Wave-length of Light. 267 



work heretofore has been done with the former ; but metallic 

 gratings possess certain advantages, notably from the ease 

 with which their temperature cau be accurately measured, and 

 the fact that they can easily be made of a size much larger 

 than glass gratings, and consequently a small inaccuracy in 

 measuring them involves much less error in the result. 



On the other hand, the coefficient of expansion of speculum 

 metal is more than twice as great as that of glass, and being a 

 good conductor it is far more sensitive to small changes of 

 temperature. And this property increases the liability to 

 irregularities in the ruling, particularly in large gratings 

 which require several days for completion. In ruling on 

 glass change of temperature is less serious, but this advantage 

 is more than offset by the faults caused by the wearing away 

 of the diamond point, which breaks down so rapidly that it 

 is enormously difficult to produce a glass grating free from 

 flaws and at all comparable in optical excellence with those 

 upon speculum metal. The determination of absolute wave- 

 length should rest on measurements made with both classes ; 

 and with sufficiently exact instruments and very careful ex- 

 perimentation, the better results can probably be obtained 

 from the metallic gratings. For the reasons previously stated, 

 this paper is confined to the results from glass ones. 



Now there are two quite distinct ways of using transmission 

 gratings — first, perpendicular, or nearly so, to the collimating 

 or the observing telescope ; and second, in the position of 

 minimum deviation. The method in the first case is familiar; 

 the properties of the second are as follows : — 



The general relation between the incident and the diffracted 



ray is 



. ... /<n .n m\ 

 sin z-i-sm (o— i) = — . 

 a 



When i=0°, this gives the ordinary formula for normal in- 

 cidence. Putting it in the form 



. 2(a) .8 {. 8\ 



the deviation represented by the angular term will evidently 



be a minimum when i= ^ ; and the wave-length will then be 

 It 



given by the formula 



« 2(a) . 8 

 X= -^ sin Ti . 



m 2 



It is not easy to say which method of procedure is prefer- 



