86 PRINCIPAL FORBES ON AN EXPERIMENTAL INQUIRY INTO 



69. The formulse used in the preceding calculations are the following :- 



Case I. < 



Case II. 



( /»% i i ~-e e -66184a; 



(A)Iog, = lo g 275-5- 1 + . 13()93j 



•3472~ 

 (Bj log v = log 4-0+ 1 _. 05 Q 6g > where *=4-a 



(C) log „=log 2605- j^g- 

 ( D ).o g „=,o g 209-08 -jS"* 



Case III. 



•4217r 

 (E) log « = log 0-47 + 1 _. 0405g . where ~ 



(F) log ,=W MM-fL^jj 



= 5 — x. 



(G) log*=log 052 + 



•4521* 

 1--0282*' 



where ~ = 5 — x. 



70. With reference to the preceding numerical Table, I may remark, First, 

 that the differences shown are not in all cases deviations from direct observations, 

 but between the formulse and the graphical interpolation of the data. There is a 

 difficulty (which will be understood from Art. 57) in comparing compendiously 

 the formulse with the single data of Table I. When the points of the curve are 

 somewhat distant from points of observation, the numbers in the preceding Table, 

 obtained from the formulse, may be, and probably are more reliable than those 

 assigned from the curve. Secondly, the curve of Case I. appears to be the most 

 reliable in all respects. And in particular I consider the portion of the curve 

 which includes the highest temperatures, or those corresponding to points on the 

 bar between and 3 inches, to be very nearly accurate. From numerous inde- 

 pendent calculations, I conclude that the value of v at the origin, or in contact 

 with the crucible, is pretty exactly 275°5 Cent., as there assigned. If we add to 

 this 12°-5 for the approximate temperature of the apartment, we have 288° for 

 that of the bar where it enters the crucible, and is supposed to have very nearly 

 the temperature of melting lead. This is a considerably lower temperature than 

 is usually attributed to melting lead * 



* Usually stated at from 320° to 330° Cent., 608° to 626° Fahr. Biot, indeed, gives it as 

 only 260°, inferentially derived from his conduction experiments (Traite de Physique, iv. 677) ; hut 

 this is on the supposition of the logarithmic law prevailing. Crichton, junior, gives 606° 5 Fahr. 

 (T. Thomson); Daniell, 612°; Kupffer, 633°. Supposing any of these last numbers to be correct, the 

 inference must be, that in the conduction experiments described in the present paper, the temperature 

 of melting lead did not extend to the outside of the iron crucible when the origin of the co-ordinates 

 has been taken, but must be sought somewhere in the interior. This conclusion is strengthened by 

 some otlier, though indirect considerations. 



