METHODS EiirLOYED IN CALlBItATIOxN OF MEECURIAL THERMOMETERS. 201 



Effect of Errors in Measurement of Threads. 



(3G) The errors introduced in a correction-method depend partly upon 

 the magnitude of the false assumptions made in the method itself, partly 

 upon errors in the measurement of thread. 



It has been shown that the former may be obviated to a great extent 

 by approximation or transference ; it remains to investigate the latter. It 

 has been thought better to treat of this subject by itself in oi-der to avoid 

 the complication which it introduces into the discussion of the various 

 methods. It is proposed here to investigate tlae probable errors of the 

 corrections of the principal points in terms of the errors in the thread- 

 measurements. The probable error of a thread-measurement will be 

 considered the same in all cases and taken = e. It must, however, be 

 remembered that, in all probability, for reasons already given, long 

 threads are less accurately measured than short. 



Gat-Lussac's Method, 



The equations (1) (p. 164) show that in the case of Gay-Lussac's 

 method the correction for the r*** principal point is 



v V n. — r 



a/; "V ™m V 1- / ' vn / V r/ ' yn i [^ .' V )* 



V'VjV rl — -.[ l^ ^1 Jf — ^1 fj; ^,-+1 '.,■ ^1 f.r' 



n n n 



Hence if e,. be the probable error of the correction at this point, since all 

 the ^s are independent measures 



E,.^ =: — (n — r)e^ + —!- re^ = -^— ~ e^. 



Hence if rt = 10 the squares of the probable errors at the first, second, 



9 16 

 &c., points are proportional to — , -— , &c. 



These numbers are plotted down and give the curve indicated in the 

 figure on p. 158. 



Rudbeeg's Method. 



It will be sufficient to consider the case of division into six parts. 

 The above formulae give at once 



g2 2 



3 — o"' ^2 — ^4 — o ^ • 



Since the shorter thread is found as the mean of three independent 



measures its (probable error) ^ = — , and since this thread is measured 



o 



independently of 0(3), and ^(1) is found from the equation 



where all the quantities on the right are independent 

 {p.e. 0(1))2 = J -f e2 + J ^ 1.83 e\ 



A curve is drawn through the points thus obtained in the figure on p. 158. 



