Apbil 15, 1910] 



SCIENCE 



589 



Ore ihe Determination of Latitude and Longitude 

 in a Balloon: Professor C. Rusge, of the Uni- 

 versity of Berlin. 



The Ruling of Diffraction Gratings: Professor A. 

 A. MiCHELSON, of the University of Chicago. 



On Certain Physical Hypotheses sufficient to ex- 

 plain an Anomaly in the Moon's Motion: Pro- 

 fessor E. W. Beowi^, of Yale University. 

 Professor Guthe's address has been printed in 

 full in Science, January 7, 1910, and an abstract 

 of that of Professor Eunge is printed in Science 

 for January 28 (Report of Section A). Abstracts 

 of the other two are given below: 



Ore tlie Ruling of Diffraction Gratings: A. A. 



MiCHELSON, University of Chicago. 



The difBculty with the echelon and other inter- 

 ferential methods of great resolving power lies in 

 the large number of overlapping spectra. In the 

 grating great regularity in spacing is required if 

 high resolving power is sought. The use of the 

 cadmium red line makes it possible to secure the 

 needed regularity in spacing, since the alterna- 

 tions of dark and light interference bands can be 

 observed through 250,000 wave-lengths. 



After long labor it has been found possible to 

 make gratings as efficient in resoh'ing power as 

 are the echelon and other interferential apparatus. 

 An idea of the accuracy required is gained from 

 the' consideration that errors must not exceed 

 ,00001 inch when not systematic; if they are sys- 

 tematic much greater accuracy than this is nec-es- 

 sary to avoid "ghosts," say to .000001 inch. 

 The best screws when they come from the lathe 

 have errors of about .001 inch. By grinding, say 

 a month, with a special nut, these can be reduced 

 to about .0001, and by further labor to .00002 

 inch. Beyond this, local processes of correction 

 become necessary. 



To secure gratings of sufficient length for the 

 great resolving power desired, it was necessary to 

 use a screw three times as large as that used in 

 Rowland's machines. His method of grinding was 

 tried for a long time without securing satisfactory 

 results. By the use of a grinding nut cut into 

 three parts and with very fine emery success was 

 finally reached. The use of too coarse emery in 

 order to save time caused the wearing out of one 

 screw before its errors were removed. Attempts 

 to grind under oil and tinder water were made, 

 but given up. Finally the following method was 

 used: grinding for several months with the nut 

 kept wet with soap and water; errors were then 



determined with the interferometer; then a cor- 

 recting nut with an arrangement for rubbing 

 harder on one side of the thread than the other 

 was applied. In this way the errors were brought 

 down to about .000002 inch. (The method for the 

 final correction was also described.) 



To work in the second-order spectrum 250,000 

 lines, or a grating fifteen inches long, was needed. 

 To secure necessary rigidity in a screw long 

 enough to rule this length, it must weigh thirty 

 or forty pounds. Nine tenths of this weight was 

 sustained by floating on mercury. Steel can not 

 be used for the nut; a yielding material is re- 

 quired. Wood was used, as by Rowland. As great 

 accuracy of ways is necessary, one bearing surface 

 only was used instead of four as in a lathe. 

 Great trouble was found in securing suitable 

 diamonds for ruling. No difficulty was found the 

 first year, after that not a good one was found 

 for sis years. Finally through Sir Wm. Crookes 

 a satisfactory diamond was obtained from a cer- 

 tain mine which yields extra hard stones. To 

 prevent undue wear very light pressure only on 

 the tracing point was used, and the ruling subse- 

 quently deepened by etching. Only flat gratings 

 have been ruled, as these can be made of higher 

 accuracy than concave gratings. 

 Ore Certain Physical Hypotheses sufficient to ex- 

 plain an Anomaly in the Moon's Motion: 

 Erin-est W. BEOwrr, Yale University. 

 Newcomb has shown that there is a difference 

 between the observed and theoretical positions of 

 the moon which can be roughly represented by a 

 term of period about 270 years and coefficient 13". 

 In the paper the author has examined numerous 

 hypotheses sufficient to explain the term, in order 

 to clear the groimd of those which seemed to be 

 of doubtful value and to bring forward those 

 which appeared sufficiently reasonable to merit 

 tests from observations of a different nature* 

 Some account of three of these hypotheses was 

 presented to the meeting. It was stated that a 

 minute libration of the moon would be sufficient, 

 provided it took place in the moon's equator and 

 had the proper period. The supposition of mag- 

 netic attraction practically demanded (a) a 

 periodic change in the magnetic movement of the 

 earth or of the moon. If (a) were rejected, it 

 was necessary to suppose that the mean place of 

 the lunar magnetic axis was near the lunar equator 

 and that the oscillations of its position took place 

 in the plane of the equator. The observed secular 

 change of the earth's magnetic axis could not 



