76 GREAT MEN OF SCIENCE 



originally descended, even when the pendulum during its 

 movement has been subjected to effects which have nothing 

 to do with its weight. Galileo had already convinced himself 

 of this in the case of the simple pendulum, by letting such a 

 pendulum swing both freely and also past a projecting peg, 

 which caught and bent the thread in the course of the move- 

 ment, so that the bob of the pendulum was forced into a new 

 circular path with the peg as centre, from the moment when 

 the thread met the latter. In such experiments the bob 

 never reached a greater height than that from which it had 

 been released, and when it attained a less height, this was 

 obviously only the result of frictional resistances which had 

 nothing to do with the main process. Huygens worked out 

 in an exactly similar manner, by means of an imaginary 

 experiment, the case of the oscillating rod. Imaginary 

 experiments became, after Stevin's time, of ever increasing 

 importance in research, but they must be of a permissible 

 description; that is to say, they must only deal with processes 

 that could be realised with sufficient approximation. We 

 imagine the rod to be let loose and to swing until it reaches its 

 lowest or vertical position, and at the moment when it reaches 

 this, we suppose that the connection between its parts is 

 abolished, so that these now continue to swing as simple 

 pendulums. Even then, the combined centre of gravity of 

 all the parts of the pendulum can only rise to the same point 

 from which it had descended. But the motions of all the 

 parts are known, since they are simple pendulums. These 

 pendulums were released with the velocities which they had 

 at the moment of separation, that is with velocities which 

 were proportional to their distances from the axis of rotation. 

 Hence if one of these velocities is known, they are all known, 

 and the motion of the whole centre of gravity while they 

 swing further as simple pendulums, is also known. The 

 question now to be settled by simple and known processes 

 of calculation is conversely the following: how great must 



