44 



THE POPULAE EDUCATOE. 



3. Are you right or wrong ? 4. I am right, I am not wrong. 5. Have 

 you my brother's good gun ? 6. I have not the gun. 7. Are you cold 

 to-day? 8. I am not cold; on the contrary, I am warm. 9. Have you 

 good bread ? 10. I have no bread. 11. Are you not hungry ? 12. I 

 am neither hungry iior thirsty. 13. Are you ashamed ? 14. I am 

 neither ashamed nor afraid. 15. Have we pepper or salt ? 16. You 

 have neither pepper nor salt. 17. What book have you ? 18. I have 

 my cousin's book. 19. Have you the iron hammer or the silver 

 hammer ? 20. I have neither the iron hammer nor the silver ham- 

 mer, I have the tinman's wooden hammer. 21. Is anything the 

 matter with you? 22. Nothing is the matter with me. 23. Have 

 you the bookseller's large book ? 21. I have neither the book- 

 seller's large book, nor the joiner's small book ; I have the captain's 

 good book. 



LESSONS IN GEOGRAPHY. XV. 



ASTRONOMICAL PRINCIPLES OP GEOGRAPHY. 



called the square of that number. But the numbers 1, 4, y, 16, 

 25, 36, 49, 64, 81, etc., are the squares of the numbers 1, 2, 3, 4, 

 5, 6, 7, 8, 9, etc., because they are found by multiplying the 

 latter numbers each by itself ; and the fractions i, J, , ^, , Jg, 

 i, i, i, etc., are called the reciprocals or inverses of the squares ; 

 and ratio means the rate at which anything increases or de- 

 creases ; hence, the force of heat, or quantity of heat received 

 from a common fire, is in the ratio of the inverses of the squares 

 of the distances ; or more shortly, in the inverse ratio of the 

 squares of the distances. 



This may be explained in another way still. Suppose A 

 to be placed at 2 feet distance from the fire, and B at 3 feet 

 distance ; then B will receive less heat than A, not in the 

 ratio of 2 to 3, the numbers which represent their distances, 

 but in the ratio of 2 times 2 to 3 times 3, that is, of 4 to 9 : in 

 other words, as 4 is contained 2| times in 9, so A will 

 receive 2^ times the quantity of heat that B receives ; and this 



IN our last lesson we endeavoured to explain to our geographi- is all that is really meant by the phrase, the inverse ratio of tht 

 cal students the nature of the motion of the earth round the squares of the distances. 



sun, and of its motion round its own axis. We there stated j Having thus explained the law of the influence of heat upon 

 the principle or law of attrac- two bodies, or any number of bodies 



the language peculiar to 



tion 



the science of astronomy, somewhat 

 modified and simplified; but as 

 some of our readers may be entire 

 novices, and may never have heard 

 or understood several of the terms 

 we made use of, we shall in this 

 lesson endeavour to make the sub- 

 ject plearer still. 



First, then, as to the said law of 

 attraction : let us illustrate this, by 

 a very familiar instance taken from 

 the heat of a common fire. Sup- 

 pose two persons, A and B, sitting 

 at the same distance from the fire, *' JU1 



both in front of it at least, the / 

 one as much as the other; it 

 is plain that they would both feel 

 the same degree of heat ; for, 

 whatever reason may be assigned 

 to show that A received more / 

 heat than B, the same reason / 

 might be assigned to show that B / 

 received more heat than A ; there- / 

 fore, they must both receive the 

 same heat. 



Now, suppose that B removes to 

 double the distance that he was at 

 when alongside of A, and that A 

 remains in the same place; it might 

 then be supposed that B would re- 

 ceive only half as much heat 

 as he did before; or that A 

 was now enjoying double the 

 heat which B was receiving in his 

 new position. Such is not the case, however ; for the degree 

 of heat does not diminish at the same rate that the distance 

 increases, as you might expect at first sight ; but it diminishes 

 at a much greater rate, and the question is how much greater ? 

 Now, well-conducted and careful experiments in Natural 

 Philosophy have proved that the heat received at the dis- 

 tances of 2, 3, 4, 5, 6, 7, 8, 9, etc., feet, is not |, |, i, |, i, \, I, i 

 of the heat received at 1 foot ; but it is i, |, i, i, , i, i, i, 

 etc., of the heat received at 1 foot. So that B will receive at 

 double the distance of A, only one-fourth of the heat which 

 A receives ; at triple the distance, only one-ninth of the heat ; 

 and so on. 



The law of progression then is as follows : Let the heat re- 

 ceived at the distance of 1 foot be denoted by 1, then the heat 

 received at the distance of 2 feet will be represented by 1 

 divided by 2 times 2, or ; the heat received at the distance of 

 3 feet will be represented by 1 divided by 3 times 3, or i ; the 

 heat received at the distance of 4 feet will be represented by 1 

 divided by 4 times 4, or ^ ; and so on. 



Now, dividing 1 by any number gives a result which in 

 mathematics is called the' reciprocal or inverse of that number ; 

 and multiplying any number by itself gives a result which is 



NEPTUNE 



DIAGRAM ILLUSTRATING THE RELATIVE POSITIONS, 

 ETC., OF THE SUN, PLANETS, AND PLANETOIDS. 



at different distances from the 

 source of heat, in the case of a 

 common fire, we again observe that 

 this law is equally true of the in- 

 fluence of light and of the influence 

 of attraction upon bodies at different 

 distances from the source of light 

 and of attraction. Thus we know 

 and feel that the sun is the great 

 source of light and heat to this 

 world of ours ; and Astronomy 

 teaches us that it is also the source 

 of attraction, or of that power 

 which has operated upon the earth 

 and the other planets, and which 

 continues still to operate upon 

 them, by causing them to revolve 

 in elliptical orbits or paths round 

 that luminary, as explained in our 

 last lesson. 



From the earliest ages up to the 

 time of Kepler, the planets (Greek, 

 irA.cn/rjTjjs, pla-ne'-tees, a wanderer), 

 or wandering stars so called in 

 opposition to the fixed stars, which 

 appear always to preserve the same 

 relative distances from each other 

 were reckoned to be in number only 

 six ; and this number being ma- 

 thematically perfect that is, equal 

 to the sum of all its factors, 1, 2, 3 

 it was imagined that no more 

 planets could exist, or could be ex- 

 pected to be found. Kepler, in- 

 deed, inquired most earnestly ifhy 

 they were only six in number ; but Galileo, who first applied 

 the telescope to astronomy, opened a new door in the temple of 

 science, by the discovery of the four satellites of Jupiter, IB 

 1610, and led by this discovery to that of the other planets 

 at a later period, which put to flight all reasons why the 

 number of the planets should be limited to any given number. 

 He would be a bold man indeed now-a-days who would try to 

 limit the number of the planets, seeing that so many have 

 been discovered within these few years past. 



The six planets known from antiquity are the following : 

 Mercury, Venus, the Earth, Mars, Jupiter, and Saturn ; no satel- 

 lite was known from antiquity but the Moon. The first addi- 

 tion to the planets of the Solar System was Uranus, at first 

 called the Georgium Sidus (the Georgian Star), in honour of 

 King George III., by Sir William Herschel, who discovered it, 

 March 13th, 1781. It was afterwards called Herschel, in honour 

 of the discoverer; but it is now called Uranus, because, for- 

 sooth, Uranus was in the Greek mythology (the fables of 

 the heathen gods) the father of Saturn! Uranus has eight 

 satellites, of which six were discovered by Sir William Herschel. 

 Of these, five have since been observed by other astronomers. 

 The planet Neptune, the third in point of size of those that 



