$4-10$ A new high efficiency air filter has been designed to be used in a secure containment facility to do re$-$

search on detection and destruction of anthrax. Before the filter is built and installed, it needs to be tested.

It is proposed to use ceramic microspheres of the same diameter as the anthrax spores for the test. One

obstacle in the test is that the efficiency of the sampling equipment is unknown and cannot be readily

tested because the rate of release of microspheres cannot be sufficiently controlled to define the num$-$

ber of microspheres entering the sampling device. The engineers propose the test apparatus shown in

Figure P$-4-10.$ The sampling filters capture the microspheres on a membrane filter that allows micro$-$

scopic counting of the captured particles. At the end of the experiment, the number of particles on the

first filter is $1941$ and the number on the second filter is $63.$ Assuming each filter has the same efficiency,

estimate the efficiency of the sampling filters. $[$Note; this problem is easily solved using the particle counts

$(C_1,C_2,C_3)$ and efficiency $().]$