RMS value of fundamental harmonic vs RMS of third harmonic
Depends on what kind of periodic signal it is. As @Andy Aka mentioned: "Amplitude Profile" or How its amplitude changes with time (Triangular, Square or others ?). 

Whatever be the complex periodic wave you have (say amplitude =\$ V_o \$ , Period = \$T = 2\pi/\omega\$), it can be represented as sum of fundamental frequency and its harmonics.

$$V(t) = V_f(t) + V_2(t)+V_3(t).....V_n(t) $$
where fundemental frequency component is -

$$V_f(t) = V_osin(\omega t)$$

Harmonics are -
 $$V_2(t) = V_2sin(2\omega t)$$
 $$V_3(t) = V_3sin(3\omega t)$$
$$.$$
 $$V_n(t) = V_nsin(n\omega t)$$
So, the nth harmonic's RMS value would be:
$$V_{n(rms)} = \sqrt{\frac{1}{T}\int_0^TV_n^2sin^2(n\omega t)dt}$$

The amplitude of the wave \$V_0\$ is not enough information to determine what would be the amplitude of the nth harmonic ie., \$V_n\$ . So you cannot formulate a direct relation between rms value of the fundamental wave and its nth harmonic just with that information.