Wave-length of Light, 273 



measurements regular and linear, and during part of the 

 time was placed directly over the grating to give a check on 

 the attached thermometer. This expedient was finally aban- 

 doned as unlikely to be of much use. 



The corrections for temperature were deduced from the 

 assumed coefficient of expansion of glass, which was taken as 

 0*0000085. This was reduced to angular correction for the 

 approximate value of <fi, and applied directly to the observed 

 angles. Since the temperatures at which observations were 

 made varied little from 20° C, and were quite equally distri- 

 buted on both sides of that figure, any error in the assumed 

 coefficient would hardly affect the average result, but would 

 appear, if at all, as a slight increase in the probable error. 



760 milliin. (reduced) was taken as standard pressure, and 

 the values for the days of observation were taken from the 

 U. S. Signal- Service observations for the hours of 11 A.M. 

 and 3 p.m. on those days. The average for the measurements 

 made with grating I. was 761 millim., and for those with 

 grating II. 760 millim.; so that corrections for pressure were 

 uncalled for. 



The effect of the velocity of the apparatus through space is 

 a subject concerning which there has been much discussion. 



Angstrom deduced a correction ; but Van der Willigen, in 

 quite a lengthy discussion of the whole matter, came to the 

 conclusion that there was no error due to the above cause. 

 Since that period the question has been raised from time to 

 time, but no decisive investigations on the subject have yet 

 been published. At present, however, it seems to be tolerably 

 well settled that no correction is needed, as the error, if there 

 be any, is of an order of magnitude entirely negligible, and 

 in the present paper none has been applied. 



The angular measurements, after all corrections were ap- 

 plied, may thus be regarded as determined with a high degree 

 of accuracy — most probably to less than one part in half a 

 million. 



Measurement of the Gratings. 



The exact determination of the grating-space is by far the 

 most difficult portion of a research on absolute wave-length, 

 and has been uniformly the most fruitful source of errors. 

 Besides the experimental difficulties of the task, it is far from 

 an easy matter to secure proper standards of length. The 

 standards used in various former investigations have proved 

 to be in error, sometimes by a very considerable amount ; and 

 indeed very few of the older standards are above suspicion. 

 As Peirce has very justly remarked in connection with this 



Phil. Mag. S. 5. Vol. 23. No. 142. March 1887. U 



