716 PROCEEDINGS OF THE AMERICAN ACADEMY. 



of a second. Five such measurements were made on different parts of 

 at least three different tracings for each case discussed, so that each of the 

 observed ratios in Table III depends on fifty measurements of each of 

 the quantities involved. This labor seemed to be necessary because, 

 under high magnification, the tracing itself was so wide as to make the 

 setting corresponding to a given vertex somewhat uncertain, and also 

 because it was hoped that this averaging would eliminate the effect of 

 local variations in the time scale of the slide due to any transverse or 

 torsional vibrations that might be present. As a matter of fact such 

 vibrations caused surprisingly little trouble even when the bridge was not 

 used. 



Three other sources of error were constantly in evidence. In the 

 first place, it is assumed above that the vertical cross-hair is perpen- 

 dicular to the axis of the screw, and an error of one degree in this 

 adjustment might, under unfavorable circumstances, cause an error of 

 more than two per cent in the observed ratio. 15 Eighteen sets of obser- 

 vations on photographic reductions of a carefully prepared drawing 

 showed that the angle of error was actually about 40' and its effect has 

 been allowed for when necessary. A second error is involved in the 

 orientation of the slide itself with respect to the axis of the screw. 

 This was harder to allow for, but the adjustment could be made with 

 considerable accuracy, and furthermore the resulting error would be 

 somewhat diminished when the results for five tracings were averaged. 

 And finally, it was difficult, with the comparatively crude apparatus 

 which was used, to be sure that the slide was moving perpendicularly to 

 the motion of the wire when the tracing was made ; but in getting slides 

 for measurement, this adjustment was repeated for each line, so as to take 

 advantage of the averaging process already mentioned. Fortunately the 

 resulting error in all three cases varies directly as the ratio of the ampli- 

 tude of a tracing to the apparent length of its period, and in all cases 

 this ratio was made very small by increasing the speed of the slide when 

 the tracings were made. 



Under the circumstances the agreement of the observed with the 

 predicted values is reasonably satisfactory, the average departure being 

 0.8%, or, if account be taken of sine, —0.1%, while the average of 

 the probable errors of the individual determinations is 0.5%, It is 

 evident that Kriger-Menzel's law holds for the longitudinal vibrations 



15 One advantage of the method of section 2 is that it involves the versed sine 

 of the corresponding angle of error rather than its sine. 



