82 Messrs. Paterson and Dudding on the 



It would seem that a definite difference in the conditions 

 in Washington and London must be looked for to account 

 for the discrepancy, and the present authors think it will be 

 found to lie in the fact that the pentane lamp really has a 

 temperature coefficient, but that its effect is almost entirely 

 masked by the method generally used of determining and 

 applying the humidity correction. In a more recent publi- 

 cation of the Bureau of Standards *, Messrs. Crittenden and 

 Taylor suggest the possibility of a temperature coefficient, 

 but they do not discuss its bearing on the constant for the 

 humidity correction. In their earlier publication also 

 (p. 768) they mention the effect which the temperature may 

 have on the humidity correction, as determined in the earlier 

 N.P.L. investigation*)*. 



The authors have not been able to determine the tempera- 

 ture coefficient of the pentane lamp. The difficulties found 

 by all investigators, and mentioned by Crittenden and Taylor, 

 of changing humidity and temperature independently Lave 

 prevented this. Nor is the matter of sufficient importance 

 to justify the prolonged and difficult investigation which 

 would be necessary. On the assumption, however, that 

 there is a temperature coefficient the work already done 

 enables an estimate to be made of its influence. 



If it may be assumed that the candle-power of the pentane 

 lamp under various atmospheric conditions is given by 



Candle-power = 10 + A(8-«) + B(760-6) + C(tl2-0» ( 3 ) 

 where A, B, and C are constants, 



e = litres of water-vapour per cubic metre, 

 b = height of barometer in millimetres, 

 t = temperature in °C, 



the method of least squares enables us to determine the 

 most probable value of the constants A, B, and C from a 

 large number of simultaneous observations of the variables, 

 candle-power, humidity, barometer, and temperature pro- 

 vided that : — 



(a) All values of humidity, barometer, and temperature 



* "The Pentane Lamp as a Working Standard," Crittenden and 

 Taylor, Bulletin of the B. of S. vol. x. p. 410. 



t In a still more recent publication (Bull. B. S. vol. x. p. 574) received 

 after the paper was written, the same authors refer to the subject again, 

 and make the suggestion which has been elaborated here, but without 

 giving actual figures connecting humidity and temperature at Washino-ton. 

 If these are obtainable and could be compared with those given here the 

 validity or otherwise of the suggested explanation would be established. 



X The normal temperature of 12° is chosen because it corresponds 

 with the previously fixed normal humidity of 8 litres per cubic metre. 



