172 



REPORT — 1808. 



As an example we will find equations connecting tM'o series o£ 

 experimental numbers (kindly furnished by Mr. Bruce Wade, of Trinity 

 College, Cambridge). 



In fig. 3 these two curves are plotted logarithmically. They are each 

 represented very nearly by straight lines, and the equations may be ob- 



FlG. 



tained from the figure at once, the power of y being a tangent and the 

 coeflBcient of x a reciprocal of an intercept. 



(a) y^-'^'^lSx. 



(b) 2/i'^=29.x-. 



When the equation connecting the values is of the form 



yP:=axf-+bx'^±&c. 

 the same method could be employed. 



Tri-dimensional Logarithmic Coordinates. 



39. The construction of a surface to represent the mutual algebraic 

 relationships of three variables is in general a matter of great labour, 

 involving the computation of a series of curves which have then to be 

 placed at appropriate distances apart, and the surface constructed so as to 

 pass through all the curves. Many equations in physics lend themselves 

 very readily to discussion by nteans of tridimensional logarithmic coordi- 

 nates. Writing down a few which occur, we have 



pv='Rd, c=-, Q=c)', T=27r V 1-. 

 R '^ g 



As one of the simplest of such equations we may take V'=gh, which is 

 the equation of seismic ocean waves. 



Regarding v, g, h all as variables, the surface representing the equa- 

 tion in logarithmic coordinates is drawn in fig. 4. This figure is a tri- 

 metric projection of a model of the logarithmically ruled planes and the 

 homologue of the surface v'^—gh. 



It is obvious that scale lines could be used to represent changes in the 

 quantities occurring in equations involving more variables. 



