DETAILED DESCRIPTION OF THE INVENTION As the starting material fatty acid for use in preparing an acyl-poly-hydroxy carboxylic acid to be employed in the non-liquid detergent composition in the present invention and expressed by the foregoing general formula, saturated or unsaturated straight-chain or branched-chain fatty acids having 6 to 20 carbon atoms are employed. Said fatty acids include fatty acids obtained from natural fats, fatty acids manufactured from olefins and carbon monoxide by oxo synthesis or the like, fatty acids manufactured by oxidation of paraffins, etc. In the case of fatty acids having 6 to 10 carbon atoms and 16 to 20 carbon atoms, it is appropriate to employ them independently as the detergency thereof is relatively minor, but it will do to employ them upon admixing with fatty acids having 11 to 15 carbon atoms. On the occasion of thus admixing, it is desirable that the ratio of said fatty acid having 11 to 15 carbon atoms is more than 70 wt. %. As the fatty acids for this purpose, there are, for instance, caproic acid, caprylic acid, lauric acid, myristic acid, palmitic acid, stearic acid, arachidic acid, oleic acid, . alpha. -methyl decanoic acid, . alpha. -methyl dodecanoic acid, . alpha. -methyl tridecanoic acid, . alpha. -methyl tetradecanoic acid, etc. . alpha. -hydroxy carboxylic acid as another constituent of acyl-poly-hydroxy carboxylic acid includes glycolic acid, lactic acid and . alpha. -hydroxy butyric acid. The degree of condensation n of . alpha. -hydroxy carboxylic acid has a grave influence upon the detergency; when n ranges from 2 to 4, the highest detergency is displayed, and as n becomes bigger, the detergency lowers gradually. Therefore, in the case of applying an acyl-poly-hydroxy carboxylic acid independently, it is appropriate to make n in the range of from 2 to 6, while in the case of applying it as a mixture, it is appropriate to make n be in the range of from 1. 7 to 6. 5 on the average, and particularly in order to obtain the highest detergency, n is to be in the range of from 1
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