, so is the difference between the given logarithm and the next less to the figures to be subjoined to those found in the table. Thus - Suppose it were required to find the natural number corresponding with 4.6968455

475	is	6766936,	and the next greater is-
		6776070
		9134	their difference.

Now take the proportion as 1 : .9134 : : 83 : 75
	83
	27302
	73072
1,0000)75.8022, or 7498 nearly which being added

The next less logarithm in the table is ................	6963564
The next greater ........................................................	6972293
Difference . .	8729

The gibem logarithm ....................	.............................	6968455
Next lees ......................................	...........................	6963564
	Difference . . .	4891

Now - As	8729 :	100 : :	4891 :	56
			100
		8729)	489100	(56
			43645
			52650
			52374

Which being subjoined to 497, the three figures found in the table opposite to the next less logarithm, give 49756 for the number of the given logarithm.

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A Table Of Logarithms Of Numbers, From 1 To 1000

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A Table Of Logarithms Of Numbers, From 1 To 1000

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