During the last few years continuous indicating electric exhaust gas analysers have been coming into use more and more for controlling the strength of the fuel/air mixture which the carburettor feeds into the engine.

These instruments have already been described in a publication (vide List of References (i)), but since they are of growing interest, especially for aviation, some further research as to their merits and shortcomings seems to be indicated.

Therefore tests have been run with an aircraft type of instrument (the “ Cambridge (N.Y.) Aero Mixture Indicator ”) and an automobile type of instrument (the “ Lantz Phelps Motor Fuel Combustion Tester ” ).

The rapid progress made in mechanical engineering during the present century has brought many troublesome problems in its wake. One of the most serious of these troubles arises from resonant and such like vibration. It has, therefore, become increasingly necessary for a designer to take account of vibration. A powerful instrument for this purpose was provided by the late Lord Rayleigh, whose method for finding an approximation to the fundamental frequency of vibration of an elastic system is fairly well known. In this paper an attempt is made inter alia to explain Rayleigh's Principle and to clarify, so far as the author is able to do so, the basis of the principle. Other devices for ascertaining approximate frequencies are also given and an appendix has been added on forced vibration experiments.

In a previous issue of this Journal (Vol. 40, pp.663-680, 1936) Mr. N. J. Hoff has investigated the buckling of an elastically encastred strut. The ingenious method used by Mr. Hoff consists in considering portions of various lengths of a rigidly encastred strut which is in a state of neutral equilibrium under the action of its critical compressive load. This load is also the critical load of an elastically encastred strut whose length is equal to the length of the considered portion, if only the rigidities of encastrement are chosen in accordance with the ratios of the slopes of the neutral axis at the ends of this portion to the bending moments there. The total length of the elastically encastred strut does not enter immediately into the formulae derived by this method, there enter only two lengths x1 and xr whose sum is equal to the total length. These quantities are the distances between the ends of the considered portion of the rigidly encastred strut and the middle of its span.