ON MATHEMATICAL NOTATION AND PRINTING, 337 



Report of the Committee, consisting of W. Spottiswoode, F.R.S., 

 Professor Stokes, F.R.S., Professor Cayley, F.R.S., Professor 

 Clifford, F.R.S., and J. W. L. Glaisher, F.R.S., appointed to 

 report on Mathematical Notation and Printing, with the view of 

 leading Mathematicians to prefer in optional cases such forms as 

 are more easily put into type, and of promoting uniformity of 

 notation. 



With a view to the questions referred to them for consideration, your Com- 

 mittee have made inquiries into the nature and processes of mathematical 

 printing, and the diiRculfcies attendant thereon ; and it appears to them that 

 a statement of the results of these inquiries will form the best introduction to 

 the suggestions which they have to make. 



The process of " composition " of ordinary matter consists in arranging 

 types uniform in height and depth (or " body" as it is termed) in simple 

 straight lines. The complications peculiar to mathematical matter are mainly 

 of two kinds. 



First, figures or letters, generally of a smaller size than those to which 

 they are appended, have to be set as indices or suffixes ; and consequently, 

 except when the expressions are of such frequent occurrence as to make it 

 worth while to have them cast upon type of the various bodies with which 

 they are used, it becomes necessary to fit these smaller types in their proper 

 positions by special methods. This process, which is called " justification," 

 consists either in filHng up the difference between the bodies of the larger 

 and smaller types with suitable pieces of metal, if such exist, or in cuttiag 

 away a portion of the larger, so as to admit the insertion of the smaller 

 types. 



The second difficulty arises from the use of lines or " rules " which occur 

 between the numerator and denominator of fractions, and (in one mode of 

 writing) over expressions contained under radical signs. In whatever part 

 of a line such a rule is used, it is necessary to fill up, or compensate, the 

 thickness of it throughout the entire line. When no letters or mathematical 

 signs occur on a line with the rule the process is comparatively simple ; 

 but when, for example, a comma or sign of equality follows a fraction, or a 

 + or — is prefixed to it, the middle of these types must be made to range 

 with the rule itself, and the thickness of the rule must be divided, and half of 

 it placed above and half below the type. 



The complications above described may arise in combination, or may be 

 repeated more than once in a single expression ; and in proportion as the 

 pieces to be "justified" become smaller and more numerous, so do the 

 difficulties of the workman, the time occupied on the work, and the chances 

 of subsequent dislocation of parts augment. 



The cost of " composing" mathematical matter may in general be estimated 

 at three times that of ordinary or plain matter. 



With a view of illustrating these remarks, we have taken as an example 

 an expression of not unfrequent occurrence in mathematics, but of consider- 

 able difficulty to the printer, and have marked out in compartments the 

 different types of which it has to be composed. The shaded parts represent 

 the "justification " spoken of 



1875. z 



