Chart monthly data sets currently across multiple columns, as a single date series

I have a sheet of numerical data, with many empty cells like:

column1 column2 column3 column4 etc
date Jan Feb March
1 23 100 123
2 25 103
3 104 125
4
5 28 108 130
6 etc
..
31 95 154

{the empty cells and formatting spaces have been removed by the webpage}
I want to plot this numerical sequence as a single line from 1st Jan to 31st Dec.
By inserting a chart, Excel automatically plots each column as a data set/line against the date 1..31.

How do I tell Excel that the data is held in multiple columns? In the series data edit box, I have tried joining columns by &, but Excel did not like that and gave an error.