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Mr. A. J. Ellis. 



[June 17, 



I find beats of all kinds most easy to count (by the seconds hand 

 of a chronometer) when about 4 in a second. They can be counted 

 well from 2 to 5 in a second. Above 5 they are too rapid for accu- 

 racy ; below 2 and certainly below 1, they are too slow, so that it is 

 extremely difficult to tell from what part of the swell of sound the 

 beat should be reckoned. Partly from this reason, perhaps, I have 

 found great variety in counting successive sets of such slow beats. I 

 never use beats of less than one in a second, if I can avoid it. When 

 the beats are slow it is difficult to discover by ear which of the two 

 beating tones is the sharper ; and even fine ears are often deceived. 

 It is easy to discover, however, by putting one of the forks under the 

 arm for a minute. This heats and flattens it by 2 or 3 beats in 10 

 seconds. Hence if the beats with the heated fork are slower, it was 

 sharper, because it has been brought nearer the other ; if faster, it 

 was flatter and has been brought further away. Count for 10, 20, or 

 40 seconds, according to the fork. Up to 20 or 30 beats in 10 seconds it 

 is easy to count in ones, but from 30 to 50 it is best to count in twos, 

 as one-ee, two-ee, &c, beginning with one, and hence throwing off one 

 at the end. When counting for 20 seconds I always count in twos, 

 and for 40 seconds in fours, as one-ee-ah-tee, two-ee-ah-tee, &c, be- 

 cause I have to divide the result by 20 or 40 ; and this division is 

 avoided by the count itself. Owing to difficulties in beginning and 

 ending the count, I find the possible error per second to be 2 divided 

 by the number of seconds through which the count extends ; and that 

 it is best to take a mean of 5 to 10 counts for each set of beats. 



Temperature plays an important part. Forks should not be touched 

 with the unprotected hand ; they otherwise easily flatten by 2 beats 

 in 10 seconds. Interpose folds of paper. I use two folds of brown 

 paper stitched between two pieces of wash-leather. Large forks are 

 generally on resonance boxes and need not be touched, otherwise the 

 same precautions should be used, as they are very sensitive, and retain 

 the heat longer than small forks. Scheibler's forks are fitted with 

 wooden handles. In tuning, the file heats and flattens ; the result, 

 therefore, can seldom be known for a day or two, when the forks have 

 cooled and "settled," as they will be sure to "jump up." I find it 

 best to leave off filing when the forks are two or three tenths of a 

 vibration too flat. In sharpening there is, therefore, great danger of 

 doing too much, as the fork remains apparently at the same pitch, the 

 flattening by heat balancing the sharpening by filing. Hence all 

 copies should be compared some days after, by means of a third fork 

 about four vibrations flatter or sharper than each, to avoid the slow 

 beats of approximate unisons. The filing also seems to interfere with 

 the molecular arrangement of the forks. 



The thermometer should be always consulted when beats are taken. 

 But if the beats are between two forks, of which the pitch of one at a 



