20 REPORT — 1841. 



III. Assumes log e ^ = — -50776, and gives — (y — 2 wi) = ^'Sll. 



1 2 3 4 



65-13 30-9 14-93 7-27 



IV. 1 2 3 4. 

 65-13 30-12 14-93 7*5 



(9.) A bar of white marble. The temperature of the air = 17-15°. 

 No. of therm. ... 12 3 4 



Exc. of temp. ... 63-91 6-08 1-95 1-47 



Calculations. 



I. 1 2 3 4 

 63-91 11-16 1-95 -3406 



II. Gives log e~^ = - -74249, A = 59*40. 



12 3 4 



63-91 10-9 1-95 -352 



no 



III. Assumes log e = — -74249, and gives -— (y — 2 wi) = -644. 



1 2 ' 3 4 



63-91 11-35 1-95 -379 



IV. 1 2 3 4 

 63-91 10-18 1-95 -37 



Of the other formulae ■which have been tested by experiment we do not 

 make much account, since it is our impression that the experiments were con- 

 ducted rather with a view to illustrate the formulae than to try the validity 

 of the principles on which they depend. We instance the following : it is 

 taken from Fourier's Memoir, which contains several others, ' Mem. de I'ln- 

 stitut/ tom. V. p. 217. See also Kelland, 'Theory of Heat,' p. 60. 



Three thermometers were placed at different points of a solid ring, at in- 

 tervals of one-eighth of the circumference : a fourth was so placed that the 

 third lay midway between it and the first. The temperatures observed were 

 66°, 50^2°, 4^*°, and 34-353° + 17f°, respectively. 



The equation which results from formula (3) is — = I — ) — 2, 



where v^, v^... are the excesses of temperature of the different thermometers 

 above that of the air. 



By computation, it appears that the first side of this equation is 3-140, and 

 the second 3-143, a difference hardly appreciable. 



The second and third hypotheses give formulse which are merely correc- 

 tions on the first. In this case, therefore, no correction is required. 



In computing the result on the fourth hypothesis, our equation is 



l-a~^'+ 1 -a~^' ^ ( 1 -g—' + l-a—a y_^^ 

 1 - a-^' 



f l - a~^' + 1 - a-^' X 

 V 1 - a-'-^ ) 



and the first side is equal to 2-96, the second to 2-875 ; a coincidence which, 

 though not so close as the former, is very far within the error due to the 

 effect of the air. We are almost inclined to believe that the veiy closeness 

 of the coincidence by the former process proves the incorrectness of the for- 

 mula to represent what it is intended to express. 



We are now, in the last place, to exhibit the results of an experiment of a 

 different kind, and one which, had it been well made, we should have deemed 

 most important. It is taken from M. Biot's work, 'Traite de Physique,' iv.676. 



