168 REPOBT— 1882. 



Gay-Lussac— Example III. 

 Application of method of transference. 



Determination of secondary points. 



(24) In this case a thread about 4° long was used, and the principal 

 points were taken 4° apart. The thread having been accurately broken 

 off, the transfer corrections are small. The curve determined in the last 

 example was used as an approximation to determine them. The positions 

 of the upper and lower ends are given in Columns II. and I. Table X. ; 

 their difference, or the uncorrected thread-length, in Column III. From 

 this the transferred thread-length 



T=t+ (<p (u + Au) - <p (u)) - if (i + M) - cp (0), 



is calculated in Columns IV., V., and VI., and from these the corrections 

 of the principal points are determined as before. 



This example offers a means of illustrating the determination of 

 secondary points. Let Pq and P be two principal points between which 

 n secondary points are to be determined. This may be done by apply- 

 ing Gay-Lussac's method to the interval by means of a thread=one n + 1"* 

 of the distance between Pg and Pj. If this thread has been used to 

 determine an approximate correction curve, transferred thread-lengths can 

 be used, and the equations 



T-r,=ni)-^(Po) 

 T-r2 = .^(2)-0(l) 

 T - 73 = (3) - ^ (2) 



&c. = &c. 

 T-r„ + . = ./.(P,)-0 W 

 give by addition 



{n + 1) T = 7, -t- 72 + 73 -f- 4- r„, + , -f (PO - (Po) 



Whence T can be determined, and the calculations proceed exactly as 

 before, except that T is not the mean of the transferred thread-lengths. 

 The calculations of a few points will suffice, the thread used in Example 

 II. being employed to bisect the intervals between the principal pointa 

 obtained in the present example. 



Thus in Table XI., Column I. gives the principal and secondary 

 points numbered as in Table VIII., Example 2. Column II. gives the un- 

 corrected thread-lengths taken from the same Table. Columns III. and 

 IV. give the values of the quantities by which the transference is 

 effected, taken from the continuous curve in Plate I., fig. 1. Column VI. 

 gives the value s oi Z correct to O'OOl taken from Table X., Column VII. 

 Column VII. gives the values of T, i.e. of ^{rj + T2 + f(Pi)}. Column 

 VIII. gives T — 7, and in Column IX. the corrections are finally ob- 

 tained, as given by the formula. 



The points given by this thread are indicated in Plate I., fig. 1. 



