INTO THE LAWS OF THE CONDUCTION OF HEAT IN BARS, ETC. 



135 



Fig. 1. 



at one end, in the following way. Take either the very bar to be used, or a 

 shorter one exactly similar; insert in it a thermometer, 

 in all respects as the thermometers are ultimately to be 

 used for finding the final temperatures. Heat the entire 



(dv\ 

 -T ) , 



corresponding to given temperatures of the thermometer. 



There will be evidently no difficulty in doing this with extreme accuracy. I 



need net insist on the details. We thus obtain for the 



given bar the proportional expenditure of heat by the 



surface, depending on the temperature of the axis of the 



bar, and on nothing else. (By temperature, of course I 



mean excess of temperature above air.) Let such a 



table be formed, or a curve constructed. 



6. " II. Let now the bar experiment [for conduction] be made in the usual 

 way, only with greater precautions than perhaps have hitherto been taken (in- 

 quiring into the effect of the number and size of 

 the holes, and correcting the thermometers for the 

 unimmersed parts of the scale). Register the final 

 temperatures at different distances from the source 

 of heat, the bar being very long. The curve ab, 

 we know, is nearly a logarithmic. Project it graphi- 

 cally, and by drawing tangents, ascertain the rate 



V 



dv 

 dt 



100 

 90 

 &c. 



5J 



5» 



he. 



a 











\ 



P-^ 



-^. 6 







u 





15 



Fig. 2. 



of decrement of temperature for a small increment of leno-th or - — for anv 

 number of points of the bar,— or else, calculate this, 

 taking thermometric indications by threes [twos], 

 and assuming a modulus for each point. Hence we 







dv 



dv 



a? 



V 



dec 



di 



1 



J5 



5» 



55 



2 











5» 



55 



55 



3 











5J 



55 



55 



II. 



form a second table, of od, v corresponding,-^^, and 



from Table I., or from a graphical curve of the 

 observations on which it was founded, we add the 

 column of the momentary loss of heat due to all 



external causes, or £, corresponding to v observed. 



7. "in. We may now construct with abscissae .2?, and ordinates ^'', the experi- 

 mental curve a/3, whose area will express the total escape of heat from the bar, or 

 from any part of it. Thus the area xos' ^^ will represent the escaped heat from the 

 portion of the bar xx'. I should have no doubt of being able to approximate to this 

 area, with fully the accuracy which the inevitable errors of apparatus and observa- 



