Experimental Determination of the Velocity of Light / Made at the U.S. Naval Academy, Annapolis

by Albert A. Michelson

The numbers in the column headed "Value of one turn of the screw" were taken from the table, page 127.

Date.	Distinctness of image.	Temperature, Fahr.	Position of deflected image.	Position of slit.	Displacement of image in divisions.	Difference between greatest and least values.	B.	Cor.	Number of revolutions per second.	Radius of measurement, in feet.	Value of one turn of the screw.	Velocity of light in air, in kilometers.	Remarks.
June 5	3	76	114.85	0.300	114.55	0.17	1.423	-0.132	257.36	28.672	0.99614	299850	Electric light.
June 7	2	72	114.64	0.074	114.56	0.10	1.533	-0.084	257.52	28.655	0.99614	299740	P.M. Frame inclined at various angles
June 7	2	72	114.58	0.074	114.50	0.08	1.533	-0.084	257.52	28.647	0.99614	299900	P.M. Frame inclined at various angles
June 7	2	72	85.91	0.074	85.84	0.12	1.533	-0.084	193.14	28.647	0.99598	300070	P.M. Frame inclined at various angles
June 7	2	72	85.97	0.074	85.89	O.07	1.533	-0.084	193.14	28.650	0.99598	299930	P.M. Frame inclined at various angles
June 7	2	72	114.61	0.074	114-53	0.07	1.533	-0.084	257.42	28.650	0.99614	299850	P.M. Frame inclined at various angles
June 9	3	83	114.54	0.074	114.47	0.07	1.533	-0.216	257.39	28.658	0.99614	299950	P.M. Frame inclined at various angles
June 9	3	83	114.54	0.074	114.46	0.10	1.533	-0.216	257.39	28.658	0.99614	299980	P.M. Frame inclined at various angles
June 9	3	83	114.57	0.074	114.47	0.08	1.533	-0.216	257.39	28.662	0.99614	299980	P.M. Frame inclined at various angles
June 9	3	83	114.57	0.074	114.50	0.06	1.533	-0.216	257.39	28.660	0.99614	299880	P.M. Frame inclined at various angles
June 9	2	83	114.61	0.074	114.53	0.13	1.533	-0.216	257.39	28.678	0.99614	300000	P.M. Frame inclined at various angles
June 10	2	90	114.60	0.074	114.52	0.11	1.517	-0.300	257.29	28.685	0.99614	299980	P.M.
June 10	2	90	114.62	0.074	114.54	0.08	1.517	-0.300	257.29	28.685	0.99614	299930	P.M.
June 12	2	71	114.81	0.074	114.74	0.09	1.450	-0.072	257.45	28.690	0.99614	299650	A.M.
June 12	2	71	114.78	0.074	114.70	0.05	1.450	-0.072	257.45	28.690	0.99614	299760	A.M.
June 12	1	71	114.76	0.074	114.68	0.09	1.450	-0.072	257.45	28.690	0.99614	299810	A.M.
June 13	3	72	112.64	0.074	112.56	0.09	1.500	-0.084	257.49	28.172	0.99614	300000	A.M.
June 13	3	72	112.63	0.074	112.56	0.10	1.500	-0.084	257.49	28.172	0.99614	300000	A.M.
June 13	2	72	112.65	0.074	112.57	0.08	1.500	-0.084	257.49	28.172	0.99614	299960	A.M.
June 13	3	79	112.82	0.260	112.56	0.06	1.517	-0.168	257.42	28.178	0.99614	299960	P.M.
June 13	3	79	112.82	0.260	112.56	0.13	1.517	-0.168	257.42	28.178	0.99614	299960	P.M.
June 13	3	79	112.83	0.260	112.57	0.07	1.517	-0.168	257.42	28.178	0.99614	299940	P.M.
June 13	3	79	112.82	0.260	112.56	0.06	1.517	-0.168	257.42	28.178	0.99614	299960	P.M.
June 13	3	79	112.83	0.260	112.57	0.11	1.517	-0.168	257.42	28.178	0.99614	299940	P.M.
June 13	3	79	113.41	0.260	113.15	11	1.517	-0.168	258.70	28.152	0.99614	299880	P.M. Set micrometer and counted oscillations.
June 13	3	79	112.14	0.260	111.88	6	1.517	-0.168	255.69	28.152	0.99614	299800	Oscillations of image of revolving mirror.
June 14	1	64	112.83	0.260	112.57	0.12	1.500	+0.012	257.58	28.152	0.99614	299850	A.M.
