48 PHOTOGRAPHIC FACTS AND FORMULAS 
to make the combined focus 16 in? Ans—(9—4)+9X 
(4—16)=5+9X %4%=—5+24%=7% in. Where a 
scale of magnification is marked, as on the ordinary type of 
adjustable mount, and another magnification is desired that 
is not marked, let M’ stand for any existing marked magnifi- 
cation, M” the magnification desired. Then f” kK (M’ — 
M’”) ~~ (M’ X M’”) will be the increase of separation re- 
quired. Example: Suppose a magnification of 5 be wanted, 
and the nearest mark is 3, the focus of the negative lens 
being 41%4. Then 4% X (5—3) + (5 X 3) = 4% X 2/15 
= 3/5 in., which is the necessary extra separation readily 
measured from the existing mark for 3 magnifications. When 
the focus of the negative lens is not known, it is easy to find 
it from the distance between any two magnification marks on 
the mount. The rule is: multiply the two magnifications 
together and divide by their difference, multiplying the quo- 
tient by the distance D between the two marks; (M’ K M”) 
— (M’—M”) xD. Example: suppose the distance be- 
tween the marks 8 and 4 on a telephoto mount is % in., then 
(8 X 4) + (8—4) XK % = 32/4 X % = 6 in., which is the 
required focus (Lockett). 
PINHOLE Exposure.—The correct exposure is, with the 
small pinholes used in practice, always greater than that cal- 
culated on a basis of relative aperture ratios. The inverse 
square law cannot be applied in calculating relative exposures 
at varying plate distances from one and the same pinhole. 
Using a pinhole made with a No. 12 needle, the pinhole 
exposure factor by which the aperture ratio numbers must 
be multiplied varies from 1.6 to 1.42 as the plate distance 
diminishes from 254 to 128mm (Carnegie). 
Watkins finds that it is better to expose with a pinhole for 
50 per cent longer than the exposure calculated on the ratio 
aperture, and gives the following table based on 1/40 instead 
