539 



dy 



-^ and on llie other hand hv the tangent of the ano,-le CMO, coiise- 



dx .o o ' 



qiiently by . 



As the tangent at any point of a parabola is expressed by 



% _ J(_ 

 dx 2x 



we get for the slope at tlie end of the string, where y =z — / and 



A 

 ÜJ := h: 



dx Ah 



As CO represents half the total lateral strain, consequently — Z 



Li 



and OM the total longitudinal strain P we may write: 



The longitudinal strain of a string can be found from the formula 

 for the vibration-frequency of a stretched string, given in Kohlrausch's 

 Handbuch der prakt. Phys. (11^'^ edition p. 245) : 



in which N represents the frequency per second, / the length in 



meters and p the weight of 1 m. of wire. We obtain from this for (he 



tension 



ANH'^p 



P= -. 



9.81 



By substituting this value of P in the equation for the latei-al 

 pressure, we find : 



_ Sh ANH'p 



which value may be equalled to the lateral pressure calculated before : 



I 9.81 



As HI! indicates the pressure in dynes, j), the weight of 1 m. of 



string, must likewise be expressed in dynes, thus: 



p z=: 9.81 jtr^fj. 



We obtain finally after this substitution : 



32 N'hjir'g 



H = — — '- . 



] 



35 



Proceedings Royal Acad. Amsterdam. Vol. XVI. 



