174 



REPORT 1882. 



In the example worked out, the lengths of the thread employed were 

 approximately 4°, 8°, 12° . . 32°. In strict accordance with the method 

 as just explained, a thread 36° long ought also to have been used. It 

 was, however, found difficult to manipulate so long a thread. Herr 

 Thiesen points out that a number of thi-eads less than the largest possible 

 number may be used, and the plan adopted below can easily be extended 

 in a case where more than one thread is wanting. 



Table XV. gives in the first and last columns the numbers of the 

 principal points between which the thread was measured. Column I. 

 gives the transferred thread-lengths. Column II. the differences between 

 the consecutive values of -. 



Thus, Thread I. gives in accordance with equations (2) 



Thread II. gives 



c (2') - c (V) 



a (3') - c (2') 



a(3')-^(l') = 

 a (4') -0(2') = 



: - 80 



: - 83, &C. 



- 166 



- 25, &c. 



These numbers are tabulated in Table XVI. 



Thus 2 (2') — c (1') is entered in Column 2, Row 1. 



„ ?(3')-o(2') „ „ 3, „ 2. 



and so on. 



It will be seen that the squares in Column 10, Row 1, and Column 1, 

 Row 10, are blank. This results from the fact that no measures were 

 taken with a thread 36° long. 



By adding the numbers in the different columns, the values of all the 

 o's, except o (1) and c (10) are found as previously explained. 



By adding Column I., however, the equation, 



9 (1') - {o (V) + c. (2') + + a (9')} = 1081 i 



is obtained, or ' 



9 S (1') + 8 (10') = 1081, 



Similarly, Column 10 gives ' j 



9 c (10') + c (V) = 34. ' 



Whence c (1') = 121-2 c (10') = - 9-7. 



