Fats and fatty oils are converted into mono- and diglycerides by alcoholysis and interesterification in the presence of an interesterification catalyst such as sodium methoxide and an organic hydroxy compound having at least one unesterified alcoholic hydroxyl group not acid enough to inactivate the catalyst, the conversion being carried out at a temperature sufficiently below 180 DEG F. to permit crystallisation of solid mono- and diglycerides as they are formed. The reaction may be conducted in the presence of an inert solvent. After separation of the solid and liquid fractions, the products may be used as such or they may be esterified with fatty or non-fatty mono- or polycarboxylic acids, or they may be split to form fatty acids and glycerol which may be reused in the alcoholysis reaction. The fatty acids may be used in soap making, while the liquid fractions may be used for preparing drying oils by esterifying the unesterified hydroxyl groups in such oils with the fatty acids of drying oils. Among fats and oils specified are palm, cotton seed, linseed, soybean, corn, rapeseed, menhaden, sardine, salmon, and pilchard oils, and tallow. Alcoholic substances referred to include glycerol, methanol, ethanol, propanol, isopropanol, butanols, amyl alcohol, acetone glycerol, allyl alcohol, glycidol, ethylene glycol, polyethylene glycol, di- and polyglycerol, penta-erythritol, sorbitol, mannitol, cyclohexanol, glycol monoethers, glycerol ethers, monoacetin, monobutyrin, lauryl alcohol, cetyl alcohol, benzyl alcohol, ethanolamine, and non-acid alcohol esters and salts of hydroxy carboxylic acids such as diethyl tartrate, potassium tartrate, ethyl lactate, and sodium glycollate. In addition to sodium methoxide, any alkali metal alkoxide from materials less acidic than phenol may be employed as catalysts including ethoxides, propoxides, butoxides, and alkoxides of lauryl alcohol, ethylene glycol, and mono- and diglycerides of the glyceride mixture; also tetramethyl ammonium methoxide, lauryl benzyl ammonium methoxide, and alkali metal organic compounds such as triphenylmethyl sodium, potassium pyrrole, and finely divided metallic suspensions of potassium or sodium in xylene. The catalyst may be added as a dispersion in xylene, toluene or petroleum naphtha. The amount of catalyst to be employed ranges from about 0.05 to 0.5 per cent in the case of sodium methoxide, while the amount of alcoholic body added may vary from about 1 per cent of the oil to amounts over and above those theoretically necessary to convert all the glycerides to fatty acid monoglycerides. At temperatures of 120 DEG F. to 80 DEG F. the greater proportion of the reaction takes place within 24 hours, but at lower temperatures a longer time such as 3 or 4 days may be necessary. If maximum conversion is desired, an even longer time such as 17 days may be occupied and the temperature may be reduced progressively for example from 90 DEG F. to 50 DEG F. as the mono- and diglycerides crystallise out. After the desired interesterification has taken place and before the temperature of the mixture is allowed to rise appreciably, the catalytic material is rendered inactive for example by the addition of hydrochloric acid, phosphoric acid, carbonic acid, glacial acetic acid, or water. In an example, glycerol containing a small amount of sodium hydroxide is added slowly to palm oil at 170 DEG C. with vigorous agitation. The product is cooled to 100 DEG C. and phosphoric acid added to neutralise the alkali. About 0.2 per cent sodium methoxide is then added with vigorous agitation and the mixture kept at 100 DEG F. in an atmosphere of nitrogen for 1 to 3 days. It is finally treated with phosphoric acid to inactivate the catalyst and filtered to give a solid fraction consisting of substantially completely saturated mono-, di- and triglycerides of palm oil fatty acids, and a liquid fraction containing the bulk of the unsaturated constituents. Other examples refer to the treatment of palm oil with methanol and of cottonseed oil with glycerol. The process can be applied to the separation of tallow and similar fats into commercial stearic acid and red oil (principally oleic acid). The mono- and diglycerides from cottonseed oil or soybean oil may be separated from the liquid constituents and the fractions converted into low and high titer soap respectively. Drying oils for paint may also be produced from the liquid fractions prepared according to the invention from linseed oil, semi-drying oils, or fish oils by esterifying unesterified hydroxyl groups in such fractions with fatty acids of drying oils. Specification 574,807 is referred to.ALSO:Fats