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"For common purposes we may without sensible error suppose the earth's motion equable and neglect the corrections, and then the rule for the parallax of will be this: Sine lat. : rad. : : cotang. A : cotang. C, or rad : sine lat. : : tang. A : tang. C; then long. star \mp C = long. of λ. Cosine C : cosine A : : semi transverse axis : z. And cosine decl. cosine (ʘ - λ) :: z : x = parallax of right ascension."

"Hitherto we have considered the apparent motion of the star about its true place, as made only in a plane parallel to the ecliptic, in which case it appears to describe a circle in that plane; but since, when we judge of the place and motion of a star, we conceive it to be in the surface of a sphere, whose centre is our eye, 'twill be necessary to reduce the motion in that plane to what it would really appear on the surface of such a sphere, or (which will be equivalent) to what it would appear on a plane touching such a sphere in the star's true place. Now in the present case, where we conceive the eye at an indefinite distance, this will be done by letting fall perpendiculars from each point of the circle on such a plane, which from the nature of the orthographic projection will form an ellipsis, whose greater axis will be equal to the diameter of that circle, and the lesser axis to the greater as the sine of the star's latitude to the radius, for this latter plane being perpendicular to a line drawn from the centre of the sphere through the star's true place, which line is inclined to the ecliptic in an angle equal to the star's latitude; the touching plane will be inclined to the plane of the ecliptic in an angle equal to the complement of the latitude. But it is a known proposition in the orthographic projection of the sphere, that any circle inclined to the plane of the projection, to which lines drawn from the eye, supposed at an infinite distance, are at right angles, is projected into an ellipsis, having its longer axis equal to its diameter, and its shorter to twice the cosine of the inclination to the plane of the projection, half the longer axis or diameter being the radius. Such an ellipse will be formed in our present case..."

"If we suppose the distance of the fixed stars from the sun to be so great that the diameter of the earth's orbit viewed from them would not subtend a sensible angle, or which amounts to the same, that their annual is quite insensible; it will then follow that a line drawn from the earth in any part of its orbit to a fixed star, will always, as to sense, make the same angle with the plane of the ecliptic, and the place of the star, as seen from the earth, would be the same as seen from the sun placed in the focus of the ellipsis described by the earth in its annual revolution, which place may therefore be called its true or real place. But if we further suppose that the velocity of the earth in its orbit bears any sensible proportion to the velocity with which light is propagated, it will thence follow that the fixed stars (though removed too far off to be subject to a parallax on account of distance) will nevertheless be liable to an aberration, or a kind of parallax, on account of the relative velocity between light and the earth in its annual motion. For if we conceive, as before, the true place of any star to be that in which it would appear viewed from the sun, the visible place to a spectator moving along with the earth, will be always different from its true, the star perpetually appearing out of its true place more or less, according as the velocity of the earth in its orbit is greater or less; so that when the earth is in its perihelion, the star will appear farthest distant from its true place, and nearest to it when the earth is in its aphelion; and the apparent distance in the former case will be to that in the latter in the reciprocal proportion of the distances of the earth in its perihelion and its aphelion. When the earth is in any other part of its orbit, its velocity being always in the reciprocal proportion of the perpendicular let fall from the sun to the tangent of the ellipse at that point where the earth is, or in the direct proportion of the perpendicular let fall upon the same tangent from the other focus, it thence follows that the apparent distance of a star from its true place, will be always as the perpendicular let fall from the upper focus upon the tangent of the ellipse. And hence it will be found likewise, that (supposing a plane passing through the star parallel to the earth's orbit) the locus or visible place of the star on that plane will always be in the circumference of a circle, its true place being in that diameter of it which is parallel to the shorter axis of the earth's orbit, in a point that divides that diameter into two parts, bearing the same proportion to each other, as the greatest and least distances of the earth from the sun."

"I would by no means attempt to infer from hence, that the longitude found by observations of this sort may in all cases be depended upon within one degree; but I beg leave to observe, that whatever extraordinary circumstances may have concurred to produce so near an agreement in this particular case, the event is such as may give reason to hope, however great the difficulties of finding the longitude by this method seem to be, that they are not insuperable, or such as ought to deter those whom it most nearly concerns from attempting to remove them."

