12 REPORT 1865. 



transmitted through any minute coloured substances. By using a parabolic reflector 

 attached to the object-glass, opaque bodies maybe examined by reflected light; 

 and, as a curious test-object, it may be mentioned that, by this means, a speck of 

 blood on white paper, which would not weigh more than one-millionth of a grain, 

 will show a perfectly characteristic spectrum. 



Heat. 



Experimental Inquiry into the Laws of the Conduction of Heat in Barn, and 

 into the Conducting -Power of Wrought Iron. By Principal Forbes, F.R.S. 



The experiments described in this paper were all made in 1850 and 1851, upon 

 a plan which was fully explained by the author in letters to Mr. Airy and Pro- 

 fessor Kelland in the former year. Some notice of them appeared in the British 

 Association Reports for 1851 and 1852, .and the apparatus was supplied by a grant 

 from the Association. 



In previous inquiries into the thermal condition of a long conducting bar heated 

 at one end, two assumptions have always been made ■.—first, that the flux of heat 

 across any transverse section of the bar is proportional throughout to the rapidity 



of the decrement of temperature reckoned along the axis of the bar (or to -=-, where 



v represents the temperature, above that of surrounding space, of any point of the 

 axis of the bar at a distance x from the origin ) : secondly, that the loss of heat 

 by radiation and convection from the surface of the bar is at every point propor- 

 tional to the same temperature n. By assuming these principles (the last of which 

 is certainly more or less inexact), the well-known solution of the problem of the 

 heated bar is, that the temperatures (or excesses of temperature) diminish in a 

 geometrical progression from the origin, and finally, of course, become insensible. 

 Previous experimenters have confined themselves to finding the constants of the 

 logarithmic curve for different substances, and thence their relative (not absolute) 

 conducting-powers. 



In the experiments now described, neither of the above-mentioned principles is 

 assumed. The external loss of heat is directly ascertained by experiment, and the 

 admissibility or otherwise of the first of the two assumptions is also directly tested. 



That assumption may be thus svmbolized : F = — ft— , where F is the flux of heat 

 r " J da? 



across unit of section, k the conducting-power for the substance employed, and v 



and x have the same signification as before. 



I. In the first instance, a bar of iron 8 feet long and \\ inch in diameter, was 

 heated at one end by means of a crucible containing melted solder. Thermometers 

 were inserted at various points of its length. The results, v in terms of x, 



were projected in a curve (approximately a logarithmic), and the values of j- 



were found by projection or calculation, or both. 



II. Next, a short bar (20 inches long), perfectly similar in section and condition 

 of surface to the long bar, is heated to above 200° Cent, in a bath of fused metal, 

 and allowed to cool in free space, a thermometer being inserted at the centre of its 

 length. This gives us the rate at which such a bar is parting with its heat from all 

 causes whatever, in terms of the temperature shown by a thermometer in its axis. 



III. The losses of heat in unit of time (one minute) last found, may be taken as 

 representing the amount of heat dissipated from each elementary section of the 

 long bar in the statical experiment (I.), being given in terms of the temperature 

 proper to each point of such a bar. A curve may thus be constructed, having for 

 its line of abscissa? the axis of the long bar, and for ordinates, the rate of dissipa- 

 tion of heat from each portion of its surface clue to both radiation and convection. 

 This curve is called by the author the statical curve of cooling. 



IV. If we can by mechanical quadrature, or otherwise, find the whole amount of 

 heat dissipated between any point of the long bar and its coolest extremity, we 



