Paragraph: A nichrome wire A B, 100 ~cm long and of uniform cross...

Paragraph: A nichrome wire $A B, 100 \mathrm{~cm}$ long and of uniform cross section is mounted on a meter scale, the ${ }_1$ and B coinciding with 0 cm and 100 cm marks respectively. The wire has a resistance $S=50 \mathrm{ohm}$. A $C$ along this wire, between $A$ and $B$ is called a variable point to which one end of an electrical ele connected. In the following questions this arrangement will be referred to as 'wire $A B$ '.Question: The 'wire AB ' is now a part of the adjacent circuit. With the resistors $\mathrm{P}=50 \Omega$ and $\mathrm{Q}=100 \Omega$, the null point is obtained at C where $\mathrm{AC}=33 \mathrm{~cm}$. When the resistors are interchanged, the null point is found at C with $\mathrm{AC}=67 \mathrm{~cm}$. The systematic error in this experiment seems to be due to noncoincidence of A and B with 0 cm mark and 100 cm mark respectively. If these end errors are equivalent to ' $a$ ' cm and ' $b$ ' cm respectively, then they are