Royal Society, 



315 



stated above, the graduation of the spirit thermometer was proceeded 

 with as follows. 



The process of calibrating the tubes was the same as for the mer- 

 curial thermometers ; as in these, also, the freezing-point and a tem- 

 perature of 90° or 95° were determined with reference to short 

 scales on the stems ; the distances OF, OH (figure, page 312) were 

 also measured ; and by comparing these measurements with the 

 numbers obtained by calibration, they were expressed in terms of 

 lengths of the calibrating column. 



'I'he equation (1.) may be put under the form N=A(T + 0T") by 



D 



making 0=—. Let^^and h be the distances OF, OH expressed in 

 A 



steps of the calibrating column ; Fll=h—/. LetT^ be the number 



of degrees above 32° corresponding to H, and let a.o 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.), 



h-f=ao (T, + 0Tr) or ao= , /"/.,., . 



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 cco, 

 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 -t-100° Fahr. : — 



The value in degrees of the step /= — =Ky. Then calling the 



numbers in the table X, since — =— , we find K^= — . — = — . 



cc/ Xf tto \/ 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 tiie values through- 

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

 sjjonding 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, 