June 14	1	64	112.83	0.260	112.57	0.05	1.517	+0.012	257.60	28.152	0.99614	299880	A.M.
June 14	1	65	112.81	0.260	112.55	0.11	1.517	0.000	257.59	28.152	0.99614	299900	A.M.
June 14	1	66	112.83	0.260	112.57	0.09	1.517	-0.012	257.57	28.152	0.99614	299840	A.M.
June 14	1	67	112.83	0.260	112.57	0.12	1.517	-0.024	257.56	28.152	0.99614	299830	A.M.
June 14	1	84	112.78	0.260	112.52	0.06	1.517	-0.228	257.36	28.159	0.99614	299790	P.M. Readings taken by Lieut. Nazro.
June 14	1	85	112.76	0.260	112.50	0.08	1.500	-0.240	257.33	28.159	0.99614	299810	P.M. Readings taken by Lieut. Nazro.
June 14	1	84	112.72	0.260	112.46	0.08	1.483	-0.228	257.32	28.159	0.99614	299880	P.M. Readings taken by Lieut. Nazro.
June 14	1	84	112.73	0.260	112.47	0.09	1.483	-0.228	257.32	28.159	0.99614	299880	P.M.
June 14	1	84	112.75	0.260	112.49	0.09	1.483	-0.228	257.32	28.129	0.99614	299830	P.M.
June 17	2	62	112.85	0.260	112.59	0.09	1.517	+0.036	257.62	28.149	0.99614	299800	A.M.
June 17	2	63	112.84	0.260	112.58	0.06	1.500	+0.024	257.59	28.149	0.99614	299790	A.M.
June 17	1	64	112.85	0.260	112.59	0.07	1.500	+0.012	257.58	28.149	0.99614	299760	A.M.
June 17	3	77	112.80	0.260	112.54	0.07	1.500	-0.144	257-43	28.157	0.99614	299800	P.M. Readings taken by Mr. Clason.
June 17	3	77	112.77	0.260	112.51	0.08	1.500	-0.144	257.43	28.157	0.99614	299880	P.M. Readings taken by Mr. Clason.
June 17	3	77	112.77	0.260	112.51	0.11	1.500	-0.144	257.43	28.157	0.99614	299880	P.M. Readings taken by Mr. Clason.
June 17	3	77	112.77	0.260	112.51	0.09	1.500	-0.144	257.43	28.157	0.99614	299880	P.M. Readings taken by Mr. Clason.
June 17	3	77	112.78	0.260	112.52	0.08	1.500	-0.144	257 43	28.157	0.99614	299860	P.M. Readings taken by Mr. Clason.
June 18	1	58	112.90	0.265	112.64	0.07	1.500	+0.084	257.65	28.150	0.99614	299720	A.M.
June 18	1	58	112.90	0.265	112.64	0.10	1.500	+0.084	257.65	28.150	0.99614	299720	A.M.
June 18	1	59	112.92	0.265	112.66	0.07	1.483	+0.072	257.62	28.150	0.99614	299620	A.M.
June 18	2	75	112.79	0.265	112.52	0.09	1.483	-0.120	257-43	28.158	0.99614	299860	P.M.
June 18	2	75	112.75	0.265	112.48	0.10	1.483	-0.120	257-43	28.158	0.99614	299970	P.M.
June 18	2	75	112.76	0.265	112.49	0.08	1.483	-0.120	257-43	28.158	0.99614	299950	P.M.
June 20	3	60	112.94	0.265	112.67	0.07	1.517	+0.063	257.65	28.172	0.99614	299880	A.M.
June 20	3	61	112.92	0.265	112.65	0.09	1.517	+0.048	257.63	28.172	0.99614	299910	A.M.
June 20	2	62	112.94	0.265	112.67	0.07	1.517	+0.036	257.62	28.172	0.99614	299850	A.M.
June 20	2	63	112.93	0.265	112.66	0.03	1.517	+0.024	257.61	28.172	0.99614	299870	A.M.
June 20	2	78	133.48	0.265	133.21	0.13	1.450	-0.156	257.36	33.345	0.99627	299840	P.M.
June 20	2	79	133.49	0.265	133.23	0.09	1.500	-0.168	257.40	33.345	0.99627	299840	P.M.
June 20	2	80	133.49	0.265	133.22	0.07	1.500	-0.180	257.39	33.345	0.99627	299850	P.M.
June 20	2	79	133.50	0.265	133.24	0.13	1.483	-0.168	257.39	33.345	0.99627	299840	P.M.
June 20	2	79	133.49	0.265	133.22	0.06	1.483	-0.168	257.38	33.345	0.99627	299840	P.M.
June 20	2	79	133.49	0.265	133.22	0.10	1.483	-0.168	257.38	33.345	0.99627	299840	P.M.
June 21	2	61	133.56	0.265	133.29	0.12	1.533	+0.048	257.65	33.332	0.99627	299890	A.M.
June 21	2	62	133.58	0.265	133.31	0.08	1.533	+0.036	257.64	33.332	0.99627	299810	A.M.
June 21	2	63	133.57	0.265	133.31	0.09	1.533	+0.024	257.63	33.332	0.99627	299810	A.M.
