Sirius is the brightest star in the night sky. Intrinsically, Sirius is over 20 times brighter than our Sun and over twice as massive. As Sirius is 8.7 light years distant, it is not the closest star system -- the Alpha Centauri system holds this distinction. Sirius is called the Dog Star because of its prominence in the constellation of Canis Majoris (Big Dog). In 1862, Sirius was discovered to be a binary star system with a companion star, Sirius B, 10,000 times dimmer than the bright primary, Sirius A. Sirius B was the first white dwarf star discovered, a type of star first understood by Subrahmanyan Chandrasekhar in 1930. While studying Sirius in 1718, Edmond Halley discovered that stars move with respect to each other. The Sirius system is shown above captured in X-ray light. From http://antwrp.gsfc.nasa.gov/apod/ap960902.html
"the great White Lodge on Sirius is the spiritual prototype of the great White Lodge on Earth" [EA350]
"It might be profitable to you to bear in mind at this point what I have often told you, that the great White Lodge on  Sirius is the spiritual prototype of the great White Lodge on Earth, of which modern Masonry is the distorted reflection, just as the personality is a distorted reflection of the soul." [EA.348]
"The first four initiations of the solar system correspond to the four "initiations of the Threshold," prior to  the first cosmic initiation. The fifth initiation corresponds to the first cosmic initiation, that of "entered apprentice" in Masonry; and makes a Master an "entered apprentice" of the Lodge on Sirius. The sixth initiation is analogous to the second degree in Masonry, whilst the seventh initiation makes the Adept a Master Mason of the Brotherhood on Sirius.[IHS.18]
"These ancient Mysteries were originally given to humanity by the Hierarchy, and were - in their turn - received by the Hierarchy from the Great White Lodge on Sirius. They contain the clue to the evolutionary process, hidden in numbers and in words; they veil the secret of man's origin and destiny, picturing for him in rite and ritual the long, long path which he must tread." [EA.331]
"Masonry, as originally instituted far back in the very night of time and long antedating the Jewish dispensation, was organized under direct Sirian influence and modeled as far as possible on certain Sirian institutions and bearing a slight resemblance also to our hierarchical life - as seen in the light of the Eternal Now. Its "Blue Lodge" with its three degrees is related to the three major groups of Lives on Sirius, for there are there no kingdoms of nature, such as we possess; these groups receive all Those Who choose the fourth Path, and train Them in the mode of existence and the type of livingness which is found on Sirius. This will make it plain to you that the least developed of the Sirian Lives are - from our standpoint - all of Them initiates of very high degree. Masonry is, therefore, connected in a peculiar way with the fourth Path. Down the ages, the Masonic tradition has been preserved, changing its nomenclature from time to time, reinterpreting its Words of Power, and consequently getting further and further removed from its original beauty and intent." [R&I.417]
"The influences of Sirius, three in number, are focused in Regulus, which is, as you know, a star of the first magnitude and which is frequently called "the heart of the Lion." There is more real occultism hidden in the names given to the various stars by astronomers down the ages than has yet been realized, and here you have a case in point." [EA.300]
"A Master, therefore, is one who has taken the seventh planetary initiation, the fifth solar initiation, and the first Sirian or cosmic initiation." [IHS.18]
"The energies coming from the sun, Sirius, are related to the love-wisdom aspect or to the attractive power of the solar Logos, to the soul of that Great Being. This cosmic soul energy is related to the Hierarchy. You have been told that the great White Lodge on Sirius finds its reflection and a mode of spiritual service and outlet in the great White Lodge of our planet, the Hierarchy." [EA.416]
Sirius. "This is the great star of initiation because our Hierarchy (an expression of the second aspect of divinity) is under the supervision or spiritual magnetic control of the Hierarchy of Sirius. These are the major controlling influences whereby the cosmic Christ works upon the Christ principle in the solar system, in the planet, in man and in the lower forms of life expression. It is esoterically called the "brilliant star of sensitivity." [EA198]
Sirius - The Star of Sensitivity - governing the Hierarchy. "Sirius - working in a sevenfold manner through the seven rays and their seven groups as these constitute the active Hierarchy". [EA.200]
[AN] value of Sirius =  . Number of stars in Leo according to AAB. is 95. [Labour of Hercules. Labour V.]
