PROBLEM WORKER

Otago Daily Times, Issue 22568, 11 May 1935, Page 19

PROBLEM WORKER

DIFFERENTIAL ANALYSER A WONDEEFUL MACHINE. The world's latest word in calculating machines —the differential analyser—which has been installed in the basement of the physics building of Manchester University to work out abstruse mathematical problems that occur m modern scientific research, was explained at the opening ceremony recently by Professor D. R. Hartree (states the Manchester Guardian). Professor Hartree explained that differential equations were mathematical formuulae expressing the relation in Which the rate of change of variable quantities stood in relation to the quantities themselves and possibly others. No previous machine could deal with these directly, because variable quantities were outside arithmetical conceptions. Some such equations could be solved by existing numerical tables, but an important minority had in the past been soluble only by graphical methods, which were limited in scope ard accuracy, or by increasingly laborious mental calculation, the labour of which no one knew better than he, who had given thousands of hours to them. The machine meant not merely a saving of time but also making, possible many investigation's which without it would be too laborious to be undertaken at all. One practical one on which he had been working referred to the regulation of the temperature of a room by hotwater apparatus. The problem of what the temperature of the room would be at a given moment involved the quantity and temperature of the water, the initial temperature of the air in the. room, and the length of time a given temperature was brought to bear on the air. If the machine was set in motion and the pointer-arm at the " input" table guided along a curve supplying the known factors, the pencils on the other side of the machine would supply, in the form of a graph on the " output" table, the information required about the temperature of the room. The mathematician using the machine knows, of course, the formula by which, the answer can be obtained, and it is merely to eliminate the sheer labour of applyiug the formula (often enormously complicated) to different sets of figures that the machine is used. The mathematician draws a detailed diagram showing exactly how each of the components of the intricate machine must be related to the others. From this the mechanic sets the machine. That may sometimes take a whole day, but once it is done the machine can be used for an indefinite number of applications of the formula and the answer to each obtained in about a quarter of an hour, whereas without the machine each might take weeks. The machine is at present set to answer a problem in atomic theory in which Professor Hartree is specially interested.