[263] APPARATUS FOR THE DELINEATION OF 

 CURVED SURFACES, IN ILLUSTRATION OF 

 THE PROPERTIES OF GASES, ETC. 1 



IN attempting the graphic representation of the relations 

 between the volume, temperature and pressure of gases, or of 

 other problems involving three variables, one is met by the 

 difficulty of properly constructing the surfaces in question. 

 Drawing isothermals, etc., as projected upon a single plane, 

 gives a very imperfect idea of the actual proportions. For 

 many years this method has been occasionally supplanted by 

 the actual construction, in papier mache or plaster, of models 

 bounded on one side by the surface in question, relief maps, 

 in other words. This plan suffers from several disadvantages. 

 Aside from the notion of solid volume which is involuntarily 

 entertained in beholding such a model, some of the surfaces 

 are too complex to be well shown in this manner. Further- 

 more, the models are rather hard to make, expensive, and 

 occupy a good deal of room. 



I have obviated most of these difficulties by obtaining a set 

 of glass plates, about 11 cm. square and 7 mm. thick, ruled in 

 squares 7mm. wide. Placed one on top of the other, these form 

 a block whose perpendicular edge may be taken for the third 

 axis in a system of rectangular coordinates. Having drawn 

 upon a sheet of paper the curves representing the relation 

 between volume and pressure as successively 0, 10, 20, 30, 

 etc., of temperature, I can trace them, with suitable grease- 

 chalks, upon the successive glass plates. When these are 



1 Reprinted from Journal of the American Chemical Society, 13, 263 (1891). Also 

 Chemical News, 66, 220 (1892). 



