and the Mode of Us Communication. 33 



point E, another perpendicular EF be erected, and EF 

 be taken equal to the difference of the temperatures 

 after the time represented by CE has elapsed ; and if 

 the perpendiculars GH and LM be drawn, representing 

 the difference of the temperatures after the times EG 

 and GL have elapsed, a curved line PQ drawn through 

 the points D, F, H, M, will be the logarithmic curve; 

 or, if it vary from that curve, its variation, within 

 the limits answering to a change of temperature amount- 

 ing to a few degrees (especially if they be taken when 

 the temperature of the hot body is about 40 or 50 

 degrees above that of the medium), will be so very 

 small that no sensible error will result from a supposi- 

 tion that it is the logarithmic curve, in supplying, by 

 computation, any intermediate observations which hap- 

 pen to have been neglected in making an experiment. 



These computations are very easily made, with the 

 assistance of a table of logarithms, in the following 

 manner. 



Supposing CD, CG, and GH, to have been deter- 

 mined by actual observation ; and that it were required 

 to ascertain, by computation, the absciss CE, corres- 

 ponding to any given intermediate ordinate EF, or 

 (which is the same thing) to determine at what time the 

 cooling body was at any given intermediate temperature 

 (= EF) between that ( CD) which it was found by 

 observation to have at the point C, and that (= GH) 

 which it was found to have after the time represented by 

 the line GC had elapsed ; 



It is log. CD log. GH is to CG as i to m 

 (= modulus the subtangent of the curve at the point 

 D.)* And CE = m X log. CD - - log. EF. 



* The subtangent shows in what time the instrument would cool down to the tem- 

 VOL. II. 3 



