METHODS EMPLOYED IN CALIBRATION OF MERCURIAL THERMOMETERS. 187 



The analogue of Table XXII. in the second approximation would there- 

 fore be drawn up as under : — 



Hence the correction for the r^^ initial point (omitting the constant) 

 would be : 



10 



0«l,r + «2»- +....+ 1tlO„) + jTj {^(«I,r) + ^(«2n) + + </'(»I0„-)} 



Bat 



— (U^„ + U.2„. + + Iho,,-) = H, = ^(C) + ir, 



plus a constant which may be neglected, and 



1 r, 



10 



{^(»i.,-) + ^(«2»-) + + fi^ho„y,■. 



is equal to the quantity entered in Table XXVI. as h',.. 



Hence ^'(iV) = Z^',- — '^,- 



The values of -ra-,. taken out from the first mean and first initial point 

 curves in figs. 2 and 1, Plate II. are entered in Table XXVII. In the 

 next column are the differences between the values of h',. — m' and •zr-,.. 



The additional correction for 11G° from the second upper point curves 

 is — -002. Hence, by adding 6 to the values of h',. — in' — tn,., the 

 ordinates of the second initial point curve are obtained which are entered 

 in the last column of Table XXVII. By taking the mean of these and 

 the upper point curves where they overlap, the following second approxima- 

 tion corrections are obtained in Table XXX. 



Table XXX. 

 Corrections of initial 2>oints {second ap2}i'oximatio')i) expressed in terms o/C-OOl. 



In order still further to correct the upper part of the scale, the follow- 

 ing method is adopted. The full corrections for the initial and upper 

 points are taken out from the second mean curve and entered in Table 

 XXXI. 



If to any mean thread-length, i.e. to the value of v,. obtained in 

 Table XIX., the mean correction for its upper points be added, and that 



