From Dr. Luther's Lectures on Galatians (1535):
"St. Paul speaks very insultingly about the Law when he calls it ‘elements’ (Galatians 4:3,9), and not simply ‘elements’ but ‘weak and beggarly elements.’ Is it not blasphemy to use such names for the Law of God? In its proper use the Law ought to support the promises and grace. If it conflicts with these, it is no longer the holy Law of God; then it is a false and diabolical doctrine that only produces despair, and therefore must be repudiated and excommunicated.
"When he calls the Law ‘weak and beggarly elements,’ therefore, he is speaking of the Law as it is used by proud and presumptuous hypocrites, who seek to be justified through it, not of the Law understood spiritually, which effects wrath. For in its proper use, as we have said so often, the Law restrains the wicked but terrifies and humbles the proud. On this score it is not only a powerful and rich element but omnipotent and extremely wealthy, in fact, an invincible omnipotence and wealth. For if you were to compare the Law with the conscience, then it is the conscience that is ‘weak and beggarly,’ while the Law is extremely powerful and rich, having more power and riches than all of heaven and earth could contain; therefore even one iota or dot (Matt. 5:18) of the Law could kill the whole human race, as the history of the giving of the Law in Exodus 19 and 20 testifies. So delicate a thing is the conscience that it trembles and turns pale even for a very minor sin. Now this is the true and theological use of the Law, but Paul is not discussing that here.
"But Paul is discussing the hypocrites who abuse the Law, that is, who have fallen away from grace or who have not yet come to grace and strive for justification through the Law, straining and wearying themselves day and night in the works of the Law. Thus Paul testifies of the Jews in Romans (10:2-3): ‘I bear them witness that they have a zeal for God, that they labor day and night. But this is not enlightened, for they are ignorant of the righteousness that comes from God.’ Such people are confident that they can be so strengthened and enriched by the Law that they will be able to set their own strength and riches of righteousness, which they have from the Law, against the wrath and judgment of God, and that thus they will be able to appease God and be saved. It is in this connection that you would be right in calling the Law ‘weak and beggarly elements,’ that is, something that cannot help and has neither aid nor counsel.
"Anyone who wanted to grow rhetorical here could develop these words further actively, passively, and neutrally. Actively: the Law is a weak and beggarly element because it makes men weaker and more beggarly. Passively: because it does not have of itself the power and ability to grant or confer righteousness. And neutrally: of itself it is weakness and poverty, which afflict and trouble the weak and the poor more and more all the time. Trying to be justified through the Law, therefore, is as though someone who is already weak and sick were to ask for some even greater trouble that would kill him completely, but meanwhile were to say that he intends to cure his disease by this very means; or as though someone suffering from epilepsy were to catch the plague in addition; or as though a leper were to come to another leper, or a beggar to another beggar, with the aim of giving him assistance and making him rich. As the proverb says, one of these is milking a billy goat and the other is holding the sieve!
"This is a lovely depreciation, by which Paul wants to indicate that those who seek to be justified through the Law receive the benefit of becoming weaker and more beggarly day by day. On their own they are already weak and beggarly, that is, they are ‘by nature children of wrath’ (Eph. 2:3), sentenced to death and to eternal damnation; and now they take hold of something that is sheer weakness and beggarhood in order to become strong and rich. Therefore everyone who falls away from the promise to the Law, from faith to works, is doing nothing but imposing an unbearable yoke upon himself in his weak and beggarly condition (Acts 15:10). By doing this he becomes ten times as weak and beggarly, until he finally despairs, unless Christ comes and sets him free." (Luther’s Works, Vol. 26, CPH 1963)