420 D. J. SCOURFIELD ON LOGARITHMIC PLOTTING. 



1, 10, 100, 1,000, 10,000, etc., the logarithms of which are 0, 1, 2, 



3, 4, etc., respectively, and then dividing the spaces so obtained 

 unequally by lines drawn at distances equal to -3010, "4771, -6021, 

 •6990, -7781, etc., which are the logarithms of the numbers 2, 3, 



4, 5, 6, etc. 



Ordinary sectional paper, ruled say in inches and tenths, can 

 be adapted to logarithmic plotting by considering the bolder lines 

 to represent the numbers 1, 10, 100, 1,000, 10,000, etc., as before, 

 and by applying to the intermediate lines the numbers of which 

 the logarithms are -1, -2, *3, '4, etc. The values of the lines, 

 commencing with the first above the base line, will therefore be 

 approximately as follows : — 



1-259 3-981 12-589 39-811 



1-585 5-012 15-849 50-119 



1-995 6-310 19-953 63-096 



2-512 7-943 25-119 79-433 



3162 10000 31-623 100000 etc. 



Typical logarithmic sectional paper should of course be ruled or 

 taken logarithmically in both directions. This, however, is not 

 required in plotting biological data as a rule, although it is 

 possible that it might be useful in certain kinds of work — perhaps, 

 for example, for data connected with the variations exhibited by 

 a rapidly increasing number of organisms. But it is only proposed 

 to consider the use of paper ruled or taken logarithmically in one 

 direction — namely, horizontally, the ruling in the other direction 

 proceeding in arithmetical progression as usual. 



On the accompanying Plate (XX.) will be seen a chart which 

 has been ruled in the manner above suggested. The horizontal 

 lines represent tenfold changes in the numbers (individuals) for 

 each unit of measurement (one inch), whilst the vertical lines 

 represent equal divisions of time (months). The latter have been 

 ruled at half-inch instead of one-inch intervals, as would perhaps 

 have seemed more natural, because in this way steeper curves are 

 produced, and also because the angles representing the various 

 changes are separated from one another more than they would 

 otherwise be. 



In addition to the advantage already referred to — namely, that 

 the graphic representation of an enormous range in the numbers 

 is rendered possible — logarithmically ruled paper as described 

 above, or ordinary sectional paper taken logarithmically, has the 



