It is unnecessary to think that Luke was really doubtful what was the age of Jesus, whether twenty-eight or thirty-two. His elaborately careful and precise dating, 3:1, 2, may be taken as an indication that he had good and accurate information on the subject; that he "had investigated all the circumstances accurately in their origin". But, like a true Greek, he says "about thirty," where the less sensitive barbarian of our northern island would use a rudely positive and definite number. The only doubt that remains is whether Luke means in his thirtieth year, or when he was thirty years old; and this doubt is resolved by the other facts recorded by Luke, as we shall see. Jesus was thirty years old, when he began his public career.
The precise statement is doubtless derived from the same authority as the whole of the first two chapters (and perhaps also 4:16-30); and the only reason for recording it is that it was given exactly by a first-rate authority, and therefore helped Luke's readers "to know the certainty concerning the things wherein they had been instructed". An authority, who was really good on such a point, would know the exact age, and Luke expressly declares his intention of setting down only such facts as he had accurately and certainly on trustworthy authority. Where his knowledge was only vague, he usually refrains from making any statement.
If the birth of Jesus occurred in BC.6, he became thirty years of age in the second half of AD.25, and his appearance as a teacher took place within the year that followed. If his birth occurred in BC.7, the date of his appearance must be placed one year earlier, but we shall find reason to reject that supposition.
Some time, but apparently quite a short time, before Jesus came forward as a teacher, John the Baptist began to preach that the Messiah was at hand; and Jesus was among the crowds who flocked to him to receive baptism. Now, as Luke mentions, "the word of God came to John" in the fifteenth year of the authority  of Tiberius Caesar. The date is given very precisely and definitely; but, unfortunately, it is by no means easy to say what year is meant by it.
It is often found that, where an ancient writer aims at making his statement most precise and exact, his words lend themselves to several interpretations.  What did Luke understand by the authority of Tiberius? In the inscriptions of that emperor's lifetime, the years of his reign are estimated according to the number of times that he had received tribunician power. On that system his fifteenth year began on 27th June, AD.13. Obviously Luke cannot intend that year.
Again, according to Velleius, the admirer and friend and faithful follower of Tiberius, associated with him in nine years of warfare, authority equal to that of Augustus in all the provinces and armies of the empire was granted to Tiberius by the senate and people, on the proposal of Augustus himself, before he returned to Rome to celebrate his triumph over the peoples of Pannonia and Dalmatia. Now this triumph was celebrated on
16th January, AD.12,  therefore the decree of equal power must have been passed before the end of AD.11. Further, the language of Velleius suggests that the decree was issued not long before Tiberius returned, and it was so closely connected with his return that Suetonius seems to place it after he reached Rome. But Velleius's authority must be ranked superior in regard to such a point.
There can be no doubt that this was the event which Tacitus had ill mind when he said that Tiberius had been created Collega Imperii during the lifetime of Augustus (Annals, 1., 3).
It follows that the first year during which Tiberius held power as colleague of Augustus with equal power in all provinces of the empire coincided with the end of AD.11 and the greater part of AD.12, and the fifteenth year with AD.25-6. 
If Luke counted the years of Tiberius according to that system, all his statements as to time in these early chapters are found to be consistent and accurate. The first enrollment must have taken place in autumn BC.6. Jesus was thirty years old in autumn BC.25. In the later months of that year, when the fifteenth year of the Hegemonia of Tiberius in the provinces had just recently begun (according to the official usage  ), John appeared announcing the coming of Christ; and very shortly thereafter Jesus came and was baptized by John in the river Jordan. A month or two thereafter occurred the Passover on 21st March, AD.26 (Lewin, Fasti Sacri, p.173).
The only reason for doubting whether Luke could have counted the years of Tiberius on that system, is that it is never employed elsewhere in reckoning the reign of that emperor. When his tribunician years are not stated, his reign is always elsewhere counted from the death of his predecessor, Augustus; and it is beyond dispute that he was not in any proper and strict sense emperor until that time. But it seems not impossible that his Hegemonia in the provinces might be counted from AD.11, when his authority began in them. Similarly, we saw that in Egypt the reign of Augustus was reckoned, not from any date when he became emperor in a strict and proper sense, but from BC.30, when his authority began in that country.
