OF ARTS AND SCIENCES. 331 



" 4. The fourth column gives the reading of the zero point when the 

 standard is inclined 90°. 



" 5. The fifth column gives the correction depending on the interior 

 figure of the standard column." 



It will be noticed that the report of Dr. "Waldo gives only the cor- 

 rections of F61 between the limits 0° and 100°. In the reduction of 

 the observations at temperatures below 0° for the determination of the 

 absolute coefficients of expansion of the bars under consideration, I 

 found a constant tendency to a positive correction, on the supposition 

 that the coefficient was constant. For example, instead of finding the 

 constant difference between bars 7^ and S in meltiuij ice to be 75.1 

 div., as determined from the equations of condition on the following 

 pages, I found continually diminishing values, until for T= — 11° 

 the value was 52.6 div. In the case of bar C. S. a similar result was 

 found. The coefficients were now assumed to be a constant, and the 

 corrections to the thermometer required to make all the values of 

 S — T and S — C. S. below 0° agree with the values derived from 

 observations above 0° were computed, with the following results. 



Corrections to YGl. 



A similar series of corrections was derived from bar C. S. Smootli 

 curves were now drawn through the points determined by these resid- 

 uals, and the following corrections were obtained. Afterwards Mr. 

 S. W. Holman. of the Institute of Technology, compared Z61 with an 

 alcohol standard thermometer by Baudin. His results are given be- 

 low. It should be noted that Mr. Holraan's values were derived before 

 he had any knowledge of the results obtained by the writer. 



