Departme= nt of Mathematics, university of Vermont

Mathematics at UVM &nbs= p;

The First Two Centuries

&= nbsp;

Rog= er Cooke

10/= 1/2007

This document sketches the people and activities that have characterized the Department of Mathematics (now the= Department of Mathematics and Statistics) at the University of Vermont.

Contents

Introduction. 2<= span style=3D'mso-no-proof:yes'>

Sources.= 2<= span style=3D'mso-no-proof:yes'>

Overview of the Subject. = 2<= span style=3D'mso-no-proof:yes'>

§1. The Early Years, 1801–1825= . <= /span>3<= span style=3D'mso-no-proof:yes'>

The Curriculum. 3<= span style=3D'mso-no-proof:yes'>

Instruction and Equipment 5<= span style=3D'mso-no-proof:yes'>

Personnel. 5<= span style=3D'mso-no-proof:yes'>

Students.= 9<= span style=3D'mso-no-proof:yes'>

§ 2. The “Benedictine” Era, 1825–1854. 9<= span style=3D'mso-no-proof:yes'>

Personnel. 9<= span style=3D'mso-no-proof:yes'>

Curriculum. 11<= span style=3D'mso-no-proof:yes'>

Students.= 12<= span style=3D'mso-no-proof:yes'>

The Mathematical Environment. 12<= span style=3D'mso-no-proof:yes'>

§ 3. A Generation of Struggle, 1854–1= 885. <= /span>13<= span style=3D'mso-no-proof:yes'>

Personnel. 13<= span style=3D'mso-no-proof:yes'>

Curriculum. 14<= span style=3D'mso-no-proof:yes'>

The Mathematical Environment. 14<= span style=3D'mso-no-proof:yes'>

§ 4. The Beginnings of Growth, 1885–1= 914. <= /span>17<= span style=3D'mso-no-proof:yes'>

Personnel. 17<= span style=3D'mso-no-proof:yes'>

Curriculum. 18<= span style=3D'mso-no-proof:yes'>

§ 5. Another Generation of Struggle, 1915–1954. 20<= span style=3D'mso-no-proof:yes'>

Personnel. 20<= span style=3D'mso-no-proof:yes'>

Curriculum. 22<= span style=3D'mso-no-proof:yes'>

The Mathematical Environment. 22<= span style=3D'mso-no-proof:yes'>

Students.= 23<= span style=3D'mso-no-proof:yes'>

§ 6. UVM Moves Toward the Mainstream, 1955–1965. 23<= span style=3D'mso-no-proof:yes'>

Personnel. 23<= span style=3D'mso-no-proof:yes'>

Curriculum. 24<= span style=3D'mso-no-proof:yes'>

Research.= 24<= span style=3D'mso-no-proof:yes'>

Conclusion. 24<= span style=3D'mso-no-proof:yes'>

References. 24<= span style=3D'mso-no-proof:yes'>

Mathematics at the University of V= ermont

By Roger Cooke

Introduction. In 1990, as the bicentennial of the founding of UVM approached, a committee was formed to organize a proper celebration of the occasion. = This committee solicited proposals from the Faculty for projects suitable to the= celebration. At the suggestion of my colleague = Jeﬀ Dinitz, I proposed to write the history of mathematics at UVM. The follo= wing pages are the result of that proposal. Being a history of mathematics, this history appropriately has the form of a matrix whose rows are indexed by historical periods and whose columns are indexed by the areas of relevance = to the mathematical history: personalities, teaching, research, students, and = the mathematical environment. Not every position in this matrix will be occupie= d, but these are the general categories that will be discussed.

Sources. The followi= ng material was gleaned from a wide variety of sources. The most important sou= rce of documentary material was of course the University Archives. I am particularly indebted to David Blow, the University Archivist, for his cons= tant and eﬃcient help and suggestions in locating the documents I needed. These documents include the personnel ﬁles on the characters involved, the minutes of the meetings of the Board of Trustees (known originally as the Corporation), and the University Catalogs. The Wilbur Collection at the Bailey–Howe Library has also been a valuable source of material. Finally I am indebted to several r= etired colleagues for their personal reminiscences: Heath Riggs, Ivan Hershner, N. Jam= es Schoonmaker, Joseph Izzo, and most especially George Nicholson,ⁱ whose mathematical career spans more than one-third of the history of mathematics at UVM.

