I'm growing tomatoes organically and need to know why the bottoms rot while the fruits are still on the vine.Jerome Moore
What you are seeing is a plant nutrition disorder called blossom-end rot. It is very common in early summer, when plants are growing rapidly and attempting to meet the demands placed on them by fruits. When they can't pump quite enough nutrients to the fruits, the blossom end of the fruit develops rot spots. Naturally, the problem is most common with large-fruited tomatoes because it's a farther trip from the stem attachment to the end of the fruit.
Acidic conditions make it difficult for tomatoes to take up calcium, so mixing dolomitic lime or slow-release rock phosphate into the soil, well before planting, will help to prevent this problem, if your soil is naturally acidic. Fluctuating soil moisture and too much nitrogen, which pushes the plants to grow, also contribute to the problem.
To reduce the disorder once it's in progress, pick off affected fruits. Lightening the fruit load will make it easier for the plants to meet the needs of flawless specimens. Also pile on plenty of mulch, which will prevent fluctuations in soil moisture.