"This fundamental and most important article being established upon such full evidence, it remained to be examined within what limits the errors arising from observations actually taken at sea could be contained. In order to determine this point, I computed the ship's longitude from each of the observations made by captain Campbell, and, upon comparing the results of several that were taken near the same time and under the like circumstances, it appeared that in general the observer was not liable to err more than one minute in judging of the apparent contact of the moon's limb and the object with which it was compared. Now this being nearly the same error that would be found to obtain, if the like observations were to be made with the same instruments on land, it may hence be inferred, that in moderate weather the motion of the ship is no otherwise an impediment in this sort of observations, than as it renders the repetition of them more tedious and troublesome to the observer, which yet ought by no means to be omitted; because if each single observation be liable to an error of a minute only, by taking the mean of five or six, the error on this head may be so far diminished as to be of small moment."

"But before I proceed farther it may be proper to take notice, that since the time when I gave their lordships an account of the near agreement of Mr. Professor Mayer's lunar tables with the observations that had been then made at the Royal Observatory, I have compared several others, which concurred to prove that the difference between the observed and computed places nowhere amounted to more than about one minute and a half; and I find that the difference (small as it is) may yet be diminished by making alterations in some of the equations, whose true quantity could not be determined without proper observations; after making the needful corrections it appeared, by the comparison of above eleven hundred observations taken here since the new instruments were fixed up, that the difference did nowhere amount to more than a minute: it may therefore be reasonably concluded, that so far as it will depend upon the lunar tables the true longitude of a ship at sea may in all cases be found within about half a degree, and generally much nearer."

"Sir, Having long deferred to make any report relating to the observations that were taken at sea by captain Campbell, in the year 1757, which you transmitted to me by order of the lords of the admiralty, I think it necessary to acquaint you, that, upon examining those observations, I perceived that they were not in all respects accompanied with such circumstances as are requisite for forming a right judgment of the accuracy and certainty with which observations proper for finding the longitude at sea by the moon can in fact be taken; for which reason I delayed giving my opinion upon this point till I could have an opportunity of comparing a greater variety of observations, made at different times, and with different instruments: such an opportunity having lately been given me by captain Campbell, who has favoured me with a copy of several observations that were made by him in 1758 and 1759, I now beg leave to lay before their lordships the result of the comparisons which I have made."

"I give all my printed books to Samuel Peach, son of Samuel Peach, in my Will named, and desire that this may be a codicil to my last Will and Testament, and taken as part thereof, as witness my hand, this third day of December. in the year of our Lord 1761."

"When the year was completed, I began to examine and compare my observations, and having pretty well satisfied myself as to the general laws of the phenomena, I then endeavored to find out the cause of them. I was already convinced that the apparent motion of the stars was not owing to the of the earth's axis. The next thing that offered itself was an alteration in the direction of the plumb-line with which the instrument was constantly rectified; but this upon trial proved insufficient. Then I considered what refraction might do, but here also nothing satisfactory occurred. At length I conjectured that all the phenomena hitherto mentioned, proceeded from the progressive motion of light and the earth's annual motion in its orbit. For I perceived that, if light was propagated in time, the apparent place of a fixed object would not be the same when the eye is at rest, as when it is moving in any other direction than that of the line passing through the eye and the object; and that, when the eye is moving in different directions, the apparent place of the object would be different."

"My Instrument being fixed, I immediately began to observe such Stars as I judged most proper to give me light into the Cause of the Motion... There was Variety enough of small ones; and not less than twelve, that I could observe through all the Seasons of the Year; they being bright enough to be seen in the Day-time, when nearest the Sun. I had not been long observing, before I perceived, that the Notion we had before entertained of the Stars being farthest North and South, when the Sun was about the Equinoxes, was only true of those that were near the solstitial Colure: And after I had continued my Observations a few Months, I discovered what I then apprehended to be a general Law, observed by all the Stars, viz. That each of them became stationary, or was farthest North or South, when they passed over my Zenith at six of the Clock, either in the Morning or Evening. I perceived likewise, that whatever Situation the Stars were in with respect to the cardinal Points of the Ecliptick, the apparent Motion of every one tended the same Way, when they passed my Instrument about the same Hour of the Day or Night; for they all moved Southward, while they passed in the Day, and Northward in the Night; so that each was farthest North, when it came about Six of the Clock in the Evening, and farthest South when it came about Six in the Morning."

"We are paternalists when we make someone act in his own interests."

"Take a Swede who is proud of his country’s peaceful record. He might have a similar divided attitude. He may not be disturbed by the thought that Sweden once fought aggressive wars; but if she had recently fought such wars he would be greatly disturbed. Someone might say, “This man’s attitude is indefensible. The wars of Gustavus, or of Karl XII, are as much part of Swedish history.” This truth cannot, I think, support this criticism. Modern Sweden is indeed continuous with the aggressive Sweden of the Vasa kings. But the connections are weak enough to justify this man’s attitude."

