The Text

1801 Constitutional Amendment III [Senate reorganized.]:
That from the first Monday in July next, the number of the senators shall be permanently thirty-two, and that the present number of senators shall be reduced to thirty-two in the following manner, that is to say: The seats of the eleven senators composing the first class, whose time of service will expire on the first Monday in July next, shall not be filled up; and out of the second class the seats of one senator from the middle district, and of one senator from the southern district, shall be vacated by the senators of those districts belonging to that class, casting lots among themselves; out of the third class the seats of two senators from the middle district, and of one senator from the eastern district shall be vacated in the same manner; out of the fourth class the seats of one senator from the middle district, of one senator from the eastern district, and of one senator from the western district, shall be vacated in the same manner; and if any of the said classes shall neglect to cast lots, the senate shall, in such case, proceed to cast lots for such class or classes so neglecting. And that eight senators shall be chosen at the next election, in such districts as the legislature shall direct, for the purpose of apportioning the whole number of senators amongst the four great districts of this state, as nearly as may be, according to the number of electors qualified to vote for senators, which shall be found to be in each of the said districts by the census above mentioned; which eight senators, so to be chosen, shall form the first class.
1801 Constitutional Amendment IV [Future apportionments of legislature.]:
That from the first Monday in July next, and on the return of every census thereafter, the number of the assembly shall be increased at the rate of two members for every year, until the whole number shall amount to one hundred and fifty; and that upon the return of every such census, the legislature shall apportion the senators and members of the assembly amongst the great districts and counties of this state, as nearly as may be, according to the number of their respective electors; Provided, that the legislature shall not be prohibited by anything herein contained, from allowing one member of assembly to each county, heretofore erected within this state.

The full provision includes both the amendment and the text it amends – NY Constitution 1777, Article XI:
That the members of the senate be elected for four years, and immediately after the first election, they be divided by lot into four classes, six in each class, and numbered, one, two, three, four; and that the seats of the members of the first class shall be vacated at the expiration of the first year; the second class the second year; and so on continually, to the end that the fourth part of the senate, as nearly as possible, may be annually chosen.