[RAN] value of Sirius = 
"First and foremost is the energy or force emanating from the sun Sirius. If it might be so expressed, the energy of thought, or mind force, in its totality, reaches the solar system from a distant cosmic center via Sirius. Sirius acts as the transmitter, or the focalizing center, whence emanate those influences which produce self-consciousness in man. During initiation, by means of the Rod of Initiation (acting as a subsidiary transmitter and as a powerful magnet) this energy is momentarily intensified, and applied to the centers of the initiate with terrific force; were it not that the Hierophant and the two sponsors of the initiate pass it primarily through their bodies, it would be more than he could stand. This increase of mind energy results in an expansion and an apprehension of the truth as it is, and is lasting in its effects. It is felt primarily in the throat center, the great organ of creation through sound." [IHS.99]
"Each one of us, in due process of evolution, forms part of one of the Heavenly Men, Who Themselves form the seven centers in that greater Heavenly Man, the Logos. Yet, though we are merged with the whole, we do not lose our identity, but forever remain separated units of consciousness, though one with all that lives or is. In like manner our Logos loses not His identity, even though He forms part of the Consciousness of the Logos of Sirius. In His turn, the Sirian Logos forms one of the seven Grand Heavenly Men, who are the centers in the body of ONE OF WHOM NOUGHT MAY BE SAID." [TCF.572]
The Intermediate Law of Karma. - There is also an intermediate law, which is the synthetic law of the system of Sirius. This law is called by the generic term, the Law of Karma, and really predicates the effect the Sirian system has on our solar system. Each of the two systems, as regards its internal economy, is independent in time and space, or (in other words), in manifestation. We have practically no effect on our parent system, the reflex action is so slight as to be negligible, but very definite effects are felt in our system through causes arising in Sirius. [TCF.570]
The system of the Sirian Logos is on the cosmic mental plane, and in a subtle way, incomprehensible to us, our Logos, with His system, forms a part of a still greater Logos. This does not involve loss of identity, though the matter is too abstruse to express more adequately. It is in this analogy that the basic idea can be found of all teaching given out about the Grand Heavenly Man. The whole conception of these laws is bound up in this idea. We have the three laws of the cosmic higher planes, holding in a synthesis of beauty the greater and the lesser system. Next we have the great law of Sirius, the Law of Karma, on the third subplane of the cosmic mental plane, which law really controls our Logos, and His actions, in the same way as the ego - in due course of evolution - controls the human personality.[TCF.572]
"We need to remember that, under the Law of Correspondences, we shall have a relationship in the Cosmos, similar to that existing in the microcosm between the ego and the personality. The suggestion holds much that we might consider with benefit. We must not, however, carry the analogy too far; as we have not yet evolved to where we have planetary consciousness, still less systemic, how can we really expect even to conceive of the A B C of cosmic truth? Just broad hints, wide conceptions, and generalities, are as yet possible. Of one thing we can be sure, and that is that identity ever remains." [TCF.572]
"Gradually, by dint of hard effort, certain Masters have qualified themselves, or are qualifying themselves, to take the place of the original members of the group, permitting of their return to a cosmic center around which our system, and the greater system of Sirius revolve." [IHS.190]
"This particular group of devas emanate from a great force center which we generalize by calling it by the name of the sun Sirius."
Reference to Sirius as a constellation:
The cosmic mental plane, and therefore with the constellation Sirius. [TCF904]
This great Sun (Sirius) which is to our solar Logos what the Monad is to the spiritual man, has a peculiar part to play where our Earth is concerned." (R&I 414)
"The consciousness of the cosmic mental plane is the goal of attainment for our solar Logos and the Sirian Logos is to our solar Logos what the human Ego (or soul) is to the human personality." (C.F. 592)
(LOM) Letter I: alignment of Ego with the personality personality: Further still the alignment may be progressed: - in the alignment of our entire solar system with the system of Sirius lies a still more remote goal. It is a point far ahead in time, but holds hid the secret of the greater cycle.
and from the same letter:
This morning, I would touch on the matter of egoic alignment again, showing you, under the Law of Correspondences, the universal application. It lies based in geometry, or in figures and numbers.
From AAB in "The Labours of
"In Canis Major we find Sirius, the Dog Star, called in many old books "the leader of the entire heavenly host", for it is ten or twelve times brighter than any other star of the first magnitude. Sirius has always been associated with great heat, hence we have the phrase of "the dog days" in the middle of the summer, when the heat is supposed to be greatest. From the standpoint of the occultist, Sirius is of profound significance. "Our God is a consuming fire", and Sirius is the symbol of the universal soul as well as of the individual soul. It is therefore, esoterically considered, the star of initiation. In the language of symbology we are told, there comes a moment when a star blazes forth before the initiate, signifying his realization of his identity with the universal soul, and this he suddenly glimpses through the medium of his own soul, his own star."
