A Young Man's Mathematics Lessons

Pages of calculations and problem-solving in the lesson book of Daniel Toll. Image from Glen-Sanders Papers, collection on microfilm in the Grems-Doolittle Library (originals at New-York Historical Society in New York City). 

This blog entry is written by Schenectady County Historical Society trustee John Gearing.

Among the manuscript treasures of the Grems-Doolittle Library lies an oft-overlooked gem: the Glen-Sanders Papers. Members of the Glen and Sanders families resided in Scotia's eponymous mansion for over 200 years. In the mid-twentieth century the estate was broken up and the remaining Glen-Sanders papers came into the possession of the New-York Historical Society. The Schenectady County Historical Society has a copy of the papers on eighteen reels of microfilm. The collection includes correspondence and notes (the earliest of which is dated 1674), account books, maps, wills, and genealogical records.

A careful reading of such papers can help us better understand what life was like in Schenectady in earlier times. While one could be excused for assuming that eighteenth century life was far simpler and much less sophisticated than it is today, a mathematics lesson book in the Glen-Sanders papers suggests otherwise. The book bears the name of Daniel Toll and is dated 1790. The mathematics taught were practical in nature and covered topics essential to every successful merchant.

The first exercise taught young Mr. Toll how to subtract the weight of a container, the “tare,” to determine the weight its contents. For example, flour was sold at the wholesale level in barrels. This sounds simple, but some goods were sold in units of “hundredweights” (or 112 pounds) and tare was sometimes set at a percentage of the whole rather than the actual weight of the container. Conversions were often necessary. Also covered was the calculation of “Brokage,” which Toll defined as “the percentage charge levied by those called Brokers who find customers and selling them the goods of other men whether strangers or natives.” A budding merchant needed to calculate “tret” as well. Tret was the amount (typically 4 pounds per hundredweight) allowed for the wastage of goods during shipment.

Page dealing with the subjects of tare and tret in the lesson book of Daniel Toll. Image from Glen-Sanders Papers, collection on microfilm in the Grems-Doolittle Library (originals at New-York Historical Society in New York City).

Both simple and compound interest were covered in Daniel Toll's subjects. He was taught how to compute interest when the percentage was not a whole number, and how to compute either the return, the term, the principal, or the percentage when the other three factors were given. Fractions, both “vulgar” and decimal, were covered, along with multiplication.

The lessons were taught using pounds, shillings, and pence. Instead of being a decimal system like today's dollar, this system was based on multiples of twelve. Twenty pennies made one shilling, and twelve shillings made a pound. Merchants' calculations required converting pounds to shillings and pence, and vice versa. Some problems required converting everything to pence, completing the calculation in pence, and then reconverting the answer to pounds, shillings and pence.

Complex computations were taught using a sort of algorithm. For example, to determine the present value of a amount due to be paid in the future, Toll wrote:

“Answer
1. As 12 months are to the rate percent
So is the time proposed to a fourth number

2. Add that fourth number to ₤100

3. As that sum is to the fourth number
So is the given sum to the rebate

4. Subtract the rebate from the given sum
and the remainder is the present worth.”

Although this “answer” may be mystifying to modern eyes, a careful perusal of the Toll's sample problem shows that four steps above were easily translated into arithmetical calculations by students of the day.

Assuming the dates (1790 and 1793) in the lesson book are accurate, Daniel Toll would have been between 14 and 17 years old when learning the practical mathematics shown in this lesson book. The difficulty and complexity of Toll's math curriculum seems to compare favorably to that of today's students of the same age, suggesting that Schenectadians 224 years ago were not all that much different, in some respects, than we are today. Assuming that Jonathan Pearson's information is correct in his Genealogies of the Descendants of the First Settlers of Schenectady, Daniel Toll, it seems, grew up to be a physician, and not a merchant after all.

An Early Schenectady Newspaper: The Western Spectator

Masthead of the Western Spectator newspaper. This particular issue is dated April 21, 1803; it is the earliest issue our library has on microfilm. Image from the collections of the Grems-Doolittle Library.

The Western Spectator, or, Schenectady Weekly Advertiser was an early newspaper published in Schenectady from 1802 to 1807. The Western Spectator is the one of the earliest known newspapers known to be published in Schenectady; the first was the Mohawk Mercury (1795-1798).

A cluster of notices from the April 21, 1803 Western Spectator. The notices include an advertisement seeking "a sober industrious man" to work in the beer brewing business, a house and lot for sale on Green Street in Schenectady, a notice of a 15-year-old enslaved girl for sale, and a notice offering a one-cent reward for the return of a runaway indentured apprentice. Image from the collections of the Grems-Doolittle Library.

Our library has seven issues of Western Spectator, from the years 1803-1805 and 1807, on microfilm. Although only a few issues of the newspaper have survived, the issues provide an interesting look at the local community. A local printer, John L. Stevenson, established a weekly paper titled the Schenectady Gazette in 1799. In December 1802, Stevenson changed the name of the Schenectady Gazette to the Western Spectator, or, Schenectady Weekly Advertiser. Publication of the Western Spectator ceased in 1807.

The Western Spectator contains numerous advertisements for local businesses. This advertisement announces the new general store of P. Brower at the corner of Washington Street (now Avenue) and Front Street, selling liquors, meats, dry goods, and dishes. Brower notes that he will "dispose of low for Cash or country produce." Image from the collections of the Grems-Doolittle Library. 

Notice of John P. Whitbeck of Niskayuna in the February 17, 1804 Western Spectator offering five dollars for the return of Jack, a slave who had escaped. Like many runaway slave notices of the time period, the notice includes an extensive description of the enslaved person. Image from the collections of the Grems-Doolittle Library. 

