10 



The angle «5 will always be small ; in Angstroms 35 observations upon the E 

 line, the only ones given in full in his memoir, its value w.is generally less than 

 3', reaching nearly 11' in one case however. Assuming ') = sin ') ami ens ') = 1 

 anil expaniliiig the above, we have 



tan <p = :, . o 



1 — CdSj' 



from which (p is compiiteil. 



The relative merits of these methoils in any particular case will (le[)i'ni1 

 largely, of course, on the construction of the instruiuMit anl the nxturj of th:j 

 grating with which the work is done. Thus, in tlvj present instance, the instru- 

 ment does not adapt itself readily to the use of the second method and I do not 

 know that it possesses any particular advantages over the first. The grating used 

 prevents the adoption of tlie fourth method, besides it is uiinejessary to resort to 

 the approximation which forms a part of the process of reduction in the use of 

 that method. The choice, therefore, seems to lie between the lir.-^t and third. 

 From a theoretical stand point tlie third method is by far the most tempting of 

 all and it certainly offers many advantages. Among these may be mentioned 

 the fact that the mass of matter to be moved in the process of making a measure- 

 ment is reduced to a minimum, being only the circle and the grating upon it. 

 This motion is also generally much smoother than that of the telescope or 

 collimator and hence, more completely under the control of the observer Thus 

 the settings will be easier and possibly more precise. Another great advantage is 

 that as the grating has a movement independent of the circle the method of 

 repetition may be introduced. The angle a is measured very easily by first mak- 

 ing the grating normal to the tele.scope, by the aid of the collimating eye-piece, and 

 then turning the grating until the image of the slit is bisected by the cross-wires. 



In spite of the numerous attractions offered by this method it was very 

 reluctantly rejected, after several hundreds of observations had been made for 

 purposes of comparisou between it and the first, and the latter was accepted as, 

 on the whole, more accurate. There are several objections to the third method, 

 not at first a[)parent, but which became evident during its use. One of these 

 was that it was found to be impossible to rely ujjon the constancy of the angle 

 between the telescope and collimator. Sometimes a change would appear to 

 occur suddenly and the magnitude of the change was often so great as to produce 

 a decidedly sensible effect on the resulting wave-length. I attribute these changes 

 to the effects of change in temperature upon various parts of the instnuuent; a 

 sudden shifiing taking place when the stress due to expansion reaches a certain 

 amount. Of course the real movement is exceedingly minute but it is sufficient 

 to produce a perceptible effect on the angular measurements. The existence of 

 these changes renders freipient measurements of the angle between the telescope 

 and collimator necessary. As the collimating eye-piece is a necessity in these 



