METHODS EMPLOYED IX CALIBRATION OF MERCURIAL THERMOMETERS. 177 



and upper ends of the threads ; Column III. the uncoxTected thread- 

 lengths ; Columns IV. and V. the principal points near the ends of the 

 threads to which the corrections are to be transferred ; Columns VI. and 

 VII. give the transfer corrections for the lower and upper ends of the 

 threads; Column VIII. the transferred thread-length. Thus, from the 

 first thread, 



T = 19-908 + i> (119-960) - </. (100-052), 

 = 19-908 + {<!> (119-960) - </> (120)}, 

 - {<!> (100-052) - <l> (100)} + f (120) - f (100), 

 = 19-908 + - -002 + f (120) - <p (100), 

 = 19-906 + <p (120) - <l> (100). 



From this table the following equations are obtained :— 



19-906 + </) (120) - <p (100) = 71 (1) 



20-171 + (j> (140) - <^ (120) = ri (2) 



12-890 + <i> (113-3) - </) (100) = r. (3) 



13-009 + i> (126-7) - <p (113-3) = r^ (4) 



13-107 + <l> (140) - ./. (126-7) = t^ (5) 



13-017 + <J> (120) - (/. (106-7) = T2 (6) 



13-097 + <p (133-3) - <j> (120) = t^ (7) 



16-492 + (j> (116-7) - f (100) = 73 (8) 



16-689 + f (133-3) - f (116-7) = 73 (9) 



16-641 + <!» (123-3) - f (106-7) = 73 (10) 



16-635 + ^ (130) - <l> (113-3) = 73 (11) 



16-729 + f (136-7) -</) (120) =73 (12) 



16-580 + </. (120) - f (103-3) = 73 (13) 



16-643 + f (126-7) - f (110) = 73 (14) 



16-730 + </. (140) - (123-3) = 73 (15) 



From (1) (2) since <{> (100) = <j> (140) = 0. 



^^,,0^^20071-29:906^ -133 (a) 



From (3) (4) (5) by addition 



3 72 = 39-006 or t^ = 13-002 



Hence from (3) (4) (5) (6) (7) 



f (113-3) = -112 (/3) 



(126-7) = -105 (y) 



</. (106-7) = -148 (g) 



<t> (133-3) = -038 (0 



From (8) and (9) by addition 



33-181 + ^ (133-3) - il> (100) = 2 73. 



Hence, since ^ (133 3) = -038, and ^ (100) = 0, 73 = 16-6095. 

 Hence, from the equations given by thread III., 



<f> (116-7) = -1175 

 from (10) <!> (123-3) = -1165 1 _ .,,g, 



from (15) <!> (123-3) = -1205 / ^^^^ - i J O'^ 



^ (130) = -0865 



f (136-7) = -0135 



f (103-3) = -1035 



^ (110) = -1385 

 1882. N 



