After evidence was obtained in the 1920s that the universe is expanding, it became reasonable to ask: [1] It can be calculated that the critical density of matter needed to brake the expansion and “close” the universe is equivalent to three hydrogen atoms per cubic meter. But the density of the observable universe [2] luminous matter in the form of galaxies comes to only a fraction of this.  [3] While the expansion of the universe were to stop, there must be enough invisible matter in the universe to exceed the luminous matter in density by a factor of roughly 70.

Our contribution to the search for this “missing matter” has been to study the rotational velocity of galaxies at various distances from [4] its center of rotation. It [5] has been known for some time that outside the bright nucleus of a typical spiral galaxy luminosity falls off rapidly with distance from the center. If luminosity [6] was a true indicator of mass, most of the mass would be concentrated toward the center. Outside the nucleus, the rotational velocity would decrease geometrically with distance from the center [7], in conformity with Kepler’s law.  [8] Moreover, we have found that the rotational velocity in spiral galaxies either remains constant with increasing distance from the center or increases slightly. This [9] unrecognized result indicates that the falloff in luminous mass with distance from the center is balanced  by an increase in nonluminous mass.

Our findings suggest that as much as 90 percent of the mass of the universe is not radiating at any wavelength with enough intensity to be detected on the Earth. Such dark matter could be in the form of either extremely dim stars [10] of low mass, of large planets like Jupiter, and of black holes, either small or massive. It has not yet been determined whether this mass is sufficient to close the universe [11], some physicists consider it significant that estimates are converging on the critical value.

World population from 10,000 BC to today

[12] A [13] confusing change: The world population today that is 1,860-times the size of what it was 12 millennia ago when the world population was around 4 million – half of the current population of London.

What is [14] impressive about this chart is of course that almost all of this growth happened just very recently. Historical demographers estimate that around the year 1800 the world population was only around 1 billion people. This implies that on average the population grew very slowly over this long time from 10,000 BCE to 1700 (by 0.04% annually). After 1800, this changed [15] basically, the world population was around 1 billion in the year 1800 and increased 7-fold since then.

Around 108 billion people have ever lived on our planet. This means that today’s population size makes up 6.5% of the total number of people ever born.

For the long period from the appearance of modern Homo sapiens [16] up until the starting point of this chart in 10,000 BCE, it is estimated that the total world population was often well under one million. In this period, our species was often seriously threatened by extinction.

A number of researchers have published estimates for the total world population over the long run.

In terms of recent developments, the data from the UN Population Division [17] provide consistent and comparable estimates (and projections) within and across countries and time, over the last century. This data starts from estimates for 1950, and is updated periodically to reflect changes in fertility, mortality and international migration.

In the section above we looked at the absolute change in the global population over time. But what about the rate of population growth?

[18] ; but since then, world population growth has halved.

For the last half-century, we have lived in a world [19] by which the population growth rate has been declining. The UN projects that this decline will continue in the coming decades.

A common question we’re asked is: [20] is the global population growing exponentially? The answer is no. For population growth to be exponential, the growth rate would have be the same over time (e.g. 2% growth every year). In absolute terms, this would result in an exponential increase in the number of people. That’s because we’d be multiplying an ever-larger number of people by the same 2%. [21] 2% of the population this year would be larger than 2% last year, and so on; this means the population would grow exponentially.

[22] However as we see in this chart, since the 1960s the growth rate has been falling. This means the world population is not growing exponentially – for decades now, growth has been more similar to a linear trend.

The Penelope Royalty Trust is a United States oil and natural gas royalty trust based in Waco, Texas.  With a market capitalization of US $620,040,000[23] and an average daily trading volume of about 237,000 shares at the end of 2007, they are one of the [24] larger royalty trusts in the United States. [25]

[26] Most of the trusts’ properties are on Jeepers Ranch in Curr County, Texas, where it owns a 75% [27] net overriding royalty interest in the fee mineral interests (in this case, oil and natural gas). [28] Other properties of the trust are in 32 other Texas counties, most are in the western portion of the state, on the High Plains; the trust owns a 95% net overriding royalty interest in all its properties outside of the Jeepers Ranch.

The principal productive zones for oil on Jeepers Ranch are in two geologic units, the Grayburg and the San Andreas, at a depth of from 2,800 to 3,400 feet (1,000 m) below ground surface; however, there [29] was a total of 12 producing zones on the ranch, including one at a depth of 10,600 feet (3,200 m). [30] As of the end of 2006, there were a total of 620 operational and productive oil wells and 142 natural gas wells on the Jeepers Ranch in the trust. On December 31, 2006, the trust claimed a lifetime of approximately 8.3 years for all mineral reserves of the trust.

Penelope Royalty Trust came into being in November 1980, with an agreement between Brickabrack Royalty Company and the Nations Star Bank of Fort Worth. As is the case with U.S. royalty trusts, the  trust cannot function as a business, and has no employees; all operations and maintenance are carried out by the trustee and its subcontractors. Currently, the assets of the trust are managed by Barnaby and Boom, Inc., [31] which acquired Melenial oil, the previous operator.

The trust pays a relatively high dividend, yielding an annual rate of 12.4% in early 2008; [32] however, it pays out monthly, a relative rarity for U.S. stocks. However, its distribution is dependent on the prices of oil and gas; thus, unlike traditional stocks [33], the dividend payout will differ each month.

[34] I now put myself under the guidance of the accomplice, Louis, who began to express doubts of his ability to find the upper glacière, administering [35] consolation by reminding us that if he could not find it no one else could.

As we walked on through the mist and rain, it became necessary to circumvent a fierce-looking bull, and Mignot and the accomplice told rival tales of the dangers [36] by which pedestrians are exposed from the violence of the cattle on some montagnes [37], where the bulls are allowed to grow to full size and fierceness. Mignot was quite motherly in his advice and his cautions, recommending as the [38] assurest safeguard a pocket-pistol, loaded with powder only, to be flashed in the bull's face as he makes his charge. When informed that in England an umbrella or a parasol is found to answer this purpose, he [39] tilted his head negatively, evidently having no confidence in his own umbrella, and doubting its obeying his wishes at the critical moment; indeed, it would require a considerable time, and much care and labour, to unfurl a lumbering instrument of that description. [40] Having the best of the tale-contest, with Renaud in the end since he had himself been grazed by a bull which came up, from a tree, springing him into a tree.

Before very long we reached a little kennel-like hut of boughs, which no decent dog would have lived in,[41] and no large man could have entered, and from this we drew a charcoal-burner. [42] A herdsman on his way from one pasturage to another could give no better help, and we began to despair, till at length Louis desired us to halt in a place sheltered from the rain, while he prosecuted the search alone. We had [43] plenty of time for observing that, like other leafy places sheltered from the rain, our resting-place was commanded by huge and frequent drops of water;[44].