From awell-know Judge article, these 31 aphorisms first appeared in the March 1893 issue of The Path. In the May and June 1893 issues of The Theosophist, a learned Hindu pandit, E. Desikacharya, somewhat critically responded by stating that these are fairly common traditional notions about Karma, providing an impressive series of quotations. Below are the aphorisms together with the passages from Hindu scripture:

(1) There is no Karma unless there is a being to make it or feel its effects. 
"If they (the afflictions) are the root (of Karma) fructification (or result) is rank, years, and enjoyment" Patanjali, Yoga Sutras (II. 1:3).

"All the creatures in the world would have been exterminated if there were no Karma. If also Karma bore no fruits, creatures would have never multiplied ......... Without Karma, the course of life itself would be impossible." (Mahabharata (Vanaparva, sec. XXXII)

"There must be a body for the Karma to operate on, and Karma to operate on a body" (Vatsyayana's Commentary on the Nyaya Sutras, III. 2, 64).

(2) Karma is the adjustment of effects flowing from causes, during which the being upon whom and through whom that adjustment is effected experiences pain or pleasure.

"These (Karmas) have joy or suffering as their fruits, according as the cause is virtue or vice." Patanjali, Yoga Sutras (II, 14)

(3) Karma is an undeviating and unerring tendency in the Universe to restore equilibrium, and it operates incessantly.

"The consequence of the Karma that is once done can never be obviated." (Mahabharata. Vanaparva CCIX)

(4) The apparent stoppage of this restoration to equilibrium is due to the necessary adjustment of disturbance at some other spot, place, or focus which is visible only to the Yogi, to the Sage, or the perfect Seer: there is therefore no stoppage, but only a hiding from view.

"The Karma done must be suffered, whether good or bad." (Suta Samhita)

"Indeed, all creatures live according to the Karma of a former life, even the Creator and the Ordainer of the Universe, like a crane that liyeth on the water (untaught by anyone)". (Mahabharata. Vanaparva, Sec. XXXII):

(5) Karma operates on all things and beings from the minutest conceivable atom to Brahma. Proceeding in the three worlds of men, gods, and the elemental beings, no spot in the manifested universe is exempt from its sway.

"Karma affects the whole Universe from Brahman to the grass," Mahabharata

See also Manu Smriti (XII, 9-51)

(6) Karma is not subject to time, and therefore he who knows what is the ultimate division of time in this Universe knows Karma.

"As it (Karma) is not controlled by Time and Space, it should not be judged by Time and Space." (Vyasadeva, Commentary on Patanjali’s Yoga Sutras - II, 1:1)

(7) For all other men Karma is in its essential nature unknown and unknowable.

" It is very difficult, to know which is Karma and which is not Karma". (Bhagavadgita, IV, 17)

"He who knows it is a wise man" (Bhagavadgita, V. 19). )

(8) But its action may be known by calculation from cause to effect; and this calculation is possible because the effect is wrapped up in and is not succedent to the cause.

See Manu (Chap. XII, 39-51)

"We have to conjecture about the nature of our previous Karma, by our present birth" (Vyasadeva, Commentary on Patanjali II,13)

"Its action can only be conjectured," (Bhojadeva, Commentary on Patanjali)

(9) The Karma of this earth is the combination of the acts and thoughts of all beings of every grade which were concerned in the preceding Manvantara or evolutionary stream from which ours flows.

Since every cause must have an effect and since the present Karma is the result of past Karma, and Karma is thus said by Sankaracharya to be with no beginning, it is reasonable to suppose that the Karma of the present Manvantara is the result of the past.

(10) And as those beings include Lords of Power and Holy Men, as well as weak and wicked ones, the period of the earth's duration is greater than that of any entity or race upon it.

(see Patanjali's Yoga Sutra II, 1, Vyasadevas Commentary)

(11) Because the Karma of this earth and its races began in a past too far back for human minds to reach, an enquiry into its beginning is useless and profitless.

"The objection would be valid if the world was had a beginning; but, as it is without beginning, merit and inequaity are like seed and sprout, caused as well as causes, and there is therefore no logical objection to their operation." (Sankara, Commentary on Bhagavadgita, II. 1. 35)

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(13) The effects may be counteracted or mitigated by the thoughts and acts of oneself or of another, and then the resulting effects represent the combination and interaction of the whole number of causes involved in producing the effects. 
"The effects (of Karma) which have not yet begun to operate will be counteracted, or will die out (Brahma Sutras.IV, 4, 1)

See also the Prayaschitka Khanda and Madhavacharya, Commentary on Parasara Smriti, chapter on Karmavipaka.