Further, Luke, the whole spirit of whose History stamps it as belonging to the Flavian period, knew that the reign of Titus was counted from the day when he was made the colleague of his father, Vespasian; and thus he may have been led to apply to the time of Tiberius the principle which was in current and official use while he was writing. 
Now the only dates that are permissible for the crucifixion are AD.29, 30 and 33. Different authorities vary between these three years. But, as it is not possible to allow that more than four Passovers occurred during the public career of Jesus, we are bound to the view that his career extended from the time preceding the Passover of 26 till the Passover of 29. The strength of the tradition that places the crucifixion in 29 has been admirably stated by Mr. C. H. Turner in his article on the "Chronology of the New Testament". 
But is this consistent with Luke's narrative? Does he permit the supposition that four Passovers occurred within the period of Jesus' teaching?
Luke does not refer to any Passover during that whole period except the last. He was not interested in the relation of Jesus to the Jewish feasts, and hardly alludes to the subject after the Passover that occurred in the Savior's twelfth year. Hence we cannot expect from him much direct evidence bearing on the Passovers during the teaching of Jesus.
Moreover, Luke had little of the sense for chronology, the value of which in clearly understanding or describing any series of incidents had not been appreciated so early as the first century. Chronology, too, was much more difficult when no era had come into general use, when dates were commonly stated by the names of annual magistrates, or the years of sovereigns, and when in Asia scores of different eras for dating had just begun to come into use side by side with one another, so that, even when one does find a date by a numbered year, it is often a difficult problem to determine what era is used.
Want of chronological sense or interest may seem a serious defect in a historian. But we are too apt to forget that Luke was not writing for us, and that he was not even writing for posterity. He wrote for the benefit of his own contemporaries. His work stands in the closest relation to the time. That which seemed most important for the requirements of the Church at the time was what Luke most desired to record with absolute accuracy and trustworthiness. Abstract scientific interest in the chronology of the Gospel did not exist among his readers. What they were concerned with was its truth; and that was gathered from the Savior's teaching, from his statements about himself, and from the facts of his Birth, Death and Resurrection. These were the points on which Luke's attention was concentrated in his first book.
Some authorities are disposed to think that Luke believed the whole period of the teaching of Jesus to have been comprised within the period of a little more than a year, lasting from shortly before one Passover till the Passover of the following year. A widely-spread opinion in the second and third centuries assigned that duration to the Savior's ministry, but I can discover nothing to show that Luke shared it. The opinion, probably, was the result of two causes. In the first place, the notes of time in the Gospels are very slight and difficult to fit together. In the second place, the saying about "the acceptable year of the Lord" was easily misunderstood.
The memory of the earliest authorities, as a rule, was entirely filled with the words and teaching of the Savior. Chronological order was little thought of; and we should probably find that most of the writings alluded to by Luke 1. I took the form of collections of sayings and parables. The only events, probably, that were vividly remembered in their historical aspect and apart from the doctrine connected with them, were the series of actions comprised within the last few days of the Savior's life. The sequence of these events was indelibly stamped on the memory of all.  But the rest of the tradition was a reproduction of past lessons and impressive sayings. These were connected with certain localities; some were associated with certain actions of the Savior or of those who were in his company. But his numerous journeys great and small were not remembered in their sequence. In this state of information, Luke evidently forbore the attempt to describe exactly the movements of Jesus during the greater part of the teaching.
In the beginning, indeed, he describes the sequence of Jesus' first journeys. He tells how Jesus was baptized by John in Jordan, 3:21; and he dates at that point the beginning of his teaching, 3:23. Then he tells of the journey into the wilderness, i.e., the country south from Jerusalem, and mentions that Jesus was actually in Jerusalem, 4:1-13. Thereafter Jesus returned to Galilee and taught there for some time, 4:14, 15, after which he returned to Nazareth for a brief visit, 4:16-30. Being rejected and threatened with death at Nazareth, he came down to Capernaum, 4:31.
