OF ARTS AND SCIENCES. 341 



It will be seen that the vahie of b derived from these equations is 

 nearly identical with the final value adopted from the subsequent 

 observations, that value being — 0.57 |U. Combining the value of 

 7^"2 — ji^„ ^^.ji^jj j.]jg value derived from the observations with Com- 

 parator No. 1, we have 



r. - Rt- = ^^^'^^t'"'"'^ = 166.1 ,,. 



The value derived from the observations which follow is 1G5.5 |m. 



Determination of Absolute Coefficients of Expansion. 



The earlier experiments made by the writer in the determination of 

 the absolute coefficients of expansion of the bars under consideration 

 were very unsatisfactory. At first, the attempt was made to determine 

 the coefficient of one end-measure bar by subjecting it to wide ranges 

 of temperature when submerged in water, and thence to determine the 

 relative coefficients between it and the remaining bars whose coefficients 

 were desired. This attempt was only moderately successful. While 

 it was possible to obtain nearly a constant value for the coefficient of 

 this bar by different combinations of the results on the same day, the 

 deviation of the values for different days was considerably greater than 

 should have been found. The chief difficulty consisted in the impossi- 

 bility of keeping the entire mass of the water at the same temperature. 

 No amount of agitation seemed to accomplish this. 



A second method gave rather better results. It was found that an 

 end-measure bar placed in the clock-room of the Observatory remained 

 at a nearly constant temperatue, the change during twenty-four hours 

 rarely exceeding a few tenths of a degree. It was also found to be 

 possible to place this bar upon Comparator No. 1, and to make a com- 

 parison with any line-measure bar in a little less than one minute. 

 Durinof this time the chanse in the ]en<i;th of the bar was found not to 

 exceed two or three divisions of the micrometer, even when the differ- 

 ence in temperature was as great as 20° Fahr. The plan of observa- 

 tion was as follows. The line bar was adjusted for position upon the 

 comparator, and the reading of the microscope for the contact of the 

 stops and the coincidence with the defining line at one end was made 

 under favorable conditions for a steady temperature. The reading of 

 the thermometer was also recorded. The end-measure bar was then 

 brought into the room, placed in position between the stops, and the 

 microscope carriage was set for contact between the stops and the end 

 of the bar. From this point the remaining part of the observation 

 could be made leisurely for any temperature lower than that of the 



