166 KEPORT— 1882. 



The ordinates of the standard curve are therefore easily obtained by 

 subtracting 0'069 from the numbers in Column VI. of the above Table 

 VII., and adding the number of degrees above 100 in Column IV. multi- 

 plied by -001025. 



It is unnecessary to give the whole of the remainder of the calcula- 

 tions ; but, as examples, the corrections for 104'55 and 135'05 may be 

 taken, all the numbers being in terms of 0°'001 :— 



f (104-55) = 195-6 - 69 + 4-6 = 131 

 <t> (135-05) = 31-8 - 69 + 35-1 x 1-025 

 .= 31-8 — 69 + 36 = — 1 approximately. 



The standard curve thus obtained is the dotted curve in Plate I. 

 fig. 1. 



Gat-Lussac. — Example II. 

 Used as a principal point method with second approximation. 



TJiermometer G. 



(23) Another example of the application of Gay-Lussac's method 

 -was carried out in a somewhat different way. 



It was now used to determine the corrections of points 2° apart — i.e. 

 as a principal point method. 



,The thread-ends always lay in the divisions next to the principal 

 point, and as a first approximation the differences between the corrections 

 at the extremities of the thread and at the principal points were neg- 

 lected. 



The calculation for the first approximation is carried out exactly as in 

 the last case. There were twenty-one principal points — -viz. 100°, 102°, 

 104°, &c. These were numbered from to 20, as shown in the Column 

 headed u' in Table VIII. Columns I. and II. give the positions of the 

 upper and lower ends of the thread ; Column III. their differences, or the 

 uncorrected thread-lengths ; Columns IV. and V. the values of S («') and 

 (u') obtained exactly as in the last example : — • 



With these values of (u') an approximate correction curve was 

 drawn, and the corrections for the positions of the upj^er and lower ends 

 of the thread were taken out in Table IX., Columns I. and II. 



Then, since the corrected thread-length 



= <i + (l> (u + Am) — <P (i + Ai), 



the differences of the numbers in Columns II. and I. are entered in III., 

 and these, when added to the corresponding numbers in Column III., 

 Table VIII., give the corrected thread-lengths entered in Table IX., 

 Column IV. The numbers in Columns V. and VI. are obtained exactly 

 like those in Columns IV. and V. in Table I. ; and, by adding the values 

 of (/)' (t/) in Table II. Column VI. to those of ^ (u') in Column V. 

 Table I., the values of fi ('^*') ^re found. 



It will be noticed that the differences between the values of f (u') 

 and 02 (^<') are not inconsiderable. 



The curve obtained is drawn in Plate I. fig. 1. It is used, hereafter, 

 as a first approximation curve for obtaining transferred thread-lengths in. 

 the other methods. 



