Month: July 2015

The Astronomy Exam at Haverford College in 1859

In the late 1850s students at Haverford College had to pass exams in three departments: English, Classics, and Mathematics.[1] They demonstrated their mastery in these divisions through a grueling set of exams at the end of the senior year.[2] First they had to pass a battery of private exams that covered all the subjects and spanned two weeks. These private exams were followed by a set of public exams.

According to the regulations established in 1855, the faculty had to determine the private exam schedule in advance and give the seniors one full week’s notice. In 1859 the seniors had to take the following test:

Private Exams at Haverford College in 1859
Week 1 Week 2
AM PM AM PM
2nd Day Antigone & Grk. Ex. Differential Calculus Dymond Lat. Prose (Cic. & Tacit.)
3rd Day Kent’s Commentaries Integral Calculus Analyt. Geometry Butler
4th Day Logic Rhetoric Horace & Lat. Ex. Mechanics
5th Day Intellect. Philosophy
6th Day Political Economy Thucydides Optics
7th Day Astronomy
At the faculty meeting on May 27, 1859, the faculty determined the schedule for the first week of private exams that year. Nearly a month later the faculty got around to finalizing the second week’s exam schedule. The Minutes of the Faculty are found in Haverford Quaker & Special Collections, Call# HCV—R4 ID 1835–1869 (see the finding aid).
At the faculty meeting on May 27, 1859, the faculty determined the schedule for the first week of private exams that year. Nearly a month later the faculty got around to finalizing the second week’s exam schedule. The Minutes of the Faculty are found in Haverford Quaker & Special Collections, Call# HCV—R4 ID 1835–1869 (see the finding aid).

Each exam was supposed to include a “series of written questions … [with] a number being annexed to each question, to represent the value assigned to a correct answer” and must include a “suitable number of questions” to test the students’ mastery. Each day students filed into the examination room where under the watchful eye of a faculty member they were prohibited from talking to each other while they took the exam. Exams lasted up to four hours.

Seemingly in an effort to reduce bias against students, the faculty had stipulated that each student should assume a motto and should sign his exams not with his name but with that motto. According to the regulations set down in 1855:

XII The papers containing the answers, must not be signed with the students [sic] name, but with a name or motto, assumed for the occasion; and a sealed envelope, inscribed with said assumed name, and containing the real one, must be handed in to the first meeting of the council, after the merit of the answers has been determined.

Predictably, some students were quite creative in the mottos they adopted, sometimes capturing, no doubt, their own anxiety about the exams:
Crocket, H. St. John, Mohawk, O!, Kit Carson, Incog., Imparatus, No Anxiety, Anxietas, √–1.

Equally predictably, others viewed it as a tedious task, choosing something trite—Greek letters were common, e.g., Omega and Beta were common.

Some of the mottos reflect the prominence of the classics in Haverford’s early curriculum:
Aeneas, Tyro, Hesperus, Ajax, Hector, Themistocles, Ὄνομα, Ἑρμῆς, Ξένος, Παραδειγμα, Φευ φευ.

Finally, and most interesting to me, some mottos seem to reflect a growing interest in astronomy, e.g., Regulus, Hipparchus, and most bluntly Telescope.

In 1859 eight students took the private exams.

The faculty always recorded student performances in the Minutes of the Faculty Meeting, listing both the student’s motto, his real name, and his grades in the three departments as well as his average. The Minutes of the Faculty are found in Haverford Quaker & Special Collections, Call# HCV—R4 ID 1835–1869 (see the finding aid).
The faculty always recorded student performances in the Minutes of the Faculty Meeting, listing both the student’s motto, his real name, and his grades in the three departments as well as his average. The Minutes of the Faculty are found in Haverford Quaker & Special Collections, Call# HCV—R4 ID 1835–1869 (see the finding aid).

The Haverford College Catalogue lists the books seniors studied and the faculty who taught the various course. From the list of books and the public lectures faculty agreed to give, we glean some idea of what seniors were supposed to have learned. In the late 1850s Moses Stevens was responsible for teaching the mathematics, which was divided into three subjects: mechanical philosophy, optics, and physical and practical astronomy. For the first two subjects, students were assigned a book by Olmsted, perhaps Dennis Olmsted’s An Introduction to Natural Philosophy (1844)). For astronomy, they read a book by Robinson, probably Horatio Robinson’s A Treatise on Astronomy, Descriptive, Physical, and Practical (1850).

