Wave-length of Light . 269 



these experiments. They are both ruled upon plane sextant 

 mirrors, and are of very nearly the same size — thirty milli- 

 metres long, with lines of about nineteen millimetres. Each 

 hundredth line is longer, and each fiftieth line shorter, than 

 the rest ; so that the gratings are very easy to examine in 

 detail. The ruling of both is smooth and firm, without breaks 

 or accidental irregularities, and almost without flaws. They 

 were ruled at different temperatures and on different parts of 

 the screw; and while one was ruled with the ordinary arrange- 

 ment of the engine, the other was ruled to a very different 

 space by means of a tangent-screw. This great diversity of 

 conditions in the two gratings is far from favouring a close 

 agreement in the results ; but tends to eliminate constant 

 errors due to the dividing-engine, and hence to increase the 

 value of the average result. It must be remembered that 

 two gratings ruled on the same part of the screw are in most 

 respects little better than one. The grating designated I. in 

 this paper contains 12,100 spaces, at the rate of very nearly 

 400 to the millimetre, and was ruled (by tangent-screw) at 

 a temperature of 6°*7 0. in January 1884. It gives excellent 

 definition with almost exactly the same focus for the spectra 

 on either side, and is quite free from ghosts or other similar 

 defects. 



The grating designated II. has 8600 spaces, at the rate of 

 about 7200 to the inch, and was ruled in November 1884, 

 at 11°' 6 C. Its definition and focusing are very nearly as 

 good as in I., and, like it, it shows no trace of ghosts or false 

 lines. They are both exquisite specimens of the work which 

 Prof. Rowland's engine is capable of doing, though, as the 

 event showed, I. is decidedly the better grating, in the 

 matter of regularity of ruling. 



Angular Measurements. 



At the beginning of the work a serious question of adjust- 

 ment arose. There are two ways of using a grating perpen- 

 dicular to one of the telescopes. In the first place it may be 

 placed and kept accurately in that position ; and, secondly, it 

 may be placed nearly in the position for normal incidence, 



and the error measured and corrected for. Angstrom used 

 the latter method, which involved a measurement on the 

 direct image of the slit as well as on the lines observed. 



Using Angstrom's notation — let a and a! be the readings on 

 the spectra, and M that on the slit. Let also 



— M = A and — - — = (p. 



