Increment In A Trigger?

I have the following table:

Code:

CREATE TABLE [dbo].[apcName](
[SysID] [int] IDENTITY(1,1) NOT FOR REPLICATION NOT NULL,
[RIN] [int] NOT NULL,
[Name] [varchar](80) NOT NULL,
[DimTab] [tinyint] NOT NULL,

[code]....

If I have an Insert trigger to set the RIN field to the next available number in the sequence of the RIN column, why does the following work for inserting 1 and only 1 record at a time but fails if doing multiple rows with a single insert?

Code:
-- Insert Trigger
UPDATE xRec
SET RIN = (Select MAX(RIN) + 1 from apcName)
FROM apcName xRec
JOIN inserted ins
ON ins.sysID = xRec.sysID

-- Works, RIN is populated correctly

Code:
Insert apcName (Name, DimTab) VALUES ('Test Name', 1)

Does Not Work. Returns 1 for all RIN's

Code:
Insert apcName (Name, DimTab) VALUES
('Test Name1', 1),
('Test Name2', 2)