378 WEIGHING THE EARTH. 



times the quantity of matter in the earth is greater than 

 that in the sliell. 



To obtain this ratio of times within a reasonable period 

 to any serviceable degree of accuracy, we must adopt 

 methods of measuring the difference of rates of the 

 pendulums by the smallest possible parts of a second. 



If the pendulums he arranged to swing in vertical 

 planes at right angles to each other, and if plane mirrors 

 be attached to them, we can optically combine their 

 movements, which combination can be shown to result 

 in an elliptical movement — at quarter phase the axes of 

 the ellipse correspond with the directions of vibration 

 of the pendulums, and their lengths with their effective 

 amplitudes of movement. . The changes of form and 

 position of those axes vary wdth the change of phase, and 

 this can be measured to small fractions of a second by 

 means of photography. 



By a suitable arrangement of things, cross wires can be 

 projected upon a very large screen, and can be instantly 

 photographed by means of an electric spark automatically 

 made by one of the clocks. 



Carefully adjusted diagrams and measured parts 

 would enable us to measure the loss of the internal clock 

 to many thousandths of a second. 



In some period between three and four years there 

 are just one hundred millions of seconds; the clock, whose 

 time is representative of the denominator of the fraction 

 which is the desired ratio of times, could be made to 

 exactly, after registering that number of seconds, record 

 the exact difference of time, at least to within the limits 

 of the possibility of optics, electricity and photography. 

 The pendulum completing the electric circuit at its lowest 

 and fastest position of movement, thus insuring the 

 greatest accuracy of time. The result would be the ratio 

 of times as a decimal fraction, i.e., in its most calculable 

 form. 



After explaining the general plan of my scheme, many 

 points of detail require attention. 



Since such extreme accuracy in the synchronising 

 of the pendulums is necessary, this must be especially 

 referred to. There can be no real synchronising unless 