Overview of the Subject. For the general histor= y of UVM there are various secondary sources, for example, that of Lindsay (1954). For that reason the g= eneral history of UVM will be touched on only where it is necessary to the narrati= ve, and no attempt will be made to render judgment on the many issues that arise. Also, before concentra= ting on the details of our own mathematical development, it may be well to expen= d a few words on the perspective within which this mathematics is to be judged. We might consider UVM= in the context of its educational mission in Vermont and Northern New England,= or as an example of an American University, or in the context of world mathematics. Each of these perspectives provides a special kind of insight into the mathematical activ= ity at UVM.

Taking the l= ocal point of view, one is pleasantly surprised to ﬁnd some rather well-educated mathematicians at UVM, even in the early nineteenth century, teaching mathematics in some depth to ordinary citizens aspiring to careers= as lawyers, physicians, clergy, or farmers.&n= bsp; As we shall see, some of these mathematicians even conducted a modest level of independent research. The national perspective reminds us that, although UVM is the twentieth oldest = university in America, there was already in existence at the time of its founding in 1= 791 a sizable number of New England institutions. Indeed, these institutions provide= d the early UVM faculty. Harvard, w= hich was founded before Newton was born, had already celebrated its sesquicenten= nial before UVM was conceived. The national point of view also brings an awarene= ss of the expansion and democratization of education after the Civil War and suggests an investigation into the extent to which UVM shared in this phenomenon. Finally, the perspective of worldwide mathematics invites comparison with European unive= rsities founded about the same time as UVM but on the periphery of the scholarly wo= rld whose primary centers were in Paris, Gőttingen, Berlin, and London, universities such as Christiania (Oslo) in Norway (founded 1807) and Kazan = in Russia (founded 1804). From this perspective one can see clearly the retard= ing inﬂuence exerted by an ocean 3,000 miles wide that separated American scholars from the great centers of European learning. The University of Oslo, for exampl= e, was hardly founded when it produced one of the giants of nineteenth-century mathematics, Niels Henrik Abel, who died in 1829 at the age of 26, but not before producing some of the most profound work ever done on elliptic functions, theory of equations, and analysis. Oslo went on to produce a steady s= tream of such ﬁgures throughout the nineteenth century, people of the stat= ure of Sylow, Lie, and Bjerknes. = Kazan, at its formation, already had the young Lobachevsky as an upper-level stude= nt. These mathematicians were geniuses, of course, but had they been in Vermont= it is unlikely that any European now alive would have heard of them. All the Norwegians mentioned above traveled to the major centers of mathematical ac= tivity. The University of Kazan imported s= uch teachers as Bartels (Gauss’ teacher) to inspire Lobachevsky and his classmates.

UVM, in contrast, was signiﬁcantly small= er than these European universities and dedicated primarily to teaching. Although UVM was founded in close cooperation with the government of the State of Vermont and the village of Burlington, these governments were not seeking to win international prestig= e by the excellence of their scholars. The aim was education for the professions. The early faculty, graduates of su= ch places as Harvard, Dartmouth, and Williams, tended to frame the curriculum = in accordance with their own background. No students from Vermont studied at the feet of the great German and French masters until late in the nineteenth century, and during the period = of this narrative no mathematicians from Europe came to UVM to share their knowledge. Nevertheless, alth= ough the very latest mathematical research has never formed a substantial part of the curriculum at UVM, from the beginning a high standard of competence was= expected of both students and faculty.