"Consider the fact that, in a few years, I shall be dead. This fact can seem depressing. But the reality is only this. After a certain time, none of the thoughts and experiences that occur will be directly causally related to this brain, or be connected in certain ways to these present experiences. That is all this fact involves. And, in that description, my death seems to disappear."

"It’s a good reason for postponing pleasures that you will then have more time in which you can enjoy looking forward to them. I remember exactly when, at the age of eight, I changed over from eating the best bits first to eating them last."

"When some principle requires us to act in some way, this principle’s acceptability cannot depend on whether such acts are often possible. We cannot defend some principle by claiming that, in the world as it is, there is no danger that too many people will act in the way that this principle requires."

"Why shouldn’t I eat toothpaste? It’s a free world. Why shouldn’t I chew my toenails? i happen to have trodden in some honey. Why shouldn’t I prance across central park with delicate sideways leaps? I know what your answer will be: “it isn’t done”. But it’s no earthly use just saying it isn’t done. If there’s a reason why it isn’t done, give the reason—if there’s no reason, don’t attempt to stop me doing it. All other things being equal, the mere fact that something “isn’t done” is in itself an excellent reason for doing it."

"Though everything is identical with itself, only I am me."

"To think about reality we must use concepts, and certain truths about concepts may reveal, or reflect, truths about reality."

"Normative concepts form a fundamental category-like, say, temporal or logical concepts. We should not expect to explain time, or logic, in non-temporal or non-logical terms. Similarly, normative truths are of a distinctive kind, which we should not expect to be like ordinary, empirical truths. Nor should we expect our knowledge of such truths, if we have ay, to be like our knowledge of the world around us."

"Even if moral truths cannot affect people, they can still be truths."

"I sometimes want to kick my car[.] Since I have this anger at material objects, which is manifestly irrational, it’s easier to me to think, when I get angry with people, that this is also irrational."

"Why do we save the larger number? Because we do give equal weight to saving each. Each counts for one. That is why more count for more."

"Naturalism and Non-Cognitivism are both...close to Nihilism. Normativity is either an illusion, or involves irreducibly normative facts."

"If we believe that there are some irreducibly normative truths, we might be believing what we ought to believe. If there are such truths, one of these truths would be that we ought to believe that there are such truths. If instead we believe that there are no such truths, we could not be believing what we ought to believe. If there were no such truths, there would be nothing that we ought to believe."

"Schopenhauer makes two curiously inconsistent claims about the wretchedness of human existence. We can object, he claims, both that our lives are filled with suffering which makes them worse than nothing, and that time passes so swiftly that we shall soon be dead. These are like Woody Allen’s two complaints about his hotel: ‘The food is terrible, and they serve such small portions!’"

"We live during the hinge of history. Given the scientific and technological discoveries of the last two centuries, the world has never changed as fast. We shall soon have even greater powers to transform, not only our surroundings, but ourselves and our successors. If we act wisely in the next few centuries, humanity will survive its most dangerous and decisive period. Our descendants could, if necessary, go elsewhere, spreading through this galaxy."

"When I consider the parts of the past of which I have some knowledge, I am inclined to believe that, in Utilitarian hedonistic terms, the past has been worth it, since the sum of happiness has been greater than the sum of suffering."

"What now matters most is how we respond to various risks to the survival of humanity. We are creating some of these risks, and we are discovering how we could respond to these and other risks. If we reduce these risks, and humanity survives the next few centuries, our descendants or successors could end these risks by spreading through this galaxy. Life can be wonderful as well as terrible, and we shall increasingly have the power to make life good. Since human history may be only just beginning, we can expect that future humans, or supra-humans, may achieve some great goods that we cannot now even imagine. In Nietzsche’s words, there has never been such a new dawn and clear horizon, and such an open sea. If we are the only rational beings in the Universe, as some recent evidence suggests, it matters even more whether we shall have descendants or successors during the billions of years in which that would be possible. Some of our successors might live lives and create worlds that, though failing to justify past suffering, would have given us all, including those who suffered most, reasons to be glad that the Universe exists."

