the term polybutadiene as used herein designates a a polymer derived from subjecting a butadiene to polymerization such as anionic polymerization using catalysts of for example na dispersants and organoalkalimetallic compounds , radical polymerization with catalysts of organoperoxides , cationic polymerization with friedel - crafts catalysts and anionic coordination reaction with ziegler - type catalysts . polybutadienes contain backbone ( trans - and cis -) double bonds in addition to vinyl double bonds . the polybutadiene used in the invention contains vinyl double bonds in an amount of more than 20 mol %, preferably more than 40 mol %, more preferably more than 50 mol % and most preferably more than 70 mol % in terms of the monomer unit . the term hardened compound as used herein refers to a hardened product resulting from crosslinking more than 10 %, preferably more than 40 %, more preferably more than 70 % and most preferably more than 90 % of the vinyl double bonds in the above defined polybutadiene . the rate of reaction of the vinyl double bonds according to the invention is represented by the formula ## equ1 ## where a is the amount of vinyl double bonds in the polybutadiene as determined by infrared spectroscopic analysis and b is the amount of vinyl double bonds in the polybutadiene after being hardened . the polybutadiene used in the invention has a number average molecular weight of 500 - 100 , 000 , preferably 1 , 000 - 20 , 000 , and more preferably 1 , 500 - 8 , 000 . smaller than 500 molecular weights would retard the hardening speed , while greater than 100 , 000 molecular weights would result in objectionably viscous product . the polybutadiene according to the invention includes copolymers having monomers other than the butadiene unit in the polymer skeleton . such comonomers are for example styrene , alpha - methylstyrene and acrylonitrile , of which styrene is particularly preferred . in any case , however , such copolymers should contain vinyl double bonds in an amount of more than 20 mol %, preferably more than 40 mol %, more preferably more than 50 mol % and most preferably more than 60 mol % in terms of the total monomer unit including the comonomer . the polybutadiene according to the invention may , if desired , be modified with acids or peroxides to introduce hydroxyl groups or carboxyl groups in the polymer . for instance , the polymer may be added with maleic anhydride , or may have intercarbon double bonds epoxidized . in any case however , the polymer should contain vinyl double bonds in an amount of more than 20 mol %, preferably more than 40 mol %, more preferably more than 50 mol % and most preferably more than 60 mol % in terms of the monomer unit . the hardened compound referred to herein may be obtained by various processes . it may for example be derived from subjecting the inventive polybutadiene to a radical hardening reaction preferably in the presence of suitable radical initiators . examples of such radical initiators include organic peroxides such as methyl ethyl ketone peroxide , 1 , 1 - bis ( t - butylperoxy ) 3 , 3 , 5 - trimethylcyclohexane , t - butylhydro peroxide , dicumyl peroxide , 2 , 5 - dimethyl - 2 , 5 - di ( t - butylperoxy ) hexyne - 3 and the like , and aromatic hydrocarbons such as 2 , 3 - dimethyl - 2 , 3 - diphenylbutane , 2 , 3 - diethyl - 2 , 3 - diphenylbutane and the like . particularly preferred are 2 , 5 - dimethyl - 2 , 5 - di ( t - butylperoxy ) hexyne - 3 , 2 , 3 - dimethyl - 2 , 3 - diphenylbutane and 2 , 3 - diethyl - diphenylbutane , of which 2 , 3 - dimethyl - 2 , 3 - diphenylbutane is best chosen . reaction temperature for radical hardening of the polybutadiene according to the invention varies with the decomposition temperature of the initiator used but is usually in the range of 50 °- 350 ° c ., preferably 150 °- 330 ° c ., more preferably 240 °- 320 ° c ., and most preferably 250 °- 310 ° c . reaction time , though dependent upon temperature , is usually in the range of 10 minutes to 10 hours , preferably 20 minutes to 3 hours . the hardened compound according to the invention may be in various forms but is preferably in the form of fine particles having a particle size of less than 100 μm , preferably less than 10 μm , more preferably less than 1 μm . it may be prepared by mechanical pulverization or by hardening while in an emulsified state . the base oil for the inventive composition may be any commercially available lubricant base oil regardless of whether it may be mineral or synthetic . mineral oils may be atmospheric or vacuum distillates which are subjected to solvent deasphalting , solvent extraction , hydrocracking , solvent dewaxing , hydrodewaxing , sulfur acid treatment , clay refining , hydrorefining and the like . eligible synthetic lubricant base oils include alpha - olefin oligomers such as normal paraffin , isoparaffin , polybutene , polyisobutylene , 1 - decene oligomer and