Plot data in descending order as appears in data frame

I've been battling to order and plot a simple dataframe as a bar chart in ggplot2.

I want to plot the data as it appears, so that the values ('count' variable) for the corresponding categories (e.g. 'humans', 'male') are plotted from high to low.

I've followed other threads on this site asking similar questions, but can't get this to work!

## Dataset (mesh2)

#Category			        Count

#Humans				62

#Male				40

#Female				38

#Adult				37

#Middle Aged			30

#Liver/anatomy & histology	        29

#Organ Size			        29

#Adolescent			        28

#Child				21

#Liver/radiography*		        20

#Liver Transplantation*		20

#Tomography, X-Ray Computed	        20

#Body Weight			18

#Child, Preschool		        18

#Living Donors*			18

#Infant				16

#Aged				14

#Body Surface Area		        14

#Regression Analysis		11

#Hepatectomy			10

## read in data (mesh2) as object (mesh2)

mesh2 <- read.csv("mesh2.csv", header = T)

## order data by count of mesh variable

mesh2$cat2 <- order(mesh2$Category, mesh2$Count, decreasing=TRUE)

## Barplot created in ggplot2

library(ggplot2)

mesh2p <- ggplot(mesh2, aes(x=cat2, y=Count)) + geom_bar (stat="identity") +     scale_x_continuous(breaks=c(1:20), labels=c("Humans", "Male", "Female", "Adult", "MAged",   "Liver anat & hist", "Organ Size", "Adolescent",	"Child", "Liver radiog", "Liver Transplnt", "Tomog X-Ray Computed", "Body Weight", "Child Preschool", "Living Donors", "Infant", "Aged", "BSA",	"Regression Analysis", "Hepatectomy"))+ theme (axis.text.x=element_text(angle=45, hjust=1))

You want reorder(). Here is an example with dummy data

set.seed(42)
df <- data.frame(Category = sample(LETTERS), Count = rpois(26, 6))

require("ggplot2")

p1 <- ggplot(df, aes(x = Category, y = Count)) +
         geom_bar(stat = "identity")

p2 <- ggplot(df, aes(x = reorder(Category, -Count), y = Count)) +
         geom_bar(stat = "identity")

require("gridExtra")
grid.arrange(arrangeGrob(p1, p2))

Giving:

Use reorder(Category, Count) to have Category ordered from low-high.