The narrative during this stage touches that of the other Gospels at occasional points; and one paragraph, 4:1-13, is perhaps founded on the same ultimate authority as Matthew 4:1-11 (though with a difference in order). No indication of the lapse of time is given; but some considerable period is likely to have elapsed even in the events implied in 4:15 alone.
But at this point, 4:31, begins a new section of the narrative. The indications of movement for a considerable period are of the vaguest kind.4:42, He went into a desert place.5:16, He withdrew himself in the deserts.5:27, He went forth.6:1, He was going through the cornfields, probably in May or June when the wheat was ripe but not cut.6:12, He went out into the mountain to pray.6:17, He came down with them.7:1, He entered into Capernaum.7:1, He went soon afterwards to a city called Nain (an episode peculiar to Luke). His return from Nain is never mentioned, but 7:18 ff. probably belongs to the coasts of the Sea of Galilee.8:1, He soon afterwards went about through cities and villages.8:22, He entered into a boat (on the Sea of Galilee).8:26, He arrived at the country of the Gerasenes, which is over against Galilee.8:38, He entered into a boat and returned.9:10, He withdrew apart to a city called Bethsaida.9:28, He went up about eight days after into the mountain to pray.9:37, On the next day when they were come down from the mountain, a great multitude met him (and here Mark's reference to the green grass, 6:39, and John's to the abundant grass, 6:10, show that the time was spring).
In this part of the narrative, the lapse of time is hardly alluded to: only the brief and vague indications just quoted are given. The marks of locality, apart from those implied in the indications of movement, are also very vague and elusive.4:44, He was preaching in the synagogues of Galilee.5:1, He was standing by the Lake of Gennesaret.5:12, He was in one of the cities.
This section of the narrative, 4:31-9:50, is as a whole (though with some considerable exceptions) closely parallel to Mark and Matthew. Great part of the section is evidently founded on an authority common to them (though we expressly avoid stating any opinion as to the nature of the connection between the three).
It is plain that though Luke, with his usual indifference to the chronological aspect of history, does not properly mark the lapse of time, yet this section must extend over some considerable period. "Preaching in the synagogues of Galilee" is the sort of phrase by which Luke sums up a considerable period; and the different movements, mentioned or implied, vague as they are, together with the intervals between them, demand time.
From 9:51 begins another new section describing the movement to Jerusalem preparatory to the culmination of Christ's teaching there. In 10:38, as they went on their way, he entered into a certain village (viz., Bethany); and in 11:1, he was praying in a certain place. In this and the following chapters there continues the same vagueness. Luke only makes it clear that the most advanced stage in the ministry has begun, and that Jesus is moving gradually towards the south and is affecting the southern half of Palestine. In 13:22, he went on his way through towns and villages teaching and journeying on unto Jerusalem. In 17:11, as they were on the way to Jerusalem, he was passing through the midst of Samaria and Galilee.8:31, We go up to Jerusalem.18:35, He drew nigh unto Jericho.19:1, He entered and was passing through Jericho.19:11, He was nigh to Jerusalem.19:28 f., He went on before, going up to Jerusalem (by the steep road from Jericho), and he drew nigh to Bethany.
Then comes the entry into Jerusalem, where the rest of the narrative has its scene.
With very slight exceptions, the section 9:51-19:28 is quite peculiar to Luke, and has hardly any points of contact with any of the other Gospels. But the same vagueness of place and time continues.
It is, however, clearly unnecessary and improbable that this section represents, or was considered by Luke to represent, the events of one single continuous approximately straight journey. The multitudes, the towns and villages, the frequent repetition of the idea of progress towards Jerusalem, imply a gradual advance of the circle of the teaching towards the south and towards the center of Jewish religion and the completion of his mission.
If, as I believe to be probably the case, Luke knew what was the "certain village" of Martha and Mary, 10:38, but for some reason (about which we need not speculate) avoided naming it, our view would be raised to complete certainty, that in this section the historian is describing a general movement southwards, accompanied and complicated by many short journeys to and fro, up and down, "through towns and villages teaching". If he is at Bethany in 10., and at Jericho in 18, and in Samaria in 17, zigzag wanderings are clearly implied. But, as many may prefer to consider that 10:38 has been put in false local and chronological order by Luke through his ignorance that the "certain village" was Bethany, we need not press an argument that is not actually required for our purpose. Even without it the view which we are stating as to Luke's intention in this section seems certain.
