420 E. Merritt — Certain Peculiarities in Behavior of a 



needle into its angular acceleration, and thus lead to the fol- 

 lowing equation of motion : 



Mp! -S- +L ^ +Ne=QT ° (1 -*" i,) (2 



The solution of this equation consists of two parts : (1) the 

 general solution of the "complementary equation " obtained by 

 equating the left hand member to zero ; (2) a special solution 

 of the complete equation. The first is readily seen to be the 

 ordinary expression for the motion of a damped needle : 



(— + v < 3 



while an easy application of the symbolic method to the com- 

 plete equation gives the following special solution : 



N Mp 2 & 2 -L& + ;N l 



The complete solution of (2) is the sum of these two parts, 

 and when simplified by the substitution of single letters for 

 the complex coefficients that arise during the integration, gives 

 the following expression for 6 : 



6= C f* cos ( — +<p\ — m T o £~ M + 1 T . (5 



The two constants of integration C and <p are determined 

 from the consideration that when t is equal to zero, both 6 and 



dO 



- T - i are also zero. 

 a t 



I — m ™ l—m 



COS(p= -^— . T = -jy-. 



It will be observed that all the coefficients in (5) contain T 

 as a factor, while <p is independent of T . The equation may 

 therefore be written : 



6 = T o \c e- u cos (— '+ cp\-m e~ u + l\ (6 



The motion represented by this equation evidently possesses 

 all the characteristics of that shown in fig. 1. It may be 

 looked upon as resulting from the combination of two motions, 

 one of them being a steady increase of deflection in accordance 

 with the logarithmic curve represented by the last two terms 

 of the equation, the other a motion of oscillation with grad- 



