116 C. Barus — Counter-twisted Curl Aneroid. 



by Prof. Worthington,* apd in a more elaborate article by 

 Prof. Greenhill.f There is not much succor to be gained 

 from theory. The most lucid expression of the case is due to 

 Lord Rayleigh.J His explanation meets the conditions of the 

 present paper very fully, since the gauges are to be constructed 

 with sharp edges and a spindle-shaped section, in order that the 

 changes of shape occurring may be pure bending. § 8. Stretch- 

 ing would necessarily introduce resistances large as compared 

 with the feeble forces to be measured. Since in the flexure of 

 an inextensible surface, the product of the principle radii of 

 curvature at a point of the surface remains constant (Gauss), 

 any uniform sectional flattening of the walls of the tube due 

 to increased external pressure must be compensated by an 

 increased curvature of the axis ; and vice versa. 



If the edges are sharp, there seems to be no advantage in 

 increasing the height of the section, for the elastic resistances 

 increase at the same time as the external pressure. There is> 

 on the other hand, a disadvantage in wide tubes, for the length 

 of the helix is thereby necessarily increased and the curl made 

 more cumbersome, while the shape of the section cannot long 

 remain regularly and uniformly arched. 



Simple cuels. 



3. Apparatus. — There is, therefore, a demand for extremely 

 thin metallic tubes, flattened nearly to the point of actual con- 

 tiguity of the walls and left with almost sharp edges. Tubes 

 made of metal as thin-walled as 0'01 cm are manufactured 

 abroad ;§ but American makers usually fall short of this 

 remarkable accomplishment. I found, however, that it was 

 quite possible to derive full advantage from the American 

 tubes by dissolving off the outside layers in a suitable acid 

 bath. 



The tube at my disposal was made of copper, being like the 

 material I formerly used in my calorimetric work.| This 

 metal is elastically unpromising, apart from the technical 

 advantages of smooth solution in diluted nitric acid, of easy 

 flattening and bending, and of a small modulus of elasticity. 

 Results, "however, which can be obtained with copper tubes, 

 can be much improved by the use of other more suitable 

 metals, and for this reason the data of sensitiveness and con- 

 stancy obtained would be an index of the possibilities of the 

 gauge erring markedly on the side of safety. 



Two methods suggest themselves for flattening : the tube 



* WorthingtoD : Nature, xli, p. 296. 1 890. 

 f Greenhill: Nature, xli, p. 517, 1890. 

 % Payleigh: Proc. Roy. Soc, Dee., 1888. 



§ I owe most of my information in relation to thin tubes to Prof. Langley. 

 I Barus: Proc. Am. Acad., xxvi, pp. 316-317, 1891. The liquid was examined 

 in a very thin tubular helix of copper, to insure rapid cooling in the calorimeter. 



