Draft of a letter from JFW Herschel to H. Goulburn, Chancellor of the Exchequer re Babbage's Difference Engine

Royal Society Herschel Collection Box 27 Item 51

September 1842

Draft of a letter from JFW Herschel to H. Goulburn, Chancellor of the Exchequer re Babbage's Difference Engine

Sir,

The Astronomer Royal [GB Airy] has communicated to me your desire to know my opinion as to the probable utility of continuing to expend upon Mr Babbage's calculating machine the sums necessary for its perfection; informing me at the same time as [del: the] a ground for the formation of such opinion that a Sum of about 16000£ has been already expended on it and that you understand from Mr Babbage that a sum not less than that will be necessary for its completion. He further states [del: as a reason for your wishing to ascertain my present views on the subject] that you understand me to have been consulted in an early stage of the business and [del: would] are therefore unwilling to proceed without endeavouring to ascertain my present views.

In reference to this latter point it is proper for me to observe that I was never individually consulted by Government on the subject in any stage of the business or called on to express an opinion on it otherwise than as a member of the Council of the Royal Society and of its Committees to whom its consideration was referred [Insert: under then circumstances and as a private friend of Mr Babbage it must be supposed that I feel the utmost delicacy in forming [del: and divulging] an opinion on a point so nearly concerning his interests and that only a permanent sense of public duty when disjointly called upon by the Government of my country which has a right to the best exercise of my judgement and faculties when seeking to be informed by them for the public advantage could decide me to enter upon such a task. To that delicacy is added a serious difficulty. During the last 10 or 12 years I have in great measure lost sight of the progress of the Engine, having resided several years out of England and since my return having been by no means in close or frequent communication with him [del: up]on its subject. Nor does my present situation permit me to enter [del: upon] fully into [del: all] the many and great developments of which would demand the requirements of a practical engineer for which I feel some months of severe [del: and arduous] application would but inadequately prepare me. It is therefore at best a birds-eye view of the subject that I can take and one in which it is very possible Mr Babbage may feel that he has a right to complain of some of his most cherished conceptions [del: not being .. ] being left unconsidered. ]

[Del: On the subject of] The utility of continuing to spend money on this machine must depend

[Insert: Take Care in Copying 1. 2. 3]

1st On the absolute utility of the machine supposing it was completed [del: or as it .,, ]

[Del: End] 3rd On the probability or certainty that its completion will be secured by the expenditure of such sums that the Government may consider itself justified in devoting to it

[Del: 3rdly] 3rdly On the total amount [del: ultimately] henceforward to be expended [del: henceforward] on it as [del: weighed] considered in realtion to the absolute utility of the machine [insert: to the claims of other branches of science on the national purse] and [del: as consideration of ] to the sum already laid out. [Del: The part of the question dependent on this point may be considered as the question of its relative utility.

On the subject of the absolute utility of the machine when completed, my own opinion coincided fully with that of the body of whose judgement it constituted an element nor have I since found the least reason to retract or alter it. I might therefore content myself with referring to the official record of that judgement as delivered in reply to references made by the Government to the Council, as the expression of my present sentiments on that head. Nevertheless I shall particularize a few cases in which its utility will be readily perceived out of many which might be selected.

But first it is necessary for me to observe that I understand by the "Calculating [del: Engine] Machine" referred to in the Astronomer Royal's communication to be intended a machine destined to accomplish the objects of the Engine brought under the notice of the Royal Society, whether by the same identical mechanical combinations, or by other simpler and more efficacious suggested by subsequent experience or which [del: may bring] have brought under its dominion tables not within its power at that epoch. An Engine in short of which the essential character is the calculating and printing series of numbers following one another in tabular order, the principle of such calculation being the successive addition of numbers one to another by mechanism which includes as a particular cases the process of multiplication [del: and] as well as the calculation of series by differences.

I make this observation because I am perfectly aware that Mr Babbage's views on the applicability of mechanism to calculatory combination in general have extended very far in advance of a simply numerical tabulation, to which however if the Engine in question be not restricted, I beg to understand as delivering no opinion whatever as to any parts of its structure which may surpass this limit. And this, not as in any way undervaluing the possible utility of such combinatory mechanism, but as being no way prepared to enter [del: into so vast a .... 3 on the [del:] new] considerations this subject suggests. This premised, I proceed to the particular instances of expected utility alluded to above.

