240 PROCEEDINGS OF THE AMERICAN ACADEMY. 



solved for p, and another was set up giving p in terms of p. The 

 form of this is exactly the same as for p in terms of p, and the procedure 

 in determining the coefficients was the same. It was not found possi- 

 ble to get quite so good an approximation, however, partly because of 

 the shape of the curve itself, which was such that a given percentage 

 error in p produces less percentage error in p than the same percentage 

 error in p produces in p. In practice, it will be found most convenient 

 to find p graphically from a curve representing the relation between 

 pressure and resistance. The form adopted was 



p = a P Wr U03 , 



a = log- 1 4.4871, 



P = log- 1 9.8836 - 10. 



Table IV shows the observed and computed values for p with the 



discrepancies. The probable error of a single reading is 0.12 per cent ; 



that of the formula itself much less. This formula holds for mercury 



in soft Jena glass No. 3880 a at 25°. 



At first sight it seems that the two empirical formulas may be com- 



v 

 bined by eliminating - so as to give a single purely exponential relation 



between p and p which may be readily solved for either. This is not 

 practical, however, because the exponential parts of the above ex- 

 pressions are only slightly affected as to percentage accuracy by 

 relatively large percentage errors in the arguments, and therefore, 

 inversely, small errors in the exponential part may produce large errors 

 in the unknown (p or p) calculated from it. Errors of as much as 20 

 per cent were found to be introduced by the suggested elimination. 



The above formulas are only empirical representations of the facts 

 throughout a given pressure range, and their use by extrapolation 

 over any considerably greater range is doubtful. No theoretical value 

 is claimed for them, and it is evident that they cannot represent the 

 actual form of the unknown function. Thus the formula for resist- 

 ance in terms of pressure predicts a negative minimum of resistance 

 of about— at 48,000 kgm. per sq. cm. Neither can extrapolation 

 be carried entirely to the origin of pressure, for the formula demands 



that -=- ( - ) be infinite when p = 0, which is almost certainly not 

 dp\pj 



the case. The error here is slight, however, and confined to the imme- 

 diate neighborhood of p = 0. - at the origin remains finite, with 