The Haverford College Catalogue for 1859 lists the books students read in the mathematics department. The books included a text by Olmsted on mechanical philosophy and optics, and a book by Robinson on astronomy. The Haverford College Catalogue for 1859 is available online here; this particular page is available here.
The Haverford College Catalogue for 1859 lists the books students read in the mathematics department. The books included a text by Olmsted on mechanical philosophy and optics, and a book by Robinson on astronomy. The Haverford College Catalogue for 1859 is available online here; this particular page is available here.

Although we don’t have Stevens’s lecture notes, we do have copies of the exams he gave the students in 1859 along with the students’ answers and marks on each section.[3] Stevens divided mathematics into six areas and tested the students on each: Analytical Geometry, Differential Calculus, Integral Calculus, Mechanics, Astronomy, Optics. The first three the students learned as juniors; the second three they studied as seniors.

Stevens tested the students in six areas. He recorded their grades in this summary table and then reported to the faculty the students’ general average on the battery of mathematics exams. Here, each area was worth 10pts for a maximum total of 60 pts. In some cases, students earned more than the maximum points—if their answers were particularly good, they could earn extra credit. The students were, apparently, most prepared for the optics exam and least prepared for the astronomy exam. These exams are found in Haverford Quaker & Special Collections, Call# 910H (this collection of materials contains all sorts of fascinating stuff, see the finding aid).
Stevens tested the students in six areas. He recorded their grades in this summary table and then reported to the faculty the students’ general average on the battery of mathematics exams. Here, each area was worth 10pts for a maximum total of 60 pts. In some cases, students earned more than the maximum points—if their answers were particularly good, they could earn extra credit. The students were, apparently, most prepared for the optics exam and least prepared for the astronomy exam. These exams are found in Haverford Quaker & Special Collections, Call# 910H (this collection of materials contains all sorts of fascinating stuff, see the finding aid).

Although all the exams—both the exams for the various mathematical subjects and the different students’ exams in each subject—would repay study, here I’ll look at just one student’s responses to the astronomy exam. The student, “Katabasis”—Benjamin H. Smith[4] was his real name—was an average student. He performed slightly better than average on the astronomy exam, but overall he was slightly below average.

When Katabasis walked in to examination room on the morning of the seventh day of the first week of exams he confronted nine questions that asked him to identify astronomical instruments and their parts, define astronomical terms, and carry out a range of calculations:

Astronomy

  1. Name the varities [sic][5] of eye-pieces in common use and describe each. Val 5.
  2. Describe the transit instrument. Val 6.
  3. How do we compute the correction for to the time of transit, for inclination of axis, for collimation and for meridian? [Val] 20.
  4. Given the R.A. and Dec. of two stars to find their distance apart. [Val] 8.
  5. Give a method for finding the lat. of a place. [Val] 10.
  6. How can we find the position of the equinoctial points? [Val] 10.
  7. What is meant by the angle of the vertical and how may it be computed? [Val] 8.
  8. Give the method of computing Rad. of earth at any point. [Val] 12.
  9. Define the parallax of a heavenly body, and show how to computer the par. of moon in R.A. [Val] 21.
Katabasis neatly copied out the astronomy examination questions. Minor spelling mistakes, e.g., “varities” for “varieties,” and abbreviations were common in the students’ copies of the questions. This exam is found in Haverford Quaker & Special Collections, Call# 910H (this collection of materials contains all sorts of fascinating stuff, see the finding aid).
Katabasis neatly copied out the astronomy examination questions. Minor spelling mistakes, e.g., “varities” for “varieties,” and abbreviations were common in the students’ copies of the questions. This exam is found in Haverford Quaker & Special Collections, Call# 910H (this collection of materials contains all sorts of fascinating stuff, see the finding aid).

Unfortunately, there’s no indication how long Katabasis and the other students had to complete the exam, though a couple of them remarked that they didn’t complete a question because “time fails.”

Although the three years of astronomy courses at Haverford used Robinson’s textbook, when Moses Stevens taught the course he had to supplement this material. For example, Robinson’s textbook said nothing about varieties of eye-pieces or transit instruments. Katabasis’ answer to question one seems to have come from Elias Loomis’s An Introduction to Practical Astronomy, which the college assigned a couple years later as the astronomy textbook. The order, the drawings, the terminology, and even the underlining in Katabasis’ answer echo that found in Loomis’s textbook.[6] Perhaps equally telling, the unnecessary information and detail Katabasis added, e.g., when he described how to “find the power of the telescope,” is exactly the detail that follows Loomis’s discussion of eye-pieces.[7]

Katabasis’ answer to question one: “Name the varities [sic] of eye-pieces in common use and describe each.” It seems likely that the source of this information was Elias Loomis’s An Introduction to Practical Astronomy. This exam is found in Haverford Quaker & Special Collections, Call# 910H (this collection of materials contains all sorts of fascinating stuff, see the finding aid).
Katabasis’ answer to question one: “Name the varities [sic] of eye-pieces in common use and describe each.” It seems likely that the source of this information was Elias Loomis’s An Introduction to Practical Astronomy. This exam is found in Haverford Quaker & Special Collections, Call# 910H (this collection of materials contains all sorts of fascinating stuff, see the finding aid).