June 21	2	64	133.57	0.265	133.30	0.11	1.533	+0.012	257.61	33.332	0.99627	299820	A.M.
June 21	2	65	133.56	0.265	133.30	0.13	1.533	0.000	257.60	33.332	0.99627	299800	A.M.
June 21	3	80	133.48	0.265	133.21	0.06	1.533	-0.180	257.42	33.330	0.99627	299770	P.M.
June 21	3	81	133.46	0.265	133.19	0.10	1.500	-0.192	257.38	33.330	0.99627	299760	P.M.
June 21	3	82	133.46	0.265	133.20	0.05	1.500	-0.204	257.37	33.330	0.99627	299740	P.M.
June 21	3	82	133.46	0.265	133.20	0.08	1.517	-0.204	257.38	33.330	0.99627	299750	P.M.
June 21	3	81	133.46	0.265	133.19	0.08	1.500	-0.192	257.38	33.330	0.99627	299760	P.M.
June 23	3	89	133.43	0.265	133.16	0.08	1.542	-0.288	257.32	33.345	0.99627	299910	P.M.
June 23	3	89	133.42	0.265	133.15	0.06	1.550	-0.288	257.33	33.345	0.99627	299920	P.M.
June 23	3	90	133.43	0.265	133.17	0.09	1.550	-0.300	257.32	33.345	0.99627	299890	P.M.
June 23	3	90	133.43	0.265	133.16	0.07	1.533	-0.300	257.30	33.345	0.99627	299860	P.M.
June 23	3	90	133.42	0.265	133.16	0.07	1.517	-0.300	257.29	33.345	0.99627	299880	P.M.
June 24	3	72	133.47	0.265	133.20	0.15	1.517	-0.084	257.50	33.319	0.99627	299720	A.M.
June 24	3	73	133.44	0.265	133.17	0.04	1.517	-0.096	257.49	33.319	0.99627	299840	A.M.
June 24	3	74	133.42	0.265	133.16	0.11	1.517	-0.108	257.48	33.319	0.99627	299850	A.M.
June 24	3	75	133.42	0.265	133.16	0.06	1.517	-0.120	257.47	33.319	0.99627	299850	A.M.
June 24	3	76	133.44	0.265	133.18	0.10	1.517	-0.132	257.45	33.319	0.99627	299780	A.M.
June 26	2	86	133.42	0.265	133.15	0.05	1.508	-0.252	257.33	33.339	0.99627	299890	P.M.
June 26	2	86	133.44	0.265	133.17	0.08	1.508	-0.252	257.33	33.339	0.99627	299840	P.M.
June 27	3	73	133.49	0.265	133.22	0.11	1.483	-0.096	257.46	33.328	0.99627	299780	A.M.
June 27	3	74	133.47	0.265	133.20	0.06	1.483	-0.108	257.44	33.328	0.99627	299810	A.M.
June 27	3	75	133.47	0.265	133.21	0.09	1.483	-0.120	257.43	33.328	0.99627	299760	A.M.
June 27	3	75	133.45	0.265	133.19	0.09	1.467	-0.120	257.42	33.328	0.99627	299810	A.M.
June 27	3	76	133.47	0.265	133.20	0.08	1.483	-0.132	257.42	33.328	0.99627	299790	A.M.
June 27	3	76	133.45	0.265	133.19	0.10	1.483	-0.132	257.42	33.328	0.99627	299810	A.M.
June 30	2	85	35.32	135.00	99.68	0.05	1.500	-0.240	193.00	33.274	0.99645	299820	P.M. Mirror inverted.
June 30	2	86	35.34	135.00	99.67	0.06	1.508	-0.252	193.00	33.274	0.99645	299850	P.M. Mirror inverted.
June 30	2	86	35.34	135.00	99.66	0.10	1.508	-0.252	193.00	33.274	0.99645	299870	P.M. Mirror inverted.
June 30	2	86	35.34	135.00	99.66	0.09	1.517	-0.252	193.00	33.274	0.99645	299870	P.M. Mirror inverted.
July 1	2	83	02.17	135.145	132.98	0.07	1.500	-0.216	257.35	33.282	0.99627	299810	P.M. Mirror inverted.
July 1	2	84	02.15	135.145	133.00	0.09	1.500	-0.228	257.34	33.282	0.99627	299740	P.M. Mirror inverted.
July 1	2	86	02.14	135.145	133.01	0.06	1.467	-0.252	257.28	33.311	0.99627	299810	P.M. Mirror inverted.
July 1	2	86	02.14	135.145	133.00	0.08	1.467	-0.252	257.28	33.311	0.99627	299940	P.M. Mirror inverted.
July 2	3	86	99.85	0.400	99.45	0.05	1.450	-0.252	192.95	33.205	0.99606	299950	P.M. Mirror erect.
July 2	3	86	66.74	0.400	66.34	0.03	1.450	-0.252	128.63	33.205	0.99586	299800	P.M. Mirror erect.
July 2	3	86	50.16	0.400	47.96	0.07	1.467	-0.252	96.48	33.205	0.99580	299810	P.M. Mirror erect.
July 2	3	85	33.57	0.400	33.17	0.06	1.450	-0.240	64.32	33.205	0.99574	299870	P.M. Mirror erect.

