ON THE MECHANICAL EQUIVALENT OF HEAT 347 



principally to that form having a graduated stem. For 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 instrument, and is placed 

 there by nearly all makers of standards. 2 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 Regnault 

 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 continuously 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 introduced. 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 represent 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 15 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 



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



