I must have my controversy ended before I publish my 'Optics and Astronomy'; for I have several things in my head, as yet only committed to memory, neither can I dispose of myself to write them in order and method till I have my mind free from other cares.
I would have a quadrant after the enclosed fashion, made of jointed wood, with a brass limb, and a ball and socket (or something else to turn upon) in the centre of gravity, three feet in the radius exactly, and as minutely divided as the quantity can suffer. I do not desire any other scales and divisions on it, save only a needle of a considerable length, for observing the declination of the same upon one of the radiuses or middle, as you think most convenient. I would also have a chain, two good compasses, and a brass sector. I desire to know the price of every one of these by themselves.
The price of the Instruments mentioned in you letter will be
Ball and socket with three-foot staff £1-8-0
Needle a foot long with graduated box £1-0-0
2 pair of compasses one to have 3 feet £0-10-0
A Brass Sector £1-5-0
I am now following out, in my public lectures, a full course of mathematics, which, if I publish, either altogether or in part, I will add to it what else of my own I think worthy of public view, and print it in Edinburgh.
Mr Barrow, in his Optics, showed himself a most subtle geometer, so that I think him superior to any that ever I looked upon: I long exceedingly to see his geometrical lectures, especially because I have some notions upon that same subject by me. I entreat you to send them to me presently as they come from the press, for I esteem the author more than you can easily imagine.
... I had ere this sent you Slusius, but I am informed the carrier goes no further than to Newcastle upon Tyne, where the books may lie long enough, unless sent to an acquaintance that may pay the carriage there and take care to send them to Edinburgh. Within three weeks or a month Mr Barrow's 'Geometrical Exercises' will be finished, and as soon as it comes out, I intend to send it as before ... Within a fortnight or three weeks after Mr Barrow's book is finished will likewise be completed Dr Wallis's book 'De Calculo Centri Gravitatis' which will be large, viz about 60 or 70 sheets of paper, and I must embrace some subsequent opportunity to send you that likewise. Fermat's Diophantus will not be extant ths year yet, and I am afraid Borelli will be disturbed in Sicily from publishing Maurolico's Archimedes with his own annotations, for Turks having got together a great naval force, it is said 80 sail of galleys and 40 sail of ships besides those of Barbary, and two Greeks were executed as spies for surveying the Plains of Palermo: Alteiri is chosen Pope a man 74 years of age, deaf and dark ...
I have read over Mr Barrow's lectures with much pleasure and attention, wherein I find him to have infinitely transcended all that ever wrote before him.
See James Gregory on equations
I can hardy believe, till I see it, that there is any general compendious and geometrical method for summing a harmonic progression ... at present I have not the leisure to examine it, but afterwards I may. I admire much the pocket tube of Mr Newton, being only 6 inches long to magnify 150 times: if it magnifies the diameter of an object so it is incredible ...
I am now much taken up, and have been so this winter past, both with my public lectures, which I have twice a week, and resolving doubts which some gentlemen and scholars propose to me. This I must comply with, nevertheless that I am often troubled with great impertinencies; all person here being ignorant of these things to admiration. These things do so hinder me, and I have but little time to spend on these studies my genius leads me to; so that it is necessary for me to delay answering you much against my own humour. I resolve, when the college rises, which will be within six weeks, to apply myself seriously to the doctrine of equations ... When I come such a length as to satisfy myself, you may be assured that I will make no secret of it to you. This inclination I find in myself to prosecute these things I had once laid up, hinders my design at present to publish any thing. Yet I cannot express how much I am sensible to your kindness, in exposing yourself freely to so much trouble upon the account of any notions my dullness can produce. ... I have had sufficient experience of the uncertainty of things ... before now, which makes me, since I came to Scotland, however mean and despicable my condition be, to rest contented and satisfy myself with that, I am at home in a settled condition, by which I can live. I have known many learned men, far above me on every account, with whom I would not change my condition.
... several gentlemen have fallen upon a method to gather contributions for mathematical instruments to the University of St Andrews, which probably may take effect. It is like upon this account I may see you within twelve months.
... proper and necessary instruments and utensils as may serve and conduce for the better, more solemn, and famous profession, teaching, and improving of natural philosophy and the mathematical science, and especially for making such observations on the heavens and other bodies of this universe, (as easily may be by such help, with the great advantage of the pure air and other accommodations of this place) whereby we may be enabled to keep correspondence with learned and inquisitive persons in solid philosophy everywhere ... we have ordered Mt James Gregory, professor of the mathematical sciences here, to go to London, and there to provide, so far as the money already received from our benefactors will reach, such instruments and utensils as he, with the advice of other skilful persons, shall judge must necessary and useful for the above mentioned design. ... And to take notice of the fabric and form of the most competent observatory, that ours here intended may be built with all its advantages.
... if the lunar eclipse of the 11th of next month be observed by any, I pray you let me have particulars of it; for by it I intend to observe the longitude of this place ...
It were tedious to write down particularly all the instruments I have brought home, even a larger letter would not contain all their names and sizes, for I have all sorts: our largest quadrant is of oak, covered with brass, 4 foot in radius and actually divided in minutes, of which we can judge
I have now abundantly satisfied myself in these things I was searching after in the analytics, which are all about reduction and solution of equations. It is possible that I flatter myself too much when I think them of value, and therefore am sufficiently inclined to know others' thoughts, both (as you say) as to the quid and quomodo of them; but that I have no ground to expect till time and leisure allow me to publish them.
... not long after your arrival in Paris, I had a letter from you; to which, the truth is, I was ashamed to answer, the affairs of the Observatory in St Andrews were in such a bad condition; the reason of which was a prejudice which the masters of the University did take against mathematics because some of their scholars, finding their courses and dictats opposed by what they had studied in mathematics, did mock their masters, and deride some of them publicly. After this the servants of the Colleges got orders not to wait on me at my observations; my salary was also kept back from me; and scholars of most eminent rank were violently kept from me, contrary to their own and their parents' wills, the masters persuading them that their brains were not able to endure it. These and many other discouragements obliged me to accept a call here to the College of Edinburgh where my salary is near double and my encouragements otherwise much greater.