TRANSACTIONS OF SECTION A, 321 
The proof can be arranged so as to cover the case of an imaginary variable. 
We have Y=O,0+6,07 +bc7+ 2... , . ° see GL) 
pal 7 Sed Ae sae | : . » (2) 
Suppose now that i= 1 +7&, and compare two series (a) the one which would 
1 
be got from (2) by successive approximation, and (4) the series got by successive 
approximation from 
rapt se Piso ele a oo ene rey 
1 
where p = |n + 7é| and 8, = |d,. 
Using the facts that the modulus of a sum is not greater than the sum of the 
moduli, and that the modulus of a product or quotient is equal to the product cr 
quotient of the moduli, we see that in the parallel processes for obtaining (a) and 
(2) any term in (4) is not less than the modulus of the corresponding term in (a). 
Hence the reversed series obtained from (1) will be convergent if that obtained 
from (4) is convergent. By the previous work the condition is 
k<4/(B, + 28)? + B?— (8, + 28) 
where x = |y|. 
The yeneral result is that the reversed series of 
y=br+b,a7 2... +d,0" . 
ts convergent for all values of y such that 
(Y)< (AB) + 2A"B,)? + N™B,2— (NB, + 2A"B,) 
where d is any quantity and XB, is the greatest of the set |Ad,| [A7B,! |A20,]. 
4. On Instruments for Stereoscopic Surveying. By H. G. Fourcanr. 
The instruments of which photographs are exhibited have been designed for 
the construction of topographical plans from stereoscopic photographs of the 
country. A preliminary account of the method was communicated to the S. A. 
Philosophical Society on October 2, 1901 (also ‘Nature,’ June 5, 1902), and a 
more complete Paper will shortly be published. 
If photographs be taken from both ends of a base, at right angles to it and 
under conditions ensuring perfect parallelism of the line of collimation of the 
camera in both positions, the co-ordinates of any point common to both pictures 
may be computed from the plate co-ordinates by means of the simple relations — 
b 
0 SF 
e 
p toes 
e 
Z aM Lave 
e 
b being the base, f the focal length of the camera lens, and e the sterecscopic 
difference—that is, the difference of the plate a’s. It is not necessary to have the 
ends of the base at the same height. 
The camera is a metal box provided with levels, a transverse telescope, and a 
very accurate réseau scale divided on the silvered surface of an optically plane and 
parallel plate of glass, which may be set in front of the senaitive film for the 
[apt of the réseau lines or raised for the exposure of the view. Two pivots 
and an end contact on the frame of the réseau plate ensure the geometrically 
1905. 4 