§1. The Early Year= s, 1801–1825

The Curriculum. The Univers= ity of Vermont was chartered in 1791 by act of the State Legislature and given = the right to collect rent from a large amount of very proﬁtable land in Vermont. Perhaps because of t= he intellectual isolation of Burlington itself, no real progress was made in acquiring a physical plant or a faculty until the citizens of Middlebury procured a rival charter in 1800 and petitioned for the transfer of the University’s lands to their institution. Thus spurred into action, Da= niel Clarke Sanders, the ﬁrst president of the University, began tutoring four students in 1800, although they were not yet formally matriculated, as= we would describe students today. Formal instruction began, with Sanders as the only faculty member, in 1801. The minutes of the Boar= d of Trustees’ meeting of January 13, 1801 (Vol. 1, p. 51) record that, “The president appointed to procure a tutor reported that no suﬃciently qualiﬁed and respectable charact= er was to be obtained in this State at present.” Because of the year of tutor= ing, Sanders ruled that these students were ready to receive their degrees in 1804. Although no recor= d of the earliest instruction has come down to the present, Lindsay (1954, pp. 85–88) gives the admission requirements and the curriculum for the four-year course of study as described in the Laws of the University from t= hat time. The admission requireme= nts were all classical: the abili= ty to translate the ﬁrst six books of the Aeneid, the four orations of Cicero against Cataline, and the four Evangelists in Greek.ⁱⁱ Admission to the University at this time, and until late in the nineteenth century, was by examination.&nb= sp; The prospective student would appear at the University at a speci= 4257;ed time—usually the week before UVM’s commencement—and prese= nt himself for examination by the faculty.

In keeping with the admission requirements, the curriculum also placed a heavy emphasis on a literary and classical educati= on. Still, mathematics was not neglected. In fact, one may well ask who today has an intimate knowledge of all these particular mathematics courses, some of which have passed out of the standard curriculum or been absorbed into more comprehensive courses:

Second year. 1st. Vulgar Arithmetickⁱⁱⁱ... 2d... Logarithms and Algebra... 3d... Geometry and Euclid’s

Elements. Plane Trigonometry. Mensuration of superﬁces and solids. Gauging. Mensurat= ion of heights and distances...

Third year. = 1st. Surveying and Levelling. Navigation. Conick Sections. Dialling. Spherical Geometry.

Projections of the Sphere. Spherical Trigonometry and Spherical Astronomy...

The emphasis= on spherical geometry, trigonometry, and astronomy is explained by the needs of navigation. These subjects, along with geography (another important obligat= ory part of the curriculum) were considered essential parts of one’s knowledge of the world. Witho= ut them, one’s appreciation of even English literature is impoverished.<= sup>iv^{Lindsay (1954, p. 69) expresses some puzzlement that the calculation=
of
eclipses was universal in all colleges of the time and considers its presen=
ce
in the curriculum “probably a hangover from the medieval
curriculum.” In fact, t=
he
calculation of eclipses has a very important function in the mundane aﬀairs of commerce, speciﬁcally in
navigation: it can be used to=
determine
terrestrial longitude. Latitude is easy to determine. One has only to go outdoors at nig=
ht and
observe the elevation of the pole star.&nb=
sp;
That elevation is the latitude of the point of observation. This last
statement is a slight oversimpliﬁcation, of course, since the
“pole star” isn’t exactly true north, but the point is th=
at
latitude is easily determined. Any
known star can be observed at its culmination (transit of the local meridia=
n),
and the local latitude can then be worked out from spherical trigonometry. =
Even
if one lives at the bottom of a mine shaft one can work out latitude; for e=
xample,
it is the arcsine of the number of revolutions a Foucault pendulum precesse=
s in
one sidereal day, and the direction of precession will distinguish northern
latitude from southern.}

