His early work on the movements of gases led him to examine the spontaneous movements of liquids, and as a result of the experiments he divided bodies into two classes--crystalloids, such as common salt, and colloids, of which gum-arabic is a type--the former having high and the latter low diffusibility. He also proved that the process of liquid diffusion causes partial decomposition of certain chemical compounds, the potassium sulphate, for instance, being separated from the aluminium sulphate in alum by the higher diffusibility of the former salt. He also extended his work on the transpiration of gases to liquids, adopting the method of manipulation devised by J. L. M. Poiseuille. He found that dilution with water does not effect proportionate alteration in the transpiration velocities of different liquids, and a certain determinable degree of dilution retards the transpiration velocity.
With regard to Graham's more purely chemical work, in 1833 he showed that phosphoric anhydride and water form three distinct acids, and he thus established the existence of polybasic acids, in each of which one or more equivalents of hydrogen are replaceable by certain metals (see ACID). In 1835 he published the results of an examination of the properties of water of crystallization as a constituent of salts. Not the least interesting part of this inquiry was the discovery of certain definite salts with alcohol analogous to hydrates, to which the name of alcoholates was given. A brief paper entitled "Speculative Ideas on the Constitution of Matter" (1863) possesses special interest in connexion with work done since his death, because in it he expressed the view that the various kinds of matter now recognized as different elementary substances may possess one and the same ultimate or atomic molecule in different conditions of movement.
Graham's _Elements of Chemistry_, first published in 1833, went through several editions, and appeared also in German, remodelled under J. Otto's direction. His _Chemical and Physical Researches_ were collected by Dr James Young and Dr Angus Smith, and printed "for presentation only" at Edinburgh in 1876, Dr Smith contributing to the volume a valuable preface and analysis of its contents. See also T. E. Thorpe, _Essays in Historical Chemistry_ (1902).