The second member of this equation shows the sum of all the external forces acting on one portion of the beam, that portion being limited by the section about which the moment _M_ acts. That sum of all the external forces, as given by the second member of equation (16_b_), is evidently the total transverse shear at the section considered. Equation (16_b_) then shows, in the language of the differential calculus, that the first derivative of _M_ in respect to _x_ is equal to the total transverse shear. It is further established in the differential calculus that whenever a function, such as _M_, the bending moment, is a maximum or a minimum, the first derivative is equal to zero. The application of this principle to equation (16_b_) shows that the bending moment in any beam or truss has its greatest value wherever the shear is zero. Hence, in order to determine at what section the bending moment has its greatest value in any loaded beam carrying a given system of loads, it is only necessary to sum up all the forces or loads, including the reaction _R_, on that beam from one end to the point where that sum or shear is zero; at this latter point the greatest moment sought will be found. This is a very simple method of determining the section at which the greatest moment in the beam exists. The preceding formulæ and diagrams may be extended to include any number of loads, and they are constantly used in engineering practice, not only for beams and girders in buildings, but also for bridges carrying railroad trains. Whatever may be the number of loads, the expressions for the bending moments at the various points of application of those loads are to be written precisely as indicated in equations (16). When the number of loads becomes great the number of terms in the equations correspondingly increase, but in reality they are just as simple as those for a smaller number of loads. The diagram for the vertical shear in this beam is the lower part of Fig. 13. As in the case of Fig. 12 the shear at _A_ is the reaction _R_, as it is _Rʹ_ at the other end of the beam. The shear in the portion _AD_ of the beam has the value _R_, but in passing the point _D_ to the right the weight _W₁_ represented by _OT_ must be subtracted from _R_, so that the shear over the section _b_ of the span is _R_ - _W₁_ or _QV_ in the diagram. Similarly, in passing the point _H_ toward the right, both _W₂_ and _W₁_ must be subtracted from _R_, giving the negative shear (the previous shear being taken positive) _VW_. The negative shear _VW_ remains constant throughout the distance _c_, but is increased by _W₃_ at the point _L_, so that throughout the distance _d_ the shear _Sʹ_ = _-Rʹ_. These shear values are all shown in the lower portion of Fig. 13 by the vertical shaded lines. Obviously it is a matter of indifference whether the shear above the straight line _GJ_ is made positive or negative; it is only necessary to recognize that the signs are different.