78 Prof. A. Anderson on the 



it must be admitted, are not very satisfactory, as the value of 

 H^Hi calculated from the focal lengths and distance apart 

 of the lenses is 2*43 cm. 



An adequate explanation of all these results is furnished 

 by a consideration of the effect of possible errors of 

 measurement which are due (1) to the instrumental error, 

 (2) to want of precision in determining whether there is any 

 motion of the image, and (3) to the error in finding the 

 position of P 2 . We may assume that the error in the 

 measurement of d is negligible. 



The formula for the focal length is 



/ d \y! yj' 



If a l5 a 2 , /3 1? /3 2 are the possible errors in # 1? a, 2 , y u y 2 , the 

 possible error in /is 



d \yx y 2 y\ ,y 2 2 /' 



all the quantities a l? a 2 , /3 1? j3 2 being taken with the positive 

 sign. Let us suppose that these errors are each equal to a 

 millimetre ; then, for the combination above described, the 

 greatest possible error in /amounts to 0*19 cm., or nearly 

 2 millimetres. For the combination referred to in my paper, 

 the error would be very nearly 3 millimetres. If instead of 

 1 millimetre the errors are each each equal to half a millimetre, 

 the largest possible error in the focal length would amount to 

 about 1*5 cm. 



Taking, now, one of the formulae referred to by Mr. Baynes, 



1 = 1M_^ J/i\ 

 / d\vi s a,)' 



f d\y 1 s x 1 

 where s = d + x 2 — X\ + yi —y 2 , we find the error in /to be 



r 



ai (^-l±-L) +l3i (lL-±-^) 

 \s 2 x l sx-f dy^J \s 2 x l sxi dy^J 



S 2 X?i 



Taking the most unfavourable case for the above com- 

 bination, and supposing the error in each case to be one 

 millimetre, this becomes 0*44 cm., or more than 4 millimetres. 

 For the combination in my paper the possible error, on the 

 supposition of a small error of 1 millimetre in each of the 