It is obvious, then, that Luke divides the teaching of Jesus, previous to the final scenes in Jerusalem, into three stages. The first and preliminary stage -- in the wilderness of Judah, in Galilee and in Nazareth -- is very briefly recorded The second -- spent in Galilee or the north continuously -- is described at much greater length: Jesus had now become a famous teacher, and attracted many hearers and followers. The third -- the extension of the sphere of influence over central Palestine as Far as Jerusalem -- is described still more fully. There is no attempt or intention to describe the movements of Jesus exactly in the second and third stages.
Further, the second stage evidently lasted a Full year, For after it has begun some time, we find ourselves in the month of May or June, and at the end we are again in spring (as we know From Mark but not from Luke).
The probability, then, is that roughly the three stages correspond to the three years; and the memory of the witnesses retained very little that was accurate and definite (except some important changes of scene and journeys) during the preliminary stage, AD.26, more about the second, AD.27, and still more about the third, AD.28.
The first Passover, AD.26 (John 2:13), falls about Luke 4:13, and the year ends about 4:31. At the feast of this year, the Jews spoke about the 46th year of the building of the Temple (John 2:20); and the 46th year had begun shortly before they spoke. 
The second Passover, AD.27 (John 5:1), falls about Luke 5. Then follows the month of May, 6:1.
The spring of AD.28 and the third Passover (John 6:4) must be placed in Luke 9. The summer of this year, however, was still spent in Galilee, according to John 7:1; but it is not inconsistent with this statement that the third stage of Luke had already begun. The characteristic of that stage was that Jesus had now set his face firmly to go to Jerusalem, 9:51; but during it, he was still passing through the midst of Samaria and Galilee, 17:11. The period in Luke's estimation is rather one of firm and definite resolution than of bodily movement continuously towards Jerusalem. The visit to the country east of Jordan (Mark 10:1 and Matthew 19:1) certainly belongs to this stage.
That there was a strong tradition to the effect that the Savior suffered at the age of thirty-three seems to follow from the agreement of Hippolytus  and Eusebius and Phlegon. The latter, as is allowed by Mr. Turner, was indebted to very early Christian authorities for his information. It is true that both Eusebius and Phlegon place the crucifixion in AD.33, but this arises from their both depending on the original Christian calculation which ultimately gave rise to the modern era of the birth of Christ. This was wrongly calculated as early as the second century; and, starting from that initial error, the chronologists had to place the beginning of the teaching in thirty and the crucifixion in thirty-three.
It is a strong confirmation of our result that it agrees with two so ancient traditions, which are quite unconnected with one another and evidently seemed to most of the ancients to be inconsistent with each other.
Starting from a very different point of view from that of Mr. Turner, and working on utterly diverse lines, we have reached nearly the same conclusion that he reached. The only differences of importance are two: --
1. I find myself obliged, on the principles of interpretation which I have followed consistently throughout, to attach a distinctly higher value than he does to Luke's statement as to the age of Jesus when he began to teach.
2. Mr. Turner is inclined to think that Luke compressed the teaching into one year; and he holds that the teaching in reality lasted only for two years, interpreting John 5:1 as referring to some unnamed minor feast.  This view cannot be disproved, but it seems to have nothing to recommend it, and it introduces quite unnecessary discord between the different Gospels. The chronological marks in the Gospels are so slight that almost anything can be made out of them, if one is bent on doing so. Hence there was in ancient time an immense variety of opinion on this point. But in four independent accounts of one series of events, a reasonable criticism will prefer the interpretation in which all the various conditions are reconciled.
At the last moment, after this chapter is in type, Professor Paterson reminds me that the result which we have attained agrees with the celebrated calculation of Kepler, who fixed on the year BC.6, because in March of that year there occurred a conjunction of Jupiter, Saturn and Mars, which would present a most brilliant appearance in the sky, and would naturally attract the attention of observers interested in the phenomena of the heavens, as were the Wise Men of the East.