"One thing that greatly matters is the failure of we rich people to prevent, as we so easily could, much of the suffering and many of the early deaths of the poorest people in the world. The money that we spend on an evening’s entertainment might instead save some poor person from death, blindness, or chronic and severe pain. If we believe that, in our treatment of these poorest people, we are not acting wrongly, we are like those who believed that they were justified in having slaves. Some of us ask how much of our wealth we rich people ought to give to these poorest people. But that question wrongly assumes that our wealth is ours to give. This wealth is legally ours. But these poorest people have much stronger moral claims to some of this wealth. We ought to transfer to these people […] at least ten per cent of what we inherit or earn."

"What now matters most is that we rich people give up some of our luxuries, ceasing to overheat the Earth's atmosphere, and taking care of this planet in other ways, so that it continues to support intelligent life."

"It has been widely believed that there are such deep disagreements between Kantians, Contractualists, and Consequentialists. That, I have argued, is not true. These people are climbing the same mountain on different sides."

"On all plausible theories, everyone’s well-being consists at least in part in being happy, and avoiding suffering."

"Nagel once claimed that it is psychologically impossible to believe the Reductionist View. Buddha claimed that, though it is very hard, it is possible. I find Buddha’s claim to be true. After reviewing my arguments, I find that, at the reflective or intellectual level, though it is very hard to believe the Reductionist View, this is possible. My remaining doubts or fears seem to me irrational. Since I can believe this view, I assume that others can do so too. We can believe the truth about ourselves."

"Certain actual sleeping pills cause retrograde amnesia. It can be true that, if I take such a pill, I shall remain awake for an hour, but after my night’s sleep I shall have no memories of the second half of this hour. I have in fact taken such pills, and found out what the results are like. Suppose that I took such a pill nearly an hour ago. The person who wakes up in my bed tomorrow will not be psychologically continuous with me as I was half an hour ago. I am now on psychological branch-line, which will end soon when I fall asleep. During this half-hour, I am psychologically continuous with myself in the past. But I am not now psychologically continuous with myself in the future. I shall never later remember what I do or think or feel during this half-hour. This means that, in some respects, my relation to myself tomorrow is like a relation to another person. Suppose, for instance, that I have been worrying about some practical question. I now see the solution. Since it is clear what I should do, I form a firm intention. In the rest of my life, it would be enough to form this intention. But, when I am no this psychological branch-line, this is not enough. I shall not later remember what I have now decided, and I shall not wake up with the intention that I have now formed. I must therefore communicate with myself tomorrow as if I was communicating with someone else. I must write myself a letter, describing my decision, and my new intention. I must then place this letter where I am bound to notice it tomorrow. I do not in fact have any memories of making such a decision, and writing such a letter. But I did once find such a letter underneath my razor."

"Until this century, most of mankind lived in small communities. What each did could affect only a few others. But conditions have now changed. Each of us can now, in countless ways, affect countless other people. We can have real though small effects on thousands or millions of people. When these effects are widely dispersed, they may be either trivial, or imperceptible. It now makes a great difference whether we continue to believe that we cannot have greatly harmed or benefited others unless there are people with obvious grounds for resentment or gratitude."

"Strawson describes two kinds of philosophy, descriptive, and revisionary. Descriptive philosophy gives reasons for what we instinctively assume, and explains and justifies the unchanging central core in our beliefs about ourselves, and the world we inhabit. I have great respect for descriptive philosophy. But, by temperament, I am a revisionist. […] Philosophers should not only interpret our beliefs; when they are false, they should change them."

"Venetian Memories. Jane has agreed to have copied in her brain some of Paul’s memory-traces. After she recovers consciousness in the post-surgery room, she has a new set of vivid apparent memories. She seems to remember walking on the marble paving of a square, hearing the flapping of flying pigeons and the cries of gulls, and seeing light sparkling on green water. One apparent memory is very clear. She seems to remember looking across the water to an island, where a white Palladian church stood out brilliantly against a dark thundercloud."

"Classical Utilitarians...would claim, as Sidgwick did, that the destruction of mankind would be by far the greatest of all conceivable crimes. The badness of this crime would lie in the vast reduction of the possible sum of happiness."

"Is the truth depressing? Some may find it so. But I find it liberating, and consoling. When I believed that my existence was a further fact, I seemed imprisoned in myself. My life seemed like a glass tunnel, through which I was moving faster every year, and at the end of which there was darkness. When I changed my view, the walls of my glass tunnel disappeared. I now live in the open air. There is still a difference between my life and the lives of other people. But the difference is less. I am less concerned about the rest of my own life, and more concerned about the lives of others."

