Step 1: Concept of Goodwill.
Goodwill is an intangible asset that represents the reputation and earning capacity of a firm. When a new partner is admitted, he must compensate existing partners for their sacrifice in profit share.
Step 2: Mode of bringing goodwill.
The new partner generally brings goodwill in the form of cash (premium for goodwill). This ensures old partners are compensated immediately.
Step 3: Capital contribution vs goodwill.
Capital contribution is different from goodwill. Capital is invested for ownership in business, whereas goodwill premium is a one-time payment for gaining entry and profit share.
Step 4: Conclude.
Therefore, a new partner brings goodwill in the form of cash.
Final Answer:
\[
\boxed{\text{Cash}}
\]