304 THE CROWFOOT FAMILY 
signs 8, o’, and 2 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 the 
formulas of Peonia, 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 b1/1,0 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 estivation of sepals or petals is indicated by two 
apostrophes, following the 5 or P, as in the formula of Pzeonia; 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, +, is to be read ‘‘more or less.” 
The algebraic symbol of infinity, ©, stands here for “many” or 
‘fan indefinite number.’ As a companion sign,o may be used to 
mean few. When the absence of an organ needs to be noted a zero, 
0, is used. A dash between numerical signs means “‘to”’; thus, 3-5 
would be read “‘three to five’”’;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 $ or 3 
(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 
