The function of the mathematical laboratory can best be understood in the light of the experience of many mathematical teachers. Anyone who has devoted even a comparatively short time to the mathematical training of workers in any branch of applied science must have had the experience that many past students return at frequent intervals for advice and consultation. The difficulties with which they are confronted appear invariably to be associated with the application in more or less concrete form of the mathematical principles and methods which they have learned. I find, as a matter of actual experience, that the complaint, when it is voiced, concerns itself not so much with the width of the mathematical field covered during training as the inability to know when to apply this or that mathematical method, how to attain the so-called solution, and how, when the mathematical solution has been obtained, to derive from it the desired information with reasonable expenditure of labour. It is partly this gap that the mathematical laboratory seeks to fill. An engineer confronted with a problem in heat conduction will not be satisfied should you provide him with an expression for the distribution in temperature in terms of a series of Bessel functions, unless he has at hand the means of immediately calculating to so many decimal places the values of these functions, either from a set of tables or by some direct mechanical process which he can apply. The form of solution provided may be to him more difficult to interpret than the original problem. It is partly because in the past mathematical teachers have been content to regard a problem as solved when, somehow or other, an analytical solution has been obtained, or to regard a problem as insoluble when such a solution cannot be obtained, that the failure exists on the part of the students of that training to utilise the mathematical weapons at their disposal, to modify them according to circumstances, and to interpret their results in actual cases.