192 Prof. Porter and Dr. Slade on the Fundamental 



conjugate curve ; then we develop until this fit is obtained.. 

 We must not develop longer or this fitting of the curves 

 would be spoiled. 



In what respects do these conclusions differ from those of 

 Hurter and Driffield ? Their great conclusion was that it 

 was necessary and sufficient that D should be a linear 

 function of log E for a sensitive plate, i. e. 



D = 7(logE— log?'). 



This conclusion appears to have been arrived at by con- 

 sidering a single kind of plate only for both negative and 

 positive, but they do not state exactly what assumptions 

 they made. If we derive from our general results, this case 

 in which the two plate curves by supposition are identical, it 

 follows that 



D=logE-logI 



for each ; or in other words 7 can only be equal to unity- 

 No other curve but this can fit its conjugate. Hence the 

 conclusion that 7 may have any value in such a case is 

 erroneous. In a later paper * on the relation between photo- 

 graphic negatives and their positives, they carry the question 

 further and conclude that 



D,=7(logP-«Di), 



which is somewhat similar to our fourth equation ; but they 

 only give arbitrary values to a and the value of 7 is also 

 quite arbitrary. It would seem, then, that as the result of a 

 somewhat quick judgment they were led to an imperfect 

 conception of the true conditions for securing a true repre- 

 sentation of gradation. The true result is in one case more 

 special than theirs because for similar plates the value of 7 

 must be unity ; it is also more general than theirs because 

 we are not constrained to keep to the linear function at all.. 

 We will examine in detail some particular cases. 



Case 1. — Suppose we follow the customary theoretical 

 practice and restrict ourselves to a negative in which the 

 straight portion of the characteristic has been utilized. 

 80 that 



I) 1 = 7(logE 1 — logi{). 



By plotting fig. 6 and viewing from the back it is seen at 

 once (fig. 7) that for the positive the necessary conjugate- 

 relation is 



D 2 = - (log E 2 — log i 2 ) . 

 7 



* Journ. Soc. Chem. Ind. 28th February, 1891. 



