The following essay contains the greater part of a series of observations, made between 1845 and 1850, by one whose recent death deprived physiology of one of its most earnest truth-loving students. The papers, as left by their author, and committed to me by his father, contained little more than a record of the observations. I have arranged them to illustrate certain general facts, and have added some of the conclusions which they plainly indicate. I have felt the more justified in making these additions, by the belief that my intimate friendship with Mr. Barlow would enable me to write what he would have written, had his life been spared. And in communicating his researches to the Royal Society, I believe I am fulfilling the design with which, not long before his death, he was preparing them for publication.—J. P.