CONTEMPORARY ADVANCES IN PHYSICS 175 



"Coincidences" — which is to say, pairs of discharges occurring so 

 close in time to one another that they seem to be simultaneous, that is, 

 within an interval which with good apparatus may be a hundredth or 

 even a thousandth of a second — are much more frecjuent than they 

 would be, if they were due only to chance. Some of course are due to 

 chance: these are the "spurious" or "casual" or "accidental" coinci- 

 dences, of which the number must be estimated and subtracted from 

 the number observed. ^^ After this is done, one is pretty safe in 

 assuming that the remainder is a measure of the number of ionizing 

 particles which have darted through both of the counters. By this 

 drastic procedure, of course, the observer limits himself to the study of 

 those corpuscles which happen to be moving along paths which 

 intersect both of the chambers. There will also be corpuscles of which 

 the paths traverse one of the counters, but not the two; it seems as 

 though the observer were throwing away his opportunity of studying 

 these, by rejecting the non-coincident discharges; but some of the 

 discharges in either tube are probably due to radioactive substances in 

 its walls, or to unknown causes inherent in the tube and not connected 

 with cosmic rays; and by accepting only the coincidences, one guards 

 to a great extent against being misled by these. Moreover, by varying 

 the relative position of the counters — for instance, by putting one of 

 them first above and then beside the other — one may study the 

 distribution-in-direction of the ionizing particles. Such studies have 

 not yet been plentiful; but it has been found that if the counters are 

 placed one above the other, the coincidences are several times more 

 numerous than if they are placed side by side. 



We have just been considering the effect of magnetic field on the 

 tracks of the corpuscles ascribed to cosmic rays, observed by the cloud- 

 chamber method: it is suitable now to review what the counting-tubes 



15 Suppose that there are xVi discharges per unit time in one of a pair of counters, 

 A^2 per unit time in the other; and that if a discharge in either starts within a time T 

 after the starting of a discharge in the other, the records of the two (whatever be 

 the way of recording them) make them appear simultaneous. Then in unit time, the 

 periods during which any discharge occurring in the first counter is not separately 

 recorded add up altogether to an amount IN^T. This is the fraction of time, dis- 

 charges occurring during which are recorded as coincidences. If the events in the two 

 counters are entirely uncorrected, then out of A^i discharges occurring per unit time in 

 the first, Ni{2N2T) or INiN^T (on the average) will coincide with discharges in the 

 second. If the discharges of each counter are recorded as peaks on tracings of 

 separate films, one may determine A^ and Nn from the films, set for T the greatest 

 time-difference which cannot surely be distinguished from zero and subtract INiN^T 

 from the total number of coincidences. Or the number of accidental coincidences, 

 together with iVi and A^2, may be observed by placing the counters so far apart that 

 no particle can traverse the two of them, and T thence computed. Or both sets of 

 discharges may be recorded on the same tracing by connecting both counters to the 

 same electrometer, in which case T will be the greatest interval for which two peaks 

 merge apparently into one; or they may be so connected that no record whatever 

 appears unless two discharges coincide. 