and fatty oils are converted into mono-and diglycerides by alcoholysis and interesterification in the presence of an interesterification catalyst such as sodium methoxide and an organic hydroxy compound having at least one unesterified alcoholic hydroxyl group not acid enough to inactivate the catalyst, the conversion being carried out at a temperature sufficiently below 180 DEG F. to permit crystallisation of solid mono- and diglycerides as they are formed. The reaction may be conducted in the presence of an inert solvent. After separation of the solid and liquid fractions, the products may be used as such, or they may be esterified with fatty or non-fatty mono- or polycarboxylic acids, or they may be split to form fatty acids and glycerol which may be re-used in the alcoholysis reaction. The fatty acids may be used in soap making, while the liquid fractions may be used for preparing drying oils by esterifying the unesterified hydroxyl groups in such oils with the fatty acids of drying oils. Among fats and oils specified are palm, cotton seed, linseed, soybean, corn, rapeseed, menhaden, sardine, salmon, and pilchard oils, and tallow. Alcoholic substances referred to include glycerol, methanol, ethanol, propanol, isopropanol, butanols, amyl alcohol, acetone glycerol, allyl alcohol, glycidol, ethylene glycol, polyethylene glycol, di- and polyglycerol, penta-erythritol, sorbitol, mannitol, cyclohexanol, glycol monoethers, glycerol ethers, monoacetin, monobutyrin, lauryl alcohol, cetyl alcohol, benzyl alcohol, ethanolamine, and non-acid alcohol esters and salts of hydroxy carboxylic acids such as diethyl tartrate, potassium tartrate, ethyl lactate, and sodium glycollate. In addition to sodium methoxide, any alkali metal alkoxide from materials less acidic than phenol may be employed as catalysts including ethoxides, propoxides, butoxides, and alkoxides of lauryl alcohol, ethylene glycol, and mono- and p diglycerides of the glyceride mixture; also tetramethyl ammonium methoxide, lauryl benzyl ammonium methoxide, and alkali metal organic compounds such as triphenylmethyl sodium, potassium pyrrole, and finely-divided metallic suspensions of potassium or sodium in xylene. The catalyst may be added as a dispersion in xylene, toluene or petroleum naphtha. The amount of catalyst to be employed ranges from about 0.05 to 0.5 per cent in the case of sodium methoxide, while the amount of alcoholic body added may vary from about 1 per cent of the oil to amounts over and above those theoretically necessary to convert all the glycerides to fatty acid monoglycerides. At temperatures of 120 DEG F. to 80 DEG F. the greater proportion of the reaction takes place within 24 hours, but at lower temperatures a longer time such as 3 or 4 days may be necessary. If maximum conversion is desired, an even longer time such as 17 days may be occupied and the temperature may be reduced progressively, for example from 90 DEG F. to 50 DEG F. as the mono- and diglycerides crystallise out. After the desired interesterification has taken place and before the temperature of the mixture is allowed to rise appreciably, the catalytic material is rendered inactive for example by the addition of hydrochloric acid, phosphoric acid, carbonic acid, glacial acetic acid, or water. In an example, glycerol containing a small amount of sodium hydroxide is added slowly to palm oil at 170 DEG C. with vigorous agitation. The product is cooled to 100 DEG C. and phosphoric acid added to neutralise the alkali. About 0.2 per cent sodium methoxide is then added with vigorous agitation and the mixture kept at 100 DEG F. in an atmosphere of nitrogen for 1 to 3 days. It is finally treated with phosphoric acid to inactivate the catalyst and filtered to give a solid fraction consisting of substantially completely saturated monodi- and triglycerides of palm oil fatty acids, and a liquid fraction containing the bulk of the unsaturated constituents. Other examples refer to the treatment of palm oil with methanol and of cottonseed oil with glycerol. The process can be applied to the separation of tallow and similar fats into commercial stearic acid and red oil (principally oleic acid). The mono- and diglycerides from cottonseed oil or soybean oil may be separated from the liquid constituents and the fractions converted into low and high titer soap respectively. Drying oils for paint may also be produced from the liquid fractions prepared according to the invention from linseed oil, semi-drying oils, or fish oils by esterifying unesterified hydroxyl groups in such fractions with fatty acids of drying oils. Specification 574,807, [Group III], is referred to.