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it has already tabulated parts of series formed

from the following equations:

 

The third differential of ux = units figur of delta ux

 

The third differential of ux = nearest whole no. to (1/10,000

delta ux)

 

The subjoined is one amongst the series which it has calculated:

 

0 3,486 42,972

0 4,991 50,532

1 6,907 58,813

14 9,295 67,826

70 12,236 77,602

230 15,741 88,202

495 19,861 99,627

916 24,597 111,928

1,504 30,010 125,116

2,340 36,131 139,272

 

The general term of this is,

 

ux = (x(x-1)(x-2))/(1 X 2 X 3) + the whole number in x/10 +

10 Sigma^3 (units figure of (x(x-1)/2)

Chapter 21

On the Cost of Each Separate Process in a Manufacture

 

253. The great competition introduced by machinery, and the

application of the principle of the subdivision of labour, render

it necessary for each producer to be continually on the watch, to

discover improved methods by which the cost of the article he

manufactures may be reduced; and, with this view, it is of great

importance to know the precise expense of every process, as well

as of the wear and tear of machinery which is due to it. The same

information is desirable for those by whom the manufactured goods

are distributed and sold; because it enables them to give

reasonable answers or explanations to the objections of

enquirers, and also affords them a better chance of suggesting to

the manufacturer changes in the fashion of his goods, which may

be suitable either to the tastes or to the finances of his

customers. To the statesman such knowledge is still more

important; for without it he must trust entirely to others, and

can form no judgement worthy of confidence, of the effect any tax

may produce, or of the injury the manufacturer or the country may

suffer by its imposition.

 

254. One of the first advantages which suggests itself as

likely to arise from a correct analysis of the expense of the

several processes of any manufacture, is the indication which it

would furnish of the course in which improvement should be

directed. If a method could be contrived of diminishing by one

fourth the time required for fixing on the heads of pins, the

expense of making them would be reduced about thirteen per cent;

whilst a reduction of one half the time employed in spinning the

coil of wire out of which the heads are cut, would scarcely make

any sensible difference in the cost of manufacturing of the

whole article. It is therefore obvious, that the attention would

be much more advantageously directed to shortening the former

than the latter process.

 

255. The expense of manufacturing, in a country where

machinery is of the rudest kind, and manual labour is very cheap,

is curiously exhibited in the price of cotton cloth in the island

of Java. The cotton, in the seed, is sold by the picul, which is

a weight of about 133 lbs. Not above one fourth or one fifth of

this weight, however, is cotton: the natives, by means of rude

wooden rollers, can only separate about 1 1/4 lb. of cotton from

the seed by one day’s labour. A picul of cleansed cotton,

therefore, is worth between four and five times the cost of the

impure article; and the prices of the same substance, in its

different stages of manufacture, are—for one picul:

 

Dollars Cotton in the seed 2 to 3

Clean cotton 10 to 11

Cotton thread 24

Cotton thread dyed blue 35

Good ordinary cotton cloth 50

 

Thus it appears that the expense of spinning in Java is 117

per cent on the value of the raw material; the expense of dying

thread blue is 45 per cent on its value; and that of weaving

cotton thread into cloth 117 per cent on its value. The expense

of spinning cotton into a fine thread is, in England, about 33

per cent. (1*)

 

256. As an example of the cost of the different processes of

a manufacture, perhaps an analytical statement of the expense of

the volume now in the reader’s hands may not be uninteresting;

more especially as it will afford an insight into the nature and

extent of the taxes upon literature. It is found economical to

print it upon paper of a very large size, so that although

thirty-two pages, instead of sixteen, are really contained in

each sheet, this work is still called octavo.

 

L s. d.

 

To printer, for composing (per sheet of 32 pages) L3 1s. 10 1/2

sheets 32 0 6 [This relates to the ordinary size of the type used

in the volume.]

 

To printer for composing small type, as in extracts and 2 0 3

contents, extra per sheet, 3s. 10d.

 

To printer, for composing table work, extra per sheet, 2 17 9

5s. 6d.

