1889.] 



On the Cavendish Experiment. 



261 



submit to the Society is nearly five times as great as the distance 

 in plan between the two small balls. 



In order to realise more fully the effect of a variety of arrange- 

 ments, I have, for my own satisfaction, calculated the values of the 

 deflecting forces in an instrument in which the distance between 

 the centres of the attracting balls is five times the length of the beam, 

 for every azimuth and for differences of levels of 0,1, 2, 3, 4, and 

 5 times the length of the beam. 



This calculation is very much facilitated by the property of the 

 circle illustrated in fig. 4. If the diameter is divided into any number 

 of equal parts, and perpendiculars drawn to cut the circle, then the 

 squares of lines drawn from any one of the points on the diameter to all 

 the intersections (including the two ends of the diameter) are in arith- 

 metrical progression, and the common difference is equal to twice 



Fig. 4. 



ililWi 



h o cc M 



the number of parts included between that point and the centre. If 

 the diameter is divided into ten parts, a and b are the positions of the 

 ends of the beam, and the semicircle is the path of the centre of the 

 large mass. When this is at any position P the resolved force at a 

 is equal to PM/Pa 3 . Now all the quantities PM 3 and Pa 2 are small 

 whole numbers, and the squares of the true distances of Pfrom a when 

 a is at different levels are small whole numbers also, so that all the 

 logarithms can be found on the first four pages of Chambers's tables. 

 It is for this reason that it is most convenient to represent the result 

 of the calculation on a diagram in which the abscissae are the projec- 

 tions of the centre of the attracting mass on a plane passing through 

 the centres of the small balls. 



In fig. 5 the dotted circle represents the possible positions of the 

 centre of the attracting mass, and a, b the small balls. The heavy 

 Curve 1 shows the value of the moment due to the ball a alone. The 

 reversed Curve 2 in the same way shows the moment of the ball b in 

 the opposite direction when that ball is at the same level as a. The 

 Curve 3 is the difference between these two, and from this actual 

 resultant moments may be found. The maximum of this curve is in 



