419 



The Logarithmic Plotting of Certain Biological Data. 



By D. J. Scourfield. 



{Read October 15th, 1807.) 



Plate XX. 



No one will dispute the great value of the graphic representa- 

 tion or plotting of many classes of facts by means of curves drawn 

 upon sectional paper. The great advantage of being able by 

 means of such curves to grasp at one view not only the relation 

 existing between the members of one series of numbers, but also 

 their relation to another series, is so evident that, in the words of 

 a well-known authority, " it needs no demonstration." 



It sometimes happens, however, that the ordinary sectional 

 paper, when used in the ordinary way, is quite powerless to cope 

 with the enormous range of figures with which one has to deal. 

 The increase in numbers of many of the lower animals and plants, 

 for example, runs up in a few weeks, or even days, from units or 

 tens to many millions. In such cases it is evidently quite im- 

 possible to plot curves showing the course of development, in the 

 usual way. If it is desired to get a graphic representation of 

 such data, some other method of plotting must be found ; and the 

 suggestion now brought forward is that for such work biologists 

 should use sectional paper ruled logarithmically, or, what comes to 

 the same thing, should use the ordinary sectional paper as if the 

 distances at which the lines are drawn represented the logarithms 

 of numbers and not the numbers themselves. 



The idea of logarithmically ruled paper is not new, but the use 

 made of it, even by mathematicians and physicists, appears to be 

 very limited. Nevertheless its great value, at least in certain 

 classes of physical work, has been fully acknowledged. (See 

 Professor Boys s article " Scale Lines on the Logarithmic Chart," 

 Nature, vol. lii., 1895, p. 272.) So far as I know, such paper has 

 not hitherto been employed in biological work. 



Logarithmically ruled sectional paper is produced by first of all 

 drawing a series of lines at equal distances apart, according 

 to any convenient scale, representing say the series of numbers 



