October 26, 1893] 



NA TURE 



6'5 



Owing to the drought the crop, greatly to the distress of poor 

 folk, proved an utter failure. Happily the wealth of the 

 season's blackberry crop atoned in some measure for the 

 cowslip failure. 



The modern taste for cut flowers has given a commercial 

 place also to the blossoms of the wood anemone, the marsh 

 marigold, the ladies' smock, and the yellow iris. 



The apple, pear, and plum crops were excellent. In some 

 plantations the gooseberry crop, through the ravages of the 

 scourge known as the red spider, was destroyed, and the bushes 

 killed. 



The hop crop was good and great, the bulk being of a 

 quality rarely, if ever, surpassed. As early as July 28 two 

 pockets reached Worcester market ; a date, save one, the earliest 

 on record. Some twenty-four years ago — I cannot put my 

 hand on the exact date — a pocket was delivered in this market 

 on July 26. 



On August 8 this season picking began to get general. On 

 .September 8, some days earlier than picking usually commences, 

 many planters had finished. 



On September 19, in ordinary years, hops begin to reach the 

 market. This season much belbre that date the public ware- 

 houses were filled with new hops. The season being in advance 

 of the hoprequiremenisof the brewers, merchants did not attend 

 to buy. For all this, waggons heavily laden with towering 

 loads of hops came pouring in, and not only were the public 

 warehouses filled, but the floor spaces of the Shirehall, the 

 Guildhall, and the Gymnasium were packed. 



The most notable feature of the year, doubtless, is the cir- 

 cumstance that during the 1 ilter part of July, as well as through 

 the month of August, and down to the present date, there was, 

 and is, a second leafing, blooming and fruiting of fruit and 

 forest trees, and blossoming of the spring and summer flora. 



In Paris the horse-chestnut trees blossomed and leafed afresh, 

 as happened with many horse-chestnut trees in Cambridgeshire. 

 In Kent orchards again put forth blossoms, while the ripening 

 fruit of the year loaded the boughs. As far north as Manchester, 

 and likewise near Wigan, the rhododendrons blossomed again. 

 Throughout England many fruit trees are in second bearing. In 

 the avenue of lindens in the New Road, in this cily, many of 

 the trees are garnished with new foliage of the exquisite vivid 

 green tincture of spring ; the leaves have attained full size. 

 Strawberries ripe and of large size (5 inches in circumference) 

 are common over a wide area of England. At Redruth, Corn- 

 wall,, primroses, gentians, and golden chain, and most of the 

 early spring llowers are again in splendid blossom ; and there 

 also fruit trees, while in full crop, are again in rich bloom. 



In the Cottenham district of Cambridgeshire a second crop of 

 various kinds of fruit is being gathered. Green gooseberries 

 have been secured during the last few days from one of the 

 gardens ; raspberries have in several places blossomed again, 

 and produced finer fruit than the first crop ; while apple-trees 

 also show a rich second bloom. In North Wales dog-roses, 

 honeysuckle, and foxgloves are again in splendid bloom. In 

 Worcestershire the midsummer flora is again in flower. Gen- 

 erally the late potato crop is growing again, and great deteriora- 

 tion of the tubers ensues. In Tenbury, Worcestershire, many of 

 the potato tubers are flabby, as though scalded, and when boiled 

 turn black and become nauseous, and the growers are wondering 

 what is the matter. 



At Medoc the vintage began on August 20, a month anterior 

 to the usual date. For generations such an early date has not 

 been known. The Girondins say the crop is splendid ; sufficient 

 casks for the crop are not procurable. 



Here, in spite, or perhaps in consequence, of the drought, 

 the familiar wayside wilding, the ladies bed straw, formed (in 

 meadows put up for mowing) a great part of the crop, and, 

 flinging lavish perfume around, lined every wayside hedgerow. 

 The humming-bird moth, of which the bed straw is a food plant, 

 was more common than ever before within my rather long ex- 

 perience. At the end of August, a month before the usual lime, 

 the thousand of Irish harvestmen left our shores for home. 



The summer of 1818 resembled greatly that of the present 

 remarkable year. 



Worcester, September. J. Lloyd Bozward. 



Asymmetrical Frequency Curves. 



Some six years ago (September i, 1887) Dr. Venn wrote to 

 you pointing out the asymmetrical character of certain frequency 



NO. 1252, VOL. 48] 



curves occurring in physical and biological measurements. I 

 have recently obtained a generalised form of the probability 

 curve which fits with a great degree of accuracy such curves, 

 and propose to discuss it at length shortly. Meanwhile I wish 

 to point out that an asymmetrical point binomial may be 

 readily fitted to such curves, although not with the complete- 

 ness of the above referred to continuous curve. Let n be the 

 number of events in a group, / the probability for single event, 

 and q that against it ; let c be the horizontal space selected as 

 the basis of each rectangle forming the point binomial, and let 

 o be the total area. Then we have the following diagram given 

 by the point system ; 



0*.j£^ <-£-> «-f-> <7-c-^ <r-'- 



where the successive heights are the terms in 



a[p" + np" 



1 I "(» 



V -I- -^ — 



I) 



/"- 



Then I premise that to fit this to any real curve we cannot 

 (i) use the length of base (« + l)c, for by trial I find this is 

 never sufficiently accurately known ; (2) use the magnitude or 

 position of the maximum ordinate of the observation curves, for 

 the first is not accurately known, and the second is dependent 

 on knowing the exact end of the observation curve. 



Accordingly I proceed not by the method suggested in Prof. 

 Edgeworth's "Law of Error and the Elimination of Chance " 

 (Phil. Ma^- p. 318, April 1886), but by a method of higher 

 moments. 



Reckoned from O, the distance ON to the vertical through 

 the centre of gravity, G, of the system of rectangles is c( 14- nq). 



I now calculate the moments of the rectangles round the 

 vertical, OY, and find for the nh moment 



Mr = oc'— q- q . • - to r differentiations {,/(/ -f (/)"}, 

 dq dq dq 



where/ -t- '/ is only to be put unity after diff^erentiation, and c 

 is supposed small. From the first four moments about OV, I 

 find the first four moments about NG iwilh the following 

 results : — 



Ml = o. 



V-i = «/'/«'-. 



M3 = "/qip - '/)«'^'. 



M4 = «/'/!• + 3(« - 2)qp]ac*. 

 Now the centre of gravity of the observation curve is found 

 at once, also its area and its first four moments by easy calcu- 

 lation. Thus the position of NG, a, yttj, fi^, and n^ are given 

 quantities. Taking the values of it„, lUj, /Jj, given above, and also 

 <i + ,/= I, I have four equations to determine/, q, n, and f. 

 Solving them, I have the following results : 



/ and q are roots of the quadratic ; 

 p'^ -p + ^ '"'''' ~ l^i)l^_±l^ = o ; 



4(3^2" - M4)Mj ■*• 6M3' 



_ 2^0' . 



(3M>- - ^4)^2 + Ms" ' 



_ V 2( ^M^" - <i4) M a + 3Ma- 

 -^. . 



As verification note that for the normal probability curve 

 3M2' = M4 and A/3 = o. 

 Thus we have 



p" - p + I = o, i e. p = i, and q = i, 

 « 

 as it should be. 



and ^ = o, 



