Mr. A. P. Trotter on a New Photometer. 87 



distance of 2 metres is perhaps a little too small ; that is, if a 

 greater distance conduces to greater precision, it might be 

 worth while to employ an intermediate distance. Again, a 

 distance of 3 metres seems suitable for comparing a pair of 

 16 c. p. lamps. This question may be considered from the 

 point of view of a gradient or fall of illumination • and it is 

 not unlikely that for any one observer, the " mean error of a 

 single observation " is a function of the gradient of illumi- 

 nation at the photometer-screen. 



With an 8 c. p. lamp at 1'5 metre, the illumination is 3*56 

 times a candle-metre; that is, it is 3* 56 times the illumination 

 which would be given by one candle at one metre. The 

 gradient is 0"0474 candle-metre per centimetre. With a 

 2-metre photometer-bar and a pair of 8 c. p. lamps, the illu- 

 mination due to one lamp is 8 candle-metres, and the gradient 

 is 0*16 candle-metre per centimetre. With a 16 c. p. lamp 

 on a 3-metre bar, the gradient at the middle, i.e. 1*5 metre, 

 is 0*948 candle-metre per centimetre. My experience with 

 the form of photometer described in this paper goes to show 

 that a gradient of less than O'l candle-metre per centimetre 

 is not desirable. It should be observed that the illumination 

 on a screen inclined at 45° to the light is about 0*7 of that of 

 a screen turned full to the light. 



To graduate a photometer-bar of unit length, and having 

 a unit light at one end, I have used the formula : — 



i 



I: 



1+ *v 



where I is a length measured on the bar, and n is propor- 

 tional to the light to be measured. With a 3-metre bar a 

 displacement of 3*9 millim. from the middle is equivalent to 

 a difference of 1 per cent, in the candle-power of the two 

 lights. Since the band of uniformity with the 3 millim. 

 strips may be said to be about 15 millim. wide, and 15*6 

 millim. are equivalent to 4 per cent., it is only by bisection 

 of this band that a precise measurement can be made. In 

 using the 8 millim. strips, if the middle of one strip or space 

 is the actual point of balance, and by error the space or strip 

 on one side of it be taken as the one indicating the balance, 

 the error is + 2 per cent. Out of several series of 12 obser- 

 vations, the mean error of a single observation has frequently 

 fallen below this. Among some results which I consider 

 satisfactory, compared with my experience with other pho- 

 tometers, are mean errors of 085 and of 1'48 per cent, calcu- 

 lated from sets of 12 readings. 



