July 12, 1883] 



NATURE 



261 



alter greatly the proportion of energy passing through the post to 

 that which is absorbed into vibrations of this side of the belly. 

 At the same time it must al-o alter slightly the nodal arrange- 

 ment of the belly, which must have an influence on the tone. If 

 from the form of construction, or relative quality of the wood of 

 the upper plate as compared with the under plate, the conditions 

 of a violin are such that the highest quality of tone of which it is 

 capable requires a relatively larger amplitude of vibration of the 

 back, the position of the sound-post should be nearer the bridge. 

 In a contrary condition of things the sound-post should be 

 farther from the bridge. The extreme range needed in different 

 violins is about a quarter of an inch. Any shift of the post must 

 affect the relative mobility of the two sides of the belly. 



If the sound-post transmits vibrations, these w 11 be in addition 

 to those received from the sides of the violin. It may be, there- 

 fore, that one condition which determines the be^t position of the 

 post is the degree in which from their form and material these 

 fulfil this duty. All the sides must share in this duty, but the 

 touch-rod shows that a large part of this action is borne by the 

 parts of the sides which curve inwards under where the strings 

 are bowed. It is in harmony with this view that Mr. Hill states 

 that if the inside blocks at the corners, which are put to 

 strengthen these parts, extend in a small degree into these 

 curved portions, the tone is injured. 



The plane of the vibrations of the strings is that in which they 

 are bowed, which is more or less oblique to the bridge. The 

 vibrations maybe considered divided into two sets at right angles 

 to each other, a and b. 



The touch-rod shows that these vibrations exist strongly in the 

 upper part of the bridge. I venture to suggest that the use of 

 the peculiar cutting of the bridge, which was finally fixed from 

 trials, by Stradiuarius, is to sift the vibrations communicated by 

 the strings and to allow those only or mainly to pass to the feet 

 which would be efficient in setting the body of the instrument 

 into vibration, the other vibrations which would be injurious in 

 tending to give a transverse rocking motion to the bridge, being 

 for the most part absorbed by the greater elasticity given to the 

 upper part of the bridge by the cutting. Below the two large 

 lateral cuts, the touch-rod shows a very great falling off of the 

 vibrations b. In the case of a violoncello these vibrations were 

 also very greatly reduced below the side openings of the bridge. 



1 he violin on which the experiments were made was without 

 a bass bar, which is a piece of pine glued to the under side of the 

 belly on the fourth string side. This bar is regarded as strengthen- 

 ing the belly and also enabling it to respond better to the lower 

 notes. The touch-rod showed no difference in the general 

 behaviour of this violin from a fine one by Stradiuarius contain- 

 ing a bass bar. 1 



On the Proportional Thickness of the Strings. — As the lengths 

 of the strings are the same, we have only the two conditions of 

 weight and tension on which their pitch depends. It is obvious 

 that for equal pressure on the feet of the bridge, as well as for 

 more convenient fingering and bowing, the strings should be at 

 the same tension. They should therefore differ in weight, so as 



1 In the " Early History of the Violin Family," Engel, speaking of the 

 Crwth, says: — "Furthermore, the contrivance of placing one foot of the 

 bridge through the sound-hole, in order to cause the pressure of the strings 

 to be resisted by th« back of the instrument, instead of by the belly, is not 

 so extraordinary and peculiar to the Crwth as most writers on Welsh music 

 maintain. It may be seen on certain Oriental instruments of the fiddle kind 

 which are not provided with a sound-post. For instance, the bridge is thus 

 placed on the three-stringed fiddle of the modern Greek, which is only a 

 variety of Ihe ordinary rabab, but which the Greeks call lyra. Inappropriate 

 as the latter designation may appear, it is suggestive, inasmuch [as it points 

 to the ancient lyra as the progenitor of the fiddle." — P. 28. 



to give fifths when brought to the same tension. The weights 

 of the strings are inversely as the squares of the number of 

 vibrations, which in the case of fifths is as 3 to 2, namely, as 9 

 to 4. As the first three strings are of the same material, it is 

 more convenient to take their diameters, which must be as 3 to 

 2, that is, each string in advancing from the first string must be 

 half as thick again as the string next to it. In the case of the 

 fourth string, covered with wire, we must find the weight of the 

 third string of gut, and take a fourth string of which the weigh! 

 is 9 to 4 for the third string. 



A good average thickness of 2nd (A) string = 0-0355 inch. 



Then the strings should be — i-t = 0x1237 , 



2nd = 00355 » 

 3rd =0-0532 ,, 



A gut string 0-0532 inch in diameter weighs, when of tht 

 same length as a fourth string, 0*98 grm., then the fourth = 2 20 

 grms. 



Ruffini sells sets of strings in sealed boxes, and these were 

 found to be in about the same relative proportion to each other 

 as the sizes indicated on the gauges sold by several makers. 



The measures of a set of Ruffini's strings were found to be : 



1st = 0^0265 inch. 

 2nd = 0-0355 „ 

 3rd = 0-0460 ,, 

 4th = 1-4100 grm. 



It will be seen that the first string is thicker, and the third 

 thinner, and the fourth much lighter than the theoretical values. 

 Therefore the tension of the first string would be greater, and 

 that of the third and fourth strings less than they should be in rela- 

 tion to that of the second string. The greater flexural rigidity of 

 the fourth string will have a small effect in the direction of making 

 the vibrations quicker, and therefore of making the tension 

 required less. 



By means of a mechanical contrivance I found the weights 

 necessary to deflect the strings to the same amount when the 

 violin was in tune. The results agreed w ith the tensions which 

 the sizes of the strings showed they would require to give fifths. 



A violin strung with strings of the theoretical size was very 

 unsatisfactory in tone. 



The explanation of thi- departure of the sizes of the strings 

 which long experience has shown to be practically most suitable, 

 from the values they should have from theory, lies probably in 

 the circumstance that the height of the bridge is different for the 

 different strings. It is obvious, where the bridge is high, there 

 is a greater downward pressure. By this modification of the 

 sizes of the strings there is not the greater pressure on the fourth 

 string side of the bridge which would otherwise be the case. 

 On the contrary, the pressure is less, which may assist the 

 setting of the belly into vibration. There is also the circum- 

 stance that the strings which go over a high part of the bridge 

 stand farther from the finger-board, and have therefore to be 

 pressed through a greater distance, which would require more 

 force than is required for the other sttings, if the tension were 

 not less. 



UNIVERSITY AND EDUCATIONAL 

 INTELLIGENCE 



Cambridge. — The next examination for Minor Scholarships 

 and Open Exhibitions at St. John's College will take place in 

 December, 18S3. There will be open for competition, besides 

 certain Exhibitions, two Minor Scholarships of 50/. per annum 

 and two of 75/. ; also such Foundation Scholarships as shall be 

 vacant, two of which may, after the commencement of residence, 

 be increased in value to 100/. each. 



Candidates may offer themselves for examination in any of 

 the following subjects : — Classics, Mathematics, Natural Science, 

 Hebrew, or Sanskrit. 



The Examinations will begin on Tuesday, December II. 



Successful candidates will be required to commence residence 

 not later than October, 1884. Further particulars of the Scho- 

 larships and Exhibitions may be obtained in October, 1883, on 

 application to one of the tutors. 



SCIENTIFIC SERIALS 



Bulletins de la Sociitid' Anthropologic de Paris, torn. v. fasc. iv. 

 18S2. — Discussion on M. Ball's caseof cretinism, in which the axiom 

 advanced by M. Lunier was generally accepted, that, while idiocy 



