purposely accepts the accumulation of non molten solid substance in the reaction medium during the course of the entire reaction in contrast to the prior known method for preparing sodium polysulfides as a result the method of the invention allows conversions up to approximately 97 of theory at temperatures which are far below the melting point of the final product of course any desired polysulfide can also be obtained from the high percentage sodium monosulfide obtained by means of melting it together with the appropriate amounts of sulfur the invention is explained in more detail below with reference to the illustrative embodiment a laboratory kneading machine with a trough of v4a formed from two semicylinders with polished inner walls was equipped with two polished blades of v4a in sigma form mounted in each instance on its own drive shaft the lower trough part was formed of a double jacket for receiving a heat conductive medium the screwed on cover of v4a was provided with a connecting piece which was able to be closed with a screw cap and with an introductory tube for introducing the protective gas argon and terminating immediately underneath the cover both sodium and sulfur were charged in and the initial product removed through the connecting piece the blade speed could be varied between 40 60 rpms a temperature sensor protective tube formed of v4a was introduced into the trough or the.