Dec. 4, 1879] 



NATURE 



121 



found a; before described. The electric fork was then started, 

 the temperature noted, and the beats between it and the standard 

 .:ed for 60 seconds. This was repeated two or three 

 times before every set of observations. 



The eyepiece of the micrometer was then set approximately, 

 and the revolving mirror started. If the image did not appear, 

 the mirror was inclined forward or backward till it came in 

 sight. 



The cord connected with the valve was pulled right or left, till 

 the images of the rev jiving mirror, represented by the two 

 round spots to the left of the cross hair, came to rest. Then the 

 screw was turned till the cross hair bisected the deflected image 

 of the slit. This was repeated till ten observations were taken, 

 when the mirror was stopped, temperature noted, and beats 

 counted. This was called a set of observations. Usually five 

 such sets were taken morning and evening. 



The steel tape used was one of Cbesterman's, 100 feet long. 

 It was carefully compared with the copy of the standard yard 

 made by Wurdemann, by a comparator. The result showed 

 that the error of the tape was 0006 foot. The true length was 

 ico - oo6 feet. 



The micrometer was also compared "with the standard yard 

 and the standard meter, the first giving for the value of one scale 

 division, o"9965omm. 



and the second, 0-99642 ,, 



Mean C99646 mm. 



One turn of the screw was found equal to 1 '0009 divisions. 

 Hence the value of one turn was 0*99655 millimeter. 



The distance between the pier for the revolving mirror and 

 the stationary mirror was measured by means of the steel tape. 

 Square lead weights were placed along the line, and measure- 

 ments taken from one to the other, the tape resting on the 

 ground and stretched by a force of 10 pounds. The measure- 

 ments, five in all, were all made at about 62° F. The results 

 are:— 1985'lj 



1985-17 

 1984-93 

 1985-09 

 198509 



True distance 1986-23 



The rate of vibration of the standard fork armed with a tip of 

 copper foil was found by allowing it to trace its record on the 

 lampblacked cylinder of a Schultz's chronoscope. The time was 

 given either by a sidereal break-circuit chronometer or by a mean 

 time clock. In the former case the break circuit worked a relay 

 which interrupted the current from three Grove cells. In the 

 latter, the circuit was broken by the pendulum. The spark from 

 the secondary coil of a Ruhmkorff was delivered from a wire 

 near the tip of the fork. The rate of the chronometer, the record 

 of which was kept at the Observatory, was very regular. It was 

 found, from observations of transits of stars during the week, to 

 be -f- 1 -3 seconds per day, which is the same as the recorded 

 rate. 



The correction for temperature was found by Prof. Mayer to 

 be + 0-012 v.s. for a diminution of l" F. 

 My own result was + 0-0125 v - s - 

 Adopted + 0-012. 



The following is the table of results: — 

 256-069 

 256-089 

 256-077 

 256-012 

 256-087 

 256-074 

 256-061 

 256-100 

 256-084 

 256-066 



Mean 



256-072 



In one of these observations I counted the beats between this 

 fork and another, first while the former was tracing its record, 

 and then when it was free and in position as for use. The dif- 

 ference, if any, was Jess than o - oi v.s. 



As the result obtained depends directly on the rate of vibration 

 of the fork, I was not willing to trust entirely to my own work, 

 and asked Prof. Mayer to make a determination. 



He kindly offered to make it together with myself. Accord- 

 ingly, I went to the Hoboken Institute, and a series often deter- 

 minations were made under the following conditions : — 



The fork was wedged into a wooden support, and the tip 

 allowed to re-t on lampblacked paper wound about a metal 

 cylinder, which was turned by hand. Break-circuit clock was 

 used, the rite of which was ascertained by comparison with the 

 Western Union time-ball. The spark from the Ruhmkorff 

 passed from the tip of metal attached to the fork, piercing the 

 paper. Size of the spark was regulated by resistances. 



Table of results was as follows : — 



256-072 

 256' 1 26 

 256-091 

 256-108 

 256-068 

 256-090 

 256-112 

 256124 

 256-080 

 256 070 



Mean 256-094 



The effect of scrape was sought for again, and found to Le 

 0-003 v - s - 



The effect of the support, however, was greater, both combined 

 being - 0-026 v.s. 



Making this correction, the result becoriies — 

 256-o6S 

 Former result ... 256-072 



Mean 



256-070 vibrations per second, at 

 65- F. 

 The formula: employed in the calculations are : — 



(1) 



(21 



. tan <p = 



r 

 Y — 2592000" 



Where tp = angle of deflection. 



d i = displacement, or r . tan <p. 

 r = radius of measurement. 

 D = twice the distance between mirrors. 

 « = number of revolutions per second, 

 o = inclination of plane of rotation. 

 V = velocity. 

 D and r are expressed in feet, and d 1 in millimetres. 

 Substituting for d 1 its value, 



d x 0-99655 x sec a, 

 where </, is the displacement in turns of screw, 

 and log sec a = o - oooo8, 

 we have, reducing to kilometres : — 



(3) tan* = <-,^ log <-, = 0-51457 



(-4) 



... V 



t 



log c = 0-49670 



In the calculations the effect of temperature on the screw, 

 scale, and tape used in finding p was neglected. It can be 

 Applied to the final result for the mean temperature, which was 

 75-6° F. 



Correction for tan <p is — 0-C00003 x 13-1 = -00004. 



Correction for V is + 12 kilometres. 



The direction of rotation was right-handed. To eliminate any 

 possible error on this account, the mirror in eight of the later 

 observations was inverted, thus making the rotation left-handed, 

 and the deflection measured to the left. The results were the 

 same as before, within the limits of error. 



To eliminate errors due to a regular variation in speed during 

 every revolution, if any such could exist, the position of the 

 frame was changed in several experiments. The results were the 

 same as before. 