1. There are constantly going forward reprints, in various forms, of logarithmic, trigonometrical, and a multitude of other useful mathematical and practical tables, in all which reprints,  [del: (especially if attended with recomputation)] there is not only danger, but almost a moral certainty of errata creeping in, whose consequences might become serious where (as in navigation) large interests, or life [del: is] are at stake. [Insert: An undetected error in a logarithmic table is like a sunken rock at sea yet undiscovered, upon which it is impossible to say what wrecks [del: may have taken place (in the literal sense of the word)] may have taken place, ] Now were an Engine capable of doing such work accessible at reasonable cost [del: might inte..] it is hardly to be supposed that it would not at least in a great many cases supersede the ordinary processes of [del: letter]press printing and [del: rending] revision.

2. I consider it by no means improbable that the present generation will not pass away without witnessing the reconstruction of the whole map of Solar Lunar and Planetary tables, based on a more complete [del: and refined] development of Newtonian theory than that which has served for the construction of those now in use, on the one hand; and on the other, on the reduction (according to a uniform system and with the best elements) of all the existing observations -at least of all the British ones- such reduction being actually in prgress, if not completed, under the direction and at the instance of the present Astronomer Royal. [Del: seems all or nearly all Astronomical tables] Tables of this nature [del: which are not] are for the most part either arithmetical progressions or tables of natural cosines to a given radius [insert: and therefore within the power of the Engine in its improved form. And its application to their calculation and printing would be the most satisfactory proof which could be afforded of its practical success. ] [Del: The great mass of such tables therefore might be written of almost currente calamis with hardly any computation, by the aid of a general table of such cosines from radius I up to 10,000 which would be the easiest task of such an Engine, or indeed of one infinitely less elaborate in its arithmetical part provided the printing part were perfect. [Footnote: Such a table for integer degrees would comprise 450000 numbers and two volumes of this extent one for cosines and one for tangents would [del: greatly facilitate...] be a vast assistance to the general computist saving logarithmic computation in every case when tabulation of such functions to integer degrees in requisite.] Now would the computation and printing of the tables in question by the direct operation of an engine such as Mr. Babbage's present any materially greater difficulty the process of multiplication of one number by a fixed succession of given numbers being the whole work of such a table. The facility with which an Arithmetical Engine could accommodate itself to all the requisites of a work of this kind so as to execute [del: the] it with convenience and cheapness would be a fair practical test of its utility.]

[Del: 3. The mathematical quantities known by the name of Elliptic Transcendents are continually acquiring [del: a] greater importance as a means of calculating the numerical results of] geometrical investigations. Tables exist for them, but should their use become more common, these would require to be revised and extended. There can be no doubt that means might be found of computing such tables by differences as in the case of logarithms and thus subjecting them to mechanical calculation and printing, This perhaps is looking too far forward into the future,]

3. [Del: In say nothing of the great number of] In the numerous tables (chiefly arithmetical progressions) which the Public Service requires, [del: for the . ... ] the guarantee of unimpeachable correctness [del: in such tables] is not without its dsitinct value. [Del: a very simple case will illustrate this] This may be instanced by a [del: simple] case of recent occurrence. In the reports [del: and ... made by] of the Commissioners [del: for considering] appointed to consider the steps to be taken for restoring the lost standards of weights and measures, it is recommended that an edition of certain tables [del: of a peculiar .,.] should be prepared and printed by Government for the use of dealers in Bullion as a probably influential means of procuring [del: publicity] the disuse of the Troy Pound. As vast sums would come to be computed [del: by such tables, a perfect reliance of their freedom from error [del: indispensable] becomes the most indispensable condition for their introduction.]by such tables it is obvious that nothing but a general impression of their absolute correctness could secure their introduction [del: and adoption] and so enable them to [del: accomplish] exert their designed [del: purpose] intent.

