350 ME. A. E. TUTTON ON A COMPENSATED INTERFERENCE DILATOMETER. 



where/' is the corrected number of bands, f the observed number, d the thickness 

 of the air layer, 1 1 and t., the limiting temperatures, and 6, and 6, the corresponding 

 barometric pressures ; a is the coefficient of expansion of air 0'00367, and n the 

 refractive index of air for the wave-length A. of the light employed. The logarithmic 



values of 2 - -" and 2 ~^r can be found once for all ; they are respectively 



3-59901 and 3'15353. The logarithms of the factors :, , and can 



7bU 1 -f- atj 1 + a.t t 



be extracted directly from LANDOLT'S tables. Hence the expression, although 

 apparently long and troublesome, lends itself to very easy computation. For the 

 purpose of the calculation of this correction it is necessary to take the reading of the 

 barometer at the time of making the observation of the exact position of the bands 

 at the initial temperature, and again when they have attained their condition of rest 

 at each of the two higher limits. These barometric observations are of particular 

 importance in the case of the determination of the expansion of the tripod, as the 

 share of the variation of pressure in the correction is then an appreciable one 

 The author employed a standard barometer suspended in the same room. 



With regard to the sign of the correction, the signs given in the above formula for 

 the temperature and pressure portions are the correct ones for use in all cases where 

 the result of the increase of temperature is to effect an increase in the separation of 

 the two reflecting surfaces, as in the case in question of the determination of the 

 expansion of the tripod. In such cases the effect of change of temperature is to 

 cause the number of observed bands to be less than it would be if such a change did 

 not occur. The contrary is the case where the thickness of the air-layer diminishes, 

 as in the cases of the determination of the expansion of an object supported on the 

 tripod table, whose expansion is greater than that of the screws, and in all 

 determinations of expansion involving the use of the compensator. In such cases 

 the signs of the temperature and pressure portions of the above formula should 

 be respectively and -)-. 



The temperature portion of the correction is usually much the larger, and 

 its sign governs that of the total correction. Indeed, in all cases when the 

 air-layer is very thin, the share of pressure can be neglected. Moreover, as 

 will be evident from the formula, the sign of the pressure portion varies according 

 as frj is less or greater than 6 2 . With regard to the sign of the more important 

 temperature portion, the fact that it follows the rule just indicated will be evident 

 from the following considerations. Rise of temperature causes a diminution in the 

 refractive index of the air, and a corresponding increase in the wave-length. The 

 same amount of separation of the surfaces will, therefore, contain fewer wave-lengths, 

 and if no expansion of the tripod and object (if one is being used) occurred, the 



