170 



EEPOKT 1882. 



Hallsteom's Method. 

 i Thermometer C. 



(25) In the application of Hallstrom's method the principal points 

 were taken 4° apart, and a thread about 8° long was measured with its 

 lower point in the neighbourhood of each of them, and a thread about 

 12° long, with its lower end in the neighbourhood of the first two. 

 S and (T have with respect to this longer thread the same meanings as 

 T and r for the shorter. The Gay-Lussac curve drawn in a continuous line 

 in Plate I., fig. 1, was used to effect the transference. Then the follow- 

 ing equations were obtained : — 



S = ^3 + </'(3')-0(O) .... (1) 



! S = a, + f (4') - <p (1') .... (2) 



T = r, + ^ (2') - V> (0) .... (3) 



T = r, + cp(3')-<p(V) .... (4) 



&c.= &c. 



T = 7,0+ 0(10')- 0(8') .... (11) 



Hence, remembering that o (n) = (p («) — (p {n — ,) from (1) and (2). 



.: c (4') = a (1') + .73 - ff, 



= a (1') + y (4') say 

 Similarly from the other equations : — 



ra - r3 = c (3') - c (1') .'. o (?,') = 3 (1') + r, - rg = 3 (1') + y (3') say 

 - c (2') = c (4;) - (r; - rj 



= I (1') + ^3 — (^4 — (''3 — '■4) 



= a (1') + y (2') say 

 can be expressed in terms of c (1'). If 



73 -r, = 3(4')-, -(2') 



c s 



Similarly all the other 



(0') and (10') are taken = zero, 



3(1') + 3(2') + 



+ 3 (10') = 0. 



Table XII. 

 Thread I. 



Hence, if all the nine equations which give the c's in terms of 3 (1') 

 be added, it follows that 



- 10 3 (1') =■ y (2') + y (3') + + y (10'). 



