COLLIGATIVE RELATIONS AND SCIENTIFIC LAWS 115 



THE EFFICIENCY OF COLLIGATIVE RELATIONS 



In Chapter II we observed that from a typical colhgative relation 

 like the law of the lever we obtain predictions that may prove only 

 approximately correct. Consider now how I will proceed when I seek 

 to draw from the law of the lever predictions exact to the limit of my 

 capacity to check them experimentally. Obviously I do well to begin 

 by checking the graduation of my meter stick and the calibration of 

 my weights; but I can hardly expect reliably to predict the behavior 

 of a system incompletely defined in any "significant" sense. I must 

 then carry through an extensive study, beginning perhaps with ex- 

 amination of the external conditions. Ideally the experiment should 

 be made in a room or enclosure free from drafts (which might dis- 

 turb the condition of balance), held at a uniform constant tempera- 

 ture ( to avoid any uneven expansions or contractions of the beam ) , 

 constant humidity ( to avoid the adsorption or desorption of water on 

 or from the beam or the weights ) , and constant pressure ( to a\'oid 

 variable buoyancy effects on beam and weights that have finite vol- 

 umes). Lacking these ideal conditions, I can still proceed, by calcula- 

 tion from measurements of the external conditions, provided that I 

 have amassed much information about the components of the sys- 

 tem: their volumes, surface areas and characteristics, coefficients of 

 thermal expansion, and so on. 



About the actual system I will in any case need very precise infor- 

 mation. Are all the bearing surfaces essentially frictionless, coplanar, 

 parallel to each other, and perpendicular to the beam? If not, further 

 measurements and calculations must supply appropriate corrections 

 for the deviations. What is the coefficient defining the rigidity of the 

 beam, what does it weigh, and where is its center of gravity? This 

 last I cannot calculate from the geometry of the beam without mak- 

 ing the potentially fallible assumption that it is perfectly homoge- 

 neous. Presumably I will prefer to make a preliminary trial to de- 

 termine the position of the fulcrum when the unloaded beam is in 

 balance; but this, rather painfully, necessitates that I assume at least 

 some part of the law of the lever in deriving the predictions by which 

 I hope to establish its exactitude. 



Completing all these preliminary studies, I can make predictions I 

 would be vastly surprised to find detectably in error. Nevertheless 

 the possibility of at least minor error always exists and occasionally 



