FREDERICK H. HOLLANDER
U. S. Naval ObservatoryTHE IBM EQUIPMENT at the United States Naval Observatory is used primarily to serve the needs of astron-omers, navigators, and aviators .. We publish annually the American EpheHteris and Nautical Almanac) the American Nautical Almanac) and the American Air AI1Jwnac.
The Ephemeris supplies data with the highest degree of accuracy. It contains theoretical positions of the sun, moon, planets and stars, with an accuracy of a tenth of a second of arc. Astronomers compare their observations with these data. The Air Almanac) on the other hand, is very rough by these standards, giving to the nearest min-ute of arc positions of the sun, three chosen planets and the moon for every ten minutes of the day. In other words, it is a highly interpolated table of relatively ·low accuracy to enable an aviator to determine his position rapidly dur-ing a flight.
The Nautical Almanac stands halfway between the other two, with an accuracy of a tenth of a minute of arc, and values given for every hour. The new form of the N auti-cal Almanac) which will be published beginning with the year 1950, is designed to facilitate use by having all the essential data for three days at one opening of the book.
The Air Almanac was designed similarly; all the informa-tion necessary for the aviator except a few tables is avail-able on one page opening. This includes corrections for the parallax of the moon, tables of moonrise and moonset, and sunrise and sunset, in addition to the values of the' Greenwich hour angle (GHA) and declination for various objects. The star tables are not included on the daily page of the Air Altnanac) because, to this accuracy, a star's position remains practically the same from day to day throughout the year.
All these data for the two almanacs are prepared by IBM machines from the accurate material of the Ephemeris. In addition, all the information is arranged on cards so that it may be printed on a special model card-operated typewriter, of which there are only two in ex-istence. The U. S. Naval Observatory has the first of these
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machines;l the other is at IRM W orId Headquarters in New York City. They are modifications of the st9-ndard card-operated typewriter, special as to keyboard, and as to the type of work they can produce.
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am going to devote some attention to the typewriter and attempt to demonstrate the versatility of its output by means of illustrations, but I want to show also how the rest of our IBM equipment fits into the picture, in supply-ing material for the typewriter.There are some special problems in setting up the cards, and that is where the other machines come in. For one thing, in a table which is published for a navigator or aviator, accuracy is essential. That means the methods of checking the results must be practically fool-proof. It is necessary that the typewriter prepare the copy from single punched cards. By that I mean each column containing numerical information must have just one punch, because our method of proofreading is to take the printer's proof as it is returned after a photo-offset plate has been made and punch the material again line for line on a new set of cards. Then those cards are compared on the 513 with the cards which had been used to prepare the copy.
That sounds like a painful process when you consider that the Air Almanac each year consists of 730 pages of 72 lines, each line consisting of a solid row of fi~ures. It requires a considerable amount of punching to duplicate all that. Yet that is the most accurate, and even turns out to be the fastest, operation. The method is applied also to the other publications, and so for any job we do, the first requirement is that the numerical data occupy single punched columns. The only double punches permitted on the detail cards are code punches, which are not puriched in proof.
In addition to the comparison with the original copy cards, a further proof against errors is made by differ-encing the fUllctions. This is carried out .on the 405.
Since we have several functions on a card, the method is limited to forming first differences, and summary
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ing these to get second, and so on. I t is a slow process to get sixth differences this way, but that is what is done, for example, in the case of the ephemeris of Mercury. moonset is possible at certain selected latitudes. The data from the eph~meris are then reproduced into new cards, and these in turn form the basis for an inverse interpola-tion to find the exact time of th~ phenomenon. Values of an hour angle preceding and of an hour angle following the moon rise or set are obtained in the 405 and summary punched. An interpolation on the-601 or 602 gives the the computed values. Other checks include differencing day by day for each latitude, and differencing values for the corresponding day with respect to latitude. The latter is a most powerful check, for if one adds the moonrise time to the moonset time for each latitude for agiven day, the sum is practically a constant for all latitudes. This check is applied also to the sunrise and twilight tables of the Nautical Almanac.
The only fault to be found with this whole procedure is that a great deal of hand manipulation of large decks of cards is required because there is no way of moving cards from one machine to another except by hand. Considerable care is necessary to prevent disarrangement of the cards.
At some stages in the process, any such disarrangement could go undetected long enough to cause serious damage.
The magnitude of the task is obvious when you consider from the daily values in the A11'lerica'1'z, Ephemeris) by com-puting the hourly differences, and. by progressive totaling these differences with appropriate starting values, thereby building up the required functions. The data for the N
au-SCIENTIFIC COMPUTATION
tical Almanac are further subtabulated to give the ten minute interval of the Air Almanac.
The original installation of the IBM machines at the the motions of the major planets and their satellites. Much of this work is annual, but some of it has been done just possible, rather than interpolate, because subtabulation goes faster and more automatically and, once it is set up, several functions can be done simultaneously. Checking is made easier by this method, also. Our intervals are usu'ally uniform, and we have no proble111s involving complex quantities or matrices.
We make one principal demand, and that is the utmost in accuracy to a large number of decimal places. In the integration of planetary orbits, ten decimal place accuracy is common. In our almanac work, extra decimals are needed to prevent accumulated rounding errors. Both the large capacity counters and the accuracy. are supplied in a satisfactory way by the Type 405 Accounting Machine and the Type 602 Calculating Punch. One handicap is the limited punching capacity of the Type 602.
N ow I would like to tell you a little about the card-operated typewriter. Perhaps the best way is to refer to the illustrations; then a few comments will give you a good idea of its capabilities. Figure 1 is a page of the Air Atmanac. It represents the time from noon to midnight of the same day for every ten minutes of time, giving for those times the GHA's and declinations of the sun,moon, and three planets, and in addition, tables of sunrise and moonrise. The summary punching which produces the GHA's also produces the cards which will go through the typewriter; the declinations and miscellaneous tables are reproduced into these cards in their proper line relation-ship. The typewriter prints the numbers from these detail cards, and the control of the spacing from column to column is taken care of by a master card which is read over again for each new line.
JUPITER -1.9