In this note the problem of random flights is considered for the case of a small number of vectors, each vector possessing the same constant magnitude. A formula is developed which permits the calculation of the probability function of the sum of N + 1 such vectors if the function of the sum of N vectors is known. The formulae for the probability distributions up to N = 8 are quoted and some of their practical applications mentioned.

No abstract

Opaque mineralogical studies of late Mesozoic dolerite dykes of Wedel-Jarlsberg Land, South Spitsbergen, show that the dykes have undergone a mild hydrothermal alteration. The alteration probably took place at the time of consolidation of the dykes, but may also have occurred as a side effect of Tertiary orogeny, which affected the western parts of Spitsbergen. Seven of these dykes were sampled during two summer seasons, when samples were collected from different exposures. A conventional procedure based on the minimum scatter principle and study of Zijderveld diagrams applied to 282 specimens demagnetized by alternating fields and thermally reveals several 'characteristic remanence' directions. In three dykes the directions are consistently reversed, but one carries both normal and reversed remanence. The reversed directions can be attributed to a geomagnetic field reversal in the late Mesozoic and K-Ar dating of one of the reversed dykes gives an age of 110 -+ 5 Myr BP in agreement with the known age of early Cretaceous field reversal.Using a least squares method of analysis of step demagnetization, low coercivity components, not separated by the conventional procedure, have been successfully isolated in two of the dykes. The analysis applied to all the other dykes confirms the results of the conventional method, yielding comparable mean directions of magnetization. The conventional method applied to 'characteristic' directions from five dykes gives a mean palaeomagnetic pole at 210.1", 78.9" N, ag5 = 3.5" and the least squares procedure applied to directions from six dykes yields a pole at 222.7", 69.7"N, ag5= 7.9". The pole positions obtained agree with those obtained for Spitsbergen dolerites by *Deceased. ipresent address:

Resistivity depth probes were made over water wells in an alluvial interior valley of Jamaica, known as the Queen of Spain' s Valley. Several types of electrode configuration were used and the observations analyzed by a technique designed to select those suitable for interpretation. The results, interpreted by standard curve matching methods, compare favorably with available well logs. They suggest that the yield is a linear function of the resistivity of the water-bearing strata. A straight line fitted to the data by the method of least squares provides a nomogram which can be used for predicting the probable yield at points where no wells exist. It is concluded that resistivity surveys can be of material assistance in a water-supply drilling program in the area. It is found that interpretation by multilayer curve-matching procedures gives more realistic results than analysis by classical two-layer master curves used in conjunction with Hummel' s rule. The results suggest also that the Wenner array gives a better resolution of small resistivity contrasts than the operationally more versatile Cooper array.

No abstract