The authors made an experimental study on tillering in paddy rice under the cultural conditions of direct sowing and transplanting. With variety Rikuu 132, cultures by both of these methods were practiced in 1947. Sowings were done on May 5. Transplantings were made on June 9 in one plot and on June 19 in another. Each plant was given a space of 1.2×0.4 shaku either in direct-sown or in transplanted plot. The numbers used for investigations per Plot were 40. In the direct-sown culture the first tiller appeared quite usually from the 2nd node (the 1st normal-leaf node) on main stem, while in the transplanted one some lower nodes remained dormant in most cases and the frst tiller appeared usually from the 4th or 5th node. Moreover, in the former, tillers appeared quite regularly in order from the lowest one to the succeeding upper ones, while in the latter, such regularity was not the case with some lower ones. In the former, however, the last tiller on main stem was that from the 9th node, while in the latter the 10th node shooted it. Lateral tillers in the transplanted culture were apparently less in number than in the direct-sown culture. Tillers appearing from a main stem are named 1st-order tillers, those from a 1st-order tiller are named 2nd-order tillers, and so on. A node on main stem and certain nodes on tillers bear mutually a corresponding relation regarding their loci. When the 1st tiller appears, from the 2nd node on main stem (node 2), the node 2 has no corresponding node. Corresponding relations of upper nodes on main stem with nodes on 1st-order tillers are: Node 3 (3rd node on main stem) with 1 node, 2p (the 1st or prophyl node on the tiller from node 2); node 4 with 2 nodes, 22 and 3p; node 5 with 3 nodes, 23, 32 and 4p; node 6 with 4 nodes, 24, 33, 42 and 5p; node 7 with 5 nodes, 25, 34, 43, 52 and 6p; and so on. WhenY=number of corresponding nodes on tillers, n=the node number of a given node on main stem, n'=number of nodes from 1st node to n-node, and loman figure I shows 1st-order tillers, then YnI is n'-2 in this case. In a case where the 1st tiller is from the 3rd node on main stem, YnI is n'-3; and in a case where the 1st tiller is from the 4th node, YnI is n'-4; and so on. So, the number of corresponding nodes on tillers is presented by a formula YnI=m, where m=n'-number of nodes from 1st node to 1st-tiller node on main stem. Corresponding relations of nodes on main stem with those on 2nd-order tillers are: When the 1st tiller appears from node 2, neither node 2 nor node 3 has corresponding node. Node 4 corresponds with 1 node, 2pp; node 5 with 3 nodes, 2p2 22p and 3pp; and node 6 with 6 nodes, 2p3, 222, 23p, 3p2, 32p and 4pp. Thus, node 7 corresponds with 10 nodes, node 8 with 15 nodes, node 9 with 21 nodes, and so on. The general formula is YnII=m(m-1)/2. Smilarly, the number of corresponding nodes on 3rd-order tillers is presented by a formula YnIII=m(m-1)(m-2)/6. Consequently, the total number of nodes on tillers of all orders corresponding with a given node on main stem is: Yn=YnI+YnII+YnIII+······or Yn=m+m(m-1)/2+m(m-1)(m-2)/6+······. Among the nodes belonging to the same group regarding corresponding relation, there is a difference in their physiological activities giving a phenomenon that new tillers from the nodes on later-order tillers as well as from those on upper tillers of the same order are apt to appear later and to be weaker. However, in spite of the fact that the prophyl node is the 1st node on a tiller, it bears in a few cases merely a comparatively weaker tiller. In the present experiment, tillers from prophyl nodes appeared rarely in the transplanted culture but none was in the direct-sown culture. The phenomenon of tillering caused by the difference of physiological activities among nodes is quite regular in the young stage of plant. [the rest omitted]