In the zodiac of Denderah, this star is called Apes, the head. We are told (in the appendix, p. 1518, of the Companion Bible) that the brightest star in Canis Major is Sirius, the Prince, called in Persian, the Chieftain. There are three other stars in the same constellation: one is called "the announcer", another the "shining one," and the third, "the glorious", all of them phrases emphasizing the magnificence of Canis Major and, esoterically, the wonder and the glory of the higher self.
In Canis Minor, the "underdog", the same writing tells us that the name of the brightest star signifies, "redeemer", that the next brightest is "the burden bearer" or "the one who bears for others". We have, therefore, in the significance of these two names, a portrayal of Hercules, as he works out his own salvation and as he bears the great burden of Atlas and learns the meaning of service.
The first of the cosmic laws is the Law of Synthesis. It is almost impossible for those of us who have not the buddhic faculty in any way developed, to comprehend the scope of this law. It is the law that demonstrates the fact that all things - abstract and concrete - exist as one; it is the law governing the thought form of that One of the cosmic Logoi  in Whose consciousness both our system, and our greater center, have a part.
August, which is ruled by Leo, is the month of the Dog-star, or of Sirius, which thus brings Sirius into close relation to Leo. Leo, in the cosmic sense (and apart from our solar system altogether) is ruled by Sirius. Sirius is the home of that greater Lodge to which our fifth initiation admits a man and to which it brings him, as a humble disciple. Later, when the new world religion is founded and is working, we shall find that the major, monthly festival in August, held at the time of the full moon, will be dedicated to the task of making contact, via the Hierarchy, with Sirian force. Each of the months of the year will later be dedicated (through accurate astrological and astronomical knowledge) to whichever constellation in the heavens governs a particular month, as Sirius governs Leo. This I shall later elaborate in the papers to be written anent the new "Approaches" to spiritual reality.[EA.299]
"Those devas who are the sumtotal of the astral light. They are the agents of the karmic lords, who are in themselves deva entities of an inconceivably advanced evolution and who, in their own substance, Record. Produce effects from cause. Direct force.
This particular group of devas emanate from a great force center which we generalize by calling it by the name of the sun Sirius. Sirius-kama-manas - the cosmic astral plane and the systemic astral plane - make a close interlocking chain, and form the line of least resistance for a particular type of negative force to pour through.[TCF.624]
References from The Secret Doctrine and A Treatise on Cosmic Fire
"Sirius was called the 'dog Star'. It was the star of Mercury, or Buddha, called the "Great Instructor of mankind." (S.D. Vol. II, 391)
"The sun, Sirius, is the
source of the Logoic mind (manas) in the same sense
as the Pleiades are connected with the evolution of mind in the Seven Heavenly Men and Venus is responsible for the coming in of mind in the Earth chain."(C.F. 347)
"Sirius, the Pleiades and our Sun form a cosmic triangle." (C.F. 375)
"Our solar system is negatively polarized as regards the sun Sirius, which influences our entire system psychically, via the three synthesizing schemes: Uranus, Neptune and Saturn." (C.F. 378) 
"Vibrations reach us from Sirius, via the cosmic mental plane." (C.F. 553)
"The Lords of Karma on our system are under the rule of a greater Lord of Karma on Sirius. We are governed by the Sirian Lord of Karma." (C.F. 570)
"The consciousness of the cosmic mental plane is the goal of attainment for our solar Logos and the Sirian Logos is to our solar Logos what the human Ego (or soul) is to the human personality." (C.F. 592)
"Three constellations are connected with the fifth logoic principle in its threefold manifestation: Sirius, two of the Pleiades and a small constellation whose name must be intuitively ascertained." (C.F. 699)
Cosmic Avatars "...represent embodied forces from the following cosmic centers: Sirius, and that one of the seven stars of the Great Bear which is ensouled by the Prototype of the Lord of the third Ray, and our own cosmic center." (C.F. 723)
Only one Being (from Sirius) has visited our system and that was at the time of individualization.
