In British parlance the Royal Navy is The Senior Service due to having been created as a permanent establishment in Tudor times, while the Army only became permanent a few centuries later.
The importance of a distinction is the need for military officers to know, at all times, who is the most senior for command purposes. Within each service officers at a specific rank assess their seniority by date of commission, both brevet and substantial. When two services are working together the same applies, except an additional tie breaker is available. - if rank are equivalent and dates of commission are the same, then the Royal Navy officer has seniority over the Army officer.
In 1913 there was as yet no Royal Air Force, and various Corps such as the Royal Artillery and Engineers were simply branches of the Army. So the only available junior service was the Army, unambiguously.
Note that it is possible to look up the effective commission date for all British Officers since 7 November 1665 on the London Gazette Archive. For example, here is the announcement of the promotion to Brevet Field Marshal of Arthur Wellesley in the July 3, 1813 Extraordinary Edition (pp 1270, lower right).
That edition also contains the after action reports filed by Wellington dated June 22 and 24, 1813, following the battle of Battle of Vitoria, including the names of all officers killed or wounded in that engagement.
The Queen's Regulations for the Army 1975 outline in Chapter 2, Parts 3 and 4 and further in Sections 9.163-9.167 the precise workings of how seniority of officers is to be determined:
a. Officers holding substantive rank are to take precedence over all those holding acting or local rank of the same
grade. They are to take precedence among themselves according to their date of promotion to that rank.
J2.041. Under the provisions of the Armed Forces Act 2006, when members of one Service are co-operating with one or both of the other Services they enjoy like power of command over members of another Service as the members of that Service of ‘corresponding rank' insofar as power of command depends upon rank or rate. The expression ‘corresponding rank' is defined in the Act by reference to The Queen's Regulations. Thus when members of different Services are acting together the superior officers of one Service become, in accordance with the scale of corresponding ranks prescribed by these Regulations at the Table
in para J2.042, superior officers of members of the other Services of lower corresponding rank or less seniority and can, consequently, give lawful commands to them.
These principles have remained unchanged over centuries, though details have become more complicated over time.