( 238 ) 



second column the values of the tangent v of the angles of incli- 

 nation existing at these moments. 



In the tliird column the values of the product rev are given, 

 calculated in the following manner. 



If of the first part of the curve the concave side is directed 

 upward, the concave part of the second half is directed downward. 

 At the point of inflection ^ =: x. 



Here b}" formula (13) 



r=^ (13) 



cv 



or 



re =— , 



V 



SO that from the values here given for q and z', the value of re 

 can be calculated. For any other point of the curve the constant 

 value re is then multiplied by the value of v for that point. 



In the fourth column the values of q, i.e. the distances of the 

 image of the string from the second position of equilibrium, are 

 given as tiie results of direct measurements. 



In the fifth column the Aalues of q are given as calculated from 

 the formula 



tifl'i — tga 

 q rrz crv -j~ ^"'^ " '' — i (28a) 



while in the sixth column the ditterences between the measured and 

 calculated values of q are given. 



The above formula (28a) requires some explanation. 



.3 



(1 + i-y- 



by 



It is obtained bv replacing in formula (11) the value 



3 



(1 + v'f cP q 



As was remarked above or — — is nothing else but the 



Q dt^ * 



expression for the acceleration. Since we used as the only method 

 for measuring o the measurement of two angles « and j?, see fig. 2, 

 we can also, these angles being known, find an approximate expres- 

 sion for the acceleration by means of their tangents. 



The velocity at the point ji^, fig. 2, is given by tga, at the point 

 ÏU ^\y ty?- '^^^^ difiereuce in velocity is ////? — tga. Assuming the 

 acceleration to be constant during the time vf, it is expressed by 



