39 



the middle vertical diameter of the body, r. is the specific gravity of the 

 body, and r the specific gravity of the fluid for the movement in air 



1 2 g h (n — r) for the movement in any liquid. 



r 

 Wiesner has done a great deal of work in determining the application 

 of the laws for different gases to epidermis with and without openings, at 

 the atmospheric pressure, and pressures above and below that of the at- 

 mosphere, and with dead and living, dry and moist membranes. He has 

 made sufficient experiments so that his conclusions, which are expressed 

 by mathematical formulae in many cases, are general, that is, his formula 



. — in which A represents the absorption coefficient, and d the density 

 I d 



of the gas is general for the epidermis, free from stomata, of any plant. 



An application of mathematics that one does not often see outside of 

 the statistician's work was made by Dr. Arthur! in his work on pear 

 blight. In this there was a set of determinations made as to the succu- 

 lency of the fruit of the Buffum pear, so as to note the relation between 

 the amount of moisture and the extent of the blight. After the deter- 

 minations were made, calculations of the probable error in the results were 

 also made, finding the variation in the determinations, and the extreme 

 variation from the mean; using the figures and applying the formula, 



± . ii74"> - . in which s is the sum of the squares of the differences be- 

 tween each separate observation and the average of all, and n is the num- 

 ber of observations. This work was done to prove its correctness, as the 

 accuracy of such work had been questioned. 



The most general application of graphic mathematics is the rectilinear 

 system of coordinates. This is so simple in the construction of diagrams 

 and so readily understood that a great many people make use of it. Be- 

 sides, one diagram will show the relation among different sets of data. 

 Take, for example, one of Sachs' diagrams showing plant growth. The ab- 

 scissa represents increments of time, the division of the ordinates, the in- 

 crements in length, the axis of abscissa' represents a certain temperature, 

 and a certain number of the divisions of the ordinates represent a degree 

 a temperature. Then spaces of the diagram are shaded for night. The 



.r. Wiesner. Versuehe iiber den Ausgleich des Gasdruckes in den Geweben der 

 Pllanzen, 187!>. .1. Weisner und H. Molisch. I'ntersuchnngen fiber dis Gasbewegung in 

 dor Pfianze, 188!>, 

 v.T. C. Arthur. 5th Ann. Rep. X. V. Exp. Sta., 1886, pp. 284-285. 



