506 Prof. R. Threlfall and Mr. J. F. Adair. On the 



accuracy of this depends, of course, on the accuracy with which the 

 groove is cut, and the accuracy of the equality of the distances 

 between the scriber and the groove and the prolonged axis of the 

 groove and the centre of the axle. Great care was taken to secure 

 these conditions both in the making of the instrument and in the 

 adjusting of the scribing point. The precise estimation in fork-beats 

 of the distance between the breaks in the scriber lines became an 

 easy matter with this table. 



The plate was dropped into the recess, and by means of the sliding 

 scriber two lines were drawn through the fork-line, each correspond- 

 ing to radii of the pendulum and each passing through its appropriate 

 epoch mark on one of the scriber lines. The estimation of the exact 

 position of the epoch mark was not easy at first, owing to the slow 

 motion of the scribers. Finally, however, by making the battery 

 very strong, the springs also strong, the magnets very powerful, and 

 the moment of inertia of the scribers very small, this difficulty was 

 partially overcome. Supposing that the two lines happened to cut 

 the fork-line in exact troughs or crests, nothing more remained than 

 to count the fork-beats. In general, however, this was not the case, 

 and then the following procedure had to be adopted. A sliding-table 

 to carry a measuring microscope was arranged over the plate, and 

 was high enough to clear the radius bar and scriber. The scriber 

 was used to draw four lines in addition to the two marked on the 

 plate already ; the lines so drawn passed through the nearest crests 

 or troughs of the fork-line, between which the line of section lay. A 

 measuring microscope, with a micrometer screw of fifty to the inch 

 and the head divided into a hundred parts, was placed on the table 

 and adjusted by a special square, so as to be tangential to the arc of 

 mean position of the fork at the point where that arc is cut by the 

 epoch line. Sometimes the arc was drawn by the radius bar, the 

 correctness of the setting of the measuring microscope was tested by 

 observing whether the arc left the cross-wires appreciably as the 

 microscope was screwed along. If all was right, three readings were 

 taken with the micrometer, thus — 



First reading, cross-wires on line through crest to right = O. 

 Second ,, „ epoch = P. 



Third „ „ crest to left = Q. 



Supposing the whole number of fork-beats has been so counted 

 that an addition has to be made at each end to get the true length, 

 we have : if T be the whole time required, r the fork period, n the 

 whole number of beats, A and A' fractions of beats, 



T = w+(A + A')t. 



Let 0, P, Q be the micrometer readings as above, then — 



