May 12, 1882.] 



♦ KNOWLEDGE ♦ 



585 



four thousand years ago, would now suffice to closely pack 

 the surfaces of about 



122,000,000,000 

 sucli globes as this earth on which we live, or tlie surface 

 of one large globe having a diameter exceeding the earth's 

 1, early .">,000 times, or the suns much more than 400 times. 

 Vet in science 4,000 years count almost as nothing. 



When we remember the rate of increase whicli is 

 customary among those whose lives are easy — this lieing 

 i.-ertainly much nearer 10 than l.l per cent per annum — 

 we see that, so far as the beiutit of the greater number of 

 surviving pei-sons at any epoeli is concerned, it is, on the 

 w hole, perhaps as well that during the last 4,000 years 

 there have been certain destroying agencies at work to pre- 

 vent the population of the earth from increasing so fast as 

 it otherwise nn'glit have done. 



It may, perhaps, be interesting, before we 'conclude, to 

 i;iijuire what would have been the actual average increase 

 per cent, per annum if the population of the earth had 

 iixcreased from 10 four thousand years ago, to 1,500,000,000 

 p.'-iw. If r be the increase per cent, per annum, we have 



/lOO + rV""" _ 



log. '^.^: 



log. (1,.J00,000,000) 



= !tl760913 

 wlience, since log. ICO = 2 we have 



4000 log. (100 + )•) = 8000 + 9-1760913 

 = 8009-irG0913 

 log. (100 + )-) = 2 0022910 

 100 + ,= 100-3304, 

 or tlie average rate of increase, on the assumptions made 

 has been little more tlian .', per cent, per annum. As it is 

 certain that tlie population of the eartli 4,000 years ago 

 consisted of many millions, the real average rate of increase 

 must have been very mucli less even than this. 



NIGHTS WITH A THREE-INCH 

 TELESCOPE. 



Bv "A Fellow of the Rov.vl Astrosojiical Society." 



'^piIE constellation Bootes, at which we now arrive (Map, 

 L p. 474), will be found a very mine of objects of in- 

 terest by the incipient observer. We will begin by turning 

 ' ur instrument, armed with a power of 160, upon f, a star 

 ■vhich Struve well described as " pulcherriina " (or most 

 'eaiitiful). So viewed it will be seen as in Fig. /', p. .")11. 



the larger star being yellow, and the companion a bluish- 

 green. 77 Bootis, an intere.sting and easy pair, when 

 viewed with a power of 160 will be found to present 

 the appearance shown in Fig. 27. ; Bootis, is a little 

 closer and somewhat more unequal pair, the colouis of the 

 components, moreover, being more strongly contrasted 

 than in the case of the previous star. It is shown in 

 Fig. a, p. 511. It is a wide and easy pair, which it 



is needless to figure. 44 Bootis, shown in Fig. 28, 

 as seen with a power of 160, is interesting from the con- 

 trasted colours of its components. It is not numbered in 

 the map, p. 474 ; but is one of two small stars forming a 

 triangle witli p and Bootis in it. Nor is our next 

 object, 39 Bootis, numbered ; but it is the north-western 

 of the pair of stars in the map, and will be found in tlie 

 sk}', a little above and to tlie right of 44. In tliis, again, 

 the coloui-s are prettily contrasted. Its aspect as viewed 

 with the same power as the preceding objects is represented 

 in Fig. 29. t: Biiotis, on tlie confines of Canes Yenatici, is a 

 wider and iiuicli more unequal pair. It is shown in Fig. 30. 

 On a line drawn from Spica A'irginis to f Bootis, and about 

 11^ south (and a little east) of Arcturus, will be found the 

 very pretty and interesting double star whicli we have 



drawn in Fig. 31. It is 69 of the fourteenth hour of 

 Piazzi's catalogue. The ditTerence in colour of the com 

 ponents of this pair will at once strike the observer. He 

 will, though, probably be puzzled to say exactly what the 

 colour of the smaller star is, very discrepant conclusions 

 on this subject having been arrived at. Some 8i° to the 

 west, and just to the north of Arcturus, we shall find a very 

 beautiful object, the star 1 Bootis, shown in Fig. 32. At 

 tlie first glance the student will observe two stars, nearly 

 of the same magnitude, and wide apart. It is the upper, 

 or southern one tif tliein, to which our attention must be 

 directed. Looking at it carefully, we shall note the minute 

 blue star shown in our figure to the south and very slightly 

 to the east of its primary. We have omitted the second 

 large star of wliicli we ha\ e just spoken from our diagram, 

 inasmuch as, using the scale to which it is drawn, such 

 star would be just out of the northern, or lower, portion of 

 the field. Finally, the student may, if he likes, look at 

 f Bootis with the very liighest power at his command ; but, 

 under the most favourable circumstances, he will only suc- 

 ceed in so far converting it into an egg-shaped object as to 

 show that it is not single. Such are a few of the most 

 easily-identifiable objects in this constellation. The number 

 of purely telescopic double stars is very large indeed, but 

 their necessary absence from our map of reference, and the 

 impossibility of recognising them without an equatoreal 

 llro^-ided with graduated circles, renders the mere mention 

 of them here sufiicient. 



PHOTOGRAPHY FOR AMATEURS. 



By A. BROTHER!?, F.R.A.S. 



'^plIE advantage of the negative form of photograph is 

 J that from it we are enabled to obtain an almost un- 

 limited number of copies on paper, having the lights and 

 sliadows, as in nature. The paper used for the purpose 

 may have a plain matt surface, that is without gloss, or 

 it may have a surface of albumen. The plain paper is used 



