Fictitious Problems in Mathematics

THE alleged inaccuracies of language in stating the assumed conditions of smoothness or roughness prevailing between two bodies in contact are unfortunately so common that it is the exception rather than the rule to find any problem in which these conditions are correctly worded. In working through a chapter of Besant's ``Dynamics'' with a class the other day, I came across no less than two problems in which a ``perfectly rough'' body was supposed to be in contact with a second body which in turn rested against a third ``perfectly smooth'' body. In these cases the framer of the question carefully avoided giving any information as to the roughness or smoothness of the middle body, so that the inaccuracy of language might easily be overlooked. But this does not apply to the following example :-