"To be a person, a being must be self-conscious, aware of its identity and its continued existence over time."

"the part of our moral theory... that covers how we affect future generations... is the most important part of our moral theory, since the next few centuries will be the most important in human history."

"R. C. O. Matthews (1986), "Presidential Address to the Royal Economic Society." as cited in Eggertsson (1990; 31-32)"

"Matthews described himself as writing economic history in the style of an economist. Sceptical of conventional economic models of "rational individualistic utility maximisation", his interests moved toward the institutional and psychological underpinnings of economic behaviour."

"The fundamental idea of transaction costs is that they consist of the cost of arranging a contract ex ante and monitoring and enforcing it ex post, as opposed to production costs, which are the costs of executing a contract."

""The chief fault in English economists at the beginning of the [nineteenth] century was... that they did not see how liable to change are the habits and institutions of industry." Thus Marshall in his inaugural lecture as Professor of Political Economy in Cambridge, referring to Ricardo (Marshall 1885, p. 155). In the circumstances of that occasion, the remark may have been intended in some part as an olive branch, because the only other serious contender for the Chair had been the High Tory economic historian William Cunningham, Archdeacon of Ely, famous as an anti-theoretical institutionalist and famous also as a polemicist - he was the clergyman who once told his congregation that for him the bliss of Heaven would be incomplete if it lacked the pleasures of controversy."

"[Neoinstitutional Economics...] theory has made an indispensable contribution in recent times to advances of understanding in this area. But it seems to me that in the economics of institutions theory is now outstripping empirical research to an excessive extent. No doubt the same could be said of other fields in economics, but there is a particular point about this one. Theoretical modelling may or may not be more difficult in this field than in others, but empirical work is confronted by a special difficulty. Because economic institutions are complex, they do not lend themselves easily to quantitative measurement. Even in the respects in which they do, the data very often are not routinely collected by national statistical offices. As a result, the statistical approach which has become the bread and butter of applied economics is not straightforwardly applicable. Examples of it do exist, the literature on the economics of slavery being perhaps the most fully developed - not surprisingly because slavery is an institution that is sharply defined. But to a large extent the empirical literature has consisted of case-studies which are interesting but not necessarily representative, together with a certain amount on legal court cases, which are almost certainly not representative. Is this the best we can do? There is a challenge here on the empirical side to economists to see what is the best way forward."

"The postwar era has not surprised Arthur Burns, for business cycles have continued their "unceasing round." although the United States recession of 1981-82 was the eighth since World War II and the deepest postwar slump by almost any measure, the 1983-84 recovery displayed an upward momentum sufficient to befuddle forecasters and delight incumbent politicians. Nor would a reincarnated Joseph Schumpeter be disappointed in the current status of business cycle research in the economics profession. To be sure, interest in business cycles decayed during the prosperity of the 1960s, as symbolized in the 1969 conference volume, Is the Business Cycle Obsolete? and in Paul Samuelson's remark the same year that the National Bureau of Economic Research "has worked itself out of one of its first jobs, namely, the business cycle.""

"This theme of mismeasurement interacts with the designation of the one hundred years between 1870 and 1970 as the “special century.” Measurement errors are greatest in the early years, both in the scope of the standard of living and in the extent of price index bias. Clearly the welfare benefits to consumers in the categories of life entirely omitted from GDP were greatest long ago: the transition from the scrub board to the automatic washing machine was a more important contributor to consumer welfare than the shift from manual to electronic washing machine controls or from a twelve-pound tub to an eighteen pound tub. The most important unmeasured benefit of all, the extension of life expectancy, occurred much more rapidly from 1890 to 1950 than afterward."

"The century of revolution in the United States after the Civil War was economic, not political, freeing households from an unremitting daily grind of painful manual labor, household drudgery, darkness, isolation, and early death. Only one hundred years later, daily life had changed beyond recognition. Manual outdoor jobs were replaced by work in air-conditioned environments, housework was increasingly performed by electric appliances, darkness was replaced by light, and isolation was replaced not just by travel, but also by color television images bringing the world into the living room. Most important, a newborn infant could expect to live not to age forty-five, but to age seventy-two. The economic revolution of 1870 to 1970 was unique in human history, unrepeatable because so many of its achievements could happen only once."

"New-classical economics has been undeniably influential, but not in the way that its three prominent creators originally imagined. Its most important contribution to macroeconomics, the assumption of rational expectations, was stolen almost immediately, and applied more fruitfully, by the new Keynesians."