172 



EEPORT — 1882. 



Using this number, the values of o («') are found in Table XIV., 

 Column II., whence in Column III. the corrections for the principal 

 points are found in the usual way. 



Thiesen's Method, 

 Thermometer G. 



(26) If the principal points be numbered from to n, Herr Thiesen 

 employs a series of threads, the lengths of which are approximately equal 

 to 1, 2, . . Ji — 1 times the distance between two consecutive principal 

 points. He deals with untransferred thread-lengths. In the following 

 example, however, transferred thread-lengths have been used, but as 

 the method of transference has been fully illustrated, it is unnecessary to 

 exhibit the calculations. Each thread gives a number of equations of 

 the form 



T = r,, + <!> {u') - f (0) 



(1) T = r,,^,+f(u + l)-<t>(V) 



T = r,,+ o + 0(n + 2)-<?.(2') 

 and so on. 



By subtracting each equation from that which precedes it, the follow- 

 ing are obtained : — 



and so on. 



Now, the thread whose length is equal to the distance between two 



principal points can be measured in n positions, and hence from it n — 1 



equations of the series (2) can be obtained. Similarly, the thread the 



length of which is twice the distance between consecutive principal points 



gives n — 2 equations ; and in all there are 



■ ^ n (n — 1) 



ji - i + u - 2 + +1 = -^ 



equations between the c's. 



These are combined to find their values as follows. 



A table is prepared, of which the following is a symbolical repre- 

 sentation : — 



The differences of the b's are given by equations (2). On adding all 

 the numbers in any column, say the ?**', an expression of the form 



n S (r') - {? (!') -f h (2') + + a («')} = S (/) 



is obtained. But if (p (0') = <p (n') = 0, the expression in the bracket 

 vanishes, and hence nc (/•') = S(r'). 



The h's being known, the values of (j) may be found as usual. 



I 