In the last two sets of June 13, the micrometer was fixed at 113.41 and 112.14 respectively. The image was bisected by the cross-hair, and kept as nearly as possible in this place, meantime counting the number of seconds required for the image of the revolving mirror to complete 60 oscillations. In other words, instead of measuring the deflection, the speed of rotation was measured. In column 7 for these two sets, the numbers 11 and 6 are the differences between the greatest and the smallest number of seconds observed.

In finding the mean value of V from the table, the sets are all given the same weight. The difference between the result thus obtained and that from any system of weights is small, and may be neglected.

The following table gives the result of different groupings of sets of observations. Necessarily some of the groups include others:

Electric light (1 set)	299850
Set micrometer counting oscillations (2)	299840
Readings taken by Lieutenant Nazro (3)	299830
Readings taken by Mr. Clason (5)	299860
Mirror inverted (8)	299840
Speed of rotation, 192 (7)	299990
Speed of rotation, 128 (1)	299800
Speed of rotation, 96 (1)	299810
Speed of rotation, 64 (1)	299870
Radius, 28.5 feet (54)	299870
Radius, 33.3 feet (46)	299830
Highest temperature, 90° Fahr. (5)	299910
Mean of lowest temperatures, 60° Fahr. (7)	299800
Image, good (46)	299860
Image, fair (39)	299860
Image, poor (15)	299810
Frame, inclined (5)	299960
Greatest value	300070
Least value	299650
Mean value	299852
Average difference from mean	60
Value found for π	3.26
Probable error	± 5

Discussion of Errors.

The value of V depends on three quantities D, n, and φ. These will now be considered in detail.

The Distance.

The distance between the two mirrors may be in error, either by an erroneous determination of the length of the steel tape used, or by a mistake in the measurement of the distance by the tape.