Longitude, on the other hand, is more di= ﬃcult to calculate. Any two points at the same latitud= e will observe the same elevation for each fixed star and planet. The problem, assuming you know that the origin of the longitude coordinate is Greenwich,= is to determine how many degrees one’s own location is west or east of t= he intersection of its circle of latitude with the Greenwich meridian. Direct measurement is precluded by= the topography of the earth. If one knew what time it was in Greenwich when it = is noon locally, of course, the longitude would be determined exactly. Each hour of time diﬀerence between local standard time and Greenwich mean time represents a diﬀerenc= e of 15º ^<=
/span>of longitude. For that reason the British government had o= 4256;ered a prize for a clock that would keep accurate time on board a sh= ip. Setting such a clock to Greenwich = time, one would then always know longitude by comparing local (sun) time with the clock time. Such clocks were = not easy to develop, and were far from cheap and reliable. The cheap way of calculating longitude, once astronomy was su= 4259;ciently sophisticated to predict planetary motion with accuracy, was= to use a big clock in the sky. F= or instance, the moon undergoes changes of phases. If one could chart these phases accurately enough, it would only be = necessary to look at the moon to know what time it is in Greenwich. Unfortunately the moon’s phases change too slowly to permit measuring any changes over = the period of a few hours. When G= alileo discovered the moons of Jupiter, he realized that their conﬁguration= s, once worked out, could be a much better “universal clock” than = the moon-related phenomena such as phases or tides. They were actually used for this p= urpose in some surveying work. The m= ost easily observable clock of this type, however, is a lunar eclipse (a solar eclipses is not visible simultaneously at widely separated places). The use= of eclipses in calculating longitude was known from very early times. A lunar eclipse on September 20, 3= 30 B. C. E. was observed at both Arbela (47ºE, in the territory of modern Iraq) and Carthage (10ºE, on the northern coast of Africa), and these observations were used by Ptolemy to calculate the diﬀerenc= e in longitude between the two places (Neugebauer 1975, p. 668). The accurate mapping of the world was still a matter of pressing practical importance in= the early nineteenth century, and scientiﬁc journals were eager to have = accurate observations of eclipses to compare with the predicted times. For that reas= on one must disagree with Lindsay’s assessment of this part of the curri= culum. As for the rest of the curriculum, it was, to be sure, not the latest in research mathematics. The calculus, already 150 years old, was not part of = the curriculum, to say nothing of the researches in mathematical physics due to Euler, Laplace, Lagrange, and others. On the other hand, Laplace and Lagran= ge were still alive at this time; it is not surprising that their work had not reached Vermont. At least Laplace’s Mécanique céleste had reached Boston and inspired a translation by Nathani= el Bowditch that far excelled the original in clarity of expression.

Instruction and Equipment<= /span>. Teaching was by lect= ure and demonstrations given by the faculty, since there was very little opportunity for hands-on laboratory work by the students. What we now call laboratory equipm= ent used for instruction was known in those days as “philosophical apparatus,” and described by ex-President John Wheeler in an address = at UVM’s semicentennial celebration in 1852:

Of astronomi= cal and philosophical apparatus, there was a telescope, planetarium, quadrants,= two sets of 24 inch Globes, and other necessary articles of value, besides seven hundred dollars worth of instruments purchased of the Rev. Dr. Prince of Sa= lem, Mass., by individuals, [Wheeler says in a footnote that the latter were Dr. John Pomeroy, David Russel Esq., and Col. W. C. Harrington—RLC] and deposited for the use of the University, in the Philosophical Chamber. The apparatus was more complete, than in any of the Colleges in New England, ex= cept Harvard and Yale. (Wheeler, 1854, p. 2)

Lindsay (195= 4, p. 106) mentions a catalog from the Rev. Dr. Prince listing objects for sal= e, including glass plates ground so as to make an airtight joint, a ﬂask beam for weighing air, a pipe of mephitic air (carbon dioxide), a long glass tube with plate and collar of leather for the Torricellian experiment (show= ing the decrease of atmospheric pressure with altitude), a model water pump of brass and glass to show the action of valves, an electric generator turned = by winch, an electrical cannon for ﬁring hydrogen gas, a battery consis= ting of nine jars, a microscope, and many other objects. Unfortunately it is not known which of these were purchased. Lindsay reports that only one of these objects remained in the early 1950’s, a compound magnet encased in brass.

There does not seem to be any record of textboo= ks, if any, used for the instruction at this period. Certainly the library was not a ri= ch source of reading material. T= he minutes of the Board of Trustees’ meeting in January 1811 (Vol. 1, p. 154), lists the entire University Library of the time. It consisted of thirty volumes, wi= th a heavy emphasis on literature and divinity studies. The few science books available we= re all devoted to the applied parts of science, such as (Erastus) Darwin’s Zoonomia, Priestley’s Corruption, Priestley’s On Air (5 volumes), and Paine̵= 7;s Geography.

Personnel. In 1807 Mr. James Dean was deemed suitably qualiﬁed and respectable to be a tuto= r of mathematics and astronomy, and in 1809 he became the ﬁrst professor = of mathematics and natural philosophy at UVM.= Dean became a scholar of some note, and his biography appears in Appleton’s Cyclopedia of Amer= ican Biography. According to i= nformation contained in the University archives in a folder bearing his name, he was b= orn at Windsor, Vermont on November 26, 1776 and received the A. B. degree from Dartmouth in 1800 and the A. M. degree, also from Dartmouth, in 1806. He left UVM in 1814, when the Univ= ersity closed and rented its buildings to the American Government for use in the w= ar against the British. In his years at UVM up to that point his salary, nomin= ally $400 per year when he was appointed in 1809, had not been regularly paid. T= he University accounts in January 1811 show that he was owed $847.15. This was surely not a sum one could easily aﬀord to forego at the time. The Unive= rsity, however, was not going to settle easily.&n= bsp; In the discussion leading up to the closing of the University (minut= es of the meetings of the Board of Trustees, Vol. II, p. 55, meeting of March = 24, 1814) we read:

