METHODS EMPLOYED IN CALIBRATION OF MERCURIAL THERMOMETERS. 195 



Table XLIII. 



</>(Uiv) + <^(U>It) = 'P'A'^tr). In terms of 0°-001 . 



Table XLIV. 

 Mean Ordinates from Initial and Ujjjyer Point Carves, in terms o/O'-OOl. 



The additional measures are then a^ain introduced. Let L, L and 

 X + Z, be an uncorrected measure of the length of a thread, and the 

 means of the ten ordinary measures of the same thread correct to a first 

 and second approximation respectively. 



Let (j> (m), <!) (i), ^., («) and ^2 (*') be the corrections for the upper 

 and initial points of the thread, correct to a first and second approxima- 

 tion respectively. 



Hence, 



L + ^2 («) — 02 (0 = ^ + ^ ; 



but ^2 («) = 00 + 0' 00, and ^0 (0 = (0 + 0' (0- 



.-. <p' {u) = (i) + f (i) + Z _ {L - i + (u)} . 



To apply this formula, Table_ XLV. is found from the second mean 

 curve, exactly as Table XXXVIT. was found from the first — i.e. the 

 columns ^ (i) and I. are completed and their means taken. As before, 

 the difference between t), and the mean of the 0(»)'s gives the correction 

 for the mean value of Thread I., and thus the corrected length of that 

 thread is found as in Table XLVI. Tlie difference between the corrected 

 lengths in Tables XLVI. and XXXVIII. give the values of I, which are 

 given in the last column of Table XLVI. The values of the corrections 

 for the upper points of the additional threads are then taken out from 

 the first mean curve and entered in Table XLVII. ; and these, being 

 added to the corresponding values of L — i in Table XXXVIII. , give 

 the values of L — L + ^ (it) entered in Table XLVIII. 



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