“Beating” was used as a method of estimation of the population density of a spider mite, Paratetranychus hondoensis EHARA, feeding on the Japanese cedar, Cryptomeria japonica D. Don. The twig (15cm long) of the Japanese cedar was loosely grasped by hand and sharply tapped against a white paper (18cm×13cm), then spider mites were beaten off by its impact onto the paper, which was immediately folded and rubbed by hand; these procedures caused the spider mites fallen to be remained on the paper as scratch spots, which could be counted at an appropriate time.
Many sharp beatings are, however, necessary to dislodge all individuals from a given twig, and it may be some trouble to work.
Assuming that the number of spider mites fallen by the tapping is proportional to that of spider mites yet to be dislodged on a given twig, the following equation may be derived,
A_n=α (S-Y_n-1), ……………………………………(1)
where A_n, is the number of spider mites fallen by tht n th beating, Y_n-1 the accumulated number of spider mites fallen till the (n-1) th beating, S initial number of spider mites at start of beating, α a proportional constant.
It may be represented in another form as follows:
Y_n=S{1-(-a)ⁿ}……………………………………(3)
The beating method was applied on 10_??_18 of October in 1957, to sixty-four twigs of the Japanese cedar growing at the Saga prefectural forest experiment station.
If points of which Y_n. and S are co-ordinates are plotted on the basis of the data obtained, linear regression passing through the origin is recognized as expected by equation (3) (Figs. 1_??_5). The larger n is, the smaller the inclination calculated by the method of least squares to the axis of Y_n (Tab. 1) is; the latter should tend to 1 in the limit of infinitely large n.
Now let the inclination of equation (3), 1-(1-α)ⁿ, be bn; then log (1-bn)=nlog (1-α)………………………………(6)
Therefore, if the assumption on which equation (1) is based is applicable, -log (1-bn) should be in proportion to n. The relation between n and -log (1-bn) based the calculation on Tab. 1 are shown in Fig. 6, which indicates the following points:
(1) the assumption is very much satisfied in beatings from the first to the third, but
(2) if beating number is more than four times, the proportion of the spider mites fallen by a beating becomes smaller; it may be due to the fact that the proportion of spider mites in the condition easily dislodged from a twig decreases with the progress of beating.