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Prof. 0. Reynolds on certain Dimensional [Feb. 6 y 



Graphic Method of comparing the Results. 



This method consists in taking as ordinates and abscissas, not the 

 thermal differences and mean pressures, but the logarithms of these 

 quantities, and the curves so formed are called the logarithmic homo- 

 logues of the curves shown in figs. 1 and 2. 



Any common ratio which exists between ordinates or abscissas of 

 corresponding points on the natural curves becomes a common differ- 

 ence between the ordinates or abscissas of their logarithmic homologues, 

 so that if the natural curves correspond after the manner that has just 

 been described, their logarithmic homologues must be precisely similar 

 curves, such that by shifting the one parallel to itself it can be made to 

 fit on to the other. 



Fig. 3. 



Log. Pressure. 



In fig. 3 a b and c cl are the logarithmic homologues respectively for 

 the air curve and the hydrogen curve with meerschaum, and e/and 

 g h are the logarithmic homologues respectively for the air and 

 hydrogen curves with stucco. By tracing e/and g h together with 

 their axes on the same paper, and moving the paper without turning 

 it, until the traced curves fit the curves for meerschaum, it is found 

 that the fit is perfect, a portion of the traced curve e f coinciding 

 with a portion of a b, and a portion of g li coinciding with c d. 



O' M and 0' N, the components of the shift, are the logarithms of 

 the ratios of the corresponding ordinates and abscissas of the natural 

 curves ; and in the particular case to which fig. 2 refers — 



O'N = -7 = log. 5 

 O'M = -77 = log. -5-9 



It is thus seen that the reason why the numerical comparison did not 



