Ancient meaning of the the character 思
Arthur Waley is indeed reflecting Chinese scholarship with this statement. In the Book of Odes 《詩經》, when 「思」 appears at the end of a line, it may be interpreted as a  modal particle (語气詞), equivalent to modern Mandarin 「啊」. For example,

《國風・漢廣》
漢之廣矣、不可泳思。
江之永矣、不可方（汸、舫）*思。
How broad, the Waters of the Hàn - they cannot be swum! 
How long, the Waters of the Jiāng - they cannot be rafted across!*
*《說文・方部》：「方，併船也。象兩舟省緫頭形。汸，方或从水。」

《小雅・鹿鳴之什・采薇》
昔我往矣、楊柳依依。
今我來思、雨雪霏霏。
Long ago, when I departed, the willows were fresh and tender;
Now, as I've returned, the rain and snow fall in torrents.


Please note that this use of 「思」 is not its earliest or original meaning. Apart from being a proper noun for a geographical region or person, 「思」's earliest usage is the same as its modern usage, meaning thoughts, contemplation, deliberation. From Guōdiàn Chǔ Slips: The Five Conducts, Slip #9:


《郭店楚墓竹簡・五行》09
……（不）（仁），恖（思）能清（精）。（智），恖能倀（長）……
...Without benevolence, one's thoughts cannot be refined; without wisdom, one's thoughts do not have foresight...


References:

《漢語大詞典》
黃德寬《古文字譜系疏證》
何琳儀《戰國古文字典：戰國文字聲系》