OF ARTS AND SCIENCES. 161 



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 — iv', A, A -\- u', A-{-ti' -\- u", &c., 



and ordinates to the corresponding corrections. 



Should it be necessary to increase the accuracy by a second cali- 

 bration with a thread of different length, it is only necessary to take 

 one of approximately an integral part of (i? — A), and when the 

 final curve of error is drawn, make the error at 2? equal to zero, dis- 

 tributing the difference at that point proportionally to the scale read- 

 ings 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. The superposition of a second curve of error 

 deduced from the same series of observations as the first, but using 

 another starting-point. A' differing from ^ by a suitable fraction of 

 the length of the thread used, will somewhat increase the accuracy 

 of the result by rendering interpolation more certain, but neither of 

 these procedures is requisite except where a very detailed study 

 of the instrument is to be made. 



This method requires for each calibration the use of but a single 

 thread. The computation is simple, and involves a minimum of ap- 

 proximation. Errors of observation are largely eliminated by the 

 number of settings made in all parts of the tube, and by the inspec- 

 tion of the curve of lengths, both of which operations tend in an 

 unusual degree to detect any mistakes or minor irregularities of the 

 capillary. It avoids the common requirement of setting the thread 

 exactly at certain definite points in the tube, or any approximate cor- 

 rection 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 cali- 

 bration 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 

 satisfiictory with which I am acquainted, except that given by Picker- 

 ing. The latter, described with some slight inaccuracies at the refer- 

 ence 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 some- 

 what more accurate. From a series of calibrations executed upon the 

 same thermometer (one with a millimetre scale by Baudin of Paris), 



VOL. xvn. (x. s. ix.j 21 



