METHODS EJirLOYED IN CALIBRATION OF MERCURIAL THERMOMETERS. 203 



A curve is, as usual, drawn in the figure on p. 158. If an bypotlieti- 

 cal 7-, is introduced, the correction may be expressed by the following 

 formulae. 



For the odd points, 



0-5 (ff^ — 0-3) - 0-5 (7, — rj + 74) + 71 



+ j^ I '■2 + '■4 + 'G + • • ■ • + 1-10 I 



- {"1 + '■3 + • • • • + ^n}, 

 and for the even points, 



J^ I 5^2 + '•4 + •••• + '■10 I - I "2 + -4 +....+ r„ j , 



where in each case n is the number of the principal point. 



Thiesen's Method. 



In the case of Thiesen's method the relation between the corrections 

 and the measures is simpler. Suppose the observations complete — i.e. no 

 threads to be wanting. 



Referring to the table on page 172, it is evident that the correction for 

 the J-* principal point is the sum of all the columns up to and including 

 the r*^ divided by 10. But the figures in any rectangle of which the O's 

 form the diagonal cancel one another. Thus the correction for any 

 point is one-tenth of the sum of the figures in all the columns np to the 

 r^^ with the rectangle in question cut off. 



For instance, if in Table XVI. (p. 174), the blank space be filled up 

 with the correct number afterwards found, the correction for i, is one- 

 tenth the sum of the figures. 



102 15 - 68 - 12 



138. 60 - 22 35 



127 "37 — 51 10 



178 77 8 57 



177 81 7 58 



, 131 49 - 39 18 



All the numbers in any diagonal sucb as that through which the 

 line is drawn are obtained from the same thread. They are the 

 differences of successive thread-lengths, and therefore their sum depends 

 only on the first and last. In other words, the number of independent 

 measures used in finding the corrections is twice the number of the 

 diagonals, i.e. it is in all cases 18. 



Hence (probable error of correction)^ = — 2e^="18e^. 

 The curve is drawn in the figure on p. 158. 



Marek's Method. 



Marek gives the formulae for finding the probable error of a correcfion. 

 When, as is the case worked out, the tube is divided into five parts, the 

 (2?. e's) ^ are 



0- 0-29 e2 0-28 e2 0-2-8e2 •0-29 e2 



