On Single-Piece Lenses. 521 



or 





1 ^o 1 Si? 



where Vj and Vo Jii'e the specific volumes of the gas at the 

 constant pressure p and at the absokite temperatures 6^ and 



We have thus a relation between the absolute temperature 

 and the temperature measured by a constant-pressure ther- 

 mometer filled with the oas under investioation. It will be 

 noticed that, as was stated above, neither J nor Op enters 

 into this equation, their place being taken by X, the measured 

 value of which depends upon two electrical units. 



The method thus briefly sketched is, of course, not appli- 

 cable to hydrogen at temperatures above —80° C, which 

 Olszewski has found to be the inversion temperature of the 

 Joule-Thomson eflect for that gas. But for other gases, 

 below their as yet unknown inversion temperatures, the 

 method appears to have certain advantages. 



U.S. Department of Agriculture, 

 Washington, D.C., June otli, 1903. 



LXII. Single-Piece Lenses. By Thomas H. Blakesley*. 



[Plate XXI.] 



IF the definition of a lens is taken to be a mass of refracting 

 material contained between two spherical surfaces, then 

 any lens is completely determined in shape and size when 

 the radii of curvature of its two end surfaces and the distance 

 between them are given. The dimensions which are mea- 

 sured at right angles to the axis do not afi'ect the focussing 

 properties of the lens except in the second order of small 

 quantities, and such dimensions are not brought into con- 

 sideration in what follows. 



If the kind of material in reference to any kind of light, 

 as defined by the index of refraction of the material for that 

 light (yLt) is supposed given, there remain only the three 

 linear matters, viz. the two radii of curvature of the surfaces 

 and the distance between the surfaces. 



Let these be symbolized under the letters ^i, r^, and cl. 



The third may be considered as always positive, and as to 

 the radii, let them be considered as having a positive value 

 when the light encounters the surfaces upon the concave side; 

 in other words, if the light as it passes generally along the 



* Communicated by the Physical Society : read May 22, 1903. 



