Intelligence and Miscellaneous Articles. 545 



(namely, the relative brightness of the two surfaces compared, 

 and an instrumental constant), it follows that only twenty-six 

 observations were effective for determining the probable error. 

 Let E be my photometric probable error of a single comparison. 

 Then the probable error of a single determination of E (which 



we may denote by r) would be ,,,,, X E, or say 55 E. Having 



made a considerable number of such determinations of E with dif-> 

 ferent coloured disks, let us ascertain their probable error from 

 their discrepancies, considering them as so many independent ob- 

 servations of the same unknown quantity, and denote this probable 

 error by >*'. If, then, E really is the same for all colours, w x e should 

 have r' — r- 



or at least the difference should not exceed p, the probable error 

 of r', which may be calculated by the formula 



_ -51 



where m is the number of sets of experiments diminished by 1. If, 

 on the other hand, E varies with the different colours, and not merely 

 accidentally, r should have a larger value. The following are the 

 values I obtained for E, the sum of the brightness of the two sur- 

 faces compared being taken as unity :— R Diff from mean 



Feb. 6. White -0041 +-0001 



Eed, just before C '0046 +'0006 



Chrome-yellow, A 2 -0032 --0008 



Feb. 7. Eed, just before C '0040 ±-0000 



Staat's emerald green -0046 +-0006 



Carmine, B -0044 +-0004 



Chrome-yellow, A 1 -0037 --0003 



Purple, Hoffmann's violet EEE -0033 --0007 



Feb. 13. Eed, just before C -0048 +-0008 



Green, complementary to carmine -0034 — -0006 



Blue-violet, No. 2 -0048 +'0008 



Yellow, A 1, mixed with black . . -0032 — -0008 



Mean -0040 



After these experiments the method of observing was changed, 



and I obtained the following :— R Diff# from mean> 



Feb. 14. White window-shade, ill. by sun -0030 — -0002 



Brown -0030 --0002 



Greenish sky-blue -0037 +-0005 



Very reddish purple -0028 --0004 



Yellow-orange '0032 +-0000 



Feb. 15. " Fundamental green of Miiller" -0030 --0002 



Vermilion, half between C and D -0034 +'0002 



Violet -2032 ±-0000 



Yellow -0036 +-0002 



Mean -0032 



Phil. Mag. S. 5. No. 21. Suppl. Vol. 3. 2 N 



