PETERS: MEASUREMENT OF SMALL DILATATIONS 283 



the reference marks at A and B. The change in these differences 

 of order is then 



(02 — bo) — (oi — bi) 

 and the relative change in the length of A and B is 



AA -AB = ^ [(a, - 62) - (ai - b,)] (4) 



Similarly, the relative change in the length of A and C is 



AA - AC = ^ [(a2 - C2) - (ai - Ci)] . (5) 



If AA is known or has been obtained from the determination of 

 (do - Gi), equation (i), the value of B and C can be com- 

 puted from these relations. 



The arrangement of the apparatus just described was used 

 at the Bureau of Standards to measure the differences in the 

 thermal expansion of steel samples, and to determine the thermal 

 expansions of steel, copper and brass simultaneously in the tem- 

 perature interval of o° to ioo° C. It is now being used in the 

 investigation of dental materials to determine the thermal ex- 

 pansion and the change in length while setting. The results 

 of these investigations will be published in the Bulletin of the 

 Bureau of Standards. This form of the apparatus is very easily 

 made and adjusted. The pins can be cut out in a few minutes 

 and their size measured with sufficient accuracy with a microm- 

 eter. They can be of almost any shape as long as the base is 

 plane and the top is brought to a conical point. The reference 

 marks can be drilled in the cover plate in a very short time and 

 it is not at all necessary to know the distances between them. 

 The fact that only a small area of the plates close to the refer- 

 ence marks and not a portion of the plates removed from the 

 samples is used in making Ithe measurements of the absolute 

 change in length of the pins, eliminates the necessity of having 

 the plates perfectly flat. They may be slightly concave or con- 

 vex. The same thing holds for the relative determinations. 

 The interference fringes denote the difference in separation 

 of the plates at the reference marks, even though the intervening 

 surfaces deviate slightly from true planes. 