Resolved, Th= at the Treasurer in paying the debts due from the Corporation to the late President and Professors, pay to them in proportion to their existing debts, provided Professor Dean withdraws his suit without Cost, at the same time having respect to what greater proportion anyone has already received. And = if said Dean does not so withdraw his suit, pay said President and Professor Chamberlain ﬁrst...

He went to Dartmouth as tutor, but because of the legal dispute that tore Dartmouth ap= art at this time (in which he backed the losing side) he came back to UVM as a professor from 1822 until 1824. He was President pro tempore of the Univers= ity brieﬂy in 1824, just before leaving to take up a position at Union College. From Union College he received an honorary Doctor of Divinity degree in 1847. He died in January 1849 and is bur= ied in Elmwood Cemetery in Burlington.

No portraits of James Dean exist, but his physi= cal appearance and character, as they appeared to President Wheeler, were descr= ibed in considerable detail in President Wheeler’s semicentennial address:=

He possessed= a mathematical mind, distinguished for its clearness and accuracy, rather than its depth and scientiﬁc insight. He devoted himself to the life of a student, and acquired much, and various knowledge, rather than comprehension and profound principles. He was rigid in his discipline, the sharp lines of which were perhaps increased, by an occasional irritability of temper, whic= h seemed to spring from his very peculiar physical constitution. He was inordinately= ﬂeshy, and in such way as to give the appearance rather of disease, than of health. His inﬂuence in the University was marked by adherence to law and or= der, in the simple and earnest pursuit of its objects. (Wheeler, 1854, p. 24)

In other wor= ds, Dean was rather a dabbler, one who preferred breadth to depth. These are precisely the qualities = needed in an institution devoted more to teaching than to research, even though Wh= eeler’s tone suggests that he thought otherwise.&n= bsp; One suspects that Wheeler felt some antipathy toward Dean.

The modest scholarly reputation that Dean attained was based on six articles by him li= sted in the Royal Society Catalogue of S= cientiﬁc Papers (Vol. 2, p. 185). = Four of these were published in 1815 in the Memoirs of the American Academy of Arts and Letters, Vol. 3, pt. 2. One of the latter is a detailed report of an observation of the solar eclipse of Septe= mber 17, 1811. Dean gives precise statements of the local solar time for the beginning and end of the eclipse as observed by himself and his companion (= see the remarks above on the signiﬁcance of eclipses for geography). The other three articles published in 1815 are connected with geometric astrono= my. One is a description of a “cometarium.” Another is “A method of displaying at one v= iew all the annual cycles of the equation of time in a complete revolution of t= he Sun’s apogee.” (T= he misnamed “equation of time” is the amount by which mean solar time—on which clocks are based—diﬀers from true solar time. It is a periodic function of time, and Dean’s article provided a small elliptical piece of paper riveted to a chart. By turning the ellipse one could determine the amount by which solar time is ahead of or behind clock time at any given moment.)

The most important of the four articles, however, was a tour de force of spherical trigonometry, “An investigation of the apparent motion of the earth viewed from the Moon arising from the Moon’s librations.” The last word here is the key to t= his paper. It is a commonplace th= at the moon always turns the same face to the earth, but this commonplace is not strictly true. The moon rotat= es on its axis at a uniform rate, but its orbit about the earth is slightly elliptical. As a result, terr= estrial astronomers get an occasional peek around the edge of the moon into its hid= den side. This is one kind of libration. The other kind occ= urs because the moon’s axis of rotation is not perpendicular to the plane= of its orbit around the earth, so that its northern and southern poles come alternately into view to the earth. Looking at these two kinds of libration from the perspective of the moon, one ﬁnds that the earth does not remain in a ﬁxed locat= ion in the sky, as would be the case if the commonly held view were accurate. Instead the earth describes a smal= l but complicated closed curve in the sky over a long period of time. Dean gave a careful analysis of th= is curve and showed that it is the curve described by a pendulum bob at the bo= ttom of a Y-shaped string, in which the vertical stroke of the Y is 40 times the distance from the fork in the Y to the line through its two tips. This article so intrigued the astr= onomer Bowditch that he was inspired to perform a detailed mathematical analysis of such a pendulum. BowditchR= 17;s article was published in the same issue of the Memoirs of the American Academy in which Dean’s four arti= cles appeared.^v

