In another step to expand its home-computer network, The Source Telecommunicating Co. will permit its 18,000 subscribers to send Mailgram messages directly from their personal computers to Western Union.

Under the new service, a subscriber can compose a message on his or her home computer and enter it into The Source's system. The Source will forward these messages electronically to Western Union's largest Mailgram processing center in New York where the messages will be routed by Zip Code to the electronically equipped post office nearest the destination. The mesage then will be printed, placed in an envelope and given preferential delivery treatment--without anyone other than the sender or receiver reading the meassage, The Source says.

If the message is placed in The Source's system by 4 p.m. EST, senders will be "virtually guaranteed" that the message will be delivered anywhere in the United States, including Alaska and Hawaii, by the next business day.

The Source, a McLean-based electronic communications company, calls this new service "a preview of nationwide electronic mail delivery." It complements a host of other Source communication services in which subscribers can send messages to one another as well as receive electronically published newsletters.

The costs for the Mailgram message service are on top of the standard usage fees of a $100 one-time registration fee and standard hourly charges, which range from $18 weekdays to $4.25 after midnight.

The rate for sending a single Mailgram is $5.15 for messages up to 100 words, with an additional $1 change for each additional 100 words. The address is considered as part of the 100-word message. If a subscriber bypassed The Source and sent a message directly to Western Union, the cost would be $4.25 for the first 50 words and $1.95 for the next 50 words.

However, The Source says its service provides some special features, such as allowing the consumer to save a copy of the message in his or her personal computer file for later reference or for another mailing.