13 



■ •!• iiii|iossil)ility of knowiii,^ exactly tlie teuii)eriiture of liis <<iatiug. Tu tlir use 

 of a traiisi»,ir('iil giatiii«^ i( is not easy to sco how its teiii|)eriiliiiv touKl In- 

 ineasiiri';!, lnit tlieie exists (lie eoniiieiisatioii (liafc the uo-elHuieiil of e\i)aiisiini 

 i.|' L^la-^s is SI) much less than that of a iiictallie reflector that it heuoines less 

 iiniMirtaiit. In these iiieasureiiieiit.s a siiinU rectangular vessel of thin eopiicr 

 was sealed to the grating which itself fonned-one side of the cn[) thus formed. 

 Tiiis Wius tilled with water in which a small theniionieter was constantly ininiersiHl. 

 As the changes in teiujieratiu'e were never very r.i|iid tliu irailiiigni' tlii< tnunnn- 

 meter can dilRr hut little from the trne temp 'ratun: of the grating, 'i'lir 

 tlu-rnioiueter w;is compared with a standard and tahlo of corrections prepared. 



As far as I eonld learn in the beginning, no determination had been madi' 

 o| till- co-efficient of expansion of the alloy from wliiih these gratings are made 

 A scries of oh.-icrvations was therefore undertaken, for the jiurpose of ascertaining 

 tliis from the grating itself hy means of angular measurements male u]>on tin- 

 same line at dilfereut temperatures. If we take the cnuatiun — 



/. = s sin 1) 



in which /. represents wave length, s the grating space and h tlie angle of <levia- 

 tion. we ohtaiii l>v ditlerentiatin^- 



./,s 



= — cot I) (( b 



W'lien till- ini'remeul of tcmperatuie is l^ the Id'i iiiud ini-iiiliri- npri'sciils the 

 co-e(Hcicnt of expansion. It will thus he seen that this can he determined with- 

 out any knowledge of the wave length of the line set upon or of the value ol' 

 the grating sp.iee. In the first series of experiments an attempt was mad<' to 

 e.irry the grating alone through a range of T;" or 10'''' of temperature, that of 

 the surrounding air remaining sensibly constant. The grating was made to 

 take the place of one side of ii wooden box which was tilled v/ith water wllo.^e 

 temperature was clianged (uj desired. It was found to be diliicult to pivvent a 

 slight shifting in the position of the grating, due to the changes in tenipei:it ure 

 of the box ami its su|i|)ort on tlie table of the spectrometer, and the tempiMalure 

 eould not be maintained constant for a suHicient length of time to enable obser- 

 vations to be made on both sides of the collimator so that the effect of this 

 sliglit change in posit iun might be eliminated. And liesides, the dilfevence of 

 teinjM'riiturv- betw(!<'n the two faces of the grating cau.sed it to warp slightly 

 which injured the delinition if it did n<(t otherwise interfere with the accuracy 

 of the results. In a brief artiele in the Aiin'iiritii ./niiriinl nf Sr'nnn' for 

 March |S,SI, I described this mode, of making tin- determination and gave the 

 results of a serii-s of ineasureinenls. Tlio objections to the methods were at 

 that time fully ujipreeiattMl ami ii more reliable process wjus indicateil. 'V\\r 

 opinion was also stated that the result there given was move likely to be too 

 lii'^li tlian too low. In fact when 1 came to ap])ly this correction to the regul.ir 



