Also, in Chapter 9 - Harmonics in the Aspect Circle, the author presents an analysis of the aspects between Sun-Saturn in the charts of 972 nonagenarians using harmonics. His conclusion is that using the traditional aspects no special relation could be found, but, by using harmonics he could identify the 24th (15 degrees), 36th (10 degrees) or the 108th (3 1/3 degrees) harmonics to be relevant.

In conclusion, harmonics gave good results in this case. In fact the author gives a very good mathematical and philosophical explanation:

"Astrology is full of circles and circular motions. Three of these are usually given precedence: first, there is the circle of the Zodiac, that is, the circle of the ecliptic in which positions of the planets in their orbits are determined. Secondly there is a circle of houses, that is, the diurnal circle of the planets as they rise, culminate and set each day. Thirdly there is the circle of aspects as a planet moves from its conjunction with another body round to the opposition and back again to the conjunction. In each of these circles the astrologer studies the relationship of one factor to another and places an interpretation upon that relationship."

"Everything in the realms of manifestation owes its existence to the dynamic power of Ideas. Ideas in their highest aspect are spiritual wholes or unities. Such wholes, existing above time and space, are yet formal causes of everything in manifestation. 

What is unitive above is multiplex below. Thus Ideas express themselves objectively through parts, the parts representing in their inter-relationships the outworking of the subjective potentialities of the whole from which they are derived, each fulfilling or expressing a function or aspect of the parent unity. The Idea, as a unity, manifests as the entire circle of the ordered relationships of the parts. In the realms of time it manifests as the whole cycle of the stages of unfoldment  of the Idea by which the inherent potentialities are actualised in the order of succession."

So, we can say that everything is the unfolding of ideas! Those are very powerful philosophical positions.

"It is a fundamental principle that the number by which the circle is divided holds the key to the interpretation of the relationship involved."

Part Two - Practical Applications

In Chapter 11, the author presents the Navamsa chart, which is an astrological technique used in Indian astrology which consist in dividing the Zodiac in nine (9) and then in 12 (twelve) parts and is said to show the marriage partner. The author show that is an application of the 9th harmonic, as there are others in Indian astrology: Hora or 2nd harmonic signify possessions, Dreshkhana or the 3th harmonic signify brothers, Chaturthamsa or the 4th harmonic signify home and property etc.  

He also writes about the number 9:

"The number 9 (nine) is associated with the Ideal to be realised and with Completion. [...] The number nine, though not identical with the idea of entelechy, yet represents the gateway to that fulfillment."

In Chapter 12, the author presents in the same manner the Panchamsa chart, an Indian technique which is based on the 5th harmonic, an indication about creativity, mental power, art.

Chapter 13 is a lesson of numerology where the author writes about the symbolism of numbers: 7 (seven) is about mysticism, sacred matters, inspiration, creativity, 6 (six) is about health, 3 (three) is about form as opposed to matter, the formal principle of a thing, 4 (four) is about the material cause, effort, will, challenges, to manifest in the world ones potential. He also gives examples, like:

"Sun - Jupiter septile (a.n. - 51 degrees 30 minutes) often tends to give an interest in mystical philosophy. Mercury - Saturn might give an interest in the mystical or symbolic aspect of numbers."