PROCEEDINGS OF THE ACADEMY AND AFFILIATED 



SOCIETIES 



THE PHILOSOPHICAL SOCIETY OF WASHINGTON 



The 746th meeting was held on November 21, 1914, at the Cosmos 

 Club, President Fischer in the chair; 31 persons present. 



Mr. W. P. White presented a paper on Electric pendulums and 

 pendulum contacts. Most methods of driving a pendulum can be 

 adequately represented mathematically by supposing that the posi- 

 tion of equilibrium is shifted for a longer or shorter time. If the de- 

 vice acts by means of a spring, it may be necessary also to consider 

 that the periodic time of the pendulum is altered through part of its 

 vibration. The resulting effect upon the motion of the pendulum can 

 very readily be handled by means of the circle of reference. A change 

 in the position of equilibrium is then graphically represented by con- 

 tinuing the line along a new circle whose center is shifted accordingly. 

 By the application of this method it is possible to show that, while a 

 strong impulse communicated to the pendulum as it passes through the 

 equilibrium position is a satisfactory method of increasing its energy 

 without affecting its period, yet the variation of the effect upon the 

 period which may occur as a result of varying amplitude is often less 

 when the pressure is changed from an impulsive one to one acting 

 for half the time of the swing. The two best forms of electric drive 

 appear to be: (1) that in which the drive is purely electric and is due to 

 an induced current which can both be made almost strictly impulsive 

 and very constant; and (2) an electrically operated arrangement in 

 which the pendulum, as it swings, raises and lowers a light weight. 

 The paper was discussed by Mr. C. A. Briggs. 



Mr. E. Buckingham then spoke on The principle of dimensional 

 homogeneity and the form of physical equations. Reasoning based on 

 the consideration of the ratios, in any two stages of a physical phenome- 

 non, of the quantities involved in it as variables, shows that the phys- 

 ical equation which describes the phenomenon by describing the 

 characteristic relation among the quantities, must necessarily have a 

 certain simple general form. This form is dimensionally homo- 

 geneous. No use is made of the other known relations among quanti- 

 ties of the kind in question, so that the result does not depend upon 

 the use of an absolute system of units but is true when the units of 

 measurement are all completely arbitrary and independent. If such 

 relations are utihzed and all measurements are made in terms of abso- 

 lute units, the necessary general form of a physical equation may be 

 still further specified, and it reduces to a form given by the speaker 



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