Average charge for corrections, per sheet, L3 2s. 10d. 33 0 0

Press work, 3000 being printed off, per sheet, L3 10s. 36 15 0

Paper for 3000, at L1 11s. 6d. per ream, weighing 28 lbs: the

duty on paper at 3d. per lb. amounts to 7s. per ream, so that the

63 reams which are required for the work will cost:

 

Paper 77 3 6

Excise Duty 22 1 0

Total expense of paper 99 4 6

 

Total expense of printing and paper 205 18 0

Steel-plate for title-page 0 7 6

Engraving on ditto, Head of Bacon 2 2 0

Ditto letters 1 1 0

Total expense of title-page 3 10 6

Printing title-page, at 6s. per 100 9 0 0

Paper for ditto, at 1s. 9d. per 100 2 12 6

Expenses of advertising 40 0 0

Sundries. 5 0 0

 

Total expense in sheets 266 1 0

 

Cost of a single copy in sheets; 3052 being printed, including

the overplus 0 1 9

Extra boarding 0 0 6

 

Cost of each copy, boarded(2*) 0 2 3

 

257. This analysis requires some explanation. The printer

usually charges for composition by the sheet, supposing the type

to be all of one kind; and as this charge is regulated by the

size of the letter, on which the quantity in a sheet depends,

little dispute can arise after the price is agreed upon. If there

are but few extracts, or other parts of the work, which require

to be printed in smaller type; or if there are many notes, or

several passages in Greek, or in other languages, requiring a

different type, these are considered in the original contract,

and a small additional price per sheet allowed. If there is a

large portion of small type, it is better to have a specific

additional charge for it per sheet. If any work with irregular

lines and many figures, and what the printers call rules, occurs,

it is called table work, and is charged at an advanced price per

sheet. Examples of this are frequent in the present volume. If

the page consists entirely of figures, as in mathematical tables,

which require very careful correction, the charge for composition

is usually doubled. A few years ago I printed a table of

logarithms, on a large-sized page, which required great

additional labour and care from the readers,(3*) in rendering the

proofs correct, and for which, although new punches were not

required, several new types were prepared, and for which

stereotype plates were cast, costing about L2 per sheet. In this

case L11 per sheet were charged, although ordinary composition,

with the same sized letter, in demy octavo, could have been

executed at thirty-eight shillings per sheet: but as the expense

was ascertained before commencing the work, it gave rise to no

difficulties.

 

258. The charge for corrections and alterations is one which,

from the difficulty of measuring them, gives rise to the greatest

inconvenience, and is as disagreeable to the publisher (if he be

the agent between the author and the printer), and to the master

printer or his foreman, as it is to the author himself. If the

author study economy, he should make the whole of his corrections

in the manuscript, and should copy it out fairly: it will then be

printed correctly, and he will have little to pay for

corrections. But it is scarcely possible to judge of the effect

of any passage correctly, without having it set up in type; and

there are few subjects, upon which an author does not find he can

add some details or explanation, when he sees his views in print.

If, therefore, he wish to save his own labour in transcribing,

and to give the last polish to the language, he must be content

to accomplish these objects at an increased expense. If the

printer possess a sufficient stock of type, it will contribute

still more to the convenience of the author to have his whole

work put up in what are technically called slips,(4*) and then to

make all the corrections, and to have as few revises as he can.

The present work was set up in slips, but the corrections have

been unusually large, and the revises frequent.

 

259. The press work, or printing off, is charged at a price

agreed upon for each two hundred and fifty sheets; and any broken

number is still considered as two hundred and fifty. When a large

edition is required, the price for two hundred and fifty is

reduced; thus, in the present volume, two hundred and fifty

copies, if printed alone, would have been charged eleven

shillings per sheet, instead of 5s. 10d., the actual charge. The

principle of this mode of charging is good, as it obviates all

disputes; but it is to be regretted that the custom of charging

the same price for any small number as for two hundred and fifty,

is so pertinaciously adhered to, that the workmen will not agree

to any other terms when only twenty or thirty copies are

required, or even when only three or four are wanted for the sake

of some experiment. Perhaps if all numbers above fifty were

charged as two hundred and fifty, and all below as for half two

hundred and fifty, both parties would derive an advantage.

 

260. The effect of the excise duty is to render the paper

thin, in order that it may weigh little; but this is counteracted

by the desire of the author to make his book look as thick as

possible, in order that he may charge the public as much as he

decently can; and so on that ground alone the duty is of no

importance. There is, however, another effect of this duty, which

both the public and the author feel; for they pay, not merely the

duty which is charged, but also the profit on that duty, which

the paper-maker requires for the use of additional capital; and

also the profit to the publisher and bookseller on the increased

price of the volume.

 

261. The estimated charge for advertisements is, in the

present case, about the usual allowance for such a volume; and,

as it is considered that advertisements in newspapers are the

most effectual, where the smallest pays a duty of 3s. 6d., nearly

one half of the charge of advertising is a tax.

 

262. It appears then, that, to an expenditure of L224

necessary to produce the present volume, L42 are added in the

shape of a direct tax. Whether the profits arising from such a

mode of manufacturing will justify such a rate of taxation, can

only be estimated when the returns from the volume are

considered, a subject that will be discussed in a subsequent

chapter.(5*) It is at present sufficient to observe, that the tax

on advertisements is an impolitic tax when contrasted with that

upon paper, and on other materials employed. The object of all

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