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 1:1MOSES NUMBERING THE MEN OF WAR. (Num. 1:1-54)
on the first day of the second month, &c.--Thirteen months had elapsed since the exodus. About one month had been occupied in the journey; and the rest of the period had been passed in encampment among the recesses of Sinai, where the transactions took place, and the laws, religious and civil, were promulgated, which are contained in the two preceding books. As the tabernacle was erected on the first day of the first month, and the order here mentioned was given on the first day of the second, some think the laws in Leviticus were all given in one month. The Israelites having been formed into a separate nation, under the special government of God as their King, it was necessary, before resuming their march towards the promised land, to put them into good order. And accordingly Moses was commissioned, along with Aaron, to take a census of the people. This census was incidentally noticed (Exo 38:26), in reference to the poll tax for the works of the tabernacle; but it is here described in detail, in order to show the relative increase and military strength of the different tribes. The enumeration was confined to those capable of bearing arms [Num 1:3], and it was to be made with a careful distinction of the tribe, family, and household to which every individual belonged. By this rule of summation many important advantages were secured: an exact genealogical register was formed, the relative strength of each tribe was ascertained, and the reason found for arranging the order of precedence in march as well as disposing the different tribes in camp around the tabernacle. The promise of God to Abraham [Gen 22:17] was seen to be fulfilled in the extraordinary increase of his posterity, and provision made for tracing the regular descent of the Messiah.
num 1:3Aaron shall number them by their armies--or companies. In their departure from Egypt they were divided into five grand companies (Exo 13:18), but from the sojourn in the wilderness to the passage of the Jordan, they were formed into four great divisions. The latter is here referred to.
num 1:4with you there shall be a man of every tribe, &c.--The social condition of the Israelites in the wilderness bore a close resemblance to that of the nomad tribes of the East in the present day. The head of the tribe was a hereditary dignity, vested in the oldest son or some other to whom the right of primogeniture was transferred, and under whom were other inferior heads, also hereditary, among the different branches of the tribe. The Israelites being divided into twelve tribes, there were twelve chiefs appointed to assist in taking the census of the people.
num 1:5these are the names of the men that shall stand with you, &c.--Each is designated by adding the name of the ancestors of his tribe, the people of which were called "Beni-Reuben," "Beni-Levi," sons of Reuben, sons of Levi, according to the custom of the Arabs still, as well as other nations which are divided into clans, as the Macs of Scotland, the Aps of Wales, and the O's and the Fitzes of Ireland [CHALMERS].
num 1:16These were the renowned--literally, "the called" of the congregation, summoned by name; and they entered upon the survey the very day the order was given.
num 1:18by their polls--individually, one by one.
num 1:19As the Lord commanded Moses, &c.--The numbering of the people was not an act sinful in itself, as Moses did it by divine appointment; but David incurred guilt by doing it without the authority of God. (See on Sa2 24:10).
num 1:20These are those that were numbered--In this registration the tribe of Judah appears the most numerous; and accordingly, as the pre-eminence had been assigned to it by Jacob [Gen 49:8-12], it got the precedence in all the encampments of Israel. Of the two half-tribes of Joseph, who is seen to be "a fruitful bough" [Gen 49:22], that of Ephraim was the larger, as had been predicted. The relative increase of all, as in the two just mentioned, was owing to the special blessing of God, conformably to the prophetic declaration of the dying patriarch. But the divine blessing is usually conveyed through the influence of secondary causes; and there is reason to believe that the relative populousness of the tribes would, under God, depend upon the productiveness of the respective localities assigned to them. [For tabular chart, see on Num 26:64.]
num 1:45all they that were numbered were six hundred thousand, &c.--What an astonishing increase from seventy-five persons who went down to Egypt about two hundred fifteen years before [see on Gen 46:8], and who were subjected to the greatest privations and hardships! And yet this enumeration was restricted to men from twenty years and upwards [Num 1:3]. Including women, children, and old men, together with the Levites, the whole population of Israel, on the ordinary principles of computation, amounted to about 2,400,000.
num 1:47But the Levites . . . were not numbered among them--They were obliged to keep a register of their own. They were consecrated to the priestly office, which in all countries has been exempted customarily, and in Israel by the express authority of God, from military service. The custody of the things devoted to the divine service was assigned to them so exclusively, that "no stranger"--that is, no person, not even an Israelite of any other tribe, was allowed, under penalty of death, to approach these [Num 16:40]. Hence they encamped round the tabernacle in order that there should be no manifestation of the divine displeasure among the people. Thus the numbering of the people was subservient to the separation of the Levites from those Israelites who were fit for military service, and to the practical introduction of the law respecting the first-born, for whom the tribe of Levi became a substitute [Exo 13:2; Num 3:12].