50 



MEMOIRS OF THE NATIONAL ACADE.MY OF SCIENCES. 



The above resiilt.s may be rediieed to a more general statement by giving the eti'ect of a change 

 of 1° Falir. on the forks' vibratory period, as follows: 



Table VI. 



+ 1- Falir. diiiiinisbcs VT.: fork's vibratory period (ji? second) ^lijj part. 

 -|- 1° Falir. diiniuishes VTi fork's vibratory period (jj^ second) -jrk^^ part. 

 + 1'^ I'alir. diminishes .S'OXs forlc's vibratory period (^ Jj secoud) xyi^it part. 

 -f- 1° Fabr. dimini.sbes VTt fork'.s vibratory period (j{-j second) ytitt part. 

 + 1° Falir. diminishes Mlt fork's vibratory period (^^^y second) yxosi part. 

 4- 1" Fabr. diminishes JJ'T,, fork's vibratory period (xoW second) yjluo part. 



From Table YI it is .«een that the effect of a change of temperatnre on the vibratory period 

 is the same for all forks made of the same steel and similarly shaped. The diflerences among the 

 fractions of a vibratory period are small and evidently owing to the necessary errors of observa- 

 tion. I have great confidence in the accuracy of this determination. Tlie mean fraction of the 

 vibratory period which one of Ka-nig's forks gains or loses by a diminution or increase of 1° Fahr. 

 is irxiTfTPart, or .00004038. 



THE LAW OF THE ErNNlNlr DOWN IN THE AMPLITUDE OF A FORK'S VIBRATION. 



Twelve sheets were carefully taken of the traces of an J'Ti fork of ll'S vibrations per second. 

 The fork was vibrated with a bow and the cylinder turned as niiiformly as possil)le by the hand. 

 The seconds were mariied off on the traces of the fork by the break circuit of the clock. At or 

 near each second mark on the sheets was measured with a microscope micrometer the amplitude 

 of the vibration. The whole number of the sheets furnished over two hundred measures, giving 

 the connection between the time the fork liad run and the amplitude of its vibration at the end of 

 that time. A curve was then plotted giving their relations. Its discussion showed that it was a 

 logarithmic curve, which has the following expression : )/=(1.119)\ 



EFFECT OF THE SUPPORT OF A FORK AND OF THE SCRAPE OF ITS TRACING-STYLE ON ITS 



VIBRATORY PERIOD. 



These experiments on the effects of the support and sci-ape of the fork were made in connec- 

 tion with Prof. Albert A. Michelson with special reference to the period of vibration of the fork 

 he used in timing the rotation of the mirror he employed in his e.xperiments on the velocity of 

 light. The fork was an TT, of Kceni"-. 



No. 1. 



Temp. SC^ Fahr. 80 



15x.0l2^.180=correction for tcuiiieratnre 



(1).... 0.3 (0).... 1289. 2 



(2).... 256.1 (7). ...1535.3 



(3).... 511.7 (8). ...1791. 5 



(4).... 767.9 (9)....2U47. 1 

 (5) .... 1023. 5 



(7)— (1)— 6^255.83 

 (8)— (2)-^6=2o5. 90 

 (9)— (3)— 6=255. 90 

 (10)— (4)— 6=255.93 

 (11)- (5)^6=255. 92 

 (12)— (6)— 6=256.01 

 (13)— (7)— 6=255.95 



.Mean 2.55.920 



Corr. for temp. .. . +.180 



2.56. 100 

 Coir, for clock ... — . 028 



256. 072 



(6)— (2)-^4=255. 97 

 (7)-(l)^6=256.93 

 (8)— (2)— 6=255. 93 

 (9)_(3)— 6=256. 03 

 (10)-(4)— 6=2.56. 10 

 [(ll)-(5)-6=25.5.95]:' 



256. 126 



