bˈækstɚ wʌz lˈɪbɚɹəl mˈɛmbɚɹ ʌv pˈɑːɹləmənt fɔːɹ mˈɔntɹoʊz bˈɜːɡz fɹʌm wˈʌn θˈaʊzənd ˈeɪthˈʌndɹɪd fˈɪfti fˈaɪv tə wˈʌn θˈaʊzənd ˈeɪthˈʌndɹɪd ˈeɪɾi fˈaɪv, ænd sˈɜːvd ˌʌndɚ wˈɪljəm jˈuːɔːɹt ɡlˈædstoʊn æz sˈɛkɹətɹi tə ðɪ ˈædmɚɹəlɾi fɹʌm wˈʌn θˈaʊzənd ˈeɪthˈʌndɹɪd sˈɪksti ˈeɪt tə wˈʌn θˈaʊzənd ˈeɪthˈʌndɹɪd sˈɛvənti wˈʌn ænd æz faɪnˈænʃəl sˈɛkɹətɹi tə ðə tɹˈɛʒɚɹi fɹʌm wˈʌn θˈaʊzənd ˈeɪthˈʌndɹɪd sˈɛvənti wˈʌn tə wˈʌn θˈaʊzənd ˈeɪthˈʌndɹɪd sˈɛvənti θɹˈiː.
Baxter was Liberal Member of Parliament for Montrose Burghs from 1855 to 1885, and served under William Ewart Gladstone as Secretary to the Admiralty from 1868 to 1871 and as Financial Secretary to the Treasury from 1871 to 1873.