I have no knowledge what is the value of Kepler's reckoning. Mr. Turner, who knows much more about the matter, speaks only of the conjunction of Jupiter and Saturn, which occurred in, May, October and December, BC.7; and I presume that he would have mentioned the triple conjunction (on which Kepler laid such stress), if he had accepted the calculation, even though it does not suit the date 7-6, to which he inclines. The coincidence, however, seems worthy of mention, but it is not presented as an argument.
But, while we lay no stress upon it as an argument, the subject is so interesting, and presents so many curious coincidences, that a few paragraphs may profitably be devoted to it.
The conjunction of Jupiter and Saturn in the constellation Pisces, according to a Jewish belief of some antiquity,  is the sign of the Messiah's coming. If there existed some belief that the coming of a King of the Jews was to be heralded thus, the occurrence of the phenomenon would necessarily arrest the attention of the astrology-loving priests in the East. Kepler's theory was, that just as the conjunction in 1604 of Jupiter and Saturn, culminated in 1605 in the conjunction of Jupiter, Saturn and Mars, and was followed by the appearance of a new and brilliant star, which disappeared again after about eighteen months, so in BC.7 and 6, the exactly singular conjunctions were followed by the appearance of a new star after the triple conjunction, and that this was the star of Matthew 2:2.
Now the visit of the Magi obviously did not occur until more than forty days after the birth of Jesus,  and may probably be placed during the winter of BC.6-5. Kepler's theory involves that they appeared before Herod at this time, and informed him of the reason of their coming. Herod thereupon consulted the Jewish priests, and heard from them that the King was to be born in Bethlehem. He also questioned the Magi privately, and learned the exact facts with regard to the appearance of the star, and doubtless also with regard to the whole phenomenon in the heavens. He would learn from the Magi that the fateful conjunction first occurred in May of the year BC.7. Then he sent the Magi away to Bethlehem, and awaited news of their discovery. When they did not return, he ordered all children under two years of age in Bethlehem to be killed. The King might have been born at any time after the first conjunction occurred; and that was at least eighteen months ago. Therefore, in order to make sure, the order included every child under two.
Now about this time, as Josephus mentions,  Herod was troubled by a prophecy that the power was about to pass away from him and from his family; and the Pharisees, from favor to the wife of Pheroras (who promised to pay their fine), predicted that the succession would come to her and her children. Obviously, the second part of the prophecy was pure invention, due to partisanship; but the first part was almost certainly connected with the Jews' deep-seated belief in the coming of a new King, the Messiah. Lewin (whose arrangement of the events in the last three years of Herod's life seems very good) places this event in BC.6; Schuerer dates it in 7. One or the other must be right. Herod put to death the ringleaders of the Pharisees, with two of his own personal attendants, and also all those of his own household that had associated themselves with the prediction of the Pharisees.
There occurred therefore a number of deaths among the family and attendants of Herod in connection with the belief in the coming of a new King.
Now Macrobius, a pagan writer about AD.400, says that when the news was brought to Augustus that Herod, King of the Jews, had ordered children under two years of age in Syria to be slain, and that among them was a son of Herod's, the Emperor remarked, "It is better to be Herod's pig than his son".  It is not probable that Macrobius was indebted to a Christian writer for this story;  and, therefore, probably the story of the Massacre of the Infants was recorded in some pagan source. The execution of the conspirators in Herod's household perhaps occurred about the same time; but among them there is not likely to have been a son of Herod's. Only a few months before, however, Herod had put to death two of his sons, and the remark of Augustus may have been prompted by hearing successively of so many barbarities, the execution of two sons, of a number of infants, and of several of his own family and personal attendants.
While all these statements furnish only vague presumptions, yet they certainly tend to show that much was going on of a remarkable character about BC.7-6, and they fit in well with both Luke and Matthew. If the narratives of these two writers are true, they throw much light on Josephus and Macrobius, and receive illustration and confirmation from them.
But that which is most certain is that our non-Christian authorities are most meager and fragmentary. It is the extreme of uncritical and unscholarly procedure to condemn the Christian authorities because they tell some things which are not mentioned in any non-Christian source.