The Western Spectator was published weekly. Issues of the paper were four pages in length and contained lengthy articles on national, international, and occasionally statewide news. The newspapers also included a number of local news items and notices. Local notices included advertisements for local businesses, legal notices, notices about mail service, notices listing property and slaves for sale, and notices of local elections. Local notices also included notices for the return of runaway slaves and apprentices. Rarely, a death notice of a local person was printed; no marriage notices appear in the newspaper.

Advertisement of the Western Mail Stage, operated by Moses Beal, which ran from Albany to Utica. This notice is rare, as it includes a small illustration; most notices of the time period did not. This notice appeared in the Western Spectator on February 17, 1804. Image from the collections of the Grems-Doolittle Library. 

An index of local people, businesses, and organizations mentioned in the Western Spectator has been compiled by one of our dedicated volunteers in the library. This index makes it possible to easily and quickly locate articles of interest to local history and genealogy researchers. An index to the issues of the Western Spectator in the library's holdings can be found by clicking this link. Have questions? Visit our library or contact our Librarian.

This cluster of notices from the November 22, 1805 Western Spectator includes a notice of the opening of a dancing school conducted by Gimbrede and Guey at the Schenectady home of James Rogers, the opening of Dr. John Dodge's medical practice on Ferry Street, and notices regarding the estates of local residents John McIntire and James Adair.

Notices related to unsettled debts, defaults on mortgages, and notices regarding money owed to or from an estate were very frequent in the Western Spectator. In this example, which appeared in the November 22, 1805 issue, Henry Corl, Jr., of Charlton, requests that any debts owed to him be paid at his store in Schenectady by March 1. Remaining unsettled debts were to be turned over to an attorney for collection after that date. Image from the collections of the Grems-Doolittle Library. 

Notice of opening of school of architecture in Schenectady that appeared in the Western Spectator on December 14, 1804. The first part of the notice had originally appeared in a previous issue of the newspaper. The second part of the notice was added in this issue to confirm that the school opened on December 1 and that they were still accepting students. Image from the collections of the Grems-Doolittle Library. 

Advertisement for sale of lottery tickets at the Schenectady post office, from the January 11, 1805 Western Spectator. Image from the collections of the Grems-Doolittle Library.

Accessing the Mohawk Mercury

Portion of an advertisement for dry goods at Charles Martin's store in the Mohawk Mercury, February 9, 1795.  Grems-Doolittle Library Collections. 

This blog entry is written by volunteer Robert J. Jones. 

The Mohawk Mercury was a weekly newspaper published in Schenectady during the last decade of the 18^th century.  In the Historical Society’s collection, we have microfilm of the paper between February 9, 1795 and March 13, 1798.  Published originally by Abraham Brockaw and Cornelius Wyckoff, Wyckoff became the sole publisher in September of 1795 according to a notice of the dissolution of their business partnership printed in the newspaper.  After this notice, no further mention is made of Brockaw, and he fades into history from the pages of his former paper.  Wyckoff, on the other hand, continues his business of selling books and doing print jobs aside from the newspaper itself.  He becomes active in various religious groups and uses his paper to promote books and publications of a religious nature.  According to an August 22, 1954 newspaper clipping from the Union-Star newspaper that we have in the library, a certain John L. Stevenson bought the paper. It is unclear if Stevenson continued printing the Mercury, but in 1799 he was publishing a newspaper under the name Schenectady Gazette (no relation to the present-day Schenectady newspaper), so it’s possible that he simply changed the name of the original publication.  In 1802 Stevenson changed the name of the Gazette to the Western Spectator and Schenectady Advertiser.  Finally in 1807, he discontinued publication. 

Published every Tuesday with essentially the same format in all the issues for which we have examples, the Mohawk Mercury was never more than four pages long; the first two pages were reserved mostly for national and international news, with some state information.  Pages three and four were almost exclusively local news and notices, generally in the form of business ads.  While the first two pages are interesting in their own right for a glimpse into the important matters of post-Revolutionary America, the real treasure of the publication for researchers of local history are the second two pages.  Given the ads and notices published, the Mohawk Mercury reads like a Who’s-Who of 1790’s Schenectady.  In total, some 1,439 individual names are printed on its pages.  Scanning the list of surnames gives an immediate impression of the ethnic make-up of the city at that time.  Not surprisingly, the overwhelming majority of names are ones we closely associate with old Schenectady: Van Antwerp, Veeder and Vedder, Van Eps, and Vrooman just to stick to the V’s.  Most of the names are of course Dutch, but names from other backgrounds are also present such as German, Welsh, Slavic (probably Polish), English, French and Scottish.

A few of those indexed in the paper have no last names.  At least four slaves, Jacob, Jap, Bawn and Joe are listed with no surnames, and of course all had run away.  Run-away wives were also a frequent subject of public notices with warnings not to harbor or help them. During election season, long lists of committee members were published showing who supported each candidate and telling us where these people lived.  Often these contain the names of many of the same businessmen and other worthies who variously ran ads in the paper.  Since the issues we have date from the founding of Union College, for several months after the institution’s founding, a series of witty essays was published lauding or decrying the college, its students and faculty.  All of them of course were published anonymously!

Considering that few other sources for Schenectady give us this kind of information for this time period, the Mohawk Mercury is a treasure trove for researchers.  Until recently, however, accessing this information has been difficult and time-consuming because no complete index existed. A partial index from issues nos. 9–30 was completed some time ago, but considering that the final issue we have was no. 170, very little information was actually accessible.  In the fall of 2012, I completed the index, and it is currently available for use at the Society’s library.  It can also be found online here.