Idaho Code § 31-135
Madison county is described as follows: beginning at the southwest corner of section thirty-four (34), township four (4) north, range forty-one (41) east (1913, ch. 26, section 2, p. 108);
Southern boundary. Thence easterly along the township line between townships three (3) and four (4) north (R.C. 23 1) to a point two (2) miles east of the range line which, when surveyed, will be between ranges forty-two (42) and forty-three (43) east (1915, ch. 8, section 2, p. 30);
Eastern boundary. Thence north to the center of the main channel of Teton river, where said river intersects the section line between sections sixteen (16) and seventeen (17), township seven (7) north, range forty-three (43) east (1915, ch. 8, section 2, p. 30);
Northern boundary. Thence down the center of the main channel of said Teton river to where the same intersects the range line between ranges forty-one (41) and forty-two (42) east; thence south to the township line between townships six (6) and seven (7) north; thence west to the southeast corner of section thirty-five (35), township seven (7) north, range forty (40) east; thence north one (1) mile, to the northeast corner of section thirty-five (35); thence west to the northeast corner of section thirty-four (34), township seven (7) north, range thirty-nine (39) east; thence north two (2) miles to the northeast twenty-one (21) and twenty-two (22), township and range last aforesaid, thence west to the northeast corner of section twenty-one (21), township seven (7) north, range thirty-eight (38) east;
Western boundary. Thence south on the section line between sections twenty-one (21) and twenty-two (22), township and range last aforesaid, to the township line between townships six (6) and seven (7) north; thence continuing in a southerly direction on the line which, when surveyed, will be the section line between sections three (3) and four (4), township six (6) north, range thirty-eight (38) east, to the southern boundary of said township; thence south along the section line between sections three (3) and four (4), township five (5) north, range thirty-eight (38) east, to where the same intersects the center of the main channel of the Snake river; thence up the center channel of said Snake river to the junction of the North and South Forks of the Snake river, and continuing up the center channel of said South Fork of Snake river to where the same intersects the section line that runs due east between sections twenty-three (23) and twenty-six (26), township four (4) north, range forty (40) east; thence east on said section line last aforesaid in said last mentioned township and range to the northeast corner of section twenty-eight (28), township four (4) north, range forty-one (41) east; thence south two (2) miles to the place of beginning (1913, ch. 26, section 2, p. 109).
County seat-Rexburg.
Idaho Code § 31-135