34 THE VOYAGE OF H.M.S. CHALLENGER. 



the use of it in the calculations preliminary to the full reduction, as in them it is A/TI 

 only which is required. 



Next, on calculating from my data the values of A and II for different temperatures, 

 I found that, within the recognised limits of errors of the observations, II might be 

 treated as sensibly constant. Thus I was enabled easily to make graphic representa- 

 tions of the average compressibility at each pressure, in terms of temperature. Again 

 I obtained curves which could, for a first trial at least, be treated as small portions of 

 rectangular hyperbolas, with the axis of temperature as one asymptote. Hence 



A— 2- 



T + t 



where T is a constant ; and B also may for a time be treated as constant. 

 Thus I arrived at the empirical expression 



E 



(n+ P )(T + t) 



whose simplicity is remarkable, and which lends itself very readily to calculation. As 

 I required it for a temporary purpose only, I found values of the constants by a tentative 



process ; which led to the result 



0-28 



{36+1)) (150 + 



This gives the average compressibility per atmosphere throughout the range of 

 additional pressure p, the latter being measured in tons' weight per square inch. 



The following brief table shows with what approximation the (unreduced) experi- 

 mental results (multiplied by 10 7 ) are represented by this formula. The nearest 

 integer is taken in the third place : — 



The agreement is tolerably close, so that the empirical formula may be used, without 

 any great error, in the hydrostatic equations, so long as the temperatures and pressures 

 concerned are such as commonly occur in lakes. 



But the columns of differences show that the form of the formula is not suitable. 

 The pressure factor seems appropriate, but it is clear that, at any one pressure, the 

 curve representing the compression in terms of the temperature has greater curvature 

 than the formula assigns. Still the formula amply suffices for the reduction of the 

 ol: ervations of any one group when the pressures or temperatures were not precisely 



