VALUE OF ACCELERATION OF GRAVITY— MENDEXHALL. 15 



shown by subsequent micrometer measurements. Such measurements showed that when tin- 

 lshed, there was with one ring- a maximum difference of about 0.001 mm. in thickness between 

 extremities of a diameter, and considerably less than this with the other. All the grinding was 

 done wet, and though chatter marks due to vibration of the machine were never eliminated, still 

 they were uniform and fine and the general surface had a surprisingly high polish (see pi. 2). 

 Though the process here described was slow (it took, with the unavoidable interruptions, about 

 a month to "finish." a ring), it proved capable of giving rings of sufficiently accurate figure for 

 the purpose in hand. 



MEASUREMENT OF THE KINGS. 



As before stated, measurements of internal diameter and thickness were made only with ordi- 

 nary micrometer gauges, care being taken about temperature disturbances, hut for the determina- 

 tion of the external diameter a special comparator was constructed. A few words will sufficiently 

 explain the points considered in its design (pi. 3). Since the general plan was to make contact 

 settings on the ring, these to be directly compared with a line-standard meter, the essential fea- 

 tures of the instrument are: A rigid end stop; accurate ways, on winch slide two carriages, one 

 (intermediate) carrying the ring (with its plane horizontal), the other a second end stop, and a 

 microscope focused on the standard bar. The one carriage has a transverse slide carrying the 

 ring, for the purpose of adjusting it so that its center is in line with the two stops. The support 

 is furthermore so arranged that the ring can be rotated around a vertical axis through its center 

 and perpendicular to its plane and to the ways (for testing "roundness"); and a vertical, linear 

 motion along this axis is provided so the diameter may be measured at various points from face 

 to face. The construction is such that to a sufficient degree of accuracy the plane of the ring- 

 is parallel to the ways and to the line of the contact points. The end stops are round steel rods, 

 hardened and ground, two sets of actual contact surfaces being provided, plane and spherical 

 (radius 4 inches). The practice was to have a spherical end abut against a plane face. There is 

 a chance for a constant error to enter here, in case the contact pieces are not symmetrical with 

 respect to the same axis, i. e., do not touch the ring and each other in the same way. Therefore 

 some measurements were also made with two plane faces abutting against each other, and. since 

 they agreed to within the limit of error with those made with one plane and one spherical surface. 

 it was concluded that this constant error was negligible. In general, "touch" contact was used 

 in bringing the ring against the fixed stop and electrical contact (single dry cell and volt-meter) 

 in bringing the moving point against the ring and against the fixed stop. The electrical method 

 is more delicate, but the other is quite satisfactory. During the observations the ring was 

 protected quite thoroughly by asbestos and cotton, and its temperature was given by two ther- 

 mometers resting directly on the upper surface. 



Standard meter. — This was a new nickel-steel bar (H form), by the Geneva society, which 

 had just been calibrated by the National Bureau of Standards, Washington; the corrections 

 determined by them have been applied to all measurements. The temperature coefficient of the 

 bar is so small that no very special precautions were necessary to control its temperature under 

 the conditions of this work. In getting the final corrected value of the diameter, however, the 

 proper correction was applied to reduce the bar interval for the temperature at which it was 

 calibrated (15.9° C.) to the temperature of the measurements (23 c ('.); this involves a slight 

 exterpolation of the temperature coefficient as given by the Bureau (for the interval 10 C. to 

 20° C), but no serious error is in all probability introduced thereby. The observing microscope 

 was of Geneva society construction, with micrometer eye-piece and objective illumination. The 

 micrometer screw was, unfortunately, not a very good one, but by using a group of one-tenth 

 mm. intervals, into which one millimeter space on the standard was divided, these being evaluated 

 by careful comparison with each other and with a known millimeter, it was possible to avoid 

 using any great interval of the screw, so that uncertainties from this source were very greatly 

 reduced. 