Madhvacharya, at the end of the chapter on Prayaschitta, observes that all of them are. only for Sancita Karma and not for Prarabdha Karma, and refers to the Brahma Sutras above quoted for his authority. He also adds that any prayaschitta undergone for counteracting or mitigating any other kind of Karma is no real prayaschitta, for, although their fruition is temporarily held in abeyance, he will have to suffer it in the future.

(14) In the life of worlds, races, nations, and individuals, Karma cannot act unless there is an appropriate instrument provided for its action.

See references to Aphorism No. 1.

(15) And until such appropriate instrument is found, that Karma related to it remains unexpended.

"In the Sanhita Karma, that which is most powerful, first begins to bear fruition, and it has body (also) as its instrument to work through." . (Madhavacharya , Prayaschitta Kanda):

See also references for Aphorism No. 13.

(16) While a man is experiencing Karma in the instrument provided, his other unexpended Karma is not exhausted through other beings or means, but is held reserved for future operation; and lapse of time during which no operation of that Karma is felt causes no deterioration in its force or change in its nature.

“Only when there are Klesas (Kama, Kroda, &c.), will Karma be able to bear fruition. When there are no Klesas, no Karma can act, just as rice which has husk and which is not fried will sprout. Thus Karma will not be operative either when the husk of the Klesas are burnt off byBrahmagnana, or when there is no such husk. The fruition of Karma is either age and experience. We shall now enquire, is one kind of Karma the cause of one birth, or many births? Or, are several kinds of Karma the causes of a single birth? If we think of saying that a single Karma is the cause of birth , that will not do, as we cannot say whether it is one of the Karmas done in the previous births, or a Karma of the present birth, that is the cause of the next birth . Hence mankind will not, as a body, have a desire to do good Karma.* If we should suppose a single Karma, then the case becomes more hopeless. If we should again suppose that several Karmas are the cause of several births, how can there be a large number of births in a single birth, the conclusion to which we are invariably driven. Thus what we should say is, that certain kinds of Karma committed between birth and death (in an incarnation) group round a more important Karma, cause the individual’s death, and give him a new birth altogether. It is those Karmas that give him sufficient age (to experience ) . How to know them we can only infer...”

“ Karma is of two kinds, viz., that which bears fruition and that which does not. That which we can infer from the mere fact of our existence, is the Karma which bears fruition (Niyatavipaka).The other kind of Karma (Aniyatavipaka) is of three kinds : (a ) That which perishes in the bud : (b) That which acts as an auxiliary to a more important karma (c) and that which does not begin to bear fruition at once , but only works after several incarnations. The Sruti says: ‘Two kinds of Karma should be known : one is bad; the virtuous make it perish . Hence shouldst thou desire to make good Karma . Gnanis know this Karma” (Vyasadeva`s Commentary on Patanjali’s Yoga Sutras , II, 13)

“The residue of works have affliction for their root, and are felt (either ) in this manifest birth , (or) in the unmanifest one”. (Sutra XII).

(17) The appropriateness of an instrument for the operation of Karma consists in the exact connection and relation of the Karma with the body, mind, intellectual and psychical nature acquired for use by the Ego in any life.

See references for Aphorism No. 14.

(18) Every instrument used by any Ego in any life is appropriate to the Karma operating through it.

(19) Changes may occur in the instrument during one life so as to make it appropriate for a new class of Karma, and this may take place in two ways: (a) through intensity of thought and the power of a vow, and (b) through natural alterations due to complete exhaustion of old causes.

In other words, the Karma which was hitherto bearing fruition has stopped doing so owing to the “repetition of Mantras, penance (under which is included Prayaschitta ) and Samadhi,”which are no other than the “ intensity of thought” and “ power of a vow”. See Bhojadeva’s or Vyasadeva’s Commentary on Patanjali’s Sutra (II, xii).

(20) As body and mind and soul have each a power of independent action, any one of these may exhaust, independently of others, some Karmic causes more remote from or nearer to the time of their inception than those operating though other channels.

(21) Karma is both merciful and just. Mercy and Justice are only opposite poles of a single whole; and Mercy without Justice is not possible in the operations of Karma. That which man calls Mercy and Justice is defective, errant, and impure. 