It is easy to imagine one of two scenarios: First, Stevens turned to Loomis’s textbook to fill in important information he thought was missing from the assigned text. Haverford had, after all, built and equipped a new observatory that it prided itself on and required students to use. In such a case, basic, practical knowledge of the instruments would be useful. Second, Katabasis had for one reason or another not learned the information in class. To make up his deficiency he had consulted Loomis’s text during his six weeks of review prior to the exam.[8]

Although the college boasted that its students had plenty of opportunity to do astronomy in its new observatory, only the first two questions gave the students a chance to demonstrate their experience working with astronomical instruments. And even these two questions don’t require working with instruments so much as being able to describe their parts—neither required the tacit knowledge that students might gain only from working with instruments. Most of the exam asked students to explain how, in principle, to carry out certain astronomical calculations. Surprisingly absent from the exam were problems that asked the student to carry out astronomical calculations.

Again, Katabasis’ answers to these latter questions seem to owe a debt to Loomis’s An Introduction to Practical Astronomy rather than Robinson’s text. For example, question 7 asks to define the “angle of the vertical” and show how to calculate it. This term is found nowhere in Robinson’s textbook. However, in Loomis’s text this problem is explained in terms remarkably similar to Katabasis’ answer, including the diagram that illustrates both Katabasis’ exam and Loomis’s textbook.

Katabasis’ answer to question 7, “What is meant by the angle of the vertical and how may it be computed?” so closely resembles the example in Loomis’s textbook that it seems likely that Loomis, not Robinson, was being used in the classroom. This exam is found in Haverford Quaker & Special Collections, Call# 910H (this collection of materials contains all sorts of fascinating stuff, see the finding aid).
Katabasis’ answer to question 7, “What is meant by the angle of the vertical and how may it be computed?” so closely resembles the example in Loomis’s textbook that it seems likely that Loomis, not Robinson, was being used in the classroom. This exam is found in Haverford Quaker & Special Collections, Call# 910H (this collection of materials contains all sorts of fascinating stuff, see the finding aid).

On closer inspection, it turns out that most of the questions are found in Loomis’s textbook but not in Robinsons. Question 6, e.g., asked how to find the equinoctial points. Whereas Robinson’s text says nothing about this problem, Loomis’s textbook discusses the issue and works three examples. Unfortunately for Katabasis, he did not recall either the discussion or the examples. For question 6 he noted, simply, “Non reminiscor.”

The astronomy exam and Katabasis’ answers give us a glimpse of Haverford’s astronomy curriculum in the mid–19th century. Together they help us see beyond the prescribed curriculum and texts—in this case, his answers suggests that the prescribed text was not the primary resource used to teach astronomy. The exam questions also give us a chance to see what the college considered valuable astronomical knowledge. Considered alongside the other students’ exams and Katabasis’ own diary, we can perhaps begin to piece together a detailed picture of astronomy education at Haverford College in the mid–19th century.[9]


  1. These departments resemble our current divisions. Mathematics, for example, included mathematics as well as mechanics, optics, and astronomy. English was divided into “Ethics etc.” and “Belles-Lettres.”  ↩

  2. During the same period the class known as “second junior” (what we now call sophomores) took a set of exams. Before long Haverford did away with it idiosyncratic “second junior” and “third junior” terms and adopted the more common (and now standard) sophomore and freshman.  ↩

  3. Unfortunately, I have not located copies of Stevens’s lecture notes, so we don’t have a clear sense of what he tried to teach the students. We do have Samuel Gummere’s lecture notes from a few years later, after he took over the teaching of mathematics. I’ve looked briefly at Gummere’s Lecture on Copernicus, but his entire set of notes merit further attention.  ↩

  4. I have just noticed that we have a copy of B.H. Smith’s diary while he was a student here at Haverford—it is also in this collection Call# 910H, which is a treasure trove of diaries, lecture notes, and other source material (it also includes another set of lecture notes by Samuel Gummere (see Samuel J. Gummere’s Lecture on Copernicus for a set of notes from Call# 910F)). I didn’t have a chance to look at it before writing this post but will look read through it as soon as I can.  ↩

