MR. A. FOWLER ON THE SPECTRUM OF MAGNESIUM HYDRIDE. 



455 



As the spectra were not normal, interpolations were made by equations of the 

 form 



X = a+bs + cs?, 



where X and s refer to corresponding wave-lengths and micrometer-scale readings, and 

 a, b, c are constants calculated from three of the standard lines. All the standard 

 lines might be made to contribute to the adopted values of a, b, c by the laborious 

 method of least squares, but the gain was found to be scarcely appreciable in a case 

 to which it was applied. 



The following example, taken from the measurements of a second-order photograph 

 of the green fluting, will show the accuracy with which the dispersion of the grating 

 over a moderate range may be represented by the above equation. It will also 

 indicate the increased precision which is made possible by the new interference wave- 

 lengths for the iron arc lines as compared with the use of ROWLAND'S values for the 

 absorption lines of iron which occur in the Fraunhofer spectrum. 



Equation for FABRY and BUISSON scale : 



X = 52GO'520-2-G75<)5s-f 0-000136*-. 

 Equation for ROWLAND'S scale : 



X = 52GO-G78-2-67544.s- + 



0-C. 



000 

 -004 

 + 002 

 + 005 



000 

 + 004 

 -001 

 -003 



000 



An alternative method of reduction was employed in duplicating the work for the 

 detection of numerical errors. In this case, the two extreme iron lines in each section 

 of the spectrum were employed as standards for the calculation of linear equations, 

 and from the values of O C for the intermediate standards, curves of error were 

 drawn, t from which the corrections to normal were readily derived. Numerous 

 additional checks were also made by simple linear interpolations between iron standards 

 not more -than 40 tenth-metres apart. 



In spite of every precaution, some of the grating photographs showed small 

 displacements of the magnesium spectrum with reference to the iron comparison, 

 probably arising from the effects of varying temperature during the longer exposures. 



