At the house formerly Sir Charles Hobby's are taught grammar, writing, after a free & easy manner in all hands usually practiced, Arithmetick Vulgar and Decimal in a concise and Practical Method, Merchants Accompts, Geometry, Algebra, Mensuration, Geography, Trigonometry, Astronomy, Navigation and other parts of the Mathematicks, with the use of the Globes and other Mathematical Instruments, by Samuel Grainger.
They whose business won't permit 'em to attend the usual School Hours, shall be carefully attended and Instructed in the Evenings.
R. F. Seybold[4] has noted that: "In advertisements of 1753 and 1754, John Lewis, of New York City, announced 'What is called a New Method of Navigation, is an excellent Method of Trigonometry here particularly applied to Navigation; But it is of great use in all kinds of measuring and in solving many Arithmetical Questions.' James Cosgrove, of Philadelphia, in 1755, taught 'geometry, trigonometry, and their application in surveying, navigation, etc.,' and Alexander Power, in 1766, 'With their Application to Surveying, Navigation, Geography, and Astronomy'." These subjects were featured also in the evening schools of the colonial period, maintained by private schoolmasters in some of the larger communities for the education of those who could not attend school in the daytime.
According to Seybold, surveying and navigation were the most popular mathematical subjects taught. Some explanation is to be derived from the statement by Schoen[5] that: "In the days when the 'bounds' of great wilderness tracts were being marked off by deep-cut blazes in the trees along a line, a knowledge of land surveying was a useful skill, and many a boy learned its elements by following the 'boundsgoer' in his work of 'running the line.' And those who did not actually take part in running the line must have attended many a gay springtime 'processioning' when neighbors made a festive occasion out of 'perambulating the bounds'." "Vague land grants and inaccurate surveys," he adds, "made the subject of boundary lines a prime issue in the everyday life of colonial homes."
At the same time there was interest in the other aspects of the mathematical sciences. As early as 1743, for instance, a Harvard mathematician named Nathan Prince advertised in Boston that if he were given "suitable Encouragement" he would establish a school to teach "Geography and Astronomy, With the Use of the Globes, and the several kinds of Projecting the Sphere" among other things.[6] A decade later, Theophilus Grew, professor in the academy at Philadelphia which has become the University of Pennsylvania, published a treatise on globes, with the title:
The Description and Use of the Globes, Celestial and Terrestrial; With Variety for Examples for the Learner's Exercises: Intended for the Use of Such Persons as would attain to the Knowledge of those Instruments; But Chiefly designed for the Instruction of the young Gentlemen at the Academy in Philadelphia. To which is added Rules for working all the Cases in Plain and Spherical Triangles without a Scheme. By Theophilus Grew, Mathematical Professor. Germantown, Printed by Christopher Sower, 1753.[7]
Thus, the need for practical mathematical instruments for the surveyor and navigator became critical in proportion to the need for men to make and use them, and it is not surprising to discover that the majority of the instruments produced and advertised by early American makers were for surveying, with nautical instruments in second place. Generally, the surveyors were not professionals; they were farmers, tradesmen, or craftsmen with a sound knowledge of basic arithmetic and occasionally with some advanced study of the subject as taught in the evening schools. The surveying of provincial and intercolonial boundaries required greater skill, however, as well as a knowledge of astronomy, and this work was relegated to the scientific men of the period.
As the increasing preoccupation with subdivision of land and with surveying led to a greater demand for suitable instruments, it was the skilled craftsmen of the community, such as the clockmaker and the silversmith, that were called upon to produce them. Superb examples also were produced by the advanced scientific men, or "mathematical practitioners," of the period.
Colonial Training in Instrument Making
One may well ask, where did these native craftsmen acquire the knowledge that enabled them to produce so skillfully the accurate and often delicate mathematical instruments? There were a number of possible sources for this knowledge. The first source lies in England, where some of these craftsmen could have studied or served apprenticeships. After completing their apprenticeship with English mathematical practitioners, they may have immigrated to the Colonies and taught the craft to others. This seems to be entirely plausible, and was probably true, for example, of Thomas Harland the clockmaker, Anthony Lamb, and perhaps several others. However, these were the exceptions instead of the rule, since a biographical study of the instrument makers in general reveals that they were for the most part native to America. It is not likely that the one or two isolated practitioners that had been trained in England could have taught so many others who worked in the same epoch.