80 PROCEEDINGS OP THE AMERICAN ACADEMY 



smallest from each of the others, and plotting the results as ordinates, 

 with the thermometer scale as abscissas, and drawing a curve through 

 the points so found, we have means of finding the area at any point. 

 The curve should not be drawn exactly through the points, but rather 

 around them, seeing they are the average areas for some distance each 

 side of the point. With good judgment, the curve can be drawn with 

 great accuracy. I then draw ordinates every 10 mm- , and estimate the 

 average area of the tube for that distance, which I set clown in a table. 

 As the lengths are uniform, the volume of the tube to any point is 

 found by adding up the areas to that point. 



But it would be unwise to trust such a method for very long tubes, 

 seeing the mercury column is so short, and the columns are not end to 

 end. Hence I use it only as supplementary to one where the column 

 is about 50 mm - long, and is always moved its own length. This estab- 

 lishes the volumes to a series of points about 50 mm - apart, and the 

 other table is only used to interpolate in this one. There seems to be 

 no practical object in using columns longer than this. 



Having finally constructed the arbitrary table of volumes, I then 

 test it by reading with the eye the length of a long mercury column. 

 No certain error was thus found at any point of any of the ther- 

 mometers which I have used in these experiments. 



"While measuring the column, great care must be taken to preserve 

 all parts of the tube at a uniform temperature, and only the extreme 

 ends must be touched with the hands, which should be covered with 

 cloth. 



If V is the volume on this arbitrary scale, the temperature on the 

 mercurial thermometer is found from the formula T = G V — ^ , 

 where C and t are constants to be determined. If the thermometer 

 contains the 0° and 100° points, we have simply 



100 



G: 



v V 



'inn r n 



Otherwise G is found by comparison with some other thermometer, 

 which must be of the same kind of glass. 



It is to be carefully noted that the temperature on the mercurial 

 thermometer, as I have defined it, is proportional to the apparent 

 expansion of mercury as measured on the stem. By defining it as 

 proportional to the true volume of mercury in the stem, we have to 

 introduce a correction to ordinary thermometers, as Poggendorf has 

 shown. As I only use the mercurial thermometer to compare with 

 the air thermometer, and as either definition is equally correct, I will 



