164 EEPoitT— 1882. 



The symbol r indicates the transferred thread-length defined in Part I. 

 (p. 150) by the equation. 



T = t + I ^(ii + A m) - (p(u) - [</.(i + A {) -i>(i)] j . 



In the case of principal point methods it is often best to indicate the 

 position of a thread by reference to the principal points nearest to which 

 its extremities lie. Let the principal points be numbered from o upwards 

 in the direction of increasing scale readings, and let u' and i' be the 

 numbers indicating the principal points nearest to the upper and lower 

 ends of the thread respectively. By the substitution of these quantities 

 for u and ^ the above system of symbols will apply without further 

 change. In cases, therefore, where ambiguity might otherwise arise, 

 1', 2', &c. mean not the first, second, &c. scale division or degree, but the 

 principal points numbered 1, 2, &c. Where no ambiguity is to be feared 

 the dashes may be dispensed with. 



Gay-Lussac's Method. 

 Thermometer C. 



(22) The following is an example of as accurate a compliance with 

 the strict conditions of this method as is possible with Mr. Brown's 

 instrument. 



The lower end of the thread was always moved into the same division 

 and generally into the same part of that division as that in which the 

 upper end previously lay. The correction is applied to the mean of these 

 two positions. The thread-length was always measured twice in each 

 position, together with the lengths of the divisions in which the extre- 

 mities lay. The length of each division was therefore measured four 

 times, twice when the upper and twice when the lower end of the thread 

 lay in it. The mean of these four readings, which rarely differed by more 

 than 0°"003, was taken as the true length. 



In Table VII., Columns I. and II. give the positions in terms of 

 uncorrected scale-divisions of the lower and upper ends of the thread. 

 Column III. gives the difierences between these quantities or the un- 

 corrected thread-lengths (<). 



Hence, if the successive values of t be indicated by i,, ^21 &c., and if T 

 be the corrected thread-length 



f T - <, = (99-66) - .i.(9805) = (99-66), 

 (1) <^ T - ^o = ^(101-27) - V(99-66) = 0(101-27), 

 [ T - ^3 = 0(102-89) - 0(101-27) = c(102-89), 

 and so on. 



If, therefore, (98-05) = 0, 



0(99-66) =c(99-66), 

 (101-27) = ^(101-27) + 0(99-66), 

 and so on. 



Now there are 26 of the equations (1), and addition gives 

 26 T - (i, +;,, + .... + ha) = 0(141-85) - 0(98-05). 

 But the corrections of these two points may be taken as zero. Hence T 

 is the mean of the uncorrected thread-lengths. 