  5. The slight variations and minor spelling mistakes in the questions across student papers suggests that the students had to copy the questions from a blackboard (one student didn’t write out the questions to the astronomy exam, just his answers, so it seems unlikely that students wrote down questions as they were read aloud at the beginning of he examination).  ↩

  6. Although the description of eye-pieces is sufficiently generic to cast doubt on finding Katabasis’ source, the underlining in his answer that corresponds to the italics in Loomis’s text certainly suggests a close link between the two. I’m not implying any malfeasance on Katabasis’ part. Just looking for sources for his information.  ↩

  7. It is interesting to see students in the 19th century doing what students still do today and perhaps have always done: bulking up answers with unnecessary information. Perhaps this practice comes from not yet knowing (or being confident that you know) what a good answer would include. Perhaps it comes from a general anxiety about having left something out. Perhaps it comes from a mistaken notion that more is better or at least not worse. Whatever the source, it’s comforting to know that what I no doubt did as a student and what I see students doing now has a long pedigree.  ↩

  8. According to the regulations established in 1855, the faculty gave the seniors and second juniors a six-week reading period to prepare for exams:

    II. The Senior and 2d Junior Classes, will be allowed the six weeks next preceding the examination, for a general review of their studies….
    Haverford’s current one-week reading period seems paltry in comparison  ↩

  9. If only we could find a copy of Moses Stevens’s lecture notes for this period, we would be set. Samuel Gummere’s notes from a few years later might also be helpful, especially because by that point Loomis’s An Introduction to Practical Astronomy was the prescribed textbook.  ↩

Astrolabes or Mariner’s Astrolabe—A Primer

Celebrations are afoot in Ontario celebrating 400 years of Francophone presence in the region. An important part of those celebrations is Samuel de Champlain’s exploration of Ontario and his early encounter with First Nations cultures. Simcoe.com has a short post on an exhibit that includes one of Champlain’s navigational instruments: “Historic astrolabe on display in Midland believed to have been Champlain’s.” Unfortunately, there’s a bit of confusion about this instrument, which is not in fact an astrolabe.

The Simcoe article faithfully reports information from the Sainte-Marie among the Hurons site. Unfortunately for the Sainte-Marie among the Hurons site, the Canadian Museum of History, which owns the instrument, contributed to the confusion. The museum lists the instrument, artifact #989.56.1, as an astrolabe (the museum also identifies its two other similar instruments—artifact #988.58.1 and artifact #LH994.142.1.2 as astrolabes). Buried toward the end of the museum’s description is a passing comment that identifies the instrument as a “mariner’s astrolabe.”

This passing comment is the only place that Champlain’s instrument in correctly identified as a “mariner’s astrolabe.” Although the two instruments share one possible function—determining the altitude of star (usually the sun or the pole star)—that’s it. The astrolabe combined observations and calculations, allowing the user to perform hundreds of operations. It was both a complex, technical device and a status symbol. The astrolabe has been compared to iPhones and more recently to a complex Rolex watch.

Astrolabes—pre-modern Rolex or iPhone, you decide.
Astrolabes—pre-modern Rolex or iPhone, you decide.

These comparisons capture the astrolabe’s status and superabundance of operations its operations. My pamphlet offers a handy introduction to the history, fabrication, and use of astrolabes. Hundreds of astrolabes survive.

The mariner’s astrolabe, by contrast, was utilitarian and singular in function. It allowed the user to determine the height of the polar star or the sun and, thus, the observer’s latitude. The instrument’s design reflects its utilitarian function. Mariner’s astrolabes are typically heavy, made from a thick brass ring (only the limb of astrolabe) to limit them from swinging too much as the ship’s deck swayed and rocked at sea. Some had a ring at the bottom of the instrument from which to hang a weight for added stability. The body of the instrument was often cut away to reduce, scholars claim, the effects of wind blowing on the body of the instrument.

On the left is a typical mariner’s astrolabe from ca. 1600, from the Museum of the History of Science, inventory #54253, found here. On the right is a planispheric astrolabe, usually called simply an astrolabe. This is an early 16th-century astrolabe from the Museum of the History of Science, inventory #52528, found here.
On the left is a typical mariner’s astrolabe from ca. 1600, from the Museum of the History of Science, inventory #54253, found here. On the right is a planispheric astrolabe, usually called simply an astrolabe. This is an early 16th-century astrolabe from the Museum of the History of Science, inventory #52528, found here.