the like , alkylbenzenes such as monoalkylbenzene , dialkylbenzene polyalkylbenzene and the like , alkyl naphthalenes such as monoalkyl naphthalene , dialkyl naphthalene , polyalkyl naphthalene and the like , diesters such as di - 2 - ethylhexyl sebacate , dioctyl adipate , diisodecyl adipate , ditridecyl adipate , ditridecyl glutarate and the like , polyol esters such as trimethylolpropane caprylate , trimethylolpropane pelargonate pentaerythritol - 2 - ethyl hexanoate , pentaerythritol pelargonate and tyhe like , polyglycols such as polyethylene glycol , polyethylene glycol monoether , polypropylene glycol , polypropylene glycol monoether and the like , polyphenyl ether , tricresyl phosphate and silicone oil . the above base oils may be used singly or in combination . the lubricant compositions of the invention are characterized by blending the base oils with the hardened compound which is used in an amount of 0 . 01 - 50 , preferably 0 . 1 - 20 and more preferably 0 . 3 - 10 parts by weight per 100 parts base oil . the hardened compound , if used in amounts smaller than 0 . 01 weight part , would lead to poor lubricating performance and , if greater than 50 weight parts , would not be sufficiently dispersed in the base oil . the inventive lubricant compositions may also be blended with various additives such as antioxidants , detergent dispersants , viscosity index improvers , pour point depressants , antiwear agents , extreme pressure additives , oiliness agents , corrosion inhibitors , metal inactivators , rust inhibitors , defoamers , emulsifiers , demulsifiers , disinfectants , colorants and the like . gelling agents may also be used to turn the compositions into greases . details as regards the above listed additives are disclosed for instance in j . soc . lubricants , japan , vol . 15 , no . 6 and &# 34 ; additives for petroleum products &# 34 ; edited by toshio sakurai , saiwai publishing co ., japan . suitable additives may be chosen to suit application of the inventive lubricant composition as engine oil , hydraulic fluid , gear oil , bearing oil or the like . the invention will be further described by way of the following examples . 100 parts by weight of liquid polybutadiene having a number average molecular weight of 3 , 000 , 65 mol % or more of vinyl double bonds and a viscosity of 500 poise at 25 ° c . were added with 1 . 0 part by weight of 2 , 3 - dimethyl - 2 , 3 - diphenylbutane , followed by heating with stirring at 80 ° c . the resulting admixture was coated uniformly over a nacl plate with use of a spinner and sandwiched by another nacl plate . this starting sample was analyzed by an infrared spectroscopic analyzer with the results shown in fig1 . the sample was heated for two hours in a constant temperature vessel having a controlled temperature of 290 ° c . and purged with nitrogen . the resulting hardened material was infrared spectroscopically analyzed with the results shown in fig2 wherein absorption of vinyl double bonds is at 910 cm - 1 . the rate of reaction of vinyl double bonds as determined by lambert - beer &# 39 ; s law with a reference absorption at 2 , 900 cm - 1 was 90 . 4 %. the sample was then placed in a brass mold and heated in a 290 ° c . constant temperature vessel for two hours . the resulting hardened product was ground by a shock - type ultrafine pulverizer to an average particle size of 16 μm and classified by a high - precision pneumatic classifier to obtain an average particle size 1 . 4 μm . 1 . 0 part by weight of the hardened compound prepared as above was added to 100 parts by weight of pentaerythritol pelargonate ( synttetic base oil ). the admixture was stirred at room temperature to obtain a pale uniform dispersion . this dispersion was tested for lubricating qualities by falex pin block tester at 80 ° c . with a load of 250 pounds for one hour . pin wear was 1 . 4 mg . seisure load was 1 , 430 pounds . the procedure of the above inventive example was followed except for the use of 1 . 0 part by weight of particulate polytetrafluoroethylene having an average particle size of 1 . 3 μm in place of the hardened particulate compound of the invention . the procedure of inventive example was followed except for the use of 1 . 0 part by weight of molybdenum disulfide having an average particle size of 0 . 3 μm in place of the inventive hardened compound . the procedure of inventive example was followed except for the use of 1 . 0 part by weight of liquid polybutadiene in place of the inventive hardened compound . lubricating quality test data on each of the above examples are shown in the following table . table______________________________________ pin wear ( mg ) seizure load ( lb ) appearance______________________________________inventive 1 . 4 1 , 430 paleexample 1comparative 36 . 5 860 paleexample 1comparative 1 . 5 1 , 410 blackishexample 2comparative 31 . 6 980 paleexample 3______________________________________