A Commentary, Critical, Practical, and Explanatory on the Old and New Testaments, by Robert Jamieson, A.R. Fausset and David Brown  at sacred-texts.com
num 29:1THE OFFERING AT THE FEAST OF TRUMPETS. (Num. 29:1-40)
in the seventh month--of the ecclesiastical year, but the first month of the civil year, corresponding to our September. It was, in fact, the New Year's Day, which had been celebrated among the Hebrews and other contemporary nations with great festivity and joy and ushered in by a flourish of trumpets. This ordinance was designed to give a religious character to the occasion by associating it with some solemn observances. (Compare Exo 12:2; Lev 23:24).
it is a day of blowing the trumpets unto you--This made it a solemn preparation for the sacred feasts--a greater number of which were held during this month than at any other season of the year. Although the institution of this feast was described before, there is more particularity here as to what the burnt offering should consist of; and, in addition to it, a sin offering is prescribed. The special offerings, appointed for certain days, were not to interfere with the offerings usually requisite on these days, for in Num 29:6 it is said that the daily offerings, as well as those for the first day of the month, were to take place in their ordinary course.
num 29:7ye shall have on the tenth day of this seventh month an holy convocation--This was the great day of atonement. Its institution, together with the observance to which that day was devoted, was described (Lev 16:29-30). But additional offerings seem to be noticed, namely, the large animal sacrifice for a general expiation, which was a sweet savor unto the Lord, and the sin offering to atone for the sins that mingled with that day's services. The prescriptions in this passage appear supplementary to the former statement in Leviticus.
num 29:12on the fifteenth day--was to be held the feast of booths or tabernacles. (See Lev 23:34-35). The feast was to last seven days, the first and last of which were to be kept as Sabbaths, and a particular offering was prescribed for each day, the details of which are given with a minuteness suited to the infant state of the church. Two things are deserving of notice: First, that this feast was distinguished by a greater amount and variety of sacrifices than any other--partly because, occurring at the end of the year, it might be intended to supply any past deficiencies--partly because, being immediately after the ingathering of the fruits, it ought to be a liberal acknowledgment--and partly, perhaps, because God consulted the weakness of mankind, who naturally grow weary both of the charge and labor of such services when they are long-continued, and made them every day less toilsome and expensive [PATRICK]. Secondly, it will be remarked that the sacrifices varied in a progressive ratio of decrease every day.
num 29:18after the manner--according to the ritual order appointed by divine authority--that for meat offerings (Num 29:3-10), and drink offerings (Num 28:7, Num 28:14).
num 29:35On the eighth day ye shall have a solemn assembly--The feast of tabernacles was brought to a close on the eighth day, which was the great day (Joh 7:37). Besides the common routine sacrifices, there were special offerings appointed for that day though these were fewer than on any of the preceding days; and there were also, as was natural on that occasion when vast multitudes were convened for a solemn religious purpose, many spontaneous gifts and services, so that there was full scope for the exercise of a devout spirit in the people, both for their obedience to the statutory offerings, and by the presentation of those which were made by free will or in consequence of vows.
num 29:39These things ye shall do unto the Lord in your set feasts--From the statements made in this and the preceding chapter, it appears that the yearly offerings made to the altar at the public expense, without taking into account a vast number of voluntary vow and trespass offerings, were calculated at the following amount:--goats, fifteen; kids, twenty-one; rams, seventy-two; bullocks, one hundred thirty-two; lambs, 1,101; sum-total of animals sacrificed at public cost, 1,241. This, of course, is exclusive of the prodigious addition of lambs slain at the passover, which in later times, according to JOSEPHUS, amounted in a single year to the immense number of 255,600.