148 T. C. MendenhaU — Use of Planes and Knife-edges 



planes forming the edge made with each other was 110°. The 

 edge was first ground until it was pronounced as perfect as was 

 practicable by the artist, Mr. E. G. Fischer, chief mechanician 

 of the Coast and Geodetic Survey, who has shown rare inge- 

 nuity and skill in the solution of the mechanical problems 

 arising during the investigation. The width of the edge was 

 then measured, using a microscope magnifying from 100 to 

 500 times. This was a difficult operation, the question of 

 illumination being troublesome. It seemed tolerably certain, 

 however, that the width of such an edge was not greater than 

 l'" ( - 001 mm ) Several different edges ground in this way were 

 measured with essentially the same result. After the vibra- 

 tion period on one of these had been ascertained it was given 

 one or two light touches upon the stone, producing an edge 

 which was found on measurement to be approximately 2*" in 

 width. After the pendulum had been swung on it it was still 

 further flattened. 



Theory shows that a pendulum will vibrate more rapidly 

 upon a slightly flattened or rounded edge than upon one which 

 is perfect. The table below shows the results of experiment 

 conducted as above described. The pendulum used was one 

 of the short, approximately half-second, pendulums of the form 

 referred to a year ago.* The numbers showing the width of 

 the knife-edge must be regarded as approximations only but 

 they are probably relatively not far from correct. 



They indicate very clearly and positively the important part 

 pla} 7 ed by the knife-edge and the importance of having it per- 

 fectly ground. There is good reason to believe that this mat- 

 ter has not hitherto received that attention in pendulum 

 researches which it is here shown to demand. While the 

 effect of a given amount of flattening on the vibration-period 

 would be less with a long seconds pendulum than with one of 

 shorter period, the tendency towards flattening, arising out of 

 greater weight and greater difficulty of handling would be 

 very much increased. There is no doubt that in some im- 

 portant gravity operations knife-edges have been used which, 

 in the light of these results must be considered intolerably 

 poor. It will be observed that going from what may be 

 accepted as a practically perfect edge to one only one two- 

 hundredth of a millimeter wide, changes the period by one 

 part in forty thousand, an amount entirely outside of a reason- 

 able limit of accuracy for work of this kind. 



The question of the best angle for the knife-edge is also 

 important and interesting. If the material of which the edge 

 is composed were physically perfect and if the faces were 

 perfect planes all angles, within certain wide limits, would be 



* This Journal, February, 1892. 



