The Mathematical Motorist.

Progress, Volume IV, Issue 6, 1 April 1909, Page 193

The Mathematical Motorist.

The following amusing skit is from a legal light shining in Wellington : — Let M be the driver of a motor car working with velocity Y. If a suffiiently high value be given to V it will eventually reach PC. In most cases V will then equal 0. For low values of V, P C may be neglected, but if V be large it will generally be necessary to square P C after which it will again assume a positive value. By a well-known elementary equation P C X £ s . d. = P C squared. But the quadrature may sometimes be effected by substituting for £ s. d. the third power of X = XXX. This is preferable where £s.d. is small with regard to M. If £ s. d. is made sufficiently large P G will vanish. If J P be substituted for P C, which may happen if the difference between M and P.C. be large the solution of the problem is more difficult because no value of £ s. d. or X can be found to effect the quadrature of J P, for as is well known, J P squared is an impossible quantity. The quantity P C is often irrational and may result in a totally arbitrary value being assigned to V differing largely from the real value. The equation may be solved by the use of logs but they must be used with care. Note. — The value of V need not suffer diminution if a circle can be described round P C. But if you cannot get round P G then the method of least possible squares should be used especially if £ ss. d. is a rapidly vanishing quantity.