354 THE CROWFOOT FAMILY 



signs S , cf , and 9 have already been explained on page 347. As 

 used in the Clematis formula they will be understood as meaning 

 that the inflorescence may consist entirely of perfect flowers (as in 

 the other genera) or may be polygamous. 



The presence of bracts more or less like foliage leaves may gener- 

 ally be taken for granted, and so need not usually be expressed in a 

 formula. Bractlets are more often absent, but it seldom matters 

 much for our purpose whether they are present or not, and they 

 rarely need to be taken into account. When either of these organs 

 present noteworthy peculiarities they may be recorded as in tliL 

 formulas of Pa'onia, Caltha, Nigella, and Anemone, following the 

 method for leaves as regards their arrangement, except that in case 

 of involucres only a denominator is used because there is but one 

 whorl. Thus in the formula for Caltha l)Vi,o would read "bractlets 

 alternate or none"; for Nigella b/5,0 means "with five bractlets 

 forming an involucre, or none"; while for Anemone B, b/2,3 means 

 "having bracts or bractlets two or three in a whorl." 



The imbricate aestivation of sepals or petals is indicated by two 

 apostrophes, following the 8 or P, as in the formula of Pa>onia; the 

 valvate, by an inverted comma opposed to an apostrophe, as in 

 Clematis. 



For each floral organ the number or numerical sign following a 

 letter tells how many of the parts represented are present. The 

 plus sign, +, means "or more," so that 5+ would be read "five or 

 more." The "plus or minus" sign, =fc, is to be read "more or less." 

 The algebraic symbol of infinity, 00, stands here for "many" or 

 "an indefinite number." As a companion sign, oc may be used to 

 mean few. When the absence of an organ needs to he noted a zero, 

 0, is used. A dash between numerical signs means "to"; thus, 3-5 

 would be read ' ' three to five " ; 0- 0° " none to many. ' ' Simply a dash 

 after a numerical sign means "or less"; thus 5- would be read "five 

 or less." 



When the numerical signs are in such fractional form as I or i 

 (Aconitum formula) it shows that the flower is irregular so far as 

 the organs so represented are concerned; otherwise, the flower is 

 understood to be regular. If the numerator be an odd number it 

 indicates that a single member of the set, more or less unlike the 

 others, is uppermost, as for example, the hooded sepal of Aconitum : 

 an even number, instead, shows that a pair of similar parts is 

 uppermost, as is the case with the staminodes in the same flower. 



Unless otherwise indicated the floral organs are understood to 

 be free and distinct. Partial coalescence of parts, as in the carpels 

 of Nigella, is indicated by placing after their numerical sign a small 

 parenthesis: thus, for the example cited CE 5 ±) would be read 

 "carpels five, more or less, partially coalescent below." 



There being no indication to the contrary it is also to be under- 

 stood that the floral organs regularly alternate, and that the anthers 



