Alfred Watkins, “Logical sizes for plates”

{3a}

LOGICAL SIZES FOR PLATES.

When a responsible committee of a large industry issues a new standard series of sizes or gauges for their commodities, some orderly method of relation or co-ordination between such sizes is looked for. One looks in vain for any trace of system in the list of standard sizes for small-plate cameras issued by the British Photographic Manufacturers’ Association in April last. There are probably good reasons why well-known old but haphazard sizes must be retained, but it is impossible in the list of new sizes to find any trace of aiming at a definite principle. The new sizes are in metric measurement, but so far from introducing any co-ordination they actually destroy the old relation of “ whole,” “half,” and “quarter” in the Continental series of 9 × 12 cm., 6 × 9 cm., and 4½ × 6 cm. by altering the two former to 8 × 12 and 6½ × 9.

I can only trace three aims in this list. “Let’s chuck out a few sizes.” “Let’s give the Decimal Association a lift by shelving inches.” “Let’s number the list to give some appearance of order.” It is safe to say that such numbers will always be ignored outside the catalogues.

The object of this paper is to give the result of an investigation into the possibility of providing a theoretically logical and co-ordinated series of sizes. It is not claimed that it is within the sphere of practical politics to adopt at once such a list; but without aiming at orderly perfection, how is it possible to attain any advance at all? Nor is this designed as an argument for the inch, for the series of sizes I arrive at are just as right in centimetres as in inches.

In the evolution of plate sizes a certain co-ordination was aimed at in the old series of whole-plate, half-plate, and quarter-plate. There are clearly great advantages in having a series in which the larger size, cut exactly in half, provides a standard smaller size, and this advantage is very apparent in the matter of sensitive paper. It leads to economy of glass and paper, both to manufacturer and user. It is fairly clear that the first “half-plate” must have really been half of 8½ × 6—namely, 6½ × 4¼, which is still a stock size. Why, then, was half-plate altered to the present 6½ × 4¾? The answer lies in the proportion between the two sides of the plate, and as this matter of proportion is a vital one, I must examine it more carefully. The ratio of short to long side in the whole plate (evidently thought satisfactory by old workers) is 1 to 1.3. If cut in half to 6½ x 4¼, the ratio of the new plate becomes 1 to 1.53, evidently much too lanky a plate for the taste of those days, and it was accordingly altered to 6½ × 4¾, which is 1 to 1.36. The true quarter of a rectangle always retains the same ratio as the large size, and therefore the quarter-plate cuts four out of a whole plate to this day, and has the same ratio of 1 to 1.3.

Many workers (myself included) prefer a plate of good length in proportion to width, and 7½ × 5 with a ratio of 1 to 1.5 is my favourite. Two of the new sizes adopted in the B.P.M.A. new list have this proportion. Now, if plates of this proportion of 1 to 1½ are cut in two, the new size has a proportion of 1 to 11/3, which, if cut in two, again results in 1 to 1½, and so on alternately.

Here let me diverge from the main theme to see what ratios appear to be favourite ones. Leaving out such special-purpose sizes as stereo and lantern, and keeping to sizes of whole-plate {3b} downwards, the range is from the dumpy 5 × 4 (1 to 1.25) to the lanky postcard, 5½ × 3½ (1 to 1.58), the average between these two being 1 to 1.415, which, as will be seen presently, is almost exactly the ratio I ultimately arrive at for a standard. But in large sizes, 10 × 8 upwards, the present sizes in use are all dumpy—chiefly a ratio of 1 to 1.2, or 1 to 1.25. Whether this is from a real need or from custom I cannot say.

To come back to the problem of devising a logical series.

At first sight a series (a) of 2 × 1½, 3 × 2, 4 × 3, 6 × 4 and so on, is good. Each plate cut in two provides a smaller size. This principle, I may say at once, seems inevitable as conferring economy in many ways in plates and paper. Then the plates are alternately of the simple 1 to 1½, and 1 to 11/3, ratios. But, unfortunately, this does not give the user a choice between squat and lanky sizes, for the 4 × 3 size man can only use a long-shaped plate by getting one of double or half the area of what he wants. It would be possible to give such free choice by adding a series (b) of 2¼ × 1½, 3 × 2¼, 4½ × 3, 6 × 4½, etc. But this, while doubling the number of sizes to be provided, would yet not provide intermediate half-way areas.

On the whole, I found it worth while investigating whether there was not some value between 11/3 and 1½ which would provide a ratio between the shorter and longer side of a plate which would remain constant when the plate was cut in half.

I soon found this perfect ratio to be √2 or 1.414, which is almost exactly the average of favourite small plate sizes, and therefore a reasonable compromise between advocates of squat and of lanky plates either of whom will only have to sacrifice a small strip of the surface of their plate (at top for the “squat” man, and at sides for the “lanky” man) to get their desired print.

It is unfortunate that this ratio, is incommeasurable, for whether we give sizes in inches or centimetres, it is inconvenient to have them in other than whole numbers or very simple fractions.

But in setting a slide rule to this ratio of 1 to 1.414, it is soon found that the simple numbers, 6 to 8½, almost exactly represent it, and can therefore be taken as a standard rectangle which, when halved, will provide two rectangles of half the area but of the same proportions.

Such a series I, therefore, think to be best for standard sizes of plates, although there remains the doubt whether the jumps to half or to double any one area of plate are not too great.

Another glance at the slide rule shows that 5 × 7, a ratio of 1 to 1.4, is the next nearest available to 1 and √2. If cut in half this becomes 3½ × 5, which has a ratio of 1 to 1.43, and halved again the ratio comes back to 1 to 1.4.

I will label this series D, and the 6 × 8½ series C.

It is a fortunate fact that the area of plates in the series D comes almost exactly half way between the area of those in series C, and that if both series are adopted within the range of most used sizes, there will be a far more uniform series in areas than ever yet provided, without, I think, providing an excessive number.

There are only eight sizes from “whole-plate” to “vest-pocket.”

{4a} It is a minor tragedy of photographic science that the early divisers of whole-plate size only missed adopting a perfect ratio by half an inch in one dimension.

I give the tables of these two logical ranges of sizes side by side, but think that in use they would form one series.

The characteristics of this complete series are as follows:—Any plate cut equally in two provides the next but one smaller size, of half its area.

All in the series have practically the same ratio of width to {4b} length, namely, not less than 1 to 1.4, not more than, 1 to 1.43. Each plate is in area near to the average area of the two nearest sizes.

Three plates in the series (7 × 5, 6 × 4¼, and 3½ × 2½) are already stock sizes in inches.

The present sheet of P.O.P. (24½ × 17), after taking half an inch from the edge, gives all the sizes in C series without waste by halving repeatedly and all the D sizes can be cut without waste from a stock width (20 or 40 inch) of bromide or P.O.P.

The same series is theoretically perfect as standards in the printing trade for books, etc., quite apart from. photography.

The proportion of the rectangle which is the basis of this series is the only proportion which remains unaltered when the rectangle is halved. Its length to its width is as the diagonal of a square is to the side of the square.

In conclusion, I repeat that such a series is equally applicable to inches or centimetres, the latter taking the higher numbers. As, however, British plate users have only bought plates in centimetre sizes for use with cameras of foreign origin, I can see no reason for abandoning our British inch.

Alfred Watkins, F.R.P.S.