He continues:--“Mathematical treatment of any problem is always analytical--attention is concentrated upon certain facts, and for the moment other facts are neglected. For example, in dealing with the thermodynamics of the steam engine, one dismisses from consideration very vital points essential to the successful working of the engine--questions of strength of parts, lubrication, convenience for repairs. But if an engineer is to succeed he must not fail to consider every element necessary to success; he must have a practical instinct which will tell him whether the engine as a whole will succeed. His mind must not be only analytical, or he will be in danger of solving bits of the problems which his work presents, and of falling into fatal mistakes on points which he has omitted to consider, and which the plainest, intelligent, practical man would avoid almost without knowing it. Again, the powers of the strongest mathematician being limited, there is a constant temptation to fit the facts to suit the mathematics, and to assume that the conclusions will have greater accuracy than the premises from which they are deduced. This is a trouble one meets with in other applications of mathematics to experimental science. In order to make the subject amenable to treatment, one finds, for example, in the science of magnetism, that it is boldly assumed that the magnetization of magnetizable material is proportionate to the magnetizing force, and the ratio has a name given to it, and conclusions are drawn from the assumption; but the fact is, no such proportionality exists, and all conclusions resulting from the assumption are so far invalid. Whenever possible the mathematical deductions should be frequently verified by reference to observation and experiment, for the very simple reason that they are only deductions, and the premises from which the deductions are drawn may be inaccurate or incomplete. We must always remember that we cannot get more out of the mathematical mill than we put into it, though we may get it in a form infinitely more useful for our purpose.”