390 



NA TURE 



[February 24, 1898 



that has ever been obtained in these regions. The skull, which 

 was sent home to me, along with a considerable number of heads 

 of antelope, lion, leopard, &c. , is now in the British Museum, 

 and Mr. Oldfield Thomas, of that institution, has compared it 

 with the skulls of both the Northern and Southern forms ; such 

 marked differences have been noticed, that opinion is in favour 

 of the possibility of its being a new species — for the time being, 

 until it has been more fully worked out, he has made it a 

 special sub-species, and named it Giraffa camelopardalis peralta. 

 The giraffe was killed south of the Benue River, north of 

 Calabar. The accompanying map will roughly show the geo- 

 graphical distribution of the two known forms, the haunts of 

 these animals being filled in. Although one or two specimens 



AFRICA 



Briiish Miles 



have been recorded on the eastern shores of Lake Chad, and 

 also on the Senegal River, from io° N. to 20° S. of the equator 

 no fact is on record of a giraffe having been seen or killed 

 within the degrees mentioned in all that part designated West 

 Africa. The map will show at a glance the immense tracts of 

 country between the habitats of these animals and the spot 

 where this single animal was killed. In a letter I had from Sir 

 George Taubman Goldie, the Governor of the Niger Company, 

 he says : " This is the only giraffe ever known in these regions ; 

 I have no doubt there are others, but they have never been seen." 

 The above facts were mentioned by me at a meeting of the 

 Linnean Society, on the 20th of last month ; and Mr. Thomas 

 exhibited the skull at the Zoological Society on the ist inst., 

 and among some of his remarks stated the skull to be the largest 

 he had ever seen. W. Hume McCorquodale. 



Abridged Long Division. 



Having been working on similar lines for some years, I was 

 very much interested in the late Mr. Dodgson's letter on 

 abridged division in Nature of January 20, and I should like 

 to offer a few observations and to give a variation of the method 

 which appears much simpler. It will be admitted that Mr. 

 Dodgson's plan is of limited application, and rather complicated 

 for general use. There is nothing to hinder the method given 

 below from being universally used, though it may not in all 

 cases be the shortest. It also has the merit, I think, of direct- 

 ness and uniformity. 



It is, of course, based on the theorem in geometrical pro- 



gression 



N 



= Ji 



ar^ + m ar" 



niN 



;«2N 



[ar"f {ar") 



e.g. (i) Divide 246813579 by 989. Here a = i, r = 10, 

 « = 3, w = II. 



NO. 1478. VOL. 57] 



10001246813579 



246813 



2714 



29 



579 X II = 2714943 

 943 X II = 29865 

 865 X II = 330 



330 



249558717 quotient. 



It will be observed that in multiplying by »i = il, we need 

 only use the figures to the left of the line, and if the first figure 

 to the right of the line be >5, call it one more ; thus, 



2715 X II = 29865, and 29-8 = 30 X 11 = 330. 



If extreme accuracy be required, the computer has only to 

 carry the process further. 



In this example we need not do so, as the divisor is 1000 

 throughout. 



(2) Divide 975318642 by 3997. 



40001975318642; 



2438296605 X 3 

 182I8722 X 3 

 11372 



244012*6699 quotient. 



Remainder in integers 



= 8642 - (2 X 4000 - 4012 X 3) = 2678. 



The 8642 and 4012 are the 11 + i figures of dividend and 

 quotient respectively. 



(3) Divide 12345678975312468 by 69993. 



70000I 1 23 456789753 1 2468 



176366842504 



1 7636684 



1763 



Quotient 176384480952 



46 X 7 -^ 7 



25 

 66 



iZ 



5 



Actual remainder 



= 312468 - (2 X 70000 - 80952 X 7) = 39132 



retaining only the last n + i figures. 

 (4) Divide 975312468 by 7003. 



7000I 975312468 



13933c 



59 



Quotient 13927c 

 Actual remainder 2468 



353 

 713 

 6 



3-^7 



7000 + 9270 X 3) = 4658, 



(O X 



retaining only last n + \ figures. 



It will be noticed here that we subtract to get the quotient. 

 The reason is evident. We actually divide by 7C00 instead of 

 7003, and therefore the quotient is too great. 



If the remainder be known, as e.g. in recurring decimals, the 

 following process, published by me some years ago, is shorter 

 than the ordinary method, besides possessing the advantage of 

 finding its own quotient. 



Divide 85296419765-1 by 9731 

 973 



The" quotient [ 87654321. It is obtained the reverse of the 



ordinary way. 



This method bears the same reverse relation to ordmary 



