534 



NATURE 



[Oct. 2 1, 1875 



tion of (/)' has almost entirely to be considered in 2. It is this 

 which constitutes the chief difference between the sliding and 

 the fixed seat, and which accounts for the sense of fatigue expe- 

 rienced in the legs in the former system. 



If we examine the problems which arise from the considera- 

 tion of Fig. I we shall find that in using the term " fixed seat " 

 we are speaking incorrectly ; that is to say, as far as there exists 

 a force to hold A in position we have none but friction ; and 

 that practically the position of A with regard to L is determined 

 by muscular action. 



Thus in Fig. 2 the seat is really more fixed than in Fig. I, or 

 there is less muscular action round t' than round T. 



The advantages of the system 2 over i are however not 

 simply mechanical, but the constancy of the angle «' affords 

 gi-eater space for the respiratory movements, and thus physio- 

 logically there is an explanation for the difference in disturbance 

 of circulation and respiration generally experienced when com- 

 paring the two systems. R. J. Lee 



St. George's Hospital 



History of the Numerals 



On reading the letter on the " Origin of the Numerals " (vol. 

 xii. p. 476) 1 was reminded of some portions of their history 

 which I had before noted down, and which are essential to any 

 consideration of their origin. 



The earliest forms which I have seen are those of the Abacus 

 (Jour. Archceol. Assoc, vol. ii.), from which our later forms are 

 mainly, if not entirely, derived. The intermediate forms are to 

 be seen in arithmetical treatises and calendars of the thirteenth 

 to sixteenth century, and on sundry quadrants, &c., of the four- 

 teenth to sixteenth century, in the British Museum. 



In the following table the earliest form of each letter and of 



Abacus 12S0 J3S0 MiSO 



1 V % 1 

 T^ ^ 1 2, 2. 



tM 5 f 



1^^ 1V75 



^ X 4- A 



^ - 14/74! jr>rd 



is (} 6 



XS30 M70 ISSi 



V A. H A 7 



JS30 13.99 



S 8 ^ % 



1339 liSO 



^99^ 



each variation is entered, with the corresponding date ; the 

 years 1280, 1320, 1420, and 1450 are only approximately 

 stated. • 



Now, with respect to the primitive forms suggested by Mr. 

 Donnisthorpe, the 2 would seem to have been two strokes at 

 right angles (not parallel), the lower stroke of our form being 

 only a tail, like that of many medial forms of Hebrew letters. 

 The 3 may have been originally three vertical strokes, which 

 were set horizontal in early times ; the flat top, however, does 

 not appear till 1574, and then only in English examples appa- 

 rently. The 4 ot the Abacus seems to have been deserted for 

 cross lines connected, which are always placed diagonal till about 

 1474, when the first turn to the present position occurs : perhaps 

 four strokes were intended, as we call cross-roads *' four roads 

 meet." 5 seems to have been inverted from the Abacus, and 

 then about 1550 the straight tail was curved towards the previous 

 figure, and the head elongated to lead to the next mark. It 

 often occurs as a perfect though very straightened S in the six- 

 teenth century, as it is now made in Belgium and other coun- 

 tries. Its form ill 1280 reminds one of the Roman V written 

 as U. 6 in the Abacus consists of six strokes ; but this, from 

 their cumbrous collocation, is probably merely a scribe's fancy. 

 7 has been apparently inverted (like 5) from the Abacus; its 

 transitions are easily traced, but its origin is not so clear ; some 

 mij^ht see a trace in the Greek Z = 7. 8 has always been very 

 near its present form, and the two squares is an explanation the 

 character of which can only be objected to on the grounds of its 

 inapplicability elsewhere. 9 has always had a straight tiil, 

 though it has been inverted since the Abacus form (as 5 and 7 

 seem changed) : its origin might be looked for in the Greek 

 possibly, as that letter has varied more in form than any other ; 

 or, more likely, in the Arabic Ta, or Tha ( = 9), which in the 

 Abacus it closely resembles ; and it is even more similar to the 

 Syriac Teth, a twin form to that of the Arabic. Perhaps the 

 ancient Arabic alphabet (in its nearer approximation to its 

 Hebrew- and Samaritan-like original) would show the origin of 

 more of these forms, and even the simple i is exactly the Arabic 

 Elif= I, for their alphabetic origin is rendered highly probable 

 from the fact that the numerical systems of the Greeks and of 

 the Semitic nations (from whom our Arabic numerals probably 

 came) were in very early times derived from the alphabet ; not, 

 like the Egyptian and Roman systems, wholly separate arrange- 

 ments. 



The apparent, though historically untrue, applicability of the 

 line + line origin of all the forms of our numerals, is an interest- 

 ing example of the fallibility of any theory which only looks to 

 present conditions, apart from past facts and history. 



Bromley, Kent W. M. Flinders Petrie 



Scarcity of Birds 



I QUITE agree with Mr. Barrington, who writes in Nature 

 (vol. xii. p. 213) concerning the scarcity of birds. I find, by 

 comparing my last year's ornithological diary with the present 

 year's one, that I have only found about three-fourths of the 

 numberof Blackbirds' {Turdus merula). Thrushes' {Tttrdus mttsi- 

 cus), Blue Titmouses' (jParus ccc7-iileus), Pied Wagtails' {Motacilla 

 alba), Greenfinches' (Coccothraustes cloris). Linnets' (Linofa can- 

 nabina) nests that I found last year. The Hirundinidse have 

 been far less plentiful than usual ; but the Goldfinch {Carduelis 

 elegans) was the rarest bird here this summer. I did not succeed 

 in finding a single nest, although our yearly average is fifteen. 

 Other birds, as the Charadriidae and the Mussel Thrush {Turdus 

 viscivorus), have been very plentiful, and I found the Mountain 

 Linnet's {Linda viontium) nest for the first time I have ever met 

 with it on the lowland south of the Humber. Will not the hard 

 frost of last winter account for the scarcity of our native birds in 

 some measure? Adrian Peacock 



Bottesford Manor, Brigg. 



OUR ASTRONOMICAL COLUMN 



H CassiopejE and Vicinity.— Smyth (Cycle ii. p. 25) 

 has the following remark with respect to stars near fi 

 Cassiope^E : — "Just 18' south of /^ is a star which, though 

 of the 6th magnitude, is not in Piazzi. It is followed 

 nearly on the parallel, about 1 1= off, by a 9th magnitude, 

 and both are remarkable from being red, of a decided 

 but not deep tint." There is no star of the 6th magnitude 

 near this position at the present time, nor so far as we 

 know is there any record of such an object having been 

 visible since the epoch of Smyth's observations, 1832 71. 



