42 R. G. WEST ON LISSAJOUS' CURVES. 



told by one of the leading opticians in London that, as a matter of 

 fact, they are not uniform. If this be so, it would seem that there 

 has been some waste of discussion upon them. If they are uniform, 

 it is surprising that M. Nobert should not have published the autho- 

 rised version of their various scales, which his machinery would 

 enable him to supply. There are two papers on Nobert's plates 

 which are of much interest, the latter from the mechanical, rather 

 than the optical point of view ; one by Mr. J. A. Brown, F.R.S., 

 read before the Royal Society, and reported in No. 163 of its Pro- 

 ceedings, extracts from which paper are given in the " Monthly 

 Microscopical Journal" for June, 1876 ; the other, a paper by Mr. 

 Wm.A. Rogers, in the "Monthly Microscopical Journal" for August, 

 1876. Mr. Brown gives elaborate measurements taken from paper- 

 photographs produced by Dr. E. Curtis. From these it would 

 seem that in the 15th band the widths of the lines, and of the spaces 

 between the lines are equal, viz., the yWa^o^h mc h. Materially finer 

 lines than these cannot, it is said, be drawn under M. Nobert's 

 pressure without the graving-point sliding into the previous grooves. 

 Mr. Rogers' estimate of the width of the lines in the 19th band is 

 iiwoo^ 1 inch, his own finest rulings being the TB a th inch wide. 

 Mr. Brown quotes the statement that lines T 6 ' th inch are visible 

 with a power of 125, and countable with a power of 160 (the stand- 

 ard of comparison with the naked eye being taken at eight inches). 

 Mr. Rogers gives the eye much greater power. He states that a 

 single line, 3 ^gth inch wide, filled with plumbago, can be seen at seven 

 inches from the unaided eye, or, if reflected irom a silvered surface, 

 at 11 inches. The former distance gives an angle of vision of 1" ; 

 the minimum angle being, according to Dr. Royston-Pigott, 

 6", and, according to other writers, 1' to 2'. Mr. Rogers places the 

 limit of visibility beyond the -^ Jo^tli inch. He says that he despairs 

 of ruling 100 consecutive lines with a less error, individual or accu- 

 mulated, than the ^oaoo^ 1 mcn j an( l puts the usual range of error in 

 stage-micrometers at from goVo^ 1 ^ loljou^h mc h> which seems high, 

 especially if referring to the thousandth divisions. He also speaks 

 of a grain in polished crown glass which causes lines sometimes to 

 become enlarged in width, and sometimes to become serrated at the 

 edges — if 25,000 to 30,000 to the inch, at once; if of coarser 

 ruling, after a time. In two instances the disruption occurred under 

 his actual observation. 



Such merit of fineness or delicacy as may attach to the tracings 