[Del: 5. By the use of Automaton wheels various tables founded on observed laws of mortality or other statistical or observational data not reducible to any known mathematical expression might be calculated and printed, I presume Mr Babbage cannot have over looked this application of his mechanism,]

These instances, [del: and a great many more which it would be tedious to recapitulate] will suffice to shew that the prospect of utility to accrue from the completion of the Engine in question is neither illusionary nor trifling, The ultimate practical utility of the Engine must however also greatly depend on the convenience and cost of working and maintaining it, on the regulations under which its accessibility to the public may be secured and on the distinctness of the direction for its use and for the repair of such parts as may in possibility get out of order as its inventor shall furnish to accompany it [del: and] which [del: direction I should observe] must be regarded as an essential part of it, [Del: These however are points on which I have no information and indeed which are [incidentally! individually] posterior to its construction.]

The second point [del: or that of relative utility] on which as already observed the utility of continuing to spend money on the machine appears to me to depend, [del: is that in which the the question of relative utility, is one on which the fact placed before me afford no data but hypothetical ones] is the total proposed expenditure, as weighed against the absolute utility of the machine, and as considered in relation both to the sums already expended and to the claims which other branches of Science theoretical and practical may be held to have on that portion of the national income (del: which .... ] be it greater or less [than] which can be devoted to such objects I should cripple my prospect of scientific utility irrecoverably in my present and future possible advocacy of any such claims if then consulted I could [del: leave out] omit so very important an element.

Now the terms [del: of any problem...] in which the question is put viz that a sum not less than 16000 will be required, leave me here without any ground to go upon except [del:up]on one assumption which therefore I am compelled to make. Viz: that the minimum named is also the [del: ultimatum] ultimum, that the least grant which will accomplish the object is the last which will be asked for. [Del: Even with this assumption] And in effect it is possible that such may be the case for, I consider that by this long and costly experience, Mr Babbage must have acquired a full practical knowledge not only of the expences attending this peculiar style of workmanship in general, but a clear view of particular items, so that it would be not unreasonable to expect that he [del: should] might be [del: enabled] able by this time to name a sum which would certainly cover the cost and with which, if granted he would pledge himself to the completion of the Engine, life being spared [insert: and that he has only been held back from doing so by the natural reluctance which every man feels to pledge himself against contingencies]. At all events I must suppose such a pledge given with respect to the sum actually actually in question, or declare myself unable to advance towards the formation of any opinion at all on this [del: point] head [del: and must be understood to decline doing so].

Making this assumption then the work, pecuniarily speaking must be regarded as half done. [Insert: As regards invention and experience I presume it must be considered much further advanced since it seems to me inconceivable that a man of Mr Babbage's talents bending his powers almost exclusively for 20 years to this object and [del: Expend?] devoting to it so vast an amount of intellectual labour as I know him to have done should not at least have fully perfected the/his idea [del: of the Engine he has undertaken] of the Engine [del: as have for those only I contemplate] he originally proposed to construct [del: whatever development his ulterior views]

[Del: And the question is as to the utility of expending the latter half of its total cost in resuscitating the former which will otherwise have been sunk.

[Del: Now] It is clear that if, in the outset of the project, it had been decided that 32000£ was not too much to expend on it, Mr Babbage is only so far advanced on the high road to his conclusion, and all is right.

If on the other hand it had been decided to expend only as far as 16000 the money is expended and the work not completed. [Del: Therefore the attempt on that supposition, and in that sense of the word has failed.] The attempt then on that supposition and in that sense of the word has proved unsuccessful.

And it [del: has] now comes to be enquired whether it be for the public benefit to make a [del: first] second attempt [underline deleted:) with the advantage of starting from the advance gained and the experience of 20 years acquired.

[Del: Now though I will not presume to state] I think it would not be becoming in me formally to deliver an opinion on this point because it is rather a moral than an abstract one, and one which it rests solely with the executive to estimate -for, (in the case which I am now arguing) [del: they have] it has [del: their] its part, and it must be purely a matter of liberality if [del: they] it volunteer a second time. Yet it is my duty to observe

1st that the advantages to the Public of such an Engine remain just what they were before its construction was attempted.

2d That I have full confidence in Mr Babbage's ability to complete the Engine if the pecuniary means be afforded him.

