187 



numbers obtained by calibration, they were expressed in terms of 

 lengths of the calibrating column. 



The equation (1.) may be put under the form N=A(T + 0T^) by 



making ^ — ^« /and h be the distances OF, OH expressed in 



steps of the calibrating column ; FH=A~/. Let be the number 

 of degrees above 32° corresponding to H, and let ao be the value, in 

 terms of a calibrating step, of one degree at the temperature 32° : 

 we have then, according to the fundamental equation (1.), 



A-/=«„ (T»+eT.^) or «o=,/~/„, . 



We may in general, without sensible error, assume that the value 

 of one degree is uniform throughout the length of a single cali- 

 brating step, or if the column of mercury has been rather too long, 

 we may subdivide the steps by interpolation. From the value of ao, 

 now obtained, we can find with sufficient exactness the temperature 

 corresponding to the middle of the step /. It will now be convenient 

 to make use of a table, derived from the values of A and B, showing 

 the relative lengths of one degree at different temperatures on the 

 supposition of uniform capacity of the tubes. The following are the 

 values for every ten degrees, from —70° to + 100° Fahr. : — 



Temp. Fahr. 



X. 



Temp. Fahr. 



X. 



o 



-70 



0-831 



+ 20 



0-980 



-60 



0-848 



30 



0-997 



-50 



0-864 



40 



1-013 



-40 



0-881 



50 



1-030 



~30 



0-897 



60 



1-046 



-20 



0-914 



70 



1-063 



-10 



0-930 



80 



1-079 







0-947 



90 



1-096 



+ 10 



0-964 



100 



M12 



iue in degrees of the step f=z~ — Kf. 



Then 



numbers in the table X, since ^=^, we find K^=i- . ?^=:?^. 



V tto X/ X/ 



This gives us the temperature corresponding to each end of the 

 step /, and we may then proceed in like manner to find the values of 

 the neighbouring steps, and so obtain successively the values through- 

 out the whole range of the thermometer. The temperature corre- 

 sponding to the point O in the figure is found by subtracting the 

 sum of all the values of K between O and F from 32°. The length, 



in turns of the dividing screw, for any degree x is ~, where R is 



the length of the step in which x occurs, and K^. the equivalent 

 number of degrees. A table can then be constructed, showing the 

 lengths of each successive degree, commencing from the point O, by 

 the aid of which the graduation may be performed. The scales ex- 

 tend to -75° Fahr. 



