298 On a Simple Method for Calibrating Thermometers. 



lation, and would be of equal accuracy, but is objectionable 

 from the fact that, in general, this volume would differ con- 

 siderably from the average volume obtained when n has a 

 greater value (always an integer), and the resulting series of 

 errors would assume larger numerical values. 



The errors or corrections are, for purposes of interpolation, 

 most conveniently represented graphically by a smooth curve 

 through points with abscissas proportional to the direct 

 readings A, A + „>, A + «' + «", &c, 



and ordinates to the corresponding corrections. 



Should it be necessary to increase the accuracy by a second 

 calibration with a thread of different length, it is only neces- 

 sary to take one of approximately an integral part of (B— A), 

 and when the final curve of error is drawn make the error at 

 B equal to zero, distributing the difference at that point pro- 

 portionally to the scale-readings among the errors at the 

 intermediate points — in other words, to shift the axis of the 

 second curve of error so that it shall make the error at B 

 zero. 



This method requires for each calibration the use of but 

 a single thread. The computation is simple, and involves a 

 minimum of approximation. Errors of observation are largely 

 eliminated by the number of settings made in all parts of the 

 tube, and by the inspection of the curve of lengths; both of 

 which operations tend in an unusual degree to detect mistakes 

 or any minor irregularities of the capillary. It avoids the 

 common requirements of setting the thread exactly at certain 

 definite points in the tube, or any approximate correction for 

 slight errors in such setting — two sources of considerable 

 error and inconvenience, especially when the thread must be 

 set near or under a line of the graduation. And, lastly, the 

 total time of calibration for a result of given accuracy is 

 reduced to one half or one third of that required by Neumann's 

 method, the quickest and most satisfactory with which I am 

 acquainted except that given by Pickering. The latter, 

 described with some slight inaccuracies, at the reference noted 

 below, is a neat application of the graphical method ; and the 

 curve of lengths of thread adopted in the method which I 

 have described is identical with the corresponding one given 

 by Professor Pickering, while the whole process is fully one 

 third shorter and somewhat more accurate. From a series of 

 calibrations executed upon the same thermometer (one with 

 a millimetre-scale, by Baudin, of Paris), using a variety of 

 methods, I have obtained slightly more concordant results 

 with the proposed method than with Neumann's or Pickering's 



