This semiannual progress report and future reports will be published as two documents to permit a wider distribution of the unclassified material. The report numbers are assigned in sequence so that the two reports will fall together when filed by report number.

On 3/14/60 the Applied Physics Corporation was awarded a subcontract for the design and development of a high-temperature high-pressure spectrophotometer system based on the Cary Model 14pm Spectrophotometer insofar as possible, and consistent with our specifications, No. CTD-2, December 16, 1959.

In the Communications of the ACM of April, 1960, p. 240, there appeared two Algol algorithms for the computation of In, the modified Bessel function of the first kind. One of these algorithms uses a convergent series and the other an asymptotic series. Their author, Dorothea S. Clarke, did not give any information with regard to which algorithm is more appropriate in a given situation (a given situation meaning the computation of In (x) for a definite pair of numbers n and x). Such information is necessary, however, if the algorithms are to be useful, particularly since the asymptotic series is in many cases not valid.