Besides the papers just discussed, Dean also published an observation of several meteor= s in Silliman’s Journal^vi= in 1823, and= an article “On the diameter of screws,” in the Boston Journal of Philosophy in 1826, which he rewrote and expa= nded in the Journal of the Franklin Inst= itute in 1845, just four years before his death.= His analysis is really an analysis of the properties of a helix, combined with some frictional considerations, and therefore applies more properly to bolts than to screws. The problem is to ﬁnd the diameter that enables the ratio of power (he seems to mean torque) to weight to be minimized. Besides these rese= arch papers, he was the author of a gazetteer of Vermont published in Montpelier= in 1808, a copy of which can be found in the Wilbur Collection of the Universi= ty of Vermont. Among the papers = in his ﬁle in the University archives is a letter of November 27, 1833 to t= he physicist Joseph Henry, reporting some meteor observations, and speculating= on ways by which it could be proved that the aurora borealis is electrical in nature.

UVM’s = ﬁrst professor of mathematics was therefore, at least by American standards of t= he times, intellectually respectable. The remaining question is, how much of his knowledge did he impart to his students? There is some evidence that he was an interesting and inspiring lecturer. When he became professor in 1809, = he delivered an inaugural speech (actually on April 24, 1810), in the manner of the German Antrittsrede entitled “An Oration on Curiosity.”&nbs= p; In my view, this 19-page summary history of natural philosophy is exceedingly inaccurate, even for its own time, and contains no memorable thoughts or sentences. It was, however, printed and published by the Samuel Mills Press in Burlington in M= ay 1810 at the request of the students= !^vii His most enduring contribution to American civilization, however, has been immortali= zed as “Dean’s Method” of apportioning the House of Represent= atives. Those familiar with the paradoxes = that can result from any system of proportional representation will appreciate t= he diﬃculty= of framing general principles of representation that will be fair under all circumstances. The most notor= ious such paradox is the so-called Alabama paradox, which arose after the 1880 census. It was discovered tha= t if the total number of representatives in Washington was increased, Alabama wo= uld actually be entitled to fewer representatives than it would get if the numb= er was left unchanged. Dean̵= 7;s Method is explained in detail in the book Fair Representation by M. L. Balinski and Y. Peyton Young (Yale University Press, 1982).

As mentioned above, James Dean left UVM when the University closed down in 1814 and did not return until 1821. His place as professor of mathemat= ics during this time was taken by the Rev. Ebenezer Burgess (1815–1817) a= nd the Rev. Gamaliel Smith Olds (1819–1821). Neither of these men was particula= rly a mathematician or scientist. T= he Historical Catalogue of Brown Universi= ty, published in 1914, lists Burgess as a tutor in the period 1811–1813.<= span style=3D'mso-spacerun:yes'> Born in Wareham, Massachusetts on = April 1, 1790, he was Preceptor at the University Grammar School in Providence 1809–1811. He graduated= from Andover Theological Seminary in 1815 and received a D. D. from Middlebury College in 1835. After leavin= g UVM he was an agent of the American Colonization Society for Africa in 1817–18. In 1821 he was ordained a Congregationalist minister and was pastor of the First Church of Dedham, Massachusetts for ﬁfty years, from 1820 until his death in 1= 870.

Somewhat less is known about G. S. Olds (1777–1848). He wrote a pamphlet now in the Wilbur Collection of UVM bearing the title, “Statement of Facts Relative to the Appointment of= the Author to the Oﬃce of Professor of Chemistry in Middlebury College and the Termination of his Connexion with that College,” published by Denio and Phelps, Green= 4257;eld, Massachusetts, 1818. As= Rev. Olds tells the story, he was approached by Middlebury College in 1816 and a= sked to take the position of professor of chemistry. Not feeling quite qualiﬁed,= he asked for a delay of one year in assuming the position, to which the Presid= ent of Middlebury assented orally. Olds w