168 REPORT— 1898. 



same setting of tlie slide rule as used for the complete elasticity curve, 

 from equation ' 



V C V k + G 



29. The Two Com2)lete Curves are Translatants. — If in the gravity 

 equation 



u-=z 



a, c, A, and u are written «', c', ^, u f. / -, the equation is unaltered. 



c \; ac 



Therefore it is a translatant with respect to a and c. 



Similarly the elasticity equation 



in 



is a translatant. 



Subsequently it will be shown how to shift the elasticity and gravity 

 curves to allow for changes in e, E, g, p, and s ; but in whatever position 

 the two curves may be on the chart the complete homologue of the equa- 

 tion in which both eflects ajipear is found by the method explained in 



30. Translation of tJie Elasticity Curve. — I. New values for e. In the 

 elasticity equation it is seen that if e becomes ne and \, n\ : u remains 

 unaltered. Thus to find new position of elasticity curve move it to the 

 right through a distance log n. 



II. New ^•alues for E. If E becomes tcE andw becomes usjn equation 



is unaltered. Thus to shift the elasticity curve move it through - log n 



upwards. 



III. New values for s. When s becomes ns, \ becomes n\ and u 

 becomes tm-i, the equation being unaltered. Thus to adapt to new 



values of s move curve log n to right, and - log ii downwards. 



' It is perhaps worth noting that the complete elasticity curve could have been 

 computed from 



„ h K 



u- = — . ■ 



A^ \ + C 



and the long wave elasticity line. Also the complete gravity curve could have been 

 obtained from 



^ A. 



A + c 



and the long wave gravity line. But in the fraction A. both numerator and 



\ + c 

 denominator change, and a separate setting of the slide rule would be necessary for 

 every new point found on the complete curve. 



