an improved ball or plug or dart dropping head 15 that is shown in fig1 8 and 10 17 in fig1 a 1 b 1 c and 2 8 ball plug dropping head 15 has an upper end portion 31 and a lower end portion 33 ball plug dropping head 15 provides a tool body 34 that can be of multiple sections that are connected together such as with threaded connections in fig1 a 1c the tool body 34 includes sections 35 36 37 38 39 the section 35 is an upper section the section 39 is a lower section ball plug dropping head 15 can be pre loaded with a number of different items to be dropped as part of a cementing operation for example in fig1 a 1 b 1 c there are a number of items that are contained in ball plug dropping head 15 these include an upper larger diameter ball dart 40 41 and smaller diameter ball 42 in fig1 26 an alternate embodiment is shown which enables very small diameter balls sometimes referred to as u201c frac balls u201d 102 which can have a diameter of between about u00bd and u215d inches to be dispensed into the well below toll body 34 the tool body 34 supports a plurality of valving members at opposed openings 90 the valving members can include first valving member 43 which is an upper valving member the valving members can include a second valving member 44 which is in between the first valving member 43 and a lower or third valving member 45 valving member 43 attaches to tool body 34 at upper opening positions 61 62.