After Woodroffe and Leadbeater, the next most influential person regarding the chakras is Christopher Hills, a spiritual philosopher and researcher who set up his own university, the University of Trees
In a very thick book, Nuclear Evolution, published in the early 1970s, Hills suggests that each of the chakras corresponds to one of the seven colours of the spectrum He then associates each chakra and colour with a particular personality type. A great deal of his book "Nuclear Evolution" is devoted to explaining each of these personality types in detail. His typology is quite fascinating, and certainly equal in profundity to the personality typology of comparable systems of character analysis, such as Carl Jung and Humanistic Astrology. The basic scheme is as follows:
|Sahasrara||crown||primordial imagination type||Imagination, shame and wonder|
|Ajna||forehead||intuitive-visionary type||Intuition, sensitivity, envy or admiration|
|Vishuddha||throat||contemplative- nostalgic||Mental concepts, authority, reverence|
|Anahata||Heart||security or self-centred type||Vital force; possession, jelousy, power|
|Manipura||Solar Plexus||intellectual||Thinking; Intellect, Change|
|Swadhistana||"Splenic Plexus"||social-gregarious||Social; Ambition|
|Muladhara||genitals||physical-sensation||Sensation; Sex, fear and anger|
Note that the positions of the chakras are a little different from the standard positions. The Muladhara is identified with the genitals (ordinarily the position of the Swadhisthana), while, following Leadbeater, the Swadhistana is identified with the "splenic plexus", although with total anatomical ignorance this centre is still located more or less beneath the navel [see diagram in Nuclear Evolution, p.435]. The Manipura is then located at the solar plexus, rather than (as in the Indian system) the Navel.
Although the psychological aspects of this theory did not catch on, the idea of matching the seven chakras with the seven colours of the spectrum was so appealing that just about every book on the chakras written since then show the chakras in rainbow colours.
It is my understanding that the chakras referred to here are not the same as the chakras referred to in Tantric yoga. All the attributes are totally different for one thing, and the chakras as described here represent major organs of the external personality, whereas in Indian and Tibetan tantra the chakras (and the tan-tiens in Taoism) represent subtle faculties that are only activated in advanced yogic practice, and that if they pertain to anything, it is the subtle inner being.
It would seem plausible to identify the rainbow chakras with the etheric body chakras in Barbara Ann Brennan's formulation, and perhaps also the focal concentration points in Mantak Chia's "Healing Tao" microcosmic orbit. The rainbow chakras therefore, if they have any validity at all, have validity inasmuch as they pertain to the etheric bodies (and if Barbara Brennan is to be believed only the second ("emotional"), fourth ("astral") and sixth ("celestial") etheric(energy field) bodies at that). They would pertain to the secondary, and even the tertiary, order of chakras.
Chakras - Wheels of Spinning Light Energy - The Seven Primary Chakras - A Comparative Study - a really fantastic page - combines a number of different contemporary explanatiosn for each chakra, also gives heaps of links
A brief introduction to the Chakra System - presents the rainbow chakra position. Nice little chakra graphics too.