ON THE CONPUCTION OP HEAT. 17 



unmelted lead was kept constantly in the vessel. The temperature of the air 

 was kept uniformly at 18° '125. The unit of length was taken as the distance 

 between the first and second thermometers. The following table contains 

 the results : 



No. of therm. Dist. from extremity. Temperature above air. 



1 2-23077 76-875 



2 3-23077 47-1875 



3 4-12019 29-375 



4 5-08172 17-8125 



5 6-02883 10-625 



6 7-89903 3-75 



7 9-78363 1-5625 



I. The result of calculation on the first hypothesis, the errors being ar- 

 ranged so that there shall be the smallest possible total error amongst the 

 first four thermometers, is given by M. Biot as follows : 



1 2 3 4 5 ■ 6 7 



77-575 46-7625 29-275 17-975 11-125 4-3125 1-6625 



II. On the second hypothesis the values of the constants are 



A = 206-9 and log e~^ = — -20955, 

 as determined from the first and third thermometers. The table is as follows : 

 1 2 3 4 5 6 7 



76-875 46-07 29-375 18-22 11-44 . 4-6 1-85 



III. By the third hypothesis, retaining the value of ^ given by the second, 

 we get y — 2 »t = -003206, a result probably too great ; and there arises the 

 following table : 



1 2 3 4 5 6 7 



76-875 47-76 29-375 18-23 11-45 4-6 1-85 



IV. The computations on the fourth hypothesis give 



12 3 4 5 6 7 



76-875 45-2 29-375 18-74 12-34 5-73 2-45 

 By selecting other observations to determine the constants, we might, had 

 it been requisite, have made the results more conformable in this case. 



(3.) M. Biot's third experiment was made on a bar of copper, plunged at one 

 extremity into melting lead. It carried fourteen thermometers, of which, 

 however, eleven only were available. The unit of distance was 101 milli- 

 metres, and the temperature of the surrounding air 15-75°. The following 

 table exhibits the result : 



No. of therm. Dist. from extremity. Temperature above air. 



4 5-25 80-5 



5 6-25 65-75 



6 7-25 53-75 



7 8-25 43-75 



8 9-25 • 35-5 



9 11-25 24- 



10 13-25 15-7 



11 15-25 Il- 

 ls 17-25 7-5 



13 19-25 5-25 



14 21-25 3-75 



I. The results of M. Biot's computation, so as to give the smallest possible 

 amount of error amongst the thermometers 4, 5, 6 and 7, are 



4 5 6 7 8 9 10 11 12 13 14 



80-6 65-78 53-82 43-8 35-75 23-81 15-85 10-56 7-03 4-68 3-12 

 1841. c 