They only appear usually and normally at the initiation of a solar Logos. (C.F. 723)
"At the planetary
initiation the Rod of Power, wielded by the solar Logos, is charged
with pure electrical force from Sirius, and was received by our Logos
during the secondary period of creation, from the hands of that great
Entity who is the presiding Lord of the Lords of Karma. He is the
repository of the law during manifestation, and he it is who is the
representative in the solar system of that greater Brotherhood on
Sirius whose Lodges are found functioning as the occult Hierarchies
in the different planets." [IHS.127]
The Rays and the Initiations - Part Two - Section One -
4. The Path to Sirius
I have frequently hinted in my various books that the Sun, Sirius, is closely related to our planetary Life; much is known in the Hierarchy anent this connection, and the particular relationship of this fourth Path to humanity, the fourth kingdom in nature, but little can be communicated to the general public. I may, however, tell you certain things which may make your imaginative rangings (if I may use so strange a phrase) creatively profitable to you.
This great Sun which is to our solar Logos what the Monad is to the spiritual man, has a peculiar part to play where our Earth is concerned. It might be considered by those with a sound sense of occult proportion that our tiny planet with its planetary Logos (one of the "imperfect Gods" of The Secret Doctrine) would be too small to enter in the slightest way into the consciousness of that Supreme Illumined Entity Who is greater even than our Solar Logos.  Such, however, is the case. There is a relationship of very ancient date between our Lord of the World, Sanat Kumara, and the Lord of Sirius, and this exists in spite of the fact that our planet is not a sacred planet. It might be added that our planet is, in the immediate cycle, owing to the factors I have lately considered with you, rapidly passing out of this category, and on the inner planes and subjectively considered is a sacred planet; the effects of this transition from non-sacred to sacred have not fully demonstrated themselves objectively. The mystery of this relationship is partially revealed at one of the higher initiations and it is then realized by the initiates that there is a good and adequate reason for the relation and that the following esoteric events, relations and happenings are simply consequences:
1. The majority of liberated humanity, and therefore a large number of the initiates who have to make decision, choose this way to the cosmic center.
2. The relationship as it expresses itself is between the Hierarchy and Sirius, and not between Shamballa and that stupendous Sun. The energy evoked in response to this relationship enters the Hierarchy via the Heart of the Sun, creating as a consequence a triangle of spiritual energy of enormous potency. You have, therefore:
Sirius * The Hierarchy * * Heart of the Sun
3. As progress is made in the course of taking the higher initiations, it becomes apparent to the initiate that two major streams of energy enter our planetary life:
"A stream of energy coming
from the cosmic mental plane and from that focal point which is to
Sanat Kumara what the egoic lotus, the soul, is to the spiritual man;
it carries the life principle of our planet and centers itself in
Shamballa. From there it is dispersed throughout all forms upon the
planet and we call it Life. It must be remembered that this life
principle embodies or is impregnated with the will and purpose 
of That which over-shadows Sanat Kumara as the soul over-shadows the
A stream of energy coming from the sun, Sirius; this enters directly into the Hierarchy and carries with it the principle of buddhi, of cosmic love. This, in a mysterious way, is the principle found at the heart of every atom. The life principle follows the line of 126.96.36.199, whilst the buddhic flow follows the line of 2.4.6. Thus atma-buddhi becomes the blended reality which is brought to full unfoldment as evolution proceeds. The energy of Sirius by-passes (to use a modern word) Shamballa and is focused in the Hierarchy. Its effect is not felt until after the third initiation, though the Masters use this energy whilst training disciples for the second, the fourth and the sixth initiations.
4. The entire work of the Great White Lodge is controlled from Sirius; the Ashrams are subjected to its cyclic inflow; the higher initiations are taken under its stimulation, for the principle of buddhi, of pure love (i.e., love-wisdom) must be active in the heart of every initiate prior to the initiation of the great decision; it is therefore only initiates of the fifth, sixth and higher initiations who can work consciously with the potent buddhic "livingness" which permeates all Ashrams, though unrecognized by the average disciple.
5. This Sirian influence was not recognized, and little of it was definitely focused in the Hierarchy, until Christ came and revealed the love of God to humanity. He is the expression, par excellence, of a Sirian initiation, and it is to that high place He will eventually go - no matter what duties or hierarchical obligations may take Him elsewhere between that time and now. The Buddha was originally to have chosen the fourth Path but other plans confront Him now and will probably claim His choice.
6. Sanat Kumara is not on the Sirian line but - to speak in symbols, not too deeply veiled - Lucifer, Son of the Morning, is closely related, and hence the large number of human beings who will become disciples in the Sirian Lodge. This [R&I.416] is the true "Blue Lodge," and to become a candidate in that Lodge, the initiate of the third degree has to become a lowly aspirant, with all the true and full initiations awaiting him "within the sunshine of the major Sun."