94 PROCEEDINGS OF THE AMERICAN ACADEMY 



portion used were determined for every centimeter, the portion of the 

 scale between the 0° and 100° points of the air thermometer being 

 assumed correct. There is no object in determining the absolute 

 value of the scale, but it should agree reasonably well with that on the 

 barometer ; for let ff , H t , and H m be the readings of the barometer, 

 and h , h t , and A 100 the readings of the cathetometer at the temperatures 

 denoted by the subfix. Then approximately 



t __ {n t +h t ) — (H + h ) _ _ H t — H + h t —h < 

 ( ^ioo + A ioo ) — ( H o ■+■ A o ) #ioo — Hq + /j ioo — h o 



As the height of the barometer varies only very slightly during an 

 experiment, the value of this expression is very nearly 



h t — h 



"inn «n 



which does not depend on the absolute value of the scale divisions. 



But the best manner of testing a cathetometer is to take readings 

 upon an accurate scale placed near the mercury columns to be 

 measured. I tried this with my instrument, and found that it agreed 

 with the scale to within two or three one-hundredths of a millimeter, 

 which was as near as I could read on such an object. 



In conclusion, every care was taken to eliminate the errors of this 

 instrument, as the possibility of such errors was constantly present in 

 my mind ; and it is supposed that the instrumental errors did not 

 amount to more than one or two one-hundredths of a millimeter on the 

 mercury column. The proof of this will be ^iown in the results 

 obtaiued. i 



The Barometer. 



This was of the form designed by Fortin, and was made by 

 James Green of New York. The tube was 2.0 cm diameter nearly 

 on the outside, and about 1.7 em on the inside. The correction for 

 capillarity is therefore almost inappreciable, especially as, when it 

 remains constant, it is exactly eliminated from the equation. The 

 depression for this diameter is about .08 min- , but depends upon the 

 height of the meniscus. The height of the meniscus was generally 

 about 1.3 mm ; but according as it was a rising or falling meniscus, 

 it varied from 1.4 to 1.2 mm . These are the practical values of the 

 variation, and would have been greater if the barometer had not been 

 attached to the wall a little loosely, so as to have a slight motion when 

 handled. Also in use the instrument was slightly tapped before read- 



