It is an ancient story. For months, the Famous-Editor had been trying to persuade the Oldest-Reporter-in-the-World to write a feature story on their mutual friend, Halstead. Since the Oldest-Reporter-in-the-World had been with the Famous-Editor since 1902 (when he was neither famous nor an editor), since the assignment was extra duty, and since, despite both of these conditions, the Oldest-Reporter and the Famous-Editor were friends of long standing, so often had the Oldest-Reporter postponed writing the story on Halstead which both of them really wanted to see in print, that the matter had become something of a joke between them.
And then one morning, the Oldest-Reporter-in-the-World pushed into the editorial sanctum. The Famous-Editor regarded his friend in amazement. Overnight a surprising change had taken place in the old man—his gray head was held high, his stride was more youthful and vigorous, the expression in his face more eager and cheerful than they had been for years. In his hand, he carried a sheaf of typewritten pages.
"Good-morning, Chief," he said, and there was a strange pride in his voice. You won't have to remind me about that Halstead story any more. Here it is, and, if I do say so, it's pretty decent."
An expression of uneasy dismay flashed across the Famous-Editor's face. "I'm sorry, Fred," he said. "It's too late." He held out a small slip of paper to the Oldest- Reporter-in-the-World. "Tear up your yarn, Fred, and write me a nice obituary."
My sensations on a certain day some months ago must have been much the same as those which in that moment overwhelmed the Oldest-Reporter-in-the-World. Ever since reporting to the Salinas as navigating officer, I have intended to write an article in appreciation of the Air Almanac. When I received orders to this duty, I made certain that a copy would be available for my use. For some months I tested the new almanac in routine navigation of this much traveled vessel and for more months I merely procrastinated writing my enthusiasm for it. And then the Pilot Chart of Central American Waters for September, 1933, came to tell me that, like the Oldest-Reporter’s friend Halstead, the Air Almanac is dead. Let this, then, be an obituary, and yet at the same time an appreciation, for, while the Air Almanac as such is quite definitely deceased, portions of its many excellencies have been admitted to the Nautical Almanac for 1934, and so its spirit (and something of its substance) lives on.
I must be careful. In my enthusiasm, I do not wish to be guilty of an overstatement. During recent years in several countries, many and distinguished have been the contributions to the science of celestial navigation—new methods for solving the old astronomical triangle, new devices for computing dead reckoning, new instruments for measuring celestial angles, new aids for keeping accurate time, new navigating machines—but not one of these has operated to simplify that most troublesome element in the solution of the astronomical triangle, that calculation where the most frequent and grievous errors are made—the time element of the problem involved in computing the local hour angle of a celestial body.
Because, aside from earlier tabulation of Greenwich hour angles of the moon in the Nautical Almanac, the Air Almanac presents to practical navigators the first improvement in computation of the local hour angle in nearly a century, it is my honest and considered opinion that the Air Almanac is the most significant contribution to the science of celestial navigation of this century. And this is said not from a theoretical standpoint but after constant and exhaustive test of this volume over a period of months as navigating officer of one of our tankers, on which celestial navigation in all its ramifications is a daily necessity.
After the above praise, I must hasten to add that I do not consider the Air Almanac as published in 1933 the final word in perfection, for refinements can be made in a number of the tables which would render use of the Almanac even less liable to error than it is at present. The excellencies which I have found and the possibilities for improvement of the tabulation of the various functions will be considered in some detail.
The sun.—For years after my first introduction to celestial navigation, I struggled with the 2-hour interval of tabulation of functions of the sun in the Nautical Almanac, and wondered why in the world the data were not tabulated every hour. The hourly differences at the bottom of the tables were useful, but, in the heat of battle, I found that not at all infrequently I added the proportional part of an hourly interval directly to the tabulated function when I should have allowed for an additional hour after the tabulated function. And so, of course, error frequently resulted. When I discovered that sun data was tabulated every hour in the Air Almanac, I was delighted. This may seem to be a small matter, but under the pressure of actual navigation, any small matter is of importance. Hourly tabulation is vastly superior to 2-hour tabulation. Upon becoming familiar with the functions as tabulated in the Air Almanac, use of the correction table for the Greenwich hour angle of the sun was unnecessary. One merely divided the minutes and seconds of G.C.T. by four and added the degrees and minutes thus obtained to the tabulated Greenwich hour angle. Furthermore, hourly tabulation renders picking out the declination much easier and less liable to error.
Use of the equation of time was entirely eliminated by the Air Almanac, and no feeling of loss was experienced. In addition, one possibility for error was removed. What navigator will not admit that he has on occasion picked out the declination for the equation of time, or vice versa?
