266 



SCIENCE 



[N. S. Vol. XLV. No. 1159 



(3) 



-*{(-5)£-('+S)f}- 



The term in D increases rapidly. 



Another approximation which is perhaps 

 equally good is much simpler. This consists 

 in regarding the angle as the mean of 0' 

 and 9" in Fig. 1; whence 



e = kxID. (4) 



Here h is constant and 



_ ,x fx b\ 

 '~''d\x DJ- 



(5) 



Values so obtained are usually too large and 

 increase in the lapse of time, whereas values of 

 equation (3) decrease. 



4. Experimental Reduction. — The difficulty 

 in correcting the results in x by the equation 

 given makes it desirable to standardize the 

 apparatus directly. This may be easily done 

 by aid of a horizontal arm AA, Fig. 2, carry- 

 ing two fine vertical wires s, s' at a distance 

 £) = 25 cm. (average arc above) apart, rotating 

 around an axis C over a graduated circle (not 

 shown). The axis C is to coincide with the 

 string of the pendulum. Fig. 1, and the lens L 



to correspond as before to the conjugate focal 

 distances u and v. In this way the angle 6 is 

 directly determined in terms of x at the screen 

 8, apart from all optic considerations. For 

 the dimensions given, s and s are adequately 

 focused at 8. The data show that within an 

 angle less than 10°, $ may be regarded as pro- 

 portional to x/D. 



This method reproduces the actual condi- 

 tions under which pendulum observations are 

 made and there seems to be no reason for 

 calling the result in question. 



Another method consists in finding the mag- 

 nification by placing a millimeter scale at C, 

 Fig. 1, and measuring its image x at 8. 



Both these methods have an advantage, as 

 they admit of reducing the individual x, D 

 values to $ values, without requiring differ- 

 ential coefficients. 



5. Ohservations. — The first experiments were 

 made with an ordinary plumb bob somewhat 

 lighter than a pound, swinging from a silk 

 thread over 4 meters long. Fair results were 

 obtained but the light bob is not always trust- 

 worthy. An example which must suffice here 

 is given in Table I. for an unnecessarily heavy 