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Keep in mind that Mr. Desikacharya is arguing from the  Dvaita Vedanta school, a very theistic, dualistic and realistic philosophy. His critique seems to be that when the Aphorisms agree with his school, then they can’t be original esoteric ideas and when they don’t agree with Vedantic scripture, then they aren’t valid.  I think that his very erudite references can just as easily show that the aphorisms are compatible with Vedantic schools in general and the ones that do not have parallels in Hindu scriptures show that they are not dependent on same.

(22) Karma may be of three sorts (a) Presently operative in this life through the appropriate instruments; (b) that which is being made or stored up to be exhausted in the future; (c) Karma held over from past life or lives and not operating yet because inhibited by inappropriateness of the instrument in use by the Ego, or by the force of Karma now operating.

This is exactly what is called Sanchita Prarabdha, by our Vedantic writers, who group the second and third classes of Karma into one, and name it Sanchita, which simply means that which is stored np for operation in future. I may here add that no notice is taken of Agami (future) Karma in the above Aphorism. The reader is referred to the Vedanta Sutras IV, 1, 13 and 15, and any Commentary thereon.

(23) Three fields of operation are used in each being by Karma: (a) the body and the circumstances; (b) the mind and intellect; (c) the psychic and astral planes.

With a slight difference in detail, this is just the same as is given in our writings, e. g ., the Bhagavadgita.

 (24) Held-over Karma or present Karma may each, or both at once, operate in all of the three fields of Karmic operation at once, or in either of those fields a different class of Karma from that using the others may operate at the same time.

This is an inference from the two preceding Aphorisms.

(25) Birth into any sort of body and to obtain the fruits of any sort of Karma is due to the preponderance of the line of Karmic tendency.

See Aphorism No. 16.

“ The important Karma, with its auxiliaries, determines the nature of enjoyment, (such as rank, age, &c.) in the next birth.” (Vyasadeva, Commentary on Patanjali, II, 13)

 (26) The sway of Karmic tendency will influence the incarnation of an Ego, or any family of Egos, for three lives at least, when measures of repression, elimination, or counteraction are not adopted.

(27) Measures taken by an Ego to repress tendency, eliminate defects, and to counteract by setting up different causes, will alter the sway of Karmic tendency and shorten its influence in accordance with the strength or weakness of the efforts expended in carrying out the measures adopted.

(28) No man but a sage or true seer can judge another's Karma. Hence while each receives his deserts appearances may deceive, and birth into poverty or heavy trial may not be punishment for bad Karma, for Egos continually incarnate into poor surroundings where they experience difficulties and trials which are for the discipline of the Ego and result in strength, fortitude, and sympathy.

 “ He who knows Karma is a wise man.” (Bhagavadgita, V. 19)

In the Chhandogyopanishad, mention is made of a great Adept, Raikwa by name, who was suffering from leprosy, as the result of bad Karma in one of his previous births, and, notwithstanding that he was a knower of Brahman, he had to experience the effects of Karmas other than Prarabdha. (See also Brahmasutras, IV, 4—15).

(29) Race-Karma influences each unit in the race through the law of Distribution. National Karma operates on the members of the nation by the same law more concentrated. Family Karma governs only with a nation where families have been kept pure and distinct; for in any nation where there is a mixture of family -- as obtains in each Kaliyuga period -- family Karma is in general distributed over a nation. But even at such periods some families remain coherent for long periods, and then the members feel the sway of family Karma. The word "family" may include several smaller families.

(30) Karma operates to produce cataclysms of nature by concatenation through the mental and astral planes of being. A cataclysm may be traced to an immediate physical cause such as internal fire and atmospheric disturbance, but these have been brought on by the disturbance created through the dynamic power of human thought.

In the Mahabharata, Yanaparva, it is said that at the end of Kaliyuga, owing to the prevalence of Adharma and neglect of religious duties, famines, pestilence, and cataclysms will take place, and carry away men and women by thousands. The whole manifested nature, whether material or astral, is governed by Karmic law. Brahma, Vishnu, Rudra and other deities do their work, towards an individual, a nation, a race, or the whole world, according to the nature of the fruits of Karma they deserve. In Sanskrit writings, thought and the deity presiding over it are identical, and so both are involved when an action relating to either of them is mentioned.

(31) Egos who have no Karmic connection with a portion of the globe where a cataclysm is coming on are kept without the latter's operation in two ways: (a) by repulsion acting on their inner nature, and (b) by being called and warned by those who watch the progress of the world.