The Air Almanac is particularly handy for determining the time of local apparent noon. All that is necessary is to plot the approximate position of noon, pick off the longitude, enter the sun table for that day and find a G.H.A. approximately equal to the longitude. One can then add mentally to the corresponding G.C.T. sufficient minutes of time to make the G.H.A. equal the longitude. If absolute accuracy is desired, a new plot should be made and the process repeated. Two such operations should take much less than a minute.
And so we see that the Air Almanac has eliminated use of the equation of time, local apparent time, and the possibility of several grievous errors, and has made the determination of the G.H.A. merely a matter of looking up a number in a table and adding to it a small correction. The improvement is decidedly advantageous.
Which of these advantages have been carried over into the Nautical Almanac for 1934?
In that publication, functions have been tabulated every two hours, which I consider less desirable than the hourly tabulation. While hourly tabulation would double the number of sun pages in the Almanac, this is an advantage rather than a handicap, for judicious use of paper clips to fix the place in the book makes a few pages more or less in the Almanac of negligible importance, when one weighs this disadvantage against the decreased possibility of error in use of the tables which hourly tabulation insures.
The equation of time has been included and therefore one still may occasionally pick out that function when the declination is desired. However, this disadvantage is outweighed by the desirability of having all navigational data combined into one Almanac, so that navigators wishing to cling to the old ways may be permitted to do so.
Determination of the G.H.A. is only slightly complicated by the 2-hour tabulation. It is more difficult to compute the correction to the G.H.A. than it was with the Air Almanac. Enough of the new data has been included in the 1934 Almanac so that the improved method of local hour angle determination may yet be used with considerable advantage over the older method.
The stars.—The manner in which the 51 common navigational stars were tabulated daily was the happiest inspiration of the Air Almanac. No longer need right ascension and sidereal time confuse the novice and confound the experienced navigator to frequent error. The G.H.A. is picked out for the Greenwich date. The correction tables for G.C.T. are simple and easy of application. Conversion of seconds of time to minutes of arc is readily accomplished mentally. All that one needs to know is how to add 3 angles together and the G.H.A. of any of the common stars is painlessly obtained. When I recall the difficulty and uncertainty which always accompanied my computation of the L.H.A. of any star with the old Almanac, my enthusiasm for the Air Almanac rises to a high pitch. When one considers that the Air Almanac also obviates the necessity for conversion of G.C.T. to G.S.T., for picking out of the Almanac the sidereal time of zero hours G.C.T., for correcting this data from Table III or its equivalent, for converting G.S.T. to G.H.A. by picking out the right ascension of the star, applying it to the G.S.T., and finally converting the G.H.A. from time into arc (all of which operations are so difficult as to be the cause of frequent error and distress even to experienced navigators), the reason for my enthusiasm for this particular feature of the Air Almanac is readily understandable.
With the Air Almanac, all that must be done is to pick out directly the G.H.A. and add to the tabulated function two readily obtained corrections and the G. H.A. is down in black and white. If one uses “H.O. 211,” one need not even write down the declination. The A and B functions from that publication are included right in the Air Almanac. The reduced trouble, pain, and worry and the increased ease of computation are amazing.
Most navigators work at least four star or planet sights at each twilight. Usually there are only 3 sun sights per day, one of which is a meridian altitude or a reduction to the meridian. Therefore, there are ordinarily 8- or 10-star or planet sights to be worked per day and only 2 or 3 sun sights. The major portion of the celestial navigation of a navigator’s day is computation of the altitudes and azimuths of stars or planets. For this reason, this new method of tabulation of star data is, in my opinion, the most significant contribution of the Air Almanac to practical navigation. The lessened strain, labor, and liability to error resulting from use of this one feature of itself makes the Air Almanac of unquestioned value.
The monthly tabulation of the G.H.A. of “additional stars” in the Air Almanac is better than the method used in the old Nautical Almanac, but it is not nearly as desirable as the daily tabulation of the 51 stars of greater magnitude. A correction table for the day of the month must be entered, which necessitates addition of a column of 4 angles to obtain the G.H.A. I have no doubt that twice as many mistakes are made in adding a column of 4 angles as are made in adding 3. Under pressure for speed in computation, the increased possibility of error is very great.
As the 51 stars which are tabulated daily in the Air Almanac are ample for all needs of practical navigation, this less desirable method of tabulation of “additional stars” would be of little importance were it not that the 1934 Nautical Almanac has included this latter method of tabulation of G.H.A. of stars as the only improvement in star computation carried over from the Air Almanac. This is to be regretted. The method of G.H.A. tabulation in the 1934 Almanac is enough clumsier than the daily tabulation in the Air Almanac greatly to reduce the advantage of the distinctive advancement in star computation which the Air Almanac contributed to celestial navigation. The 24 additional pages necessary to tabulate daily the star data (as in the Air Almanac) would be of inestimable value to practical navigators using the G.H.A. method of computing their star data. If it is not considered desirable to increase the bulk of the Almanac by 24 pages, 24 stars could be tabulated daily on 12 additional pages without crowding. Judicious choice of these 24 stars would provide ample data for celestial navigation in clear weather and would include most of the stars used in any weather or latitude. Certainly the increased convenience to navigators would be worth the price of 12 additional pages.
Inclusion in the Air Almanac of the A and B functions of declination from “H.O. 211” has occasioned considerable favorable comment from navigators using that method. One entry in the navigation table and recording the declination were eliminated. I found this feature of the daily star tabulation most convenient. Apparently lack of space prevented inclusion of the “H.O. 211” functions in the 1934 Almanac. Navigators using “H.O. 211” during the coming year will find it desirable each month to enter in pencil in the margin opposite the declination of stars frequently observed the A and B functions from that publication.
The planets.—Frankly, I liked the arrangement of the planets in the Air Almanac so little that, after a few trials, 1 observed the planets only when sufficient stars were not in evidence at morning and evening twilight. The correction table on page 209 of the Air Almanac is innocent looking and appears simple to use, but in the higher hours a very tedious and difficult interpolation is necessary to obtain the correction for the G.H.A. No correction table is provided for declination. To obtain the correction for declination, one has to multiply the variation per minute by the G.C.T., which must first be converted to hundredths of hours. Both of these computations are unpleasant mathematical operations. With stars so easy to compute, working a few planet problems made the effort and exertion by comparison seem to be not at all worth while.
After considerable study, two solutions became apparent.
- Expand the main tables to tabulate the functions every hour.
- Expand the correction table on page 209 so that such interpolation as is necessary can be done by inspection. Devise a correction table for declination.
The first solution would require 276 additional pages of tables, which is obviously impractical. However, the second solution was found to be entirely practical. The table on page 209 was expanded 5 times, but, since values were tabulated every hour instead of every 20 minutes, only two additional pages were required. The tables on page 210 are entirely satisfactory. A 3-page correction table for declination was constructed which rendered picking out the correction for declination merely a matter of inspection. If considered desirable, a correction table for right ascension of planets of 5 pages could be easily computed. Since I would never use I have not constructed one.
In actual use in daily solution of several planet problems, these tables were found to be eminently satisfactory. This is of considerable importance, as the data for planets in the 1934 Almanac have been tabulated daily just as they were in the Air Almanac. The planet correction tables on pages 152 and 153 of the 1934 Almanac are practically identical to those in the Air Almanac. A portion of my improved correction tables for the year 1934 is given at the end of this article.
The moon.—In the Air Almanac entirely too much space was devoted to this celestial body for the use which will ever be made of it. Despite the increased convenience of tabulation in the Air Almanac most navigators with whom I have discussed the matter state that they still avoid observation of the moon except in extraordinary cases, such as in circumstances where simultaneous sights of the sun and moon may be obtained or when the moon is the only heavenly body available at twilight. If such be the consensus of opinion, the infrequent occasion when observation of the moon seems desirable or is forced upon one does not appear to warrant devoting so much space to that body in an already crowded Almanac. I was glad to see that the 1934 Almanac tabulates the moon data only every hour. This is entirely adequate, but I would like to see more complete interpolation tables covering all the phases of the moon, instead of the small tables included in the 1934 Almanac opposite to each day's tabulation of data. These small interpolation tables take up entirely too much space.
Such new correction tables should be based on the principle of the moon correction tables given on page 211 of the Air Almanac, but I would suggest that they be extended to tabulate data every minute during the hour instead of every 10 seconds as at present and that columns for every 0.02 variation per minute of G.H.A. be provided. This would require one more page than in the Air Almanac, but would provide interpolation by inspection of these 2 tables. If considered desirable, an additional table of one page for correction of the right ascension could very easily be constructed, as the variation per minute of this function is only between 1.8 and 2.7.
There are two important advantages to be obtained by construction of such correction tables for the moon: (1) interpolation between hours for the tabulated data would be vastly simplified; (2) 6 days’ data could be tabulated per page instead of 4, reducing the number of moon pages from 90 to 60, and this without serious crowding or omission of essential data. The variation per minute of each function could be tabulated at the bottom of each column as was done in the Air Almanac. Thus, by inclusion of such correction tables, 3 pages would be added and 30 pages saved.
Polaris.—The data for Polaris as tabulated in the Air Almanac are excellent. I was happy to see that identical tabulation has been carried over into the 1934 Almanac. This method of computation of latitude from observation of Polaris is a great improvement over the method of the old Almanac. The L.H.A. is computed with much less difficulty and the correction to be applied to the true altitude of Polaris is taken from the Almanac with much greater facility due to the less complex arrangement of the second table.
Sunrise and sunset.—Ordinarily I like diagrams and curves less than tables. The “Sunset, Sunrise, and Twilight Diagram” of the Air Almanac, particularly as issued in a larger scale as “H.O. 5175,” is splendid. I recommend it highly for ease and speed of use. With this diagram published as a Hydrographic Office chart, it would seem to be unnecessary to continue to include it in the Almanac.
Arrangement.—Particularly happy was the arrangement of correction tables on the back covers of the Air Almanac and on pages at the front and rear of the book. Upon becoming familiar with the publication, finding the desired correction table was almost automatic. I like the location of correction tables in the Air Almanac much better than in the 1934 Nautical Almanac. In the latter publication, the tables are found at the end of the pages of the data to which they apply. Each entry to these tables results in “thumbing the pages” and consequent annoyance and loss of time, unless one resorts to an old familiar use of paper clips and marginal indexing to space off the book so that it falls open to the desired places in the 4 tables commonly used. Even with the Almanac so marked off, it would be more desirable to have the correction tables at the front and back of the book where they are readily available. The cover could be bound more ruggedly, true enough. Had I not secured my covers with adhesive tape last year, they would have pulled off before the year was half out.
No difficulty was experienced with the narrower margins of the Air Almanac. The crowded pages presented no problem in finding the desired functions. In my opinion, with arrangement of data in columns and the functions spaced off by cross and vertical lines, the desired data were even more readily picked out of the book than they were from the old Almanac.
During the past year, I have discussed the Air Almanac with a number of merchant officers and was pleasantly surprised to hear the major portion of them express enthusiasm for the new publication. Invariably they added, “Of course, I must keep up with the old Almanac until I have taken my master’s examinations, but the Air Almanac certainly makes it easier for an officer at sea.”
In my opinion, the conservatism of merchant navigators has been overstressed. I believe that they are as eager as the next person to learn improved methods. Such has been my experience with those I have encountered. And so I consider it a decided step forward to have combined the Air Almanac data into the Nautical Almanac, where curiosity will lead navigators at least to try the new method, and a fair trial will inevitably convince them that they have come upon something easier and finer. Even navigators think that the Air Almanac is applicable only to the newer methods of navigation! In the time sight and the cosine-haversine methods we invariably needed to know t, declination and latitude, and what is t but the longitude applied to the G.H.A. (which is now tabulated in the Nautical Almanac for 1934)? We should not, for the present at least, drop the older data from the Almanac, but I would feel deep regret should we fail to include in the Nautical Almanac the distinctive improvements which the new method of tabulation has brought to celestial navigation.
Desirable improvements.—From a practical angle, what can be done to improve the arrangement of data in the 1934 Almanac? Naturally, I can express only my own opinion, but it is my earnest belief that the following constructive improvements can be made at no cost in efficiency and with decided assistance to the officers, merchant and naval, who navigate our ships from place to place across the surface of the sea:
- Tabulate the sun data every hour instead of every 2 hours.
- Add 24 pages of star data tabulating daily the G.H.A. of as many stars as possible.
- Include A and B functions of declination from “H.O. 211.”
- Expand the G.H.A. correction table for planets as previously described and include a new declination correction table for planets.
- Add 3 pages of moon correction tables.
- Delete small interpolation tables on each page of moon data and tabulate 6 days of moon data per page.
- Group all correction tables at front and rear of book as was done in the Air Almanac.
- Bind the Almanac more raggedly so that the covers will be able to stand up under a year of routine usage.
Incorporation of these improvements would add some pages, save others. The result would be a slight increase in the bulk of the Almanac, but the practical navigator would gladly welcome these added pages if he knew that when he turned to the proper page he would have less difficulty picking out the desired data.
I wish to reiterate the firm conviction that this new method of tabulation of data, in my opinion, is the most distinctive contribution to the art and science of celestial navigation of this century. Certainly, the Air Almanac has made my cruise as navigator infinitely more enjoyable than it could ever have been without that splendid publication. While realizing that it would be folly to change the method of tabulation of the Nautical Almanac prematurely, still I hate to see the science of navigation retrogress, when definite progress has already been made and the way indicated to further improvement. I would like to see the Nautical Almanac incorporate into itself all of the advantages of the Air Almanac.
At any rate, and whatever may eventuate, I am happy to have been navigator of a Navy ship when the Air Almanac was my helpful and efficient shipmate.