348 HENEY A. EOWLAND 



the length of the column. We shall thus have a series of figures nearly 

 equal to each other, if the tube is good. By subtracting the 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 aver- 

 age area of the tube for that distance, which I set down 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 thermom- 

 eters 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 = C V t , where 

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

 the and 100 points, we have simply 



r _ 100 

 T~^T" * 



'100 '0 



Otherwise C 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 ex- 

 pansion of mercury as measured on the stem. By defining it as pro- 

 portional to the true volume of mercury in the stem, we have to intro- 

 duce a correction to ordinary thermometers, as Poggendorff has shown. 



