Money available for investigation but two other factors should determine its choice. It should be sufficiently sensitive to detect the object of the search and it should not be so sensitive that it continually gives false alarms of discovery. It is important to check regularly that the detection equipment is working as the search proceeds(iii) choose the optimum search path:Attempt, if possible, to show that the object does lie in the search area before you begin to search-many faultless pieces of equipment have been stripped only to have the fault discovered later elsewhere. In many cases it is best to use a convergent procedure in which a test for the existence of the object in one half of region is first applied, and having located the faulty half, to take finer and finer divisions until the object is located.Alternatively, if there is a region in which the object most probably lies, start in this region of greatest probability. The optimum path would go through the most likely places first and you should concentrate your search involves moving among many variables, as for instance in tuning a piece of electronic equipment , you should devise a one-dimensional path trough the many dimensions of the search area. The starting point should be marked and the path which is followed should be recorder because it is often necessary to retrace a path to regain a peak that has been passed. Search systematically. Sometimes it is possible to devise a way of obtaining the approximate direction and position of thje object at each search point; when this can be done, graphical or mathematical methods may sometimes help to home on to the object.(iv) allow that you may have missed the object:If a new technique or a better piece of detection equipment becomes available, check back through rejected regions in case the object may have been missed.Replication and the spacing of test pointsIt is seldom in experimental work that a single observation is regarded as conclusive. Confidence comes with repeatability.The word replication means the complete repetition of a measurement and it involves not just repeated glances at a dial to record a series of similar values but a repetition of all the steps that led up to that measurement so that when the repeated measurement is made, it tests all the steps previously made in the experiment. There are two views that may be taken about replication and these depend upon whether the replication is made with conditions as near as possible unaltered or whether some quantity is changed before the replicated measurement is made.The reason for replicating with conditions unchanged are either to test for or to reduce the random error in a measurement. The precision (the inverse of the random error) of a result is measured by the standard deviation (p.89), where it may be seen that the precision increases as the square root of the number of replications, so that to double the precision of a test point it is necessary to make four times as many replications. Clearly a case of diminishing returns. While random error may be reduced by replication, systematic error ( see p. 84) is unchanged and one must strike a balance between them. There is no point in trying to obtain a precision greater than the systematic error that is likely to be present in a particular measurement. A statistical guide to this topic is given in the next chapter under the heading assessment but again we urge you to spend thought on refining your experimental technique rather than to rely on many replications and statistics. The best economy is gained if the errors are reduced in those measurements which have the greatest effect on the results. For example, the deflections which occur when a rectangular beam is loaded depend upon the second moment of area of the beam section(bd3)/12, where b and d are breadth and depth, respectively. Here a given error in measuring d will have a much greater effect on the final result than the same error in measuring b(seep.97).The idea of changing some quantity before a replication is made may at first appear to defeat the purpose of replication, but there are good arguments for adopting this approach in some circumstances. The object is to cast the experimental net more widely and so obtain information additional to that gained by straightforward replication. If a quantity (c) is thought haveno effect in experiment and c is varied before each replication, the measurements will serve both to assess the precision of the measured quantity and to check whether c does have an effect. Clearly a single replication would not suffice because it would not separate an effect of c from a random variation in the measured quantity, but if several replication were made, each with c varied, we should say that c had an effect, if the readings showed a trend, apart from the presence of random variations. Again, where a quantity which would normally be held constant, not being one of the variables of the results, this quantity could be changed before each replication and test readings corrected for the predicted change. If it is considered that there is a significant discrepancy by measurement, then further investigation may reveal faults in the apparatus or sources of bias which might otherwise have been overlooked.The number and spacing of test points to define a curve is a matter of judgment. Preliminary tests may be required in order to find whether there are any parts of the curve in which rapid changes occur (as for instance, in the tensile yielding of a mild steel rod, the change from laminar to turbulent flow in fluids or the elastic buckling of a member)which require a concentration of test points to define them. Where rapid changes do not occur, the test points should be uniformly spaced. Sometimes it is advantageous to plot the results logarithmically, for instance, where a relation of the form y = k x a exists, a plot of log y=log k+ a log x will give a straight line from which k and a may be obtained. Where available information shows that log plots are to be employed, test points should be chosen closer together at the lower and of the range so that, when plotted, the points become evenly spaced along the curve.