MR, A. E. TUTTON ON A COMPENSATED INTERFERENCE DILATOMETER. 351 



observer would perceive the transit of the bands to the extent indicated by the 

 correction, and in the same direction as the bands move when the two surfaces 

 approach each other ; so that the effect of rise of temperature on the refraction of 

 the air is similar to that produced by approach of the two surfaces. Hence the 

 correction requires to be added when the effect of rise of temperature is to cause 

 recession of the surfaces, and to be subtracted when the surfaces approach each other. 



After the conclusion of the observations of the number of bands which effect their 

 transit for the two intervals of temperature, it is the author's practice to leave the 

 apparatus untouched for about sixteen hours, during which time it regains the 

 ordinary temperature of the air, and subsequently to repeat the whole series of 

 operations and observations for two similar temperature intervals on the following 

 day, and on as many succeeding days as it is desired to make independent deter- 

 minations. After the completion of the series, and the final slow cooling of the 

 apparatus during the night, the measurement of the exact length of the screws of 

 the tripod above the reflecting surface of the table is made, with the aid of the thick- 

 ness measurer. In the case of the determination of the expansion of the tripod, this 

 is the only additional quantity required before being able to proceed with the 

 calculation of the results. 



The full data now available for this determination are as follows : 



Lt lt length of platinum-iridium screws at the initial temperature, t l ; in this case 



= d thickness of air-layer. 



t i} initial temperature ; t 2 , first higher limit, about 70 ; t t , highest limit, about 120. 

 6,, & 2 , &a> corresponding barometric readings. 

 f z , observed number of bands for interval 2 < : . 

 f s , observed bands for interval t 3 t t . 



By means of the correction formula and these data we first calculate f 2 ' and/,', the 

 corrected number of bands for the two intervals. These quantities, when multiplied 

 by ^X, in this case, for green mercury light, 0'000273 millitn., afford the amounts of 

 expansion of the screws, or alteration of thickness of the air-layer for the two intervals 

 of temperature ; and therefrom, by addition to the measured initial length, Lt lt we 

 obtain the lengths Lt 2 and Lt 3 , at the first and second higher limits (near 70 and 

 120) respectively. That is to say, the length of the platinum-iridium screws is now 

 known at three temperatures in the neighbourhood of 10, 70, and 120. 



The author's object in making observations for two different temperature intervals 

 is to be able to determine not only the mean coefficient of expansion between 

 two limits of temperature, but also the absolute coefficient of expansion at any 

 given temperature, and the variation of the coefficient with change of temperature. 

 For it is well known that, in general, the linear coefficient of expansion is not a 

 constant quantity but varies slightly with the temperature ; the increment of the 

 coefficient per degree, however, remains practically constant. If, therefore, the 