3d That although at the outset of this matter [insert: as a member of the Council of the Royal Society and bearing in mind the claim of other branches of Science to [del: the] public aid] I should certainly have viewed with dismay the idea of recommending [del: as a member of the Council of the Royal Society] an expenditure of 32000£ of the public money on this object -yet [insert: judging from my present impressions] I am disposed to think I should not have [del: regarded] considered the [del: half] moiety of that sum wholly inadmissible, if regarded as an absolutely as final and under proper understanding as to the accordance to the public of the privilege [2 under [del: reasonable] proper regulations][1 of using the Engine when completed].

4th That, as 20 years have elapsed in proceeding so far, and [del: that] as doubtless a considerable time must still elapse before the completion of the work and the Total Expenditure being therefore spread over a very long period, a corresponding enlargement of the period within which the equivalent benefits are to accrue, ought to be allowed. A tree of slow growth must repay its culture by a long maturity.

5th [Del: That I have hitherto forborne to advert to the immitiga] That although ultimate success may be damped in the minds of some by an impression of excessive cost, yet there can be no dissentient opinion as to the immitigated evil[del:s] of an outlay of 16000£ terminating in an abandonment of the undertaking.

[Deleted with the note "Out decidedly": So far in reference to the Expenditure already incurred, in weighing a proposed public erpenditure for useful purposes against the expected it is necessary [insert: in so far as those benefits can be estimated as a matter of pecuniary value] in order to turn the scales to shew either 1st a certainty of a saving accruing to Government itself of a sum at least equal in a short time, or 2d of a much longer saving or profit in a long one or 31y a highly probable gain or saving to the Community to an amount so great as to render the Expenditure comparatively insignificant. In none of these points of view however do I feel prepared [del: to give any opinion much less to] with such a demonstration in the actual state of the data, and to hazard [del: an unsupported] a merely conjectural opinion and expect it to be received as valid would be idle.

Of benefits not [del: so] distinctly capable of pecuniary estimation I have already stated my opinion that they are neither illusionary nor trifling.

[Deleted with note "Out ??" and in pencil: "Out but do not hope it rewritten": As respects the claims of othr branches of Science I can have only one remark to make that Science consists of parts in harmony and not in jealous conflict or competition with each other and that the most desireable and advantageous way in which it can be advanced by public aid is by an application of such aid to all its branches, liberal in proportion to their relative importance [del: until a comparatively void period.

The Third [del: point] element into which I have resolved the question submitted to my consideration is the probability of success, the means being granted. I have already stated my opinion of Mr. Babbage's full ability to complete the machine satisfactorily, [del: life being spared]. But in an event to be deplored equally by his friends and by the world, should this great work not be finished or very nearly so [deleted with note "Out": I know not when the task of completing it could .. .. .

the case being one altogether peculiar ......... its completion by a successor could ahrdly be looked for considering the rare combination of inventive power, [del:zeal] and devotion to this particular object which would be required. A son indeed might complete what the Father began, but the public would have no right to expect it at his hands.

It would be fortunate indeed if a successor should arise possessing the same combination of inventive powers and [del: absolute] devotion to the task which [del: so eminently] distinguish Mr. Babbage himself.

I ought further to add that I have felt it my duty, being so applied to, to [del: form and deliver] give the subject the best consideration I am able without reference to [del: those] the opinions whatever they may be of my scientific colleagues. This, though necessary to secure the singleness and independence [del: of] which I think an opinion so demanded ought to have, yet tends to render me diffident [del: in .. * in its delivery] of its value [del: even in its present modified form] and disposed to wish that as the principle of individual has been preferred to that of public reference, that principle should be extended further than to myself alone supposing it not already done.

Neither have I communicated on the subject with Mr. Babbage himself for a similar reason though as [del: my personal] a friend [del: whose] from whom I am desirous to have no concealment on a matter so nearly [del: relating to his interests] affecting him I can have no objection but rather the contrary [del: that a copy of this letter should be transmitted to him] to his being made acquainted with the contents of this letter,

I have the honor [del: to be] most respectfully [del: Sir] to remain

[del: with the utmost respect]

Sir

Your most obedt & humble Servt

JFW Herschel

Note on back of letter:

Box A5, no 13

Letter to Goulbourn

Re Babbage's Calculating Engine