On the Focometry of Lens- Combinations. 77 



Mr. Baynes points out that the relation 



<*(i-ffWi-yi-fe-y 2 ) 



must hold between the five quantities measured. The left- 

 hand side, when the numbers are substituted, gives 111'65 

 and the right-hand side Hl'8. This is also satisfactory. 

 The above formula may be also written 



d + x 2 —x 1 +y 1 —y 2 = dy^/x^, 

 which becomes 



2 = 2-15, 



and this is, apparently, less satisfactory. With the lens to 

 the left of B, and with a diverging combination whose focal 

 length is small and in which HgHi is small, d is nearly equal 

 to Xi — x 2 and y l and y 2 do not differ by very much. Thus 

 the quantity d -f x 2 - x 1 +y x — ;/ 2 will be small, and small errors 

 in the five quantities involved may have a considerable effect 

 on the amount of the error in it compared with its correct 

 value. In the example at the end of my paper the value of 

 this quantity is — O'l, the right-hand side of the equation 

 being 0'067. The right-hand side being always positive it 

 is impossible for the left-hand side to have a negative value. 

 xrlr. Baynes points out that the focal length may be obtained 

 by getting only one centre of rotation, that is, only one 

 value of the magnification, together with three other mea- 

 surements. Denoting the quantity d x 2 — x 1 +y 1 —y 2 hvs 

 the formula? are 



f =di(^- d ^)=d!( d ^-*A 



iVJi s xj l\s x 2 y 2 ) 



In the first formula the magnification is — , and the other 



x ± 



measurements to be made are x 1 —y 1 , x 2 —y 2 , d, and similarly 

 for the second formula. But, as has been pointed out, s is 

 liable to a large relative error, which may have a great effect 

 on the value of /. Substituting the numerical values, the 

 first formula gives /= 10 cm._, and the second /= 8 -95 cm. 

 The utterly incorrect values of / obtained by Mr. Baynes 

 from the data given in the example at the end of my paper 

 are explained by the value —0*1 of s, which is quite wrong 

 and could not possibly be negative. The value of B^Hx 

 obtained from x u y { , and /is 3'38 cm., and that from x 2 , y 2 , 

 and/ 3'23 cm., /being taken to be 9*81 cm. These values, 



