98 
Miscellanea 
because as we are there dealing with a third-dimension body we should require a fourth 
dimension in order to enable us to represent the values of u^^^ as well as their positions. For 
the same reason we cannot give a graphical illustration of interpolation with four variables. 
3. Some particular cases. It will probably be useful to give the "interpolation-lines" in the 
case of a function of two variables where the values proceed by small differences. 
We shall assume that only integral values are required, and in our diagrams a heavy dot will 
stand for the position of a given value and a small dot for the position of a value obtained by 
interpolation, while the lines show the "interpolation-lines." 
Difference in ^ =3. 
Fig. 5. 
In this case the line between AB m an obvious interpolation, and similar lines will be 
neglected in other diagrams ; in fact there is only one "interpolation-line," since AC and BD are 
the same in principle ; they have merely different starting-points. 
Difference in ./; =4. 
» v y =4- 
Fig. 6. 
