Retirement benefits - Retirement Cost (Details) - USD ($) $ in Millions	3 Months Ended		9 Months Ended
	Sep. 30, 2018	Sep. 30, 2017	Sep. 30, 2018	Sep. 30, 2017
Pension Plan
Defined Benefit Plan Disclosure [Line Items]
Service cost	$ 2.6	$ 2.8	$ 8.2	$ 8.5
Interest cost on projected benefit obligation	10.5	12.0	33.8	38.7
Return on assets – expected	(16.1)	(15.9)	(48.6)	(47.3)
Amortization of losses	7.8	7.7	24.1	22.7
Amortization of prior service cost	0.0	0.4	0.2	0.8
Settlement loss	0.4	0.6	1.4	1.4
Net periodic pension cost	5.2	7.6	19.1	24.8
Other Postretirement Benefits Plan
Defined Benefit Plan Disclosure [Line Items]
Service cost			0.1	0.1
Interest cost on projected benefit obligation	4.9	5.5	15.2	16.1
Return on assets – expected	(4.1)	(4.1)	(12.5)	(12.4)
Amortization of losses	6.5	6.2	19.7	17.6
Amortization of prior service cost	(1.0)	(0.7)	(2.7)	(2.2)
Net periodic pension cost	6.3	6.9	19.8	19.2
U.S. Plans | Pension Plan
Defined Benefit Plan Disclosure [Line Items]
Service cost	0.0	0.0	0.0	0.0
Interest cost on projected benefit obligation	8.0	8.8	24.0	26.4
Return on assets – expected	(13.4)	(13.3)	(40.2)	(39.9)
Amortization of losses	6.8	6.3	20.8	18.7
Amortization of prior service cost	0.0	0.0	0.0	0.0
Settlement loss	0.0	0.0	0.0	0.0
Net periodic pension cost	1.4	1.8	4.6	5.2
Non-U.S. Plans | Pension Plan
Defined Benefit Plan Disclosure [Line Items]
Service cost	2.6	2.8	8.2	8.5
Interest cost on projected benefit obligation	2.5	3.2	9.8	12.3
Return on assets – expected	(2.7)	(2.6)	(8.4)	(7.4)
Amortization of losses	1.0	1.4	3.3	4.0
Amortization of prior service cost	0.0	0.4	0.2	0.8
Settlement loss	0.4	0.6	1.4	1.4
Net periodic pension cost	3.8	5.8	14.5	19.6
UMWA Plans | Other Postretirement Benefits Plan
Defined Benefit Plan Disclosure [Line Items]
Service cost			0.0	0.0
Interest cost on projected benefit obligation	4.2	4.6	12.9	13.7
Return on assets – expected	(4.1)	(4.1)	(12.5)	(12.4)
Amortization of losses	4.9	5.2	15.4	14.6
Amortization of prior service cost	(1.2)	(1.2)	(3.5)	(3.5)
Net periodic pension cost	3.8	4.5	12.3	12.4
Black Lung and Other Plans | Other Postretirement Benefits Plan
Defined Benefit Plan Disclosure [Line Items]
Service cost			0.1	0.1
Interest cost on projected benefit obligation	0.7	0.9	2.3	2.4
Return on assets – expected	0.0	0.0	0.0	0.0
Amortization of losses	1.6	1.0	4.3	3.0
Amortization of prior service cost	0.2	0.5	0.8	1.3
Net periodic pension cost	$ 2.5	$ 2.4	$ 7.5	$ 6.8