In a spirit as judicial Sir William Anderson has said:--“There is a tendency among the young and inexperienced to put blind faith in formulæ, forgetting that most of them are based upon premises which are not accurately reproduced in practice, and which in many cases are unable to take into account collateral disturbances, which only experience can foresee, and common sense guard against.” Do Not Pay More than 100 Cents for a Dollar. That, with regard to a new machine, all the facts of constructive and working cost should be in view, and after tests in practice, is the conviction of Professor A. B. W. Kennedy:--“Machines cannot be finally criticized, pronounced good or bad, simply from results measurable in a laboratory. One wishes to use a steam plant, for example, by which as little coal shall be burnt as possible. But clearly it would be worth while to waste a certain amount of coal if a less economical machine would allow a larger saving in the cost of repairs or of interest. Or, it might be worth while to use a machine in which a certain amount of extra power was obviously employed, if only by means of such a machine the cost of attendance could be measurably reduced. The ‘worth-whileness’ of economies comes out only in practical experience. A careful training in comparatively simple parts fits a man more than anything else to gauge accurately the importance of such parts as those named. No doubt there are many men in whom the critical faculty is insufficiently developed to allow them ever to be of use in these matters, but to those who are intellectually capable of ‘the higher criticism’ it is of inestimable value to have had a systematic training in the lower.” To the same effect are remarks by Professor J. Hopkinson:--“Doubling the thickness of a cylinder by no means doubles its strength. Conversely, doubling the strength of the material will permit the thickness to be diminished to much less than one half. Until 1869 hydraulic presses were mostly made of cast iron. There was much astonishment at the great reduction in thickness and weight which became possible when steel was substituted for the weaker material. In the case of guns it is well-known that greater strength can be obtained if the outer hoops are shrunken on the inner ones. Mathematical theory tells us what amount of shrinkage should give the best results. A gun may have a shrinkage so great as to weaken it.”