16 REPORT — 1841. 



The distance of the end of the bar from the mercury was ST'S^S deci- 

 metres. 



I. The following table exhibits the temperatures which should exist, as 

 calculated by the Cor. to formula 2 ; i. e. on the first, or Fourier's hypothesis. 

 It is copied from Biot, vol. iv. p. 672, and reduced to the cent, scale. The 

 constants are determined by thermometers 1 and 3. 



Therm.... 12 3 4. 5 67 



Result.... 85-6 29'375 17-7 11-25 6-9375 4--3125 1-6625 -6375 



II. Let us calculate the temperatures on Libri's hypothesis, by means of 

 formula 9. 



We have log^ a = -00763606, and if we denote one-sixth of this by c, our 

 equation becomes 



V = A e~^^ + c (A e'^'^y, which, being solved, 



4 -gx V^cv + \- 1 



gives Ae " := ; 



2 c 



V'4cj;„ + 1 — 1 



and therefore e~^*^*'3-^i)= 



'V4c»i + 1 — 1 



These two equations determine g and A by means of the first and third 

 thermometers; viz. 



e ^ = -6093, and A = 80-855. 



The results of the calculation are the following : 



12 3 4 5 6 7 



89-2 29-375 17-6 11-25 6-95 4-358 1-72 -67 



III. On M. Poisson's hypothesis we have formula 8, viz. 



« = |l - y (y - 2»0 }0e-^'' + y (y-2m)e 2^*': 



where d is the temperature at the heated extremity of the bar, and y, as cor- 

 rected above, is -OOSSIS. To compare this formula with experiment, we have 

 supposed that g has the same value as we found it to have according to the 

 preceding hypothesis. This supposition cannot, to any considerable extent, 

 affect the results ; and we could not obtain g by any other direct means. We 

 get from thermometers and \, y — 2m = -00153, and thence obtain the 

 following table of results : 



1 2 3 4 5 6 7 



86-25 29-375 17-78 11-36 7-05 4-43 1-75 -69 



IV. Lastly, on the hypothesis that the flow of v is proportional to v, both 

 within and at the surface of the medium. We reduce v to thermometric 



temperature by means of the equation t» = A (1 — a~ ) which is not strictly 

 accurate except for the air thermometer ; and we determine the constants 

 from thermometers 3 and 5. Tlie following are the results : 



12 3 4 5 6 7 



90-3 27-7 17-2 11-25 7-19 4-6875 2 -86 

 It may be proper to remark, that although we have adopted MM. Dulong 

 and Petit's value of a, we are aware that for radiation in air, so far as the 

 formula approximates to the circumstances, this value of a is too small. 

 (2.) The next experiment given by M. Biot (p. 673) is the following : 

 A bar of iron was held for many hours plunged in melting lead. The ves- 

 sel containing the lead was heated from below by means of a lamp and cur- 

 rent of air. To prevent the temperature from increasing, a small bar of 



