HOLMAN. — PYROMETRY. 237 



made mentally, since a is seldom more than one twentieth of a small 

 division of the scale. 



Calibration, and Computation of Unknown Temperature. — Let d^ 

 represent the corrected deflection for the sulphur temperature t^ (com- 

 puted from the reduced barometric pressure H Sit the time by the 

 foregoing formula) and let d^ be that for the assumed melting tem- 

 perature t^ of copper or the metal used. Plot two points with log d 

 as abscissa and log t as ordinate respectively. Draw through these 

 two points a straight line. Then within the limits of error of the ap- 

 paratus, the ordinate of this line corresponding to any abscissa log d 

 will be log t, the log of the desired temperature of the hot junction, d 

 being any observed deflection corrected to 20° or 0° as above. That 

 is, the number corresponding to this logarithm will be t. 



By far the most convenient way to effect this plotting and subsequent 

 interpolation, instead of employing logarithm tables and the ordinary 

 co-ordinate or plotting paper I'uled with equidistant lines, is to use 

 plotting paper with a logarithmic ruling, that is, with lines spaced at 

 distances progressively diminishing according to the logarithmic law, 

 like the divisions of the ordinary slide rule. By suitably numbering 

 the axes of such a sheet the desired quantities can be plotted directly 

 without the aid of the logarithm tables. Subsequent interpolation 

 then becomes exceedingly easy, since it is merely necessary to enter 

 the plot with the corrected deflection as abscissa, and read off the cor- 

 responding ordinate on its numbered axis, this giving directly the un- 

 known temperature t. Unfortunately such paper (which would be 

 useful in many physical and practical problems) is nowhere on sale so 

 far as the author is aware. 



In default of such paper, and instead of using the plot of logarithms 

 for continuous interpolation, a direct reading plot of deflections and 

 temperatures may be made from it once for all. On the logarithmic 

 plot look out the ordinate for every ten (or twenty) divisions of the 

 scale, i. e. corresponding to log 10, log 20, log 30, etc. (smallest 

 divisions). Look out in the log tables the numbers corresponding to 

 these ordinates, thus obtaining <,g, <oq, etc. Make a new plot, with 10, 

 20, 30, etc. as abscissas, and <,g, <.,g, ^„q, etc. as just found, as ordi- 

 nates. These points can be taken at such short intervals that a relia- 

 ble smooth curve may easily be drawn through them, and this is then 

 available for subsequent direct interpolations. 



In the absence of logarithmic plotting paper, log plots may very 

 conveniently be made by a straight edge, graduated with a logarithmic 

 scale. Four of such rulers (two of single and two of double scale) 