The limb was typically graduated from 0°–90° in the upper quadrants, once again reflecting its use as a basic observational instrument. A simple alidade with rather crude sighting vanes was attached to the front of the instrument. At night the navigator would look through the holes in the alidade to align them with the pole star. Then he could read the altitude of the star from the graduation on the limb, which altitude was, roughly, his latitude. If he wanted to know his latitude during the day, at noon he rotated the alidade until the sun shown down through the holes in the vanes (he would not look at the sun for obvious reasons). He read the sun’s altitude from the scale on the limb, added or subtracted the earth’s tilt based on the day of the year, and subtracted the result from 90° to obtain his latitude.

The mariner’s astrolabe was a nautical/navigational tool. Although an astrolabe could have been used at sea as a navigational tool, it is unclear that they were. The instrument’s many functions and finely graduated limb would have made it unnecessarily complicated and difficult to use on the deck of moving ship. Moreover, the astrolabe’s cost and status make it seem unlikely that a mariner would have owned one when there were other, more specialized and less expensive instruments that did the same thing. There are a few illustrations of astrolabes being used on ships, but whether these are idealized or meant to reflect contemporary practice is unclear. The various instruction manuals that include canons on how to use astrolabes at sea, e.g., Johannes Stöffler’s Elucidatio fabricae ususque astrolabii (1513), do not demonstrate that they were so used. Authors of such manuals sought to distinguish themselves and demonstrate their expertise by cataloging as many possible uses for astrolabes as they could imagine, regardless of whether or not anybody actually used astrolabes in those ways.

Surely few people used an astrolabe to make the many observations Cosimo Bartoli cataloged in his Del modo di misurare (1564). Google has scanned it here.
Surely few people used an astrolabe to make the many observations Cosimo Bartoli cataloged in his Del modo di misurare (1564). Google has scanned it here.

Whereas traditional astrolabes were expensive, status symbols and were, therefore, collected and displayed, mariner‘s astrolabes were working tools. They were not, as a rule, collected or displayed. Consequently, much rarer today—only about 100 survive and most of those were recovered from shipwrecks (the Museum of the History of Science has a nice audio guide to the mariner’s astrolabe here).

Champlain’s instrument was graduated from 0°–90° in each quadrant. The body has largely been cut away. And on the front is a large alidade for sighting.

From this photo it is clear that Champlain’s instrument was a mariner’s astrolabe. From the Canadian Museum of History description—direct link to photo.
From this photo it is clear that Champlain’s instrument was a mariner’s astrolabe. From the Canadian Museum of History description—direct link to photo.

It is plausible that he brought a mariner’s astrolabe with him as he explored Canada. But the story of Champlain losing his instrument by a lake, it having lain there in the forest for 250 years before a 14-year-old boy found it, and its subsequent sale to different collectors, seems almost too good to be true. And the instrument’s remarkable shape, having spent more than two centuries in the dirt, is equally surprising.[1] Whether or not it was ever owned by Champlain, his instrument is clearly a mariner’s astrolabe.


  1. In its description of the instrument’s provenance, Canadian Museum of History expresses some but not much skepticism about the story (my emphasis):

    In May 1613, Samuel de Champlain, the French explorer-cartographer, travelled up the Ottawa River. To avoid the rapids, he chose a course through a number of small lakes near Cobden, Ontario. Champlain and his men were forced to portage and to climb over and under fallen logs at one particularly difficult point by Green Lake, now also known as Astrolabe Lake. It was here, according to several nineteenth-century authors, that Champlain lost his astrolabe. If this is correct, the astrolabe remained where it had fallen for 254 years. Eventually a 14-year-old farm boy named Edward Lee found it in 1867 while helping his father clear trees by Green Lake. Captain Cowley, who ran a steamboat on nearby Muskrat Lake, offered Lee ten dollars for the astrolabe. Lee never received the money nor saw the astrolabe again. Cowley sold the astrolabe to his employer, R.W. Cassels of Toronto, President of the Ottawa Forwarding Company. He in turn sold it to a New York collector, Samuel Hoffman. The astrolabe was willed to the New York Historical Society in 1942 where it remained until June 1989, when it was acquired by the Department of Communications for the Canadian Museum of Civilization. This astrolabe is unique. It is the smallest of 35 mariner’s astrolabes surviving from the early part of the seventeenth century and the only one from France. It is in excellent condition, except for one missing piece, a small ring on the bottom edge of the disk, to which a weight was likely attached to help keep the instrument plumb. The ring was probably broken off sometime in the late nineteenth century, since it appears in an 1879 photograph of the astrolabe.

    For a more thorough analysis of the connection between Champlain and this instrument, see “The Mystery of Champlain’s Astrolabe” or, more recent, “19th century manuscript sheds new light on ‘Champlain’s Astrolobe [sic]’ thought lost by French explorer.”  ↩