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The ExpeditionPhiladelphia ConnectionsAstronomy Notebook
Lewis's Notes
Biddle's Opinions

Hassler's Dilemmas

Page 10 of 13

"The Proper Person"


Lithograph by Charles Fenderich

from a painting by Wm. G. Williams (c. 1835)1

Image theb3475, NOAA People Collection
Courtesy, Association of Commissioned Officers

erdinand Rudolph Hassler (1770-1843) was the person selected to complete the longitude calculations from the observational data that Lewis and Clark brought back. Upon him rested the ultimate materialization of Jefferson's plan for a map of the Missouri and Columbia Rivers that would be as accurate as modern science could produce. Upon him also rested much of the blame for the plan's failure.

Hassler was born in Switzerland where, as a youth in Bern, he studied mathematics, astronomy, and surveying. He emigrated to the U.S. in 1805, and soon became associated with Robert Patterson, and John Vaughan of the American Philosophical Society. When Congress established the United States Coast Survey in 1807, Hassler was hired as supervisor, on Patterson's recommendation. Meanwhile, President Jefferson appointed him as Acting Professor of Mathematics at the new U. S. Military Academy. He was dismissed on December 31, 1809, after the new Secretary of War, John Calhoun, discovered that Congress had not authorized the hiring of civilians to staff the Academy. For the next three years he taught mathematics and Natural Philosophy at Union College in Schenectady, New York.

He was unpopular as a teacher, and was dismissed as the first superintendent of the U.S. Coast Survey after only two years in that very important position. From 1817 until 1830, however, he proved his worth as a theorist, publishing two influential books, Elements of Analytical Trigonometry, and Elements of Arithmetik, Theoretical and Practical. In 1830, President Andrew Jackson appointed him United States gauger, responsible for regulating the national standards of weights and measures. Meanwhile, he was reappointed as superintendent of the United States Coast Survey in 1832, and served successfully in that role also, until his death in 1843.

At Jefferson's behest Lewis evidently delivered at least some of his and Clark's records of celestial observations to Hassler early in the spring of 1807, for on May 3rd he advanced the mathematician $100 to begin computing the longitudes. On 26 January 1810, three months after Lewis's death, Clark wrote to Hassler: "The Calculations which you made of the Celistial Observations taken by the late Govr. Lewis (& myself) on the late expedition to the Pacific, are not found among his papers. . . . I flatter my self with a hope that those Calculations with the M[em]orandoms are in your possession." He requested that Hassler send them to the publisher who was to issue the journals, John Conrad of Philadelphia. Nearly seven months later Hassler sent the following letter to his friend Robert Patterson, still uncertain as to what had been expected of him. (A copy of a map by Clark was immediately forwarded to him; Hassler returned it to Nicholas Biddle, but it has since been lost.) By the following December 20th, despite the free time the mathematician expected to have in late August, Clark had given up. "I am sorry that I could not get the Calculations from Mr. Hosler[sic] to Correct the Map," he wrote to Biddle, "but, I hope [the final map] will doe without." Biddle was exasperated with Hassler too, as the next letter suggests.

Hassler's work with Lewis and Clark's celestial observations was intermittent and perfunctory, which made it unproductive in the long run. It was unsatisfying to all concerned, for reasons which are implied in the two letters that follow. Hassler's writing is sometimes difficult to understand, owing to his somewhat limited facility with the English language.

--Robert R. Bergantino and Joseph Mussulman


Florian Cajori, The Chequered Career of Ferdinand Rudolph Hassler (Boston: Christopher Publishing House,1929).

V. Frederick Rickey, "Ferdinand Rudolph Hassler," http://www.dean.usma.edu/math/about/history/hassler.htm. Accessed October 6, 2005.

Letter 1: Ferdinand Hassler to Robert Patterson

Schenectady [New York] 12th August 18102

Dear Sir

Some few days ago I received a letter from Mr. Vaughan by which I am very sorry to be informed that he is considerably unwell, I hope it will not be of serious consequences and only transitory, I shall be happy to hear soon of his entire recovery.

This circumstance obliges me to disturb You with these lines, relating to the calculations of Capt. Lewis Voyage of which Mr. Vaughan3 sent me lately the chart, which I compared now with the results before obtained and was now some time ingaged in scrutinising the whole as far as my means reached.I could not go at it before because of the severe sickness of my younger girl who is now recovered from death and in full restablishment, after more than 2 month’s severe sickness.

