Are you saying the Catholic Encyclopedia article on Baptism is mistaken?

I don't really trust the Catholic Encyclopedia, though I do read it sometimes. The reason I do not really trust it is because of an article I read about salvation where it says that more than half of mankind will probably be saved. Considering the fact that nowhere near half of mankind was even baptized, I cannot trust a source that would say something like that. It reminds me of the story that Pope Pius X was reading the encyclopedia and someone asked him what he thought about it and he said one word, "modernism" and threw it on the ground.

The Catholic Encyclopedia denies the doctrine of extra ecclesiam nulla salus when it says Baptism can be effected without water.  Canons in Trent teach otherwise. As does Christ.  As have the popes.

While the quote may conflict with your own personal interpretation of Church teaching, it is absolutely absurd to imagine that this quote is in conflict with a proper understanding of the timeless truth you mention.  

Quote from: The Catholic Encyclopedia, 1907

The Fathers and theologians frequently divide baptism into three kinds: the baptism of water (aquæ or fluminis), the baptism of desire (flaminis), and the baptism of blood (sanguinis). However, only the first is a real sacrament. The latter two are denominated baptism only analogically, inasmuch as they supply the principal effect of baptism, namely, the grace which remits sins. It is the teaching of the Catholic Church that when the baptism of water becomes a physical or moral impossibility, eternal life may be obtained by the baptism of desire or the baptism of blood.

This quote is no surprise to me. The Catholic encyclopedia is was printed in the USA and the writers are American clergy. Not a one Americanist contributed to the encyclopedia, was it protected by God?

By the way, the teaching style above is in every way like the modern Catechism of the Catholic Church (CCC), it states a false exception to the rule, then creates a solution to for it:

when the baptism of water becomes a physical or moral impossibility, eternal life may be obtained by the baptism of desire or the baptism of blood

This exception to the rule does not exists, there are no physical or moral impossibility that God has not allowed or that He can't conquer:

St. Augustine on the Errors of Pelagius said:

"If you wish to be a catholic, do not venture to believe, to say, or to teach that “they whom the Lord has predestinated for baptism can be snatched away from his predestination, or die before that has been accomplished in them which the Almighty has predestined.” There is in such a dogma more power than I can tell assigned to chances in opposition to the power of God, by the occurrence of which casualties that which He has predestinated is not permitted to come to pass. It is hardly necessary to spend time or earnest words in cautioning the man who takes up with this error against the absolute vortex of confusion into which it will absorb him, when I shall sufficiently meet the case if I briefly warn the prudent man who is ready to receive correction against the threatening mischief. Now these are your words: “We say that some such method as this must be had recourse to in the case of infants who, being predestinated for baptism, are yet, by the failing of this life, hurried away before they are born again in Christ.” Is it then really true that any who have been predestinated to baptism are forestalled before they come to it by the failing of this life? And could God predestinate anything which He either in His foreknowledge saw would not come to pass, or in ignorance knew not that it could not come to pass, either to the frustration of His purpose or the discredit of His foreknowledge? You see how many weighty remarks might be made on this subject; but I am restrained by the fact of having treated on it a little while ago, so that I content myself with this brief and passing admonition".