in Pendulums for Gravity Measurements. 145 



formed by the intersection of two perfectly plane surfaces, a 

 condition which can never be quite realized in practice. It is 

 important, therefore, to inquire how it may be most nearly 

 approached and especially by what disposition of parts, both as 

 to form and arrangement, a given departure from it will pro- 

 duce the minimum effect upon the period of the pendulum 

 and upon the value of the force of gravity obtained by its use. 



What is believed to be an important departure from the 

 universal practice in regard to the arrangement of parts has 

 recently been experimentally investigated and with very satis- 

 factory results. It consists in an exchange in place of the 

 knife-edge and plane, the latter being attached to the pendu- 

 lum and the former to the fixed support. This arrangement 

 offers many advantages to which it is desirable to invite atten- 

 tion. It will be best, however, to refer in the beginning to 

 what will at once suggest itself to many as a serious objection 

 to this plan. When the knife-edge is attached to the pendu- 

 lum it may be assumed to have a constant relation to its mass, 

 at least so long as the pendulum does not suffer an injury 

 which alters its configuration. The axis about which vibra- 

 tion takes place may therefore be regarded as constant as 

 far as relates to different sets of swings, and it will be prac- 

 tically indifferent as to what part of the supporting plane it 

 rests upon. When the plane is attached to the pendulum this 

 axis of vibration is entirely determined by the position of the 

 plane upon the knife-edge. 



This difficulty, which at first sight appears to be formidable, 

 readily disappears in practice. In fact, a little calculation will 

 show that the line of contact between the knife-edge and the 

 plane must vary in position by a relatively large amount in 

 order to effect sensibly the period of the pendulum. Even if 

 the placing of the pendulum for successive swings were accom- 

 plished by no more accurate devices than the eye and hand, it 

 would not be difficult to avoid sensible error from this source. 

 The apparatus by means of which the pendulum is lifted from 

 and lowered upon the knife-edge is readily made adjustable so 

 that any desired line of contact can be secured and retained 

 indefinitely. 



As an illustration of the constancy of period of a pendulum 

 arranged in this way, as well as showing the ease and accuracy 

 with which the period of vibration is ascertained, the follow- 

 ing results are exhibited. 



They show the period of the pendulum derived from indi- 

 vidual swings extending through about an hour each. Twelve 

 such swings were distributed nearly uniformly through a 

 period of twenty-four hours, in order to eliminate any effect 

 of irregular hourly rate of the chronometer. The figures as 



