T o t a l i n v e n t o l i e s ancl nzethocls of volzime summa7.y zuhich facilitate conzpilation of t w e and log v o l u m e s t o a n y desi7.ed stancla?.d of utilization a?-e neeclecl. I t shoz~ld be possible t o filzd v o l u m e pel. t~e e t o a n y specified s t a n , d a~d o f zitilization exp).essecl a s stzcm p h e i g h t , to11 clib ancl t o e s t i m a t e component zueights in biomass a n d o t h e~ stziclies. T h e fzinctions developed in t h i s pape.1. ancl based zipon clbh, total h e i g h t , ancl section h e i g h t a s a f~aaction of total h e i g h t c a n m e e t nzost o f t h e s e 7.eqzcir.e)nents. Resume Les fonctions de defilement et leur application dans les inventaires forestiers O n ct besoin cl'in.r;entcii).es fo?-estie?.s conzplets e t d e w~hthocles poztv facilitel-la co?npilation cle volzimes ligne7~n: cl'ar.b?~es e n t i e i s o u cle billes COT-~.esponclant ci cles niveazix d'zitilisation c l h t e~n~i n k s . I1 clev?c~it i t~e possible d'kvalzie7~ le volzinze total pa). ~7.b7.e szsivant cles n i v e a u e cl'zitilisation e ep).imks e n t w m e cle hazitezt?. cle sozicke, cle cliam e t r e ?)zininzunz cl'zitilisation, e t / o u cle f action cle l a hazitezcv totale. D e plzcs, la techniqz~e ~l e v 7~a i t p o u v o i~* fozc?-ni7. la p7,opo7.tion clzt volzime total d e la tige conzp7'ise cla~zs les billes d e tozite longzcezt?~ o z~ clianzkt~e, qz~elqzse soit le s y s t & m e cle nzeszivage enzployk (pieel nzeszwe cle planche, pied czcbe 021 pozcls). L a me'thocle dem3ait azissi pozivoi7. &tm zitiliske pozu. clhc~i)*e l'inflzience cles facteznss biologiqzies s z t~ la f o l w e dzc fzit e t s o n clhfilenzent, e t p o z c~ estime?. les co.l?zposantes dzi poicls clans les ktzicles d e bionzasse e t azttres. L e s f o n c t i o n s cle clkf i l e m e n t p~~k s e n t h e s i c i sont baskes szoP le d h p , l a hazitelo. totale e t des f~~a c t i o n s cle lci haliteln3 totale. Elles pezivent ~~e n c o n t 7 -e ) . la plzipa).t cles e r igences knzsmk?*kes.Modern manufacturing methods, coupled with the multiplicity of possible end-uses of a single log in an integrated operation, require that the forester provide detai!ed information regarding the raw material supply. Data for the modern forest inventory must be collected in a manner that permits flexible and comprehensive analyses. Estimates of total volume per acre no longer suffice. Now the volume of material available in certain sizes and qualities must be estimated with high standards of precision and accuracy.A t the 1963 annual meeting of the Canadian In-

A new growth function, which is flexible enough in shape to accommodate most biological growth behavior, is created by adding an expanding factor to the Weibull distribution function. Many monotonically increasing biological growth phenomena can be excellently modelled by this function with various numerical values for the scale, the shape, and the upper asymptote parameters. The function is illustrated with height–age and volume–age curves for single trees and two polymorphic stand volume–age curves.

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With few exceptions the lateral extent of roots in relation to crown width has been studied only incidentally during research which had as its main goal the description of root systems. Yet the relative spread of roots in relation to crown is of vital importance in plans for controlling space among trees for optimum stand development. For example, if root spread were more limiting than crown spread it would be necessary to plan for a suitable amount of surplus space for roots to spread beyond the edge of crowns. On

Six methods of determining parabolic expressions of height-diameter relationships have been compared with two other mathematical methods of curve-fitting. It has been shown that short-cut approximations of the least-squares solution of the parabola are accurate; they are useful because of their ease of application and good conformance with the true height-diameter relationship. In this example the short-cut approximation methods have provided more desirable solutions than those secured using Henricksen's semi-logarithmic method, Stoffel's log-log method, H. A. Meyer's exponential solution of the parabola, and Staebler's precise least-squares solution of the parabolic equation with "a" variable. Three short-cut methods for calculating parabolic curves have been illustrated with data from the Campus Forest of the University of British Columbia. Special uses of the parabolic relationship have been described. Construction of site-class volume tables has been demonstrated with data for a number of commercial tree species in the Arrow Lakes District of British Columbia. The short-cut methods of determining parabolic height-diameter relationships have so many advantages that they are recommended for general use in forest inventory and for permanent plot studies.