THE BIANCHI–DARBOUX TRANSFORM OF L-ISOTHERMIC SURFACES

We study an analogue of the classical Bäcklund transformation for L-isothermic surfaces in Laguerre geometry, the Bianchi–Darboux transformation. First we show how to construct the Bianchi–Darboux transforms of an L-isothermic surface by solving an integrable linear differential system, then we establish a permutability theorem for iterated Bianchi–Darboux transforms.

Limitations to Productivity of Some Ultisol and Oxisol Subsoils

Greenhouse experiments with maize were carried out to see if the reported infertility of some subsoils could be improved with mineral fertilization and efficient watering. It was shown that the Nipe soil series (Typic Acrorthox; clayey, oxidic, isohyperthermic) exposed subsoil was as productive as the Carreras series (Aquic Tropohumult; clayey, kaolinitic, isohyperthermic) surface soil when N, K, micronutrients and 600 ppm P were added and the pots were watered by means of wicks. Carreras subsoil, when limed and fertilized with N, K, 300 ppm P, 100 ppm Mg and 36 ppm Zn produced as well as Carreras surface soil, even though it contained only about one-third as much organic matter. A comparison among eight surface and subsoils showed that yields on limed, liberally fertilized, well-watered Los Guineos series (Epiaquic Humoxic Tropohumult; clayey, kaolinitic, isothermic) surface soil, Carreras surface soil, Piña series (Psammentic Haplorthox; sandy, isohyperthermic) surface soil, Los Guineos subsoil, Piña subsoil and Catalina series (Tropeptic Haplorthox; clayey, oxidic, isohyperthermic) surface soil were not significantly different. However, the yield on the least productive of two Catalina subsoils was only 64 percent of the yield on the Los Guineos surface soil. But with the addition of Zn and slightly over 1,000 ppm P, greenhouse pot yields on the two soils were essentially the same. Field experiments will be necessary to determine optimum P rates under field conditions. It was concluded that the productivity in greenhouse pots of surface and subsoils of the Ultisols and Oxisols studied can all be brought to the same high level, provided adequate mineral fertilization (including Zn and high P rates), lime and water management are used.