I had many preparatory Calculations to make to ascertain different points relating to the Elements of the calculation, in calculating backwards from the circumstances & times given what ought to have been observed, so the Err:s Ind:as were otherwise indicated than usually in Math: Obs: the needle was re[a]d once at the north, once at south point &c. &c. After this having made what I could without a chart, which had been promised in the begining, together with the other journals (having only one, in a fair copy, which I see has many faults in writing) I am now in the following difficulties relating to the positions of some interesting points.4

1. The point of Departure, Mouth of River Dubois opposite Missouri Ct. Lewis determines Lat: 38° 55' 20" Longit: 89° 57' 45" and so I admitted it till I had the chart. But this gives long: about 93° 11' to this place and sets it opposite Illinois west of the Mississippi. A large map of Hutchins 1778[,]5 an other large map copy of Arrowsmith6 &c. what I could consult[,] gives this place about 2° more west Long: than the confluent of Ohio in MissisIpi, this point is determined by Mr. Ferrere7 89°06' which will not agree well together. I therefore tryed to conclude backwards from further points which gives me as follows

Table 22

which would place this point nearer the determination of other maps and the chart itself. So does also the comparison taken from No. 3 by a similar operation; the Departure is = 91 07 05. These results fall all between Chart numerical Datas given and pretty near the commun maps. But C. L. sais that his Long. is the result of 7 Sets of Dist: "and may be depended on with safety to 2 or 3 minutes of a degree." He gives the chronometrical determination 90° 00' 20" wherefore the chronometers rate of going was determined at the mouth of the Ohio, with which I just compared it. Which result would you advise me to adopt? The latitude is in the Chart some minutes more south but upon that I think is not to see it (it agrees there about with Hutchins, & Arrowsmith copy).

2. My journal in hands goes till Fort Mandan No. 51. The latit: of it Capt. L. gives by mean 47° 21' 04" but the Chart 46° 15' about[,] where lais the error, I must think in the Chart because C. L. has different results which I calculated over and found only such differences as show me that he was not full equal to me in his prop. parts &c. The longitude he determines by the Eclipse 14th Jany. 1805. The two ends only =

Table 23

But taking the time he indicates for the observation and supposing it corrected (therefore reduced, as he has made the calcul.) I find there a mistake of just 1h which gives reduced for these two results when compared with the nautical Almanac

Table 24

without saying if true, mean or watch, time. The Chart places this point nearly 103°. The Lunar Distances give somewhat diverging results above 114° -- but I will calculate them once more, having discovered the above error, with the new suppositions for the full accuracy of the prop: parts. What do You advise me to relay [rely] upon here? For the intermediate parts I have no mean[s] of comparison till I have some further Elements; when I come to the south Sea I have some again, by Cooks and Portlof & Dixons Voyages,8 for his Chart leads him just about 1° and 2° south of Nutka sound and between two determined points of C. Cook.

I have constructed a Chart Projection upon the principles which I mentioned You on occasion of that of Mr. Garnett,9 for the Lat. 38°-48° upon the Elements from the last measurements compared &c. &c. in the scale [1/2,000,000] where I could therefore make all the constructions with accuracy & ease. In less than a fourthnight I shall have pillaged fully the journal I have in hand and to do more I want the subsequent journ: and if a chart is wished containing all the determinations and a sketch which Gen. Clark can then fill with more particulars if wished. I want also the journal of Courses and bearings over the whole, this might give me besides this the, allmost absolutely necessary, advantage of determining those intermediate points of this journal, for which I have not Elements enough; which are numerous, and correct others, or decide on the choice of the observations.

But I should wish to have the originals if possible, be they how they will, they will direct far better than fair copies, which are never faultless. The work is tedious in itself and much more [so] when the very elements must on all possible supposition be tried. I have made more than double the calculations for this purpose than for what will appear in the results.

We have now about 4 weeks more vacancies which would be the the most convenient time for me to give to this work. I should therefore wish to have it as soon as possible, with directions upon the way in which one wished the result, if map & astron: Result, or only the last. If I had had all means, above, I should have done with it about 3. years ago. I shall make as much haste as possible to compleat the whole, when I have the other Elements.

Pray to give our best compliments to Mrs. Patterson and family, and accept my best wishes for Your constant welfare. I remain allways with perfect esteem and sincere attachment Dear Sir Your devoted St.

F. R. Hassler

1. Maryland State Archives, http://www.mdarchives.state.md.us/msa/speccol/sc2200/
sc2269/html/cartographers.html. Accessed November 15, 2005.

2. Autograph letter signed, recipient's copy; Library of Congress. Jackson, Letters, 2:556-59.

3. John Vaughan (1755-1841) was the secretary and librarian of the American Philosophical Society for more than 50 years. It was Vaughan who notified Lewis — via Thomas Jefferson — in late November of 1804, that he had been elected to the American Philosophical Society. The notification would not have reached Lewis, of course, until his return from the expedition. Jackson, Letters 1:166n.

4. Poor Hassler! All the mapping he had done in his life, and all the observations he had taken "followed the book." It's one thing to start your calculations from a reasonably well known latitude and longitude, and with a chronometer that remains at a single spot for days, where one can be absolutely certain of its rate of going. But it could not be so on a voyage such as that of Lewis and Clark.

Not only that, but Lewis obviously was instructed in the simplest methods to make and calculate the observations, involving procedures that worked just by following them through step-by-step without really knowing why they were done.

What Hassler is referring to with "Err:as Ind:as" and "Math:Obs" is that Lewis's Index Errors (Erratas Indicas) had the wrong sign from that generally accepted in mathematical or celestial observational practices. For example, on 22 July 1804, when Lewis describes his scientific instruments he gives the sextant's error as 8'45"--; actually, the sextant's error was +8'45" because it read high by that amount. Thus to correct an observation made with the sextant one had to subtract 8'45" from the observed angle. It all comes out the same if you know what the situation is, but that wasn't made clear to Hassler.

Another example: On 22 July 1804 Lewis gives the error of the octant in the back observation as 2 11' 40.3+. The octant error in the back observation actually was twice that (4 23'20.6"), and the error was minus because it read low by that amount. But since Lewis always divided the observed angle by two before anything else, he merely added the 2 11' 40.3 to the observed half angle and everything worked out okay (except during 1805 when he made his calculations using the wrong index error, and didn't discover it until he was at Fort Clatsop).

5. Thomas Hutchins (1730-89) was a surveyor and geographer who had published a map titled A new map of the western parts of Virginia, Pennsylvania, Maryland and North Carolina; comprehending the River Ohio, and all the rivers, which fall into it; part of the River Mississippi, the whole of the Illinois River, Lake Erie, part of the Lakes Huron, Michigan, &c., and all the country bordering on these lakes and rivers (London, 1778). It is considered one of the most important maps of 18th-century America. Hutchins later became the first Geographer of the United States. www.davidrumsey.com/maps6355.html, accessed October 8, 2005.

6. Aaron Arrowsmith (1750-1823) was the most distinguished cartographer of his era. His maps of North America, especially the editions of 1795 and 1802, were considered the most accurate representations of the parts of the continent which had yet been explored. John Logan Allen, Lewis and Clark and the Image of the American Northwest (Urbana: University of Illinois Press, 1975), 78-83.

7. Not identified.

8. Captain Nathaniel Portlock (1748?-1817), a veteran of Cook's third voyage, and himself captain of HMS King George, and George Dixon (d. 1800?), captain of HMS Queen Charlotte, were British explorer-traders who visited the northwest coast of North America several times between 1785 and 1788 in search of a Northwest Passage. Portlock's account was published in 1798 as Voyage Around the World; But More Particularly to the Northwest Coast of America. www.americanjourneys.org/aj-089, accessed October 8, 2005.

9. John Garnett was a well-known publisher of tables requisite and nautical almanacs used in astronomical observations, including an American edition of The Nautical Almanac.

Funded in part by a grant from the NPS Challenge-Cost Share Program.

Lewis's Notes
Biddle's Opinions

From Discovering Lewis & Clark ®, http://www.lewis-clark.org © 1998-2014
by The Lewis and Clark Fort Mandan Foundation, Washburn, North Dakota.
Journal excerpts are from The Journals of the Lewis and Clark Expedition, edited by Gary E. Moulton
13 vols. (Lincoln: University of Nebraska Press, 1983-2001)