OF ARTS AND SCIENCES. 79 



convenience in use and in calibration, the principal bulb should be 

 elongated, and another small bulb should be blown at the top. This 

 latter is also of the utmost importance to the accuracy of the instru- 

 ment, and is placed there by nearly all makers of standards.* It is 

 used to place some of the mercury in while calibrating, as well as 

 when a high temperature is to be measured ; also, the mercury in the 

 larger bulb can be made free from air-bubbles by its means. 



Most standard thermometers are graduated to degrees ; but Reg- 

 nault preferred to have his thermometers graduated to parts of equal 

 capacity whose value was arbitrary, and others have used a single 

 millimeter division. As thermometers change with age, the last two 

 methods are the best ; and of the two I prefer the latter where the 

 highest accuracy is desired, seeing that it leaves less to the maker and 

 more to the scientist. The cross-section of the tube changes continu- 

 ously from point to point, and therefore the distribution of marks 

 on the tube should be continuous, which would involve a change of the 

 dividing engine for each division. But as the maker divides his tube, 

 he only changes the length of his divisions every now and then, so as 

 to average his errors. This gives a sufficiently exact graduation for 

 large ranges of temperature ; but for small, great errors may be intro- 

 duced. Where there is an arbitrary scale of millimeters, I believe it 

 is possible to calibrate the tube so that the errors shall be less than 

 can be seen with the naked eye, and that the table found shall repre- 

 sent very exactly the gradual variation of the tube. 



In the calibration of my thermometers with the millimetric scale, I 

 have used several methods, all of which are based upon some graphical 

 method. The first, which gives all the irregularities of the tube with 

 great exactness, is as follows. 



A portion of the mercury having been put in the upper bulb, so as 

 to leave the tube free, a column about I5 mm- long is separated off. 

 This is moved from point to point of the tube, and its length carefully 

 measured on the dividing engine. It is not generally necessary to 

 move the column its own length every time, but it may be moved 

 20 mm - or 25 mm -, a record of the position of its centre being kept. To 

 eliminate any errors of division or of the dividing engine, readings 

 were then taken on the scale, and the lengths reduced to their value 

 in scale divisions. The area of the tube at every point is inversely as 

 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 



* Geissler and Casella omit it, which should condemn their thermometers. 



