Oy THE USE OF LOGARITHMIC COORDINATES, 159 



Otb the Use of Loqanthmic Coordinates. 

 By J. H. Vincent, I).8c., A.B.G.Sc. 



[Ordered by the General Committee to be printed in extemo.'] 

 PLATES L-III. 



SECT. 

 INTBODUCTION 1-3 



Definition and (in example of a translatant ....... 4-G 



CONSTBUCTION OF AX IMPEDANCE CHAET 



The eqnation represents a translatant ........ 7 



Tlw resistance line . ........... 8 



The self- induct 1071. line 9 



The complete impedance curve . . . . . . . . .10 



Mechanical device for drawing above 11 



Scale lines 12, 13 



Horn to use the chart 14 



Discussion op a Non-tbanslatant 15, 16 



CONSTEUCTION OP A CHAET FOE WAVES ON A FEOZEN SEA 



Sliort ware gravity and elasticity lines 17 



Short wave curve 18 



Above to he made general . . . . , . . . . .19 



The scale lines 20-23 



Recapitulation . . 24 



Anothbb Method of treating the same Non-tbanslatant 



The long wave elasticity line .......... 25 



Slwrt wave elasticity line 26 



Complete elasticity curve 27 



The two gravity lines and complete gravity curve 28 



The two complete curves are translatants ....... 29 



Translation of the elasticity and gravity curves 30, 31 



Scale lines for the two complete curves . 32 



Scale lines for thickness .......... 33 



0?i several outstanding matters connected with the chaH . . . 34-37 



The Use op Logarithmic Coordinates to find an Appeoximate 



Equation connecting a Series op Experimental Results . . 38 



Tbi-dimensional Logarithmic Coobdinates 39 



Semi-logarithmic Coobdinates 40 



The Gbaphical Computation op the Hypebbolic Functions . 41-49 

 The meaning of a straight line on the chart ....... 42 



The eu line 43 



Other lines ............. 44 



Semi-logarithmic graph of sink u . . . . . . . . .45 



Of cosh u 46 



Of cosech u and seeh u 47 



Of tanh u and coth u 48 



Points in the geometry of these curves 51-54 



Conclusion . 55 



Introduction. 



1. In discussing experiments upon the passage of gases through porous 

 plates Professor Osborne Reynolds employed a method of plotting curves, ' 

 in which the logarithms of two variables are used to find the points on a 

 new curve. This new curve Professor Reynolds calls the logarithmic 

 homologue of the one from which it is derived, and pointed out the 



' Sir John Herschel used the logarithmic chart in reducing photometric observa- 

 tions. Art. 285, Cape